Finite Group Databasebeta

← D7×#3501 #14261691

Subgroups — D7×#3501 #14261691

Order 1792.

7738 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3501C211yesmaximal, characteristic, complemented
2#11744017C218yesmaximal, complemented
3#11744016C214yesmaximal, complemented
4D7×#554C218yesmaximal, complemented
5D7×#554C214yesmaximal, complemented
6#11743829C214yesmaximal, complemented
7D4×Q8×D7C214yesmaximal, complemented
8#11743667C212yesmaximal, complemented
9D7×#544C212yesmaximal, complemented
10D7×#543C214yesmaximal, complemented
11#11743642C214yesmaximal, complemented
12#11743348C212yesmaximal, complemented
13D7×#533C212yesmaximal, complemented
14#11743054C214yesmaximal, complemented
15C2×D7×C22⋊Q8C214yesmaximal, complemented
16D7×#518C212yesmaximal
17#11742928C212yesmaximal, complemented
18C2×C4×D4×D7C211yesmaximal, characteristic
19#11742834C211yesmaximal, characteristic, complemented
20C22×Q8×D7C2214yescomplemented
21C22×D4×D7C2211yescharacteristic
22C23×C4×D7C2212yes—
23C7×#554C2214yescomplemented
24C7×#554C2218yescomplemented
25C7×D4×Q8C2214yescomplemented
26C7×#544C2212yescomplemented
27C7×#543C2214yescomplemented
28C7×#533C2212yescomplemented
29C2×C7×C22⋊Q8C2214yescomplemented
30C7×#518C2212yes—
31C2×C4×C7×D4C2211yescharacteristic
32Q8×C22⋊D7C2218yescomplemented
33C2×#6509C2214yescomplemented
34#90489C2212yes—
35C2×D4×Dic7C2211yescharacteristic
36C2×C4×C22⋊D7C2212yes—
37C2×#6487C2214yescomplemented
38#90421C2214yescomplemented
39#90421C2218yescomplemented
40#90420C2218yescomplemented
41#90419C2212yescomplemented
42#90419C2212yescomplemented
43#90418C2218yescomplemented
44#90418C2214yescomplemented
45D7×C4⋊Q8C2212yescomplemented
46D7×C4⋊Q8C2218yescomplemented
47D7×C4⋊Q8C2212yescomplemented
48#90381C2218yescomplemented
49#90381C2218yescomplemented
50#90381C2218yescomplemented
51#90380C2218yescomplemented
52#90379C2214yescomplemented
53D7×#125C2214yescomplemented
54D7×#125C2218yescomplemented
55#90327C22116yescomplemented
56#90327C22116yescomplemented
57#90327C22116yescomplemented
58#90326C22116yescomplemented
59#90326C2218yescomplemented
60#90325C2218yescomplemented
61#90325C2218yescomplemented
62#90325C22116yescomplemented
63#90325C22116yescomplemented
64#90323C2218yescomplemented
65#90323C22116yescomplemented
66D7×C22⋊Q8C2214yes—
67D7×C22⋊Q8C2218yes—
68D7×C22⋊Q8C2214yes—
69D7×C22⋊Q8C2218yescomplemented
70D7×C22⋊Q8C2218yescomplemented
71D7×C22⋊Q8C2218yescomplemented
72D7×C22⋊Q8C22116yescomplemented
73D7×C22⋊Q8C2218yescomplemented
74D7×C22⋊Q8C22116yescomplemented
75D7×C22⋊Q8C2218yescomplemented
76D7×C22⋊Q8C2218yescomplemented
77#90314C2218yescomplemented
78#90313C2214yescomplemented
79#90313C2214yescomplemented
80#90270C2218yescomplemented
81#90270C2214yescomplemented
82#90269C2214yescomplemented
83#90269C2214yescomplemented
84Q8×D28C2214yescomplemented
85C4×Q8×D7C2214yescomplemented
86C4×Q8×D7C2214yescomplemented
87#90236C2218yes—
88#90236C2218yes—
89C4×D4×D7C2214yes—
90C4×D4×D7C2218yes—
91C4×D4×D7C2214yes—
92C4×D4×D7C2218yes—
93C4×D4×D7C2214yes—
94C4×D4×D7C2214yes—
95#90234C2218yescomplemented
96#90234C2214yescomplemented
97#90230C2218yescomplemented
98#90230C2218yescomplemented
99#90230C2218yescomplemented
100D4×Dic14C2214yescomplemented
101D4×Dic14C2218yescomplemented
102#90212C2214yes—
103D7×#117C2214yes—
104#90210C2214yescomplemented
105#90208C2214yescomplemented
106#90202C2218yescomplemented
107#90202C22116yescomplemented
108C2×#6460C2214yescomplemented
109C2×#6459C2218yescomplemented
110C2×#6456C2211yescharacteristic
111C2×D7×C4⋊C4C2211yescharacteristic
112C2×D7×C4⋊C4C2214yescomplemented
113C2×D7×C4⋊C4C2218yescomplemented
114#90191C2212yescomplemented
115#90177C2218yes—
116C2×(C22⋊D7)⋊C4C2212yes—
117C2×D7×C22⋊C4C2218yes—
118C2×D7×C22⋊C4C2212yes—
119#90174C2218yescomplemented
120#90174C2214yescomplemented
121C2×#6441C2218yescomplemented
122C2×C4×D28C2211yescharacteristic
