Finite Group Databasebeta

← C2×#11743605 #14261513

Subgroups — C2×#11743605 #14261513

Order 1792.

6446 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#542C211yesmaximal, characteristic
2#11743605C2132yesmaximal, direct product factor
3C2×#90413C211yesmaximal, characteristic, complemented
4C2×#90412C211yesmaximal, characteristic, complemented
5C2×#90392C212yesmaximal, complemented
6C2×#90392C212yesmaximal, complemented
7C2×#90363C212yesmaximal, complemented
8C2×#90362C211yesmaximal, characteristic, complemented
9C2×#90362C211yesmaximal, characteristic, complemented
10C2×#90362C212yesmaximal, complemented
11C2×#90342C212yesmaximal, complemented
12C2×#90341C212yesmaximal, complemented
13C2×#90314C212yesmaximal, complemented
14C2×#90316C212yesmaximal, complemented
15C2×#90316C211yesmaximal, characteristic, complemented
16C2×#90313C211yesmaximal, characteristic, complemented
17C2×#90294C211yesmaximal, characteristic
18C2×#90291C211yesmaximal, characteristic
19C2×#90260C211yesmaximal, characteristic, complemented
20C2×#90258C211yesmaximal, characteristic, complemented
21C2×#90233C211yesmaximal, characteristic, complemented
22C2×#90230C211yesmaximal, characteristic, complemented
23C2×#90209C211yesmaximal, characteristic, complemented
24C2×#90208C211yesmaximal, characteristic, complemented
25C7×#542C22116yes—
26C2×C7×C4⋊Q8C2211yescharacteristic
27C2×C7×#126C2212yes—
28C2×C7×#124C2211yescharacteristic
29C2×C7×#124C2212yes—
30C2×C7×#123C2212yes—
31C2×C7×C22⋊Q8C2211yescharacteristic
32C2×C7×C22⋊Q8C2212yes—
33C2×C7×#121C2211yescharacteristic
34C2×C4×C7×Q8C2211yescharacteristic
35C2×C4×C7×D4C2211yescharacteristic
36C2×C7×#117C2211yescharacteristic
37C2×Q8×Dic7C2212yes—
38C2×Q8×Dic7C2211yescharacteristic
39C2×Q8×Dic7C2211yescharacteristic
40C2×#6507C2212yes—
41C2×#6507C2212yes—
42C2×#6507C2212yes—
43C2×#6507C2211yescharacteristic
44C2×#6507C2211yescharacteristic
45C2×#6499C2211yescharacteristic
46C2×#6499C2212yes—
47C2×#6499C2211yescharacteristic
48C2×#6498C2212yes—
49C2×#6498C2212yes—
50C2×D4×Dic7C2212yes—
51C2×D4×Dic7C2211yescharacteristic
52C2×D4×Dic7C2211yescharacteristic
53C2×#6489C2211yescharacteristic
54C2×#6489C2212yes—
55C2×#6487C2211yescharacteristic
56C2×#6487C2211yescharacteristic
57C2×#6487C2212yes—
58C2×#6487C2212yes—
59C22×Dic7⋊C4C2212yes—
60C22×C4×Dic7C2211yescharacteristic
61#90413C22116yescomplemented
62#90412C22116yescomplemented
63#90392C22132yescomplemented
64#90392C22132yescomplemented
65#90363C22132yescomplemented
66#90362C22132yescomplemented
67#90362C22116yescomplemented
68#90362C22116yescomplemented
69#90342C22132yescomplemented
70#90341C22132yescomplemented
71#90316C22132yescomplemented
72#90316C22116yescomplemented
73#90314C22132yescomplemented
74#90313C22116yescomplemented
75#90294C22116yes—
76#90291C22116yes—
77#90260C22116yescomplemented
78#90258C22116yescomplemented
79#90233C22116yescomplemented
80#90230C22116yescomplemented
81#90209C22116yescomplemented
82#90208C22116yescomplemented
83C2×#6453C2211yescharacteristic
84C2×#6453C2211yescharacteristic
85C2×#6453C2211yescharacteristic
86C2×#6453C2212yes—
87C2×#6453C2212yes—
88C2×#6453C2211yescharacteristic
89C2×#6452C2212yes—
90C2×#6452C2212yes—
91C2×#6452C2212yes—
92C2×#6452C2212yes—
93C2×#6452C2212yes—
94C2×#6452C2212yes—
95C2×#6452C2212yes—
96C2×#6452C2212yes—
97C2×#6451C2211yescharacteristic
98C2×#6451C2211yescharacteristic
99C2×#6451C2212yes—
100C2×#6451C2211yescharacteristic
101C2×#6451C2212yes—
102C2×#6451C2211yescharacteristic
103C2×#6450C2211yescharacteristic
104C2×#6450C2211yescharacteristic
105C2×#6450C2211yescharacteristic
106C2×#6450C2211yescharacteristic
107C2×#6450C2212yes—
108C2×#6450C2212yes—
109C2×#6442C2212yes—
110C2×#6442C2212yes—
111C2×#6442C2212yes—
112C2×#6442C2212yes—
113C2×#6442C2212yes—
114C2×#6442C2212yes—
115C2×#6442C2212yes—
116C2×#6442C2212yes—
117C2×#6442C2212yes—
118C2×#6442C2212yes—
119C2×#6442C2212yes—
120C2×#6442C2212yes—
121C2×#6441C2212yes—
122C2×#6441C2212yes—
123C2×#6441C2212yes—
124C2×#6441C2211yescharacteristic
125C2×#6441C2211yescharacteristic
126C2×#6441C2211yescharacteristic
127C2×#6441C2211yescharacteristic
128C2×#6441C2212yes—
129C2×#6441C2212yes—
130C2×#6441C2212yes—
131C2×#6440C2212yes—
132C2×#6440C2212yes—
133C2×#6440C2212yes—
134C2×#6440C2212yes—
135C2×#6433C2211yescharacteristic
136C2×#6433C2212yes—
137C2×#6433C2212yes—
138C2×#6432C2211yescharacteristic
139C2×C4×Dic14C2211yescharacteristic
140C2×C4×Dic14C2211yescharacteristic
141C2×C4×Dic14C2211yescharacteristic
142C2×C4×Dic14C2211yescharacteristic
143C2×C4×Dic14C2211yescharacteristic
144C2×C4×Dic14C2211yescharacteristic
145C2×C4×Dic14C2212yes—
146C2×C4×Dic14C2212yes—
147C2×#3555—71nomaximal, Sylow
148C22×C7×Q8C2311yescharacteristic
149C22×C7×Q8C2312yes—
150C22×C7×D4C2311yescharacteristic
151C22×C7×D4C2312yes—
152C23×C4×C7C2311yescharacteristic
153C23×C4×C7C2312yes—
154C23×Dic7C2311yescharacteristic
155C23×Dic7C2312yes—
156C23×Dic7C2312yes—
157C23×Dic7C2311yescharacteristic
158C22×Dic14C2311yescharacteristic
159C22×Dic14C2311yescharacteristic
160C22×Dic14C2311yescharacteristic
161C22×Dic14C2311yescharacteristic
162C22×Dic14C2311yescharacteristic
163C22×Dic14C2311yescharacteristic
164C22×Dic14C2312yes—
165C22×Dic14C2312yes—
166C7×C4⋊Q8C2318yes—
167C7×#126C23116yes—
168C7×#124C2318yes—
169C7×#124C23116yes—
170C7×#123C23116yes—