123C2×C42×D7C2211yescharacteristic
124#90161C2212yescomplemented
125C2×#3501—71nomaximal, Sylow
126C24×D7C2312yes—
127C22×C7×Q8C2314yescomplemented
128C22×C7×D4C2311yescharacteristic
129C23×C4×C7C2312yes—
130C22×C22⋊D7C2312yes—
131C23×Dic7C2312yes—
132C2×Q8×D7—416no—
133C2×Q8×D7C2314yes—
134C2×Q8×D7C2318yes—
135C2×Q8×D7C2314yes—
136C2×Q8×D7C2318yescomplemented
137C2×Q8×D7C2318yescomplemented
138C2×D4×D7Q8116yescomplemented
139C2×D4×D7C2314yes—
140C2×D4×D7C2314yes—
141C22×D28C2311yescharacteristic
142C22×C4×D7—48no—
143C22×C4×D7C2311yescharacteristic
144C22×C4×D7C2314yes—
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2312yes—
147C22×C4×D7C2312yes—
148C22×C4×D7C2318yes—
149C22×C4×D7C2318yes—
150C22×C4×D7C2312yes—
151C22×C4×D7C2314yes—
152C22×C4×D7C2314yes—
153C22×C4×D7C2314yes—
154C22×C4×D7C2311yescharacteristic
155C22×Dic14C2318yescomplemented
156C22×Dic14C2314yescomplemented
157C7×C4⋊Q8C2312yescomplemented
158C7×C4⋊Q8C2318yescomplemented
159C7×C4⋊Q8C2312yescomplemented
160C7×#125C2314yescomplemented
161C7×#125C2318yescomplemented
162C7×C22⋊Q8C2314yes—
163C7×C22⋊Q8C2318yes—
164C7×C22⋊Q8C2314yes—
165C7×C22⋊Q8C2318yescomplemented
166C7×C22⋊Q8C2318yescomplemented
167C7×C22⋊Q8C23116yescomplemented
168C7×C22⋊Q8C23116yescomplemented
169C4×C7×Q8C2314yescomplemented
170C4×C7×Q8C2314yescomplemented
171C4×C7×D4C2318yes—
172C4×C7×D4C2314yes—
173C4×C7×D4C2314yes—
174C4×C7×D4C2318yes—
175C7×#117C2314yes—
176C2×C7×C4⋊C4C2311yescharacteristic
177C2×C7×C4⋊C4C2318yescomplemented
178C2×C7×C4⋊C4C2314yescomplemented
179C2×C7×C22⋊C4C2318yes—
180C2×C7×C22⋊C4C2312yes—
181C2×C42×C7C2311yescharacteristic
182C2×C22⋊Dic7C2318yes—
183C2×C22⋊Dic7C2312yes—
184#6509C2314yes—
185#6509C2314yes—
186#6509C2318yes—
187#6509C23116yescomplemented
188#6509C2318yescomplemented
189#6509C2318yescomplemented
190#6509C23116yescomplemented
191Q8×Dic7C2314yescomplemented
192Q8×Dic7C2314yescomplemented
193#6507C23116yescomplemented
194#6507C2314yescomplemented
195#6507C2314yescomplemented
196D4×Dic7C2314yes—
197D4×Dic7C2318yes—
198D4×Dic7C2318yes—
199D4×Dic7C2314yes—
200C4×C22⋊D7C23116yes—
201C4×C22⋊D7C23116yes—
202C4×C22⋊D7C2318yes—
203C4×C22⋊D7C2318yes—
204C2×(C2×D7)⋊C4C2312yes—
205C2×(C2×D7)⋊C4C2312yes—
206C2×(C2×D7)⋊C4C2318yes—
207C2×(C2×D7)⋊C4C2318yes—
208#6489C2314yes—
209C2×C4⋊Dic7C2311yescharacteristic
210C2×C4⋊Dic7C2318yescomplemented
211C2×C4⋊Dic7C2314yescomplemented
212#6487C2314yes—
213#6487C2314yes—
214#6487C2318yes—
215#6487C23116yescomplemented
216#6487C23116yescomplemented
217#6487C2318yescomplemented
218#6487C2318yescomplemented
219C2×Dic7⋊C4C2312yes—
220C2×Dic7⋊C4C2318yescomplemented
221C2×Dic7⋊C4C2318yescomplemented
222C2×Dic7⋊C4C2318yescomplemented
223C2×C4×Dic7C2311yescharacteristic
224C2×C4×Dic7C2311yescharacteristic
225C2×C4×Dic7C2311yescharacteristic
226#6460C2318yes—
227#6460C2314yes—
228#6460C2314yes—
229#6460C2318yescomplemented
230#6460C23116yescomplemented
231#6460C23116yescomplemented
232#6460C2318yescomplemented
233#6459C2318yes—
234#6459C2318yes—
235#6459C23116yes—
236#6459C23116yescomplemented
237#6459C23116yescomplemented
238#6459C23116yescomplemented
239#6459C23116yescomplemented
240#6459C23116yescomplemented
241#6459C23116yescomplemented
242#6456C2318yes—
243#6456C2314yes—
244#6456C2314yes—
245#6456C2318yes—
246#6455C2314yes—
247#6455C2314yes—
248D7×C4⋊C4C2314yes—
249D7×C4⋊C4C2314yes—
250D7×C4⋊C4C2318yes—
251D7×C4⋊C4C2314yes—
252D7×C4⋊C4C23116yes—
253D7×C4⋊C4C2318yes—
254D7×C4⋊C4C2318yes—
255D7×C4⋊C4C2314yes—
256D7×C4⋊C4C2314yes—
257D7×C4⋊C4C2314yes—
258D7×C4⋊C4C2318yescomplemented
259D7×C4⋊C4C23116yescomplemented
260D7×C4⋊C4C23116yescomplemented
261D7×C4⋊C4C2318yescomplemented
262#6453C2318yescomplemented
263#6453C2314yescomplemented
264#6453C2318yescomplemented
265#6453C2314yescomplemented
266#6452C23116yescomplemented
267#6452C23116yescomplemented
268#6452C2318yescomplemented
269#6452C2318yescomplemented
270#6451C2314yescomplemented
271#6451C2314yescomplemented
272#6451C2318yescomplemented
273#6451C23116yescomplemented
274#6451C2318yescomplemented
275#6451C2314yescomplemented
276#6451C2314yescomplemented
277#6450C2318yescomplemented
278#6450C2318yescomplemented
279#6450C2314yescomplemented
280#6450C2314yescomplemented
281(C22⋊D7)⋊C4C2318yes—
282(C22⋊D7)⋊C4C2318yes—
283(C22⋊D7)⋊C4C23116yes—
284(C22⋊D7)⋊C4C23116yes—
285D7×C22⋊C4C2318yes—
286D7×C22⋊C4C23116yes—
287D7×C22⋊C4C2318yes—
288D7×C22⋊C4C23116yes—
289D7×C22⋊C4C2318yes—
290D7×C22⋊C4C23116yes—
291#6441C2318yes—
292#6441C23116yes—
293#6441C2318yes—
294#6441C23116yescomplemented
295#6441C23116yescomplemented
296#6441C23116yescomplemented
297#6441C23116yescomplemented
298#6441C23116yescomplemented
299#6441C23116yescomplemented
300#6440C2318yes—
301C4×D28C2314yes—
302C4×D28C2318yes—
303C4×D28C2318yes—
304C4×D28C2314yes—
305#6435C2318yes—
306C42×D7C2312yes—
307C42×D7C2318yes—
308C42×D7C2312yes—
309C42×D7C2312yes—
310C42×D7C2312yes—
311#6433C2314yescomplemented
312#6433C2318yescomplemented
313#6432C2318yescomplemented
314#6432C2312yescomplemented
315#6432C2312yescomplemented
316C4×Dic14C2314yescomplemented
317C4×Dic14C2318yescomplemented
318C4×Dic14C2318yescomplemented
319C4×Dic14C2314yescomplemented
320#3501—74no—
321#3501—78no—
322#3501—74no—
323#3501—72no—
324#3501—74no—
325#3501—72no—
326#3501—74no—
327#3501—72no—
328#3501—71no—
329#3501D711yescharacteristic, direct product factor
330C2×#554—74no—
331C2×#554—78no—
332C2×D4×Q8—74no—
333C2×#544—72no—
334C2×#543—74no—
335C2×#533—72no—
336C22×C22⋊Q8—74no—
337C2×#518—72no—
338C22×C4×D4—71no—
339C24×C7C2412yes—
340C23×D7—44no—
341C23×D7—44no—
342C23×D7C2×Q8116yescomplemented
343C23×D7C2411yescharacteristic
344C23×D7C2414yes—
345C23×D7C2412yes—
346C23×D7C2414yes—
347C2×C7×Q8—48no—
348C2×C7×Q8C2414yes—
349C2×C7×Q8C2418yes—
350C2×C7×Q8C2414yes—
351C2×C7×D4C2×Q818yescomplemented
352C2×C7×D4C2414yes—
353C22×C4×C7—44no—
354C22×C4×C7C2411yescharacteristic
355C22×C4×C7C2414yes—
356C22×C4×C7C2411yescharacteristic
357C22×C4×C7C2412yes—
358C22×C4×C7C2414yes—
359C22×C4×C7C2418yes—
360C22×C4×C7C2418yes—
361C22×C4×C7C2411yescharacteristic
362C2×C22⋊D7C2×Q8116yescomplemented
363C2×C22⋊D7C2418yes—
364C22×Dic7—44no—
365C22×Dic7C2411yescharacteristic
366C22×Dic7C2414yes—
367C22×Dic7C2411yescharacteristic
368C22×Dic7C2412yes—
369C22×Dic7C2418yes—
370C22×Dic7C2414yes—
371C22×Dic7C2418yes—
372C22×Dic7C2411yescharacteristic
373Q8×D7—216no—
374Q8×D7—416no—
375Q8×D7—416no—
376Q8×D7—416no—
377Q8×D7—48no—
378D4×D7C2×Q8132yescomplemented
379D4×D7C2×Q8132yescomplemented
380C2×D28C2×Q818yescomplemented
381C2×D28C2414yes—
382C2×C4×D7—24no—
383C2×C4×D7—216no—
384C2×C4×D7—48no—
385C2×C4×D7—44no—
386C2×C4×D7—48no—
387C2×C4×D7—44no—
388C2×C4×D7—48no—
389C2×C4×D7—44no—
390C2×C4×D7—416no—
391C2×C4×D7—42no—
392C2×C4×D7—416no—
393C2×C4×D7C2×Q818yescomplemented
394C2×C4×D7C2412yes—
395C2×C4×D7C2411yescharacteristic
396C2×C4×D7C2411yescharacteristic
397C2×C4×D7C2411yescharacteristic
398C2×C4×D7C2418yes—
399C2×C4×D7C2418yes—
400C2×C4×D7C2414yes—
401C2×C4×D7C2414yes—
402C2×C4×D7C2414yes—
403C2×C4×D7C2412yes—
404C2×C4×D7C2414yes—
405C2×C4×D7C24116yes—
406C2×C4×D7C24116yes—
407C2×C4×D7C2414yes—
408C2×C4×D7C2414yes—
409C2×C4×D7C2412yes—
410C2×C4×D7C2412yes—
411C2×C4×D7C2411yescharacteristic
412C2×Dic14—416no—
413C2×Dic14—48no—
414C2×Dic14C2414yes—
415C2×Dic14C2418yes—
416C2×Dic14C2414yes—
417C2×Dic14C2418yes—
418C2×Dic14C24116yes—
419C2×Dic14C2418yes—
420C7×C4⋊C4C2414yes—
421C7×C4⋊C4C2414yes—
422C7×C4⋊C4C2418yes—
423C7×C4⋊C4C2418yes—
424C7×C4⋊C4C2414yes—
425C7×C4⋊C4C2414yes—
426C7×C4⋊C4C24116yes—
427C7×C4⋊C4C2414yes—
428C7×C4⋊C4C2418yes—
429C7×C22⋊C4C2418yes—
430C7×C22⋊C4C2418yes—
431C7×C22⋊C4C24116yes—
432C42×C7C2412yes—
433C42×C7C2418yes—
434C42×C7C2412yes—
435C22⋊Dic7C2418yes—
436C22⋊Dic7C2418yes—
437C22⋊Dic7C24116yes—