171C7×C22⋊Q8C2318yes—
172C7×C22⋊Q8C23116yes—
173C7×#121C2318yes—
174C4×C7×Q8C2318yes—
175C4×C7×D4C2318yes—
176C7×#117C2318yes—
177C2×C7×C4⋊C4C2311yescharacteristic
178C2×C7×C4⋊C4C2311yescharacteristic
179C2×C7×C4⋊C4C2312yes—
180C2×C7×C4⋊C4C2312yes—
181C2×C7×C4⋊C4C2311yescharacteristic
182C2×C7×C4⋊C4C2311yescharacteristic
183C2×C7×C4⋊C4C2312yes—
184C2×C7×C22⋊C4C2312yes—
185C2×C7×C22⋊C4C2312yes—
186C2×C7×C22⋊C4C2312yes—
187C2×C7×C22⋊C4C2312yes—
188C2×C7×C22⋊C4C2311yescharacteristic
189C2×C7×C22⋊C4C2311yescharacteristic
190C2×C7×C22⋊C4C2312yes—
191C2×C42×C7C2311yescharacteristic
192C2×C42×C7C2311yescharacteristic
193C2×C42×C7C2312yes—
194C2×C22⋊Dic7C2312yes—
195C2×C22⋊Dic7C2312yes—
196C2×C22⋊Dic7C2312yes—
197C2×C22⋊Dic7C2312yes—
198C2×C22⋊Dic7C2311yescharacteristic
199C2×C22⋊Dic7C2311yescharacteristic
200C2×C22⋊Dic7C2312yes—
201C2×C22⋊Dic7C2312yes—
202C2×C22⋊Dic7C2312yes—
203C2×C22⋊Dic7C2312yes—
204Q8×Dic7C23116yes—
205Q8×Dic7C2318yes—
206Q8×Dic7C2318yes—
207#6507C23116yes—
208#6507C23116yes—
209#6507C23116yes—
210#6507C2318yes—
211#6507C2318yes—
212#6499C2318yes—
213#6499C2318yes—
214#6499C23116yes—
215#6498C23116yes—
216#6498C23116yes—
217D4×Dic7C2318yes—
218D4×Dic7C2318yes—
219D4×Dic7C23116yes—
220#6489C2318yes—
221#6489C23116yes—
222C2×C4⋊Dic7C2312yes—
223C2×C4⋊Dic7C2311yescharacteristic
224C2×C4⋊Dic7C2311yescharacteristic
225C2×C4⋊Dic7C2311yescharacteristic
226C2×C4⋊Dic7C2311yescharacteristic
227C2×C4⋊Dic7C2311yescharacteristic
228C2×C4⋊Dic7C2311yescharacteristic
229C2×C4⋊Dic7C2312yes—
230C2×C4⋊Dic7C2312yes—
231C2×C4⋊Dic7C2312yes—
232C2×C4⋊Dic7C2312yes—
233C2×C4⋊Dic7C2311yescharacteristic
234C2×C4⋊Dic7C2312yes—
235C2×C4⋊Dic7C2311yescharacteristic
236#6487C2318yes—
237#6487C2318yes—
238#6487C23116yes—
239#6487C23116yes—
240C2×Dic7⋊C4C2311yescharacteristic
241C2×Dic7⋊C4C2312yes—
242C2×Dic7⋊C4C2311yescharacteristic
243C2×Dic7⋊C4C2311yescharacteristic
244C2×Dic7⋊C4C2311yescharacteristic
245C2×Dic7⋊C4C2312yes—
246C2×Dic7⋊C4C2311yescharacteristic
247C2×Dic7⋊C4C2312yes—
248C2×Dic7⋊C4C2312yes—
249C2×Dic7⋊C4C2311yescharacteristic
250C2×Dic7⋊C4C2311yescharacteristic
251C2×Dic7⋊C4C2311yescharacteristic
252C2×Dic7⋊C4C2312yes—
253C2×Dic7⋊C4C2312yes—
254C2×Dic7⋊C4C2312yes—
255C2×Dic7⋊C4C2312yes—
256C2×Dic7⋊C4C2312yes—
257C2×Dic7⋊C4C2312yes—
258C2×Dic7⋊C4C2312yes—
259C2×Dic7⋊C4C2312yes—
260C2×Dic7⋊C4C2312yes—
261C2×Dic7⋊C4C2312yes—
262C2×Dic7⋊C4C2312yes—
263C2×Dic7⋊C4C2312yes—
264C2×Dic7⋊C4C2312yes—
265C2×Dic7⋊C4C2312yes—
266C2×Dic7⋊C4C23116yes—
267C2×C4×Dic7C2311yescharacteristic
268C2×C4×Dic7C2311yescharacteristic
269C2×C4×Dic7C2311yescharacteristic
270C2×C4×Dic7C2311yescharacteristic
271C2×C4×Dic7C2312yes—