438(C2×D7)⋊C4C2418yes—
439(C2×D7)⋊C4C2418yes—
440(C2×D7)⋊C4C2418yes—
441(C2×D7)⋊C4C24116yes—
442(C2×D7)⋊C4C24116yes—
443(C2×D7)⋊C4C2418yes—
444C4⋊Dic7C2414yes—
445C4⋊Dic7C2414yes—
446C4⋊Dic7C2418yes—
447C4⋊Dic7C2418yes—
448C4⋊Dic7C2414yes—
449C4⋊Dic7C2414yes—
450C4⋊Dic7C2414yes—
451C4⋊Dic7C24116yes—
452C4⋊Dic7C2418yes—
453Dic7⋊C4C2418yes—
454Dic7⋊C4C2418yes—
455Dic7⋊C4C2418yes—
456Dic7⋊C4C2418yes—
457Dic7⋊C4C2418yes—
458Dic7⋊C4C2418yes—
459Dic7⋊C4C24116yes—
460Dic7⋊C4C24116yes—
461Dic7⋊C4C2418yes—
462Dic7⋊C4C2418yes—
463Dic7⋊C4C24116yes—
464Dic7⋊C4C2418yes—
465C4×Dic7C2412yes—
466C4×Dic7C2412yes—
467C4×Dic7C2418yes—
468C4×Dic7C2412yes—
469C4×Dic7C2412yes—
470C4×Dic7C2412yes—
471C4×Dic7C2412yes—
472C4×Dic7C2418yes—
473C4×Dic7C2418yes—
474C23×Q8—74no—
475C23×D4—71no—
476C24×C4—72no—
477#554—78no—
478#554—74no—
479#554—78no—
480#554—78no—
481#554—78no—
482#554—78no—
483#554—716no—
484#554—716no—
485#554—716no—
486#554—716no—
487#554—74no—
488#554—78no—
489#554—78no—
490#554—78no—
491#554—78no—
492#554—78no—
493#554—74no—
494#554—78no—
495#554—716no—
496#554C2×D714yescomplemented
497#554C2×D718yescomplemented
498D4×Q8—78no—
499D4×Q8—78no—
500D4×Q8—74no—
501D4×Q8—78no—
502D4×Q8—716no—
503D4×Q8—74no—
504D4×Q8—78no—
505D4×Q8—74no—
506D4×Q8C2×D714yescomplemented
507#544—78no—
508#544—78no—
509#544—78no—
510#544—74no—
511#544—72no—
512#544C2×D712yescomplemented
513#543—78no—
514#543—78no—
515#543—716no—
516#543—716no—
517#543—78no—
518#543—74no—
519#543C2×D714yescomplemented
520#533—72no—
521#533—72no—
522#533—74no—
523#533—74no—
524#533—74no—
525#533—74no—
526#533—74no—
527#533—74no—
528#533—72no—
529#533C2×D712yescomplemented
530C2×C4⋊Q8—72no—
531C2×C4⋊Q8—72no—
532C2×C4⋊Q8—78no—
533C2×#125—74no—
534C2×#125—78no—
535C2×C22⋊Q8—74no—
536C2×C22⋊Q8—74no—
537C2×C22⋊Q8—74no—
538C2×C22⋊Q8—78no—
539C2×C22⋊Q8—78no—
540C2×C22⋊Q8—78no—
541C2×C22⋊Q8—74no—
542C2×C22⋊Q8—78no—
543C2×C22⋊Q8—78no—
544C2×C22⋊Q8—78no—
545C2×C22⋊Q8—78no—
546C2×C22⋊Q8—716no—
547C2×C22⋊Q8—716no—
548C2×C22⋊Q8—78no—
549C2×C22⋊Q8—74no—
550C2×C22⋊Q8—78no—
551C2×C22⋊Q8C2×D714yescomplemented
552#518—72no—
553#518—78no—
554#518—78no—
555#518—74no—
556#518—78no—
557#518C2×D712yes—
558C2×C4×Q8—74no—
559C2×C4×Q8—74no—
560C2×C4×D4—71no—
561C2×C4×D4—72no—
562C2×C4×D4—74no—
563C2×C4×D4—74no—
564C2×C4×D4—74no—
565C2×C4×D4—74no—
566C2×C4×D4—78no—
567C2×C4×D4—78no—
568C2×C4×D4—71no—
569C2×C4×D4—72no—
570C2×C4×D4—71no—
571C2×C4×D4C2×D711yescharacteristic
572C2×#117—74no—
573C22×C4⋊C4—71no—
574C22×C4⋊C4—78no—
575C22×C4⋊C4—74no—
576C22×C22⋊C4—72no—
577C22×C22⋊C4—78no—
578C22×C42—71no—
579C23×C7—42no—
580C23×C7—42no—
581C23×C7C22×Q818yescomplemented
582C23×C7C2511yescharacteristic
583C23×C7C2514yes—
584C22×D7—28no—
585C22×D7—22no—
586C22×D7—28no—
587C22×D7—22no—
588C22×D7—432no—
589C22×D7—42no—
590C22×D7—44no—
591C22×D7—42no—
592C22×D7—44no—
593C22×D7C22×Q814yes—
594C22×D7C22×Q8116yes—
595C22×D7C22×Q818yescomplemented
596C22×D7C22×Q8116yescomplemented
597C22×D7C2511yescharacteristic
598C22×D7C2514yes—
599C22×D7C2511yescharacteristic
600C7×Q8—28no—
601C7×Q8—48no—
602C7×Q8—44no—
603C7×D4C22×Q8116yescomplemented
604C2×C4×C7—28no—
605C2×C4×C7—22no—
606C2×C4×C7—48no—
607C2×C4×C7—42no—
608C2×C4×C7—44no—
609C2×C4×C7—41no—
610C2×C4×C7—48no—
611C2×C4×C7C22×Q814yescomplemented
612C2×C4×C7C2511yescharacteristic
613C2×C4×C7C2512yes—
614C2×C4×C7C2518yes—
615C2×C4×C7C2518yes—
616C2×C4×C7C2514yes—
617C2×C4×C7C2512yes—
618C2×C4×C7C2511yescharacteristic
619C22⋊D7C22×Q8132yescomplemented
620C2×Dic7—28no—
621C2×Dic7—22no—
622C2×Dic7—48no—
623C2×Dic7—42no—
624C2×Dic7—44no—
625C2×Dic7—41no—
626C2×Dic7—48no—
627C2×Dic7C22×Q814yescomplemented
628C2×Dic7C2511yescharacteristic
629C2×Dic7C2512yes—
630C2×Dic7C2518yes—
631C2×Dic7C2518yes—
632C2×Dic7C2514yes—
633C2×Dic7C2512yes—
634C2×Dic7C2511yescharacteristic
635D28C22×Q8116yescomplemented
636C4×D7—22no—
637C4×D7—28no—
638C4×D7—216no—