272C2×C4×Dic7C2312yes—
273C2×C4×Dic7C2312yes—
274C2×C4×Dic7C2312yes—
275C2×C4×Dic7C2312yes—
276C2×C4×Dic7C2312yes—
277C2×C4×Dic7C2311yescharacteristic
278C2×C4×Dic7C2312yes—
279C2×C4×Dic7C2311yescharacteristic
280C2×C4×Dic7C2312yes—
281C2×C4×Dic7C2318yes—
282#6453C2318yes—
283#6453C23116yes—
284#6453C2318yes—
285#6453C2318yes—
286#6453C2318yes—
287#6453C23116yes—
288#6452C23116yes—
289#6452C23116yes—
290#6452C23116yes—
291#6452C23116yes—
292#6452C23116yes—
293#6452C23116yes—
294#6452C23116yes—
295#6452C23116yes—
296#6451C2318yes—
297#6451C23116yes—
298#6451C2318yes—
299#6451C2318yes—
300#6451C2318yes—
301#6451C23116yes—
302#6450C23116yes—
303#6450C23116yes—
304#6450C2318yes—
305#6450C2318yes—
306#6450C2318yes—
307#6450C2318yes—
308#6442C23116yes—
309#6442C23116yes—
310#6442C23116yes—
311#6442C23116yes—
312#6442C23116yes—
313#6442C23116yes—
314#6442C23116yes—
315#6442C23116yes—
316#6442C23116yes—
317#6442C23116yes—
318#6442C23116yes—
319#6442C23116yes—
320#6441C23116yes—
321#6441C23116yes—
322#6441C23116yes—
323#6441C23116yes—
324#6441C2318yes—
325#6441C2318yes—
326#6441C2318yes—
327#6441C2318yes—
328#6441C23116yes—
329#6441C23116yes—
330#6440C23116yes—
331#6440C23116yes—
332#6440C23116yes—
333#6440C23116yes—
334#6433C23116yes—
335#6433C23116yes—
336#6433C2318yes—
337#6432C2318yes—
338C4×Dic14C23116yes—
339C4×Dic14C23116yes—
340C4×Dic14C2318yes—
341C4×Dic14C2318yes—
342C4×Dic14C2318yes—
343C4×Dic14C2318yes—
344C4×Dic14C2318yes—
345C4×Dic14C2318yes—
346#3555—732no—
347C2×#563—72no—
348C2×#563—72no—
349C2×Q82—71no—
350C2×#557—71no—
351C2×#557—71no—
352C2×#557—71no—
353C2×#556—72no—
354C2×#556—71no—
355C2×#556—71no—
356C2×#556—71no—
357C2×#554—71no—
358C2×#552—72no—
359C2×#544—72no—
360C2×#542—71no—
361C2×#542D711yescharacteristic
362C2×#541—72no—
363C2×#541—72no—
364C2×#541—71no—
365C2×#541—72no—
366C2×#541—71no—
367C2×#533—71no—
368C2×#533—71no—
369C2×#529—71no—
370C24×C7C2411yescharacteristic
371C24×C7C2412yes—
372C2×C7×Q8—24no—
373C2×C7×Q8—44no—
374C2×C7×Q8C2414yes—
375C2×C7×Q8C2418yes—
376C2×C7×D4—24no—
377C2×C7×D4—44no—
378C2×C7×D4C2414yes—
379C2×C7×D4C2418yes—
380C22×C4×C7—24no—
381C22×C4×C7—44no—
382C22×C4×C7C2412yes—
383C22×C4×C7C2411yescharacteristic
384C22×C4×C7C2411yescharacteristic
385C22×C4×C7C2411yescharacteristic
386C22×C4×C7C2412yes—
387C22×C4×C7C2412yes—
388C22×C4×C7C2414yes—
389C22×C4×C7C2411yescharacteristic
390C22×C4×C7C2411yescharacteristic
391C22×C4×C7C2418yes—
392C22×C4×C7C2411yescharacteristic
393C22×Dic7—24no—
394C22×Dic7—28no—
395C22×Dic7—42no—
396C22×Dic7—44no—
397C22×Dic7C2414yes—
398C22×Dic7C2418yes—
399C22×Dic7C2411yescharacteristic
400C22×Dic7C2412yes—
401C22×Dic7C2412yes—