639C4×D7—216no—
640C4×D7—24no—
641C4×D7—22no—
642C4×D7—28no—
643C4×D7—22no—
644C4×D7—28no—
645C4×D7—44no—
646C4×D7—44no—
647C4×D7—44no—
648C4×D7—42no—
649C4×D7—416no—
650C4×D7—416no—
651C4×D7C22×Q818yes—
652C4×D7C22×Q818yescomplemented
653C4×D7H(5,𝔽2)14yes—
654Dic14—28no—
655Dic14—216no—
656Dic14—48no—
657Dic14—416no—
658Dic14—48no—
659Dic14—44no—
660C25—72no—
661C22×Q8—74no—
662C22×Q8—74no—
663C22×Q8—78no—
664C22×Q8—78no—
665C22×Q8—78no—
666C22×Q8—78no—
667C22×Q8—74no—
668C22×Q8—2816no—
669C22×Q8C22×D714yescomplemented
670C22×D4—72no—
671C22×D4—716no—
672C22×D4—74no—
673C22×D4—74no—
674C22×D4—71no—
675C22×D4C22×D711yescharacteristic
676C23×C4—71no—
677C23×C4—72no—
678C23×C4—74no—
679C23×C4—71no—
680C23×C4—71no—
681C23×C4—78no—
682C23×C4—78no—
683C23×C4—72no—
684C23×C4—74no—
685C23×C4—72no—
686C23×C4—74no—
687C23×C4—72no—
688C23×C4—74no—
689C23×C4—288no—
690C23×C4C22×D712yes—
691C4⋊Q8—74no—
692C4⋊Q8—74no—
693C4⋊Q8—716no—
694C4⋊Q8—74no—
695C4⋊Q8—74no—
696C4⋊Q8—74no—
697C4⋊Q8—74no—
698C4⋊Q8—716no—
699C4⋊Q8—78no—
700C4⋊Q8—78no—
701C4⋊Q8—72no—
702C4⋊Q8—72no—
703C4⋊Q8—78no—
704C4⋊Q8C22×D712yescomplemented
705C4⋊Q8C22×D712yescomplemented
706C4⋊Q8C22×D718yescomplemented
707#125—78no—
708#125—78no—
709#125—74no—
710#125—74no—
711#125—716no—
712#125—716no—
713#125—78no—
714#125—78no—
715#125—74no—
716#125—78no—
717#125C22×D714yescomplemented
718#125C22×D718yescomplemented
719C22⋊Q8—74no—
720C22⋊Q8—78no—
721C22⋊Q8—78no—
722C22⋊Q8—78no—
723C22⋊Q8—74no—
724C22⋊Q8—716no—
725C22⋊Q8—716no—
726C22⋊Q8—74no—
727C22⋊Q8—78no—
728C22⋊Q8—78no—
729C22⋊Q8—78no—
730C22⋊Q8—74no—
731C22⋊Q8—716no—
732C22⋊Q8—716no—
733C22⋊Q8—78no—
734C22⋊Q8—74no—
735C22⋊Q8—716no—
736C22⋊Q8—78no—
737C22⋊Q8—716no—
738C22⋊Q8—78no—
739C22⋊Q8—716no—
740C22⋊Q8—78no—
741C22⋊Q8—78no—
742C22⋊Q8—74no—
743C22⋊Q8—716no—
744C22⋊Q8—716no—
745C22⋊Q8—716no—
746C22⋊Q8—716no—
747C22⋊Q8—716no—
748C22⋊Q8—716no—
749C22⋊Q8—78no—
750C22⋊Q8—716no—
751C22⋊Q8—716no—
752C22⋊Q8—716no—
753C22⋊Q8—78no—
754C22⋊Q8—716no—
755C22⋊Q8—716no—
756C22⋊Q8—716no—
757C22⋊Q8—716no—
758C22⋊Q8C22×D714yes—
759C22⋊Q8C22×D718yes—
760C22⋊Q8C22×D714yes—
761C22⋊Q8C22×D718yescomplemented
762C22⋊Q8C22×D718yescomplemented
763C22⋊Q8C22×D7116yescomplemented
764C22⋊Q8C22×D7116yescomplemented
765C4×Q8—74no—
766C4×Q8—74no—
767C4×Q8—78no—
768C4×Q8—74no—
769C4×Q8—74no—
770C4×Q8—78no—
771C4×Q8—78no—
772C4×Q8—74no—
773C4×Q8—78no—
774C4×Q8—74no—
775C4×Q8C22×D714yescomplemented
776C4×Q8C22×D714yescomplemented
777C4×D4—74no—
778C4×D4—74no—
779C4×D4—78no—
780C4×D4—78no—
781C4×D4—78no—
782C4×D4—78no—
783C4×D4—716no—
784C4×D4—716no—
785C4×D4—74no—
786C4×D4—74no—
787C4×D4—78no—
788C4×D4—78no—
789C4×D4—78no—
790C4×D4—78no—
791C4×D4—716no—
792C4×D4—716no—
793C4×D4—74no—
794C4×D4—74no—
795C4×D4—78no—
796C4×D4—78no—
797C4×D4C22×D714yes—
798C4×D4C22×D714yes—
799C4×D4C22×D718yes—
800C4×D4C22×D718yes—
801#117—74no—
802#117—74no—
803#117—74no—
804#117—78no—
805#117—78no—
806#117C22×D714yes—
807C2×C4⋊C4—72no—
808C2×C4⋊C4—71no—
809C2×C4⋊C4—78no—
810C2×C4⋊C4—78no—
811C2×C4⋊C4—78no—
812C2×C4⋊C4—78no—
813C2×C4⋊C4—74no—
814C2×C4⋊C4—78no—
815C2×C4⋊C4—74no—
816C2×C4⋊C4—74no—
817C2×C4⋊C4—74no—
818C2×C4⋊C4—78no—
819C2×C4⋊C4—716no—
820C2×C4⋊C4—716no—
821C2×C4⋊C4—716no—
822C2×C4⋊C4—78no—
823C2×C4⋊C4—78no—
824C2×C4⋊C4—74no—
825C2×C4⋊C4—74no—
826C2×C4⋊C4—78no—
827C2×C4⋊C4—74no—
828C2×C4⋊C4C22×D711yescharacteristic
829C2×C4⋊C4C22×D718yescomplemented
830C2×C4⋊C4C22×D714yescomplemented
831C2×C22⋊C4—72no—
832C2×C22⋊C4—78no—
833C2×C22⋊C4—72no—
834C2×C22⋊C4—72no—
835C2×C22⋊C4—78no—
836C2×C22⋊C4—78no—
837C2×C22⋊C4—78no—
838C2×C22⋊C4—78no—
839C2×C22⋊C4—716no—
840C2×C22⋊C4—78no—
841C2×C22⋊C4—716no—
842C2×C22⋊C4—716no—
843C2×C22⋊C4C22×D712yes—
844C2×C22⋊C4C22×D718yes—
845C2×C42—71no—
846C2×C42—71no—
847C2×C42—71no—
848C2×C42—78no—
849C2×C42—72no—
850C2×C42—72no—
851C2×C42—72no—
852C2×C42—72no—
853C2×C42C22×D711yescharacteristic
854C22×C7—24no—