402C22×Dic7C2411yescharacteristic
403C22×Dic7C2411yescharacteristic
404C22×Dic7C2411yescharacteristic
405C22×Dic7C2412yes—
406C22×Dic7C2411yescharacteristic
407C22×Dic7C2411yescharacteristic
408C22×Dic7C2412yes—
409C22×Dic7C2411yescharacteristic
410C22×Dic7C2418yes—
411C22×Dic7C2414yes—
412C22×Dic7C2411yescharacteristic
413C2×Dic14—24no—
414C2×Dic14—24no—
415C2×Dic14—24no—
416C2×Dic14—24no—
417C2×Dic14—42no—
418C2×Dic14—44no—
419C2×Dic14—44no—
420C2×Dic14—42no—
421C2×Dic14C2414yes—
422C2×Dic14C2414yes—
423C2×Dic14C2414yes—
424C2×Dic14C2414yes—
425C2×Dic14C2414yes—
426C2×Dic14C2414yes—
427C2×Dic14C2418yes—
428C2×Dic14C2418yes—
429C7×C4⋊C4C2414yes—
430C7×C4⋊C4C2414yes—
431C7×C4⋊C4C2418yes—
432C7×C4⋊C4C2418yes—
433C7×C4⋊C4C2414yes—
434C7×C4⋊C4C2414yes—
435C7×C4⋊C4C2418yes—
436C7×C22⋊C4C2418yes—
437C7×C22⋊C4C2418yes—
438C7×C22⋊C4C2418yes—
439C7×C22⋊C4C2418yes—
440C7×C22⋊C4C2414yes—
441C7×C22⋊C4C2414yes—
442C7×C22⋊C4C2418yes—
443C42×C7C2414yes—
444C42×C7C2414yes—
445C42×C7C2418yes—
446C22⋊Dic7C2418yes—
447C22⋊Dic7C2418yes—
448C22⋊Dic7C2418yes—
449C22⋊Dic7C2418yes—
450C22⋊Dic7C2414yes—
451C22⋊Dic7C2414yes—
452C22⋊Dic7C2418yes—
453C22⋊Dic7C2418yes—
454C22⋊Dic7C2418yes—
455C22⋊Dic7C2418yes—
456C4⋊Dic7C2418yes—
457C4⋊Dic7C2414yes—
458C4⋊Dic7C2414yes—
459C4⋊Dic7C2414yes—
460C4⋊Dic7C2414yes—
461C4⋊Dic7C2414yes—
462C4⋊Dic7C2414yes—
463C4⋊Dic7C2418yes—
464C4⋊Dic7C2418yes—
465C4⋊Dic7C2418yes—
466C4⋊Dic7C2418yes—
467C4⋊Dic7C2414yes—
468C4⋊Dic7C2418yes—
469C4⋊Dic7C2414yes—
470Dic7⋊C4C2414yes—
471Dic7⋊C4C2418yes—
472Dic7⋊C4C2414yes—
473Dic7⋊C4C2414yes—
474Dic7⋊C4C2414yes—
475Dic7⋊C4C2418yes—
476Dic7⋊C4C2414yes—
477Dic7⋊C4C2418yes—
478Dic7⋊C4C2418yes—
479Dic7⋊C4C2414yes—
480Dic7⋊C4C2414yes—
481Dic7⋊C4C2414yes—
482Dic7⋊C4C2418yes—
483Dic7⋊C4C2418yes—
484Dic7⋊C4C2418yes—
485Dic7⋊C4C2418yes—
486Dic7⋊C4C2418yes—
487Dic7⋊C4C2418yes—
488Dic7⋊C4C2418yes—
489Dic7⋊C4C2418yes—
490Dic7⋊C4C2418yes—
491Dic7⋊C4C2418yes—
492Dic7⋊C4C2418yes—
493Dic7⋊C4C2418yes—
494Dic7⋊C4C2418yes—
495Dic7⋊C4C2418yes—
496C4×Dic7C2414yes—
497C4×Dic7C2414yes—
498C4×Dic7C2414yes—
499C4×Dic7C2414yes—
500C4×Dic7C2418yes—
501C4×Dic7C2418yes—
502C4×Dic7C2418yes—
503C4×Dic7C2418yes—
504C4×Dic7C2418yes—
505C4×Dic7C2418yes—
506C4×Dic7C2414yes—
507C4×Dic7C2418yes—
508C4×Dic7C2414yes—
509C4×Dic7C2418yes—
510#563—732no—
511#563—732no—
512Q82—716no—
513#557—716no—
514#557—716no—
515#557—716no—
516#556—732no—
517#556—716no—
518#556—716no—
519#556—716no—
520#554—716no—
521#552—732no—
522#544—732no—
523#542—716no—
524#542C2×D7116yes—
525#541—732no—
526#541—732no—
527#541—716no—
528#541—732no—
529#541—716no—
530#533—716no—
531#533—716no—
532C2×C4⋊Q8—71no—
533C2×C4⋊Q8—71no—
534C2×C4⋊Q8—72no—
535C2×C4⋊Q8—72no—
536C2×C4⋊Q8—72no—
537C2×C4⋊Q8—71no—
538C2×C4⋊Q8—71no—
539C2×C4⋊Q8—71no—
540C2×C4⋊Q8—72no—
541C2×C4⋊Q8—71no—
542C2×C4⋊Q8—72no—
543C2×C4⋊Q8—71no—
544C2×C4⋊Q8C2×D711yescharacteristic
545#529—716no—
546C2×#126—72no—
547C2×#126—72no—
548C2×#126—72no—
549C2×#126—72no—
550C2×#126—72no—
551C2×#126—72no—
552C2×#126—72no—
553C2×#126—72no—
554C2×#126—72no—
555C2×#126—72no—
556C2×#126—72no—
557C2×#126—72no—
558C2×#126C2×D712yes—
559C2×#125—72no—
560C2×#125—72no—
561C2×#125—72no—
562C2×#125—72no—
563C2×#125—72no—
564C2×#125—72no—
565C2×#125—72no—
566C2×#125—72no—
567C2×#125—71no—
568C2×#125—71no—
569C2×#125—71no—
570C2×#125—72no—
571C2×#125—72no—
572C2×#125—71no—
573C2×#125—71no—
574C2×#125—72no—
575C2×#125—72no—
576C2×#124—71no—
577C2×#124—71no—
578C2×#124—72no—
579C2×#124C2×D711yescharacteristic
580C2×#124C2×D712yes—
581C2×#123—72no—
582C2×#123—72no—
583C2×#123C2×D712yes—
584C2×C22⋊Q8—71no—
585C2×C22⋊Q8—71no—
586C2×C22⋊Q8—72no—
587C2×C22⋊Q8—72no—
588C2×C22⋊Q8—71no—
589C2×C22⋊Q8—71no—
590C2×C22⋊Q8—71no—
591C2×C22⋊Q8—72no—
592C2×C22⋊Q8—71no—
593C2×C22⋊Q8—72no—
594C2×C22⋊Q8—72no—
595C2×C22⋊Q8—72no—
596C2×C22⋊Q8—72no—
597C2×C22⋊Q8—72no—
598C2×C22⋊Q8C2×D711yescharacteristic
599C2×C22⋊Q8C2×D712yes—
600C2×#121C2×D711yescharacteristic
601C2×C4×Q8—71no—
602C2×C4×Q8—72no—
603C2×C4×Q8—71no—
604C2×C4×Q8—71no—
605C2×C4×Q8—72no—
606C2×C4×Q8—71no—
607C2×C4×Q8—72no—
608C2×C4×Q8—71no—
609C2×C4×Q8—71no—
610C2×C4×Q8—71no—
611C2×C4×Q8—71no—
612C2×C4×Q8—71no—
613C2×C4×Q8—71no—
614C2×C4×Q8—72no—
615C2×C4×Q8—72no—
616C2×C4×Q8—71no—
617C2×C4×Q8—71no—
618C2×C4×Q8C2×D711yescharacteristic
619C2×C4×D4—72no—
620C2×C4×D4—71no—
621C2×C4×D4—71no—
622C2×C4×D4C2×D711yescharacteristic
623C2×#117—71no—
624C2×#117—72no—
625C2×#117—72no—
626C2×#117—72no—
627C2×#117—72no—
628C2×#117—72no—
629C2×#117C2×D711yescharacteristic
630C22×C4⋊C4—72no—
631C22×C42—71no—
632C23×C7—22no—
633C23×C7—24no—
634C23×C7—22no—
635C23×C7—24no—
636C23×C7—24no—
637C23×C7—22no—
638C23×C7C2512yes—
639C23×C7C2514yes—
640C23×C7C2511yescharacteristic
641C7×Q8—28no—
642C7×Q8—48no—
643C7×D4—28no—
644C7×D4—48no—
645C2×C4×C7—22no—
646C2×C4×C7—22no—
647C2×C4×C7—22no—
648C2×C4×C7—24no—
649C2×C4×C7—22no—
650C2×C4×C7—24no—
651C2×C4×C7—24no—
652C2×C4×C7—22no—
653C2×C4×C7—28no—
654C2×C4×C7—48no—
655C2×C4×C72−1+414yes—
656C2×C4×C7C2514yes—
657C2×C4×C7C2512yes—
658C2×C4×C7C2512yes—
659C2×C4×C7C2512yes—
660C2×C4×C7C2514yes—
661C2×C4×C7C2514yes—
662C2×C4×C7C2512yes—
663C2×C4×C7C2512yes—
664C2×C4×C7C2512yes—
665C2×Dic7—24no—
666C2×Dic7—24no—
667C2×Dic7—22no—
668C2×Dic7—22no—
669C2×Dic7—22no—
670C2×Dic7—24no—
671C2×Dic7—22no—
672C2×Dic7—22no—
673C2×Dic7—24no—