855C22×C7—21no—
856C22×C7—24no—
857C22×C7—21no—
858C22×C7—48no—
859C22×C7C23×Q812yes—
860C22×C7C23×Q818yes—
861C22×C7C2611yescharacteristic
862C2×D7—24no—
863C2×D7—21no—
864C2×D7—24no—
865C2×D7—21no—
866C2×D7—28no—
867C2×D7—232no—
868C2×D7—416no—
869C2×D7—48no—
870C2×D7C23×Q812yes—
871C2×D7C23×Q818yes—
872C2×D7C23×Q812yes—
873C2×D7C2×H(5,𝔽2)12yes—
874C2×D7#58512yes—
875C4×C7—28no—
876C4×C7—24no—
877C4×C7—21no—
878C4×C7—22no—
879C4×C7—28no—
880C4×C7C23×Q814yes—
881C4×C7C2×H(5,𝔽2)12yes—
882Dic7—28no—
883Dic7—24no—
884Dic7—21no—
885Dic7—22no—
886Dic7—28no—
887Dic7C23×Q814yes—
888Dic7C2×H(5,𝔽2)12yes—
889C24—71no—
890C24—74no—
891C24—716no—
892C24—74no—
893C24—72no—
894C24—284no—
895C24—284no—
896C24C23×D712yes—
897C2×Q8—48no—
898C2×Q8—78no—
899C2×Q8—74no—
900C2×Q8—78no—
901C2×Q8—74no—
902C2×Q8—78no—
903C2×Q8—716no—
904C2×Q8—1416no—
905C2×Q8—288no—
906C2×Q8—2816no—
907C2×Q8—288no—
908C2×Q8—2816no—
909C2×Q8—2816no—
910C2×Q8—2816no—
911C2×Q8C23×D714yes—
912C2×Q8C23×D714yes—
913C2×Q8C23×D718yes—
914C2×D4—716no—
915C2×D4—78no—
916C2×D4—732no—
917C2×D4—732no—
918C2×D4—78no—
919C2×D4—74no—
920C2×D4Q8×D718yescomplemented
921C2×D4C23×D714yes—
922C22×C4—44no—
923C22×C4—71no—
924C22×C4—78no—
925C22×C4—72no—
926C22×C4—71no—
927C22×C4—72no—
928C22×C4—71no—
929C22×C4—74no—
930C22×C4—71no—
931C22×C4—78no—
932C22×C4—78no—
933C22×C4—72no—
934C22×C4—74no—
935C22×C4—72no—
936C22×C4—71no—
937C22×C4—71no—
938C22×C4—71no—
939C22×C4—78no—
940C22×C4—78no—
941C22×C4—74no—
942C22×C4—74no—
943C22×C4—74no—
944C22×C4—72no—
945C22×C4—716no—
946C22×C4—716no—
947C22×C4—74no—
948C22×C4—74no—
949C22×C4—74no—
950C22×C4—144no—
951C22×C4—1416no—
952C22×C4—284no—
953C22×C4—288no—
954C22×C4—288no—
955C22×C4—284no—
956C22×C4—2816no—
957C22×C4—282no—
958C22×C4—288no—
959C22×C4—284no—
960C22×C4—2816no—
961C22×C4—284no—
962C22×C4C23×D711yescharacteristic
963C22×C4C23×D714yes—
964C22×C4C23×D711yescharacteristic
965C22×C4C23×D718yes—
966C22×C4C23×D712yes—
967C22×C4C23×D718yes—
968C22×C4C23×D714yes—
969C22×C4C23×D711yescharacteristic
970C4⋊C4—78no—
971C4⋊C4—78no—
972C4⋊C4—78no—
973C4⋊C4—78no—
974C4⋊C4—716no—
975C4⋊C4—716no—
976C4⋊C4—716no—
977C4⋊C4—78no—
978C4⋊C4—78no—
979C4⋊C4—78no—
980C4⋊C4—78no—
981C4⋊C4—78no—
982C4⋊C4—78no—
983C4⋊C4—74no—
984C4⋊C4—74no—
985C4⋊C4—78no—
986C4⋊C4—716no—
987C4⋊C4—74no—
988C4⋊C4—74no—
989C4⋊C4—78no—
990C4⋊C4—74no—
991C4⋊C4C23×D718yes—
992C4⋊C4C23×D714yes—
993C4⋊C4C23×D714yes—
994C4⋊C4C23×D718yes—
995C4⋊C4C23×D7116yes—
996C4⋊C4C23×D714yes—
997C4⋊C4C23×D714yes—
998C4⋊C4C23×D718yes—
999C4⋊C4C23×D714yes—
1000C22⋊C4—78no—
1001C22⋊C4—78no—
1002C22⋊C4—716no—
1003C22⋊C4—78no—
1004C22⋊C4—78no—
1005C22⋊C4—78no—
1006C22⋊C4—716no—
1007C22⋊C4—716no—
1008C22⋊C4—78no—
1009C22⋊C4C23×D718yes—
1010C22⋊C4C23×D718yes—
1011C22⋊C4C23×D7116yes—
1012C42—72no—
1013C42—72no—
1014C42—72no—
1015C42—72no—
1016C42—72no—
1017C42—72no—
1018C42—78no—
1019C42—78no—
1020C42—78no—
1021C42C23×D712yes—
1022C42C23×D712yes—
1023C42C23×D718yes—
1024C2×C7—22no—
1025C2×C7—28no—
1026C2×C7C24×Q811yescharacteristic
1027C2×C7C22×H(5,𝔽2)11yescharacteristic
1028C2×C7C2×#58511yescharacteristic
1029D7—22no—
1030D7—28no—
1031D7#350114yesdirect product factor
1032C23—42no—
1033C23—42no—
1034C23—71no—
1035C23—71no—
1036C23—74no—
1037C23—74no—
1038C23—716no—
1039C23—716no—
1040C23—78no—
1041C23—148no—
1042C23—142no—
1043C23—148no—
1044C23—142no—
1045C23—284no—
1046C23—282no—
1047C23—284no—
1048C23—282no—
1049C23—2832no—
1050C23C2×Q8×D718yescomplemented
1051C23C24×D711yescharacteristic
1052C23C24×D714yes—
1053Q8—28no—
1054Q8—48no—
1055Q8—44no—
1056Q8—1416no—
1057Q8—148no—
1058Q8—288no—
1059Q8—284no—
1060Q8—288no—
1061Q8—2816no—
1062D4—732no—
1063D4—716no—
1064D4C2×Q8×D7116yescomplemented
1065C2×C4—22no—
1066C2×C4—28no—
1067C2×C4—44no—
1068C2×C4—42no—
1069C2×C4—48no—
1070C2×C4—41no—
1071C2×C4—48no—
1072C2×C4—72no—
1073C2×C4—71no—
1074C2×C4—74no—
1075C2×C4—78no—
1076C2×C4—78no—
1077C2×C4—74no—
1078C2×C4—72no—
1079C2×C4—71no—
1080C2×C4—78no—
1081C2×C4—78no—
1082C2×C4—74no—
1083C2×C4—142no—
1084C2×C4—148no—
1085C2×C4—142no—
1086C2×C4—148no—
1087C2×C4—1416no—
1088C2×C4—1416no—
1089C2×C4—144no—
1090C2×C4—142no—
1091C2×C4—148no—
1092C2×C4—142no—
1093C2×C4—148no—
1094C2×C4—2816no—
1095C2×C4—282no—
1096C2×C4—284no—
1097C2×C4—284no—
1098C2×C4—284no—
1099C2×C4—2816no—
1100C2×C4—288no—
1101C2×C4—281no—
1102C2×C4—284no—
1103C2×C4—282no—
1104C2×C4—288no—
1105C2×C4C2×Q8×D714yescomplemented
1106C2×C4C24×D712yes—
1107C2×C4C24×D711yescharacteristic
1108C2×C4C24×D718yes—
1109C2×C4C24×D718yes—
1110C2×C4C24×D714yes—
1111C2×C4C24×D712yes—
1112C2×C4C24×D711yescharacteristic
1113C7C2×#350111yescharacteristic, complemented, Sylow
1114C22—24no—
1115C22—21no—
1116C22—24no—
1117C22—21no—
1118C22—48no—
1119C22—72no—
1120C22—72no—
1121C22—72no—
1122C22—72no—
1123C22—78no—
1124C22—148no—
1125C22—1432no—
1126C22—144no—
1127C22—141no—
1128C22—144no—
1129C22—141no—
1130C22—288no—
1131C22—2816no—
1132C22C22×Q8×D712yes—
1133C22C22×Q8×D718yes—
1134C22C25×D711yescharacteristic
1135C4—21no—
1136C4—24no—
1137C4—28no—
1138C4—28no—
1139C4—22no—
1140C4—74no—
1141C4—72no—
1142C4—141no—
1143C4—144no—
1144C4—148no—
1145C4—148no—
1146C4—142no—
1147C4C22×Q8×D714yes—
1148C4D7×H(5,𝔽2)12yes—
1149C2—22no—
1150C2—28no—
1151C2—74no—
1152C2—142no—
1153C2—148no—
1154C2C23×Q8×D711yescharacteristic
1155C2C2×D7×H(5,𝔽2)11yescharacteristic
1156C2D7×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D7
commutator, socle, cosocleC22×C7C26
FittingC7×#3501C2
prime radicalC22×D4×D7C22
hypercenter#3501D7
hypocenterC7C2×#3501
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ #3501

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C7×#3501C2semidirect
2. #11744017C2semidirect
3. #11744016C2semidirect
4. D7×#554C2semidirect
5. D7×#554C2semidirect
6. #11743829C2semidirect
7. D4×Q8×D7C2semidirect
8. #11743667C2semidirect
9. D7×#544C2semidirect
10. D7×#543C2semidirect
11. #11743642C2semidirect
12. #11743348C2semidirect
13. D7×#533C2semidirect
14. #11743054C2semidirect
15. C2×D7×C22⋊Q8C2semidirect
17. #11742928C2semidirect
19. #11742834C2semidirect
20. C22×Q8×D7C22semidirect
23. C7×#554C22semidirect
24. C7×#554C22semidirect
25. C7×D4×Q8C22semidirect
26. C7×#544C22semidirect
27. C7×#543C22semidirect
28. C7×#533C22semidirect
29. C2×C7×C22⋊Q8C22semidirect
32. Q8×C22⋊D7C22semidirect
33. C2×#6509C22semidirect
37. C2×#6487C22semidirect
38. #90421C22semidirect
39. #90421C22semidirect
40. #90420C22semidirect
41. #90419C22semidirect
42. #90419C22semidirect
43. #90418C22semidirect
44. #90418C22semidirect
45. D7×C4⋊Q8C22semidirect
46. D7×C4⋊Q8C22semidirect
47. D7×C4⋊Q8C22semidirect
48. #90381C22semidirect
49. #90381C22semidirect
50. #90381C22semidirect
51. #90380C22semidirect
52. #90379C22semidirect
53. D7×#125C22semidirect
54. D7×#125C22semidirect
55. #90327C22semidirect
56. #90327C22semidirect
57. #90327C22semidirect
58. #90326C22semidirect
59. #90326C22semidirect
60. #90325C22semidirect
61. #90325C22semidirect
62. #90325C22semidirect
63. #90325C22semidirect
64. #90323C22semidirect
65. #90323C22semidirect
69. D7×C22⋊Q8C22semidirect
70. D7×C22⋊Q8C22semidirect
71. D7×C22⋊Q8C22semidirect
72. D7×C22⋊Q8C22semidirect
73. D7×C22⋊Q8C22semidirect
74. D7×C22⋊Q8C22semidirect
75. D7×C22⋊Q8C22semidirect
76. D7×C22⋊Q8C22semidirect
77. #90314C22semidirect
78. #90313C22semidirect
79. #90313C22semidirect
80. #90270C22semidirect
81. #90270C22semidirect
82. #90269C22semidirect
83. #90269C22semidirect
84. Q8×D28C22semidirect
85. C4×Q8×D7C22semidirect
86. C4×Q8×D7C22semidirect
95. #90234C22semidirect
96. #90234C22semidirect
97. #90230C22semidirect
98. #90230C22semidirect
99. #90230C22semidirect
100. D4×Dic14C22semidirect
101. D4×Dic14C22semidirect
104. #90210C22semidirect
105. #90208C22semidirect
106. #90202C22semidirect