674C2×Dic7—22no—
675C2×Dic7—22no—
676C2×Dic7—28no—
677C2×Dic7—216no—
678C2×Dic7—44no—
679C2×Dic7—48no—
680C2×Dic72−1+414yes—
681C2×Dic7C2512yes—
682C2×Dic7C2514yes—
683C2×Dic7C2514yes—
684C2×Dic7C2512yes—
685C2×Dic7C2512yes—
686C2×Dic7C2512yes—
687C2×Dic7C2514yes—
688C2×Dic7C2512yes—
689C2×Dic7C2512yes—
690C2×Dic7C2514yes—
691C2×Dic7C2512yes—
692C2×Dic7C2512yes—
693Dic14—28no—
694Dic14—28no—
695Dic14—28no—
696Dic14—28no—
697Dic14—44no—
698Dic14—48no—
699Dic14—48no—
700Dic14—44no—
701C22×Q8—71no—
702C22×Q8—71no—
703C22×Q8—71no—
704C22×Q8—71no—
705C22×Q8—71no—
706C22×Q8—72no—
707C22×Q8—71no—
708C22×Q8—72no—
709C22×Q8C22×D711yescharacteristic
710C22×Q8C22×D712yes—
711C22×D4C22×D711yescharacteristic
712C22×D4C22×D712yes—
713C23×C4—72no—
714C23×C4—71no—
715C23×C4—72no—
716C23×C4—71no—
717C23×C4C22×D711yescharacteristic
718C23×C4C22×D712yes—
719C4⋊Q8—78no—
720C4⋊Q8—78no—
721C4⋊Q8—716no—
722C4⋊Q8—716no—
723C4⋊Q8—716no—
724C4⋊Q8—78no—
725C4⋊Q8—78no—
726C4⋊Q8—78no—
727C4⋊Q8—716no—
728C4⋊Q8—78no—
729C4⋊Q8—716no—
730C4⋊Q8—78no—
731C4⋊Q8C22×D718yes—
732#126—716no—
733#126—716no—
734#126—716no—
735#126—716no—
736#126—716no—
737#126—716no—
738#126—716no—
739#126—716no—
740#126—716no—
741#126—716no—
742#126—716no—
743#126—716no—
744#126C22×D7116yes—
745#125—78no—
746#125—78no—
747#125—78no—
748#125—716no—
749#125—716no—
750#125—716no—
751#125—716no—
752#125—716no—
753#125—716no—
754#125—716no—
755#125—78no—
756#125—716no—
757#125—716no—
758#125—716no—
759#125—78no—
760#125—716no—
761#125—716no—
762#124—78no—
763#124—78no—
764#124—716no—
765#124C22×D718yes—
766#124C22×D7116yes—
767#123—716no—
768#123—716no—
769#123C22×D7116yes—
770C22⋊Q8—78no—
771C22⋊Q8—78no—
772C22⋊Q8—716no—
773C22⋊Q8—716no—
774C22⋊Q8—78no—
775C22⋊Q8—78no—
776C22⋊Q8—78no—
777C22⋊Q8—716no—
778C22⋊Q8—78no—
779C22⋊Q8—716no—
780C22⋊Q8—716no—
781C22⋊Q8—716no—
782C22⋊Q8—716no—
783C22⋊Q8—716no—
784C22⋊Q8C22×D718yes—
785C22⋊Q8C22×D7116yes—
786#121C22×D718yes—
787C4×Q8—78no—
788C4×Q8—716no—
789C4×Q8—78no—
790C4×Q8—78no—
791C4×Q8—716no—
792C4×Q8—78no—
793C4×Q8—716no—
794C4×Q8—78no—
795C4×Q8—78no—
796C4×Q8—78no—
797C4×Q8—78no—
798C4×Q8—78no—
799C4×Q8—78no—
800C4×Q8—716no—
801C4×Q8—716no—
802C4×Q8—78no—
803C4×Q8—78no—
804C4×Q8C22×D718yes—
805C4×D4—716no—
806C4×D4—78no—
807C4×D4—78no—
808C4×D4C22×D718yes—
809#117—78no—
810#117—716no—
811#117—716no—
812#117—716no—
813#117—716no—
814#117—716no—
815#117C22×D718yes—
816C2×C4⋊C4—71no—
817C2×C4⋊C4—72no—
818C2×C4⋊C4—72no—
819C2×C4⋊C4—72no—
820C2×C4⋊C4—716no—
821C2×C4⋊C4—71no—
822C2×C4⋊C4—71no—
823C2×C4⋊C4—72no—
824C2×C4⋊C4—71no—
825C2×C4⋊C4—71no—
826C2×C4⋊C4—72no—
827C2×C4⋊C4—72no—
828C2×C4⋊C4—72no—
829C2×C4⋊C4—72no—