107. #90202C22semidirect
108. C2×#6460C22semidirect
109. C2×#6459C22semidirect
112. C2×D7×C4⋊C4C22semidirect
113. C2×D7×C4⋊C4C22semidirect
114. #90191C22semidirect
119. #90174C22semidirect
120. #90174C22semidirect
121. C2×#6441C22semidirect
124. #90161C22semidirect
127. C22×C7×Q8C23semidirect
136. C2×Q8×D7C23semidirect
137. C2×Q8×D7C23semidirect
138. C2×D4×D7Q8semidirect
155. C22×Dic14C23semidirect
156. C22×Dic14C23semidirect
157. C7×C4⋊Q8C23semidirect
158. C7×C4⋊Q8C23semidirect
159. C7×C4⋊Q8C23semidirect
160. C7×#125C23semidirect
161. C7×#125C23semidirect
165. C7×C22⋊Q8C23semidirect
166. C7×C22⋊Q8C23semidirect
167. C7×C22⋊Q8C23semidirect
168. C7×C22⋊Q8C23semidirect
169. C4×C7×Q8C23semidirect
170. C4×C7×Q8C23semidirect
177. C2×C7×C4⋊C4C23semidirect
178. C2×C7×C4⋊C4C23semidirect
187. #6509C23semidirect
188. #6509C23semidirect
189. #6509C23semidirect
190. #6509C23semidirect
191. Q8×Dic7C23semidirect
192. Q8×Dic7C23semidirect
193. #6507C23semidirect
194. #6507C23semidirect
195. #6507C23semidirect
210. C2×C4⋊Dic7C23semidirect
211. C2×C4⋊Dic7C23semidirect
215. #6487C23semidirect
216. #6487C23semidirect
217. #6487C23semidirect
218. #6487C23semidirect
220. C2×Dic7⋊C4C23semidirect
221. C2×Dic7⋊C4C23semidirect
222. C2×Dic7⋊C4C23semidirect
229. #6460C23semidirect
230. #6460C23semidirect
231. #6460C23semidirect
232. #6460C23semidirect
236. #6459C23semidirect
237. #6459C23semidirect
238. #6459C23semidirect
239. #6459C23semidirect
240. #6459C23semidirect
241. #6459C23semidirect
258. D7×C4⋊C4C23semidirect
259. D7×C4⋊C4C23semidirect
260. D7×C4⋊C4C23semidirect
261. D7×C4⋊C4C23semidirect
262. #6453C23semidirect
263. #6453C23semidirect
264. #6453C23semidirect
265. #6453C23semidirect
266. #6452C23semidirect
267. #6452C23semidirect
268. #6452C23semidirect
269. #6452C23semidirect
270. #6451C23semidirect
271. #6451C23semidirect
272. #6451C23semidirect
273. #6451C23semidirect
274. #6451C23semidirect
275. #6451C23semidirect
276. #6451C23semidirect
277. #6450C23semidirect
278. #6450C23semidirect
279. #6450C23semidirect
280. #6450C23semidirect
294. #6441C23semidirect
295. #6441C23semidirect
296. #6441C23semidirect
297. #6441C23semidirect
298. #6441C23semidirect
299. #6441C23semidirect
311. #6433C23semidirect
312. #6433C23semidirect
313. #6432C23semidirect
314. #6432C23semidirect
315. #6432C23semidirect
316. C4×Dic14C23semidirect
317. C4×Dic14C23semidirect
318. C4×Dic14C23semidirect
319. C4×Dic14C23semidirect
329. #3501D7direct (N × H)
342. C23×D7C2×Q8semidirect
351. C2×C7×D4C2×Q8semidirect
362. C2×C22⋊D7C2×Q8semidirect
378. D4×D7C2×Q8semidirect
379. D4×D7C2×Q8semidirect
380. C2×D28C2×Q8semidirect
393. C2×C4×D7C2×Q8semidirect
496. #554C2×D7semidirect
497. #554C2×D7semidirect
506. D4×Q8C2×D7semidirect
512. #544C2×D7semidirect
519. #543C2×D7semidirect
529. #533C2×D7semidirect
551. C2×C22⋊Q8C2×D7semidirect
581. C23×C7C22×Q8semidirect
595. C22×D7C22×Q8semidirect
596. C22×D7C22×Q8semidirect
603. C7×D4C22×Q8semidirect
611. C2×C4×C7C22×Q8semidirect
619. C22⋊D7C22×Q8semidirect
627. C2×Dic7C22×Q8semidirect
635. D28C22×Q8semidirect
652. C4×D7C22×Q8semidirect
669. C22×Q8C22×D7semidirect
704. C4⋊Q8C22×D7semidirect
705. C4⋊Q8C22×D7semidirect
706. C4⋊Q8C22×D7semidirect
717. #125C22×D7semidirect
718. #125C22×D7semidirect
761. C22⋊Q8C22×D7semidirect
762. C22⋊Q8C22×D7semidirect
763. C22⋊Q8C22×D7semidirect
764. C22⋊Q8C22×D7semidirect
775. C4×Q8C22×D7semidirect
776. C4×Q8C22×D7semidirect
829. C2×C4⋊C4C22×D7semidirect
830. C2×C4⋊C4C22×D7semidirect
920. C2×D4Q8×D7semidirect
1031. D7#3501direct (N × H)
1050. C23C2×Q8×D7semidirect
1064. D4C2×Q8×D7semidirect
1105. C2×C4C2×Q8×D7semidirect
1113. C7C2×#3501semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#35012
#117440172
#117440162
D7×#5542
#117438292
D4×Q8×D72
#117436672
D7×#5442
D7×#5432
#117436422
#117433482
D7×#5332
#117430542
C2×D7×C22⋊Q82
D7×#5182
#117429282
C2×C4×D4×D72
#117428342
C2×#35017