830C2×C4⋊C4—71no—
831C2×C4⋊C4—71no—
832C2×C4⋊C4—71no—
833C2×C4⋊C4—72no—
834C2×C4⋊C4—71no—
835C2×C4⋊C4—71no—
836C2×C4⋊C4—71no—
837C2×C4⋊C4—71no—
838C2×C4⋊C4—72no—
839C2×C4⋊C4—72no—
840C2×C4⋊C4—72no—
841C2×C4⋊C4—72no—
842C2×C4⋊C4—72no—
843C2×C4⋊C4—72no—
844C2×C4⋊C4—72no—
845C2×C4⋊C4—72no—
846C2×C4⋊C4—72no—
847C2×C4⋊C4—71no—
848C2×C4⋊C4—71no—
849C2×C4⋊C4—72no—
850C2×C4⋊C4—71no—
851C2×C4⋊C4—72no—
852C2×C4⋊C4—71no—
853C2×C4⋊C4—72no—
854C2×C4⋊C4—72no—
855C2×C4⋊C4—72no—
856C2×C4⋊C4—72no—
857C2×C4⋊C4C22×D711yescharacteristic
858C2×C4⋊C4C22×D711yescharacteristic
859C2×C4⋊C4C22×D711yescharacteristic
860C2×C4⋊C4C22×D711yescharacteristic
861C2×C4⋊C4C22×D712yes—
862C2×C4⋊C4C22×D712yes—
863C2×C4⋊C4C22×D712yes—
864C2×C22⋊C4—72no—
865C2×C22⋊C4—71no—
866C2×C22⋊C4—72no—
867C2×C22⋊C4—72no—
868C2×C22⋊C4—71no—
869C2×C22⋊C4—72no—
870C2×C22⋊C4—72no—
871C2×C22⋊C4—72no—
872C2×C22⋊C4—72no—
873C2×C22⋊C4—72no—
874C2×C22⋊C4C22×D712yes—
875C2×C22⋊C4C22×D712yes—
876C2×C22⋊C4C22×D712yes—
877C2×C22⋊C4C22×D712yes—
878C2×C22⋊C4C22×D711yescharacteristic
879C2×C22⋊C4C22×D711yescharacteristic
880C2×C22⋊C4C22×D712yes—
881C2×C42—72no—
882C2×C42—72no—
883C2×C42—71no—
884C2×C42—72no—
885C2×C42—71no—
886C2×C42—71no—
887C2×C42—72no—
888C2×C42—72no—
889C2×C42—72no—
890C2×C42—72no—
891C2×C42—71no—
892C2×C42—71no—
893C2×C42—72no—
894C2×C42—71no—
895C2×C42—78no—
896C2×C42C22×D711yescharacteristic
897C2×C42C22×D711yescharacteristic
898C2×C42C22×D712yes—
899C22×C7—22no—
900C22×C7—24no—
901C22×C7—22no—
902C22×C7—24no—
903C22×C7—24no—
904C22×C7—22no—
905C22×C7—44no—
906C22×C7—48no—
907C22×C7C2×2−1+412yes—
908C22×C7C2×2−1+412yes—
909C22×C7#58512yes—
910C22×C7C2611yescharacteristic
911C4×C7—22no—
912C4×C7—22no—
913C4×C7—22no—
914C4×C7—24no—
915C4×C7—22no—
916C4×C7—24no—
917C4×C7—24no—
918C4×C7—22no—
919C4×C7C2×2−1+414yes—
920Dic7—24no—
921Dic7—24no—
922Dic7—22no—
923Dic7—22no—
924Dic7—22no—
925Dic7—24no—
926Dic7—22no—
927Dic7—22no—
928Dic7—24no—
929Dic7—22no—
930Dic7—22no—
931Dic7C2×2−1+414yes—
932C24C23×D711yescharacteristic
933C24C23×D712yes—
934C2×Q8—24no—
935C2×Q8—44no—
936C2×Q8—74no—
937C2×Q8—74no—
938C2×Q8—74no—
939C2×Q8—74no—
940C2×Q8—74no—
941C2×Q8—78no—
942C2×Q8—74no—
943C2×Q8—78no—
944C2×Q8—144no—
945C2×Q8—144no—
946C2×Q8—144no—
947C2×Q8—144no—
948C2×Q8—282no—
949C2×Q8—284no—
950C2×Q8—284no—
951C2×Q8—282no—
952C2×Q8C23×D714yes—
953C2×Q8C23×D718yes—
954C2×D4—24no—
955C2×D4—44no—
956C2×D4C23×D714yes—
957C2×D4C23×D718yes—
958C22×C4—24no—
959C22×C4—44no—
960C22×C4—71no—
961C22×C4—74no—
962C22×C4—78no—
963C22×C4—71no—
964C22×C4—72no—
965C22×C4—72no—
966C22×C4—71no—
967C22×C4—71no—
968C22×C4—71no—
969C22×C4—72no—
970C22×C4—72no—
971C22×C4—71no—
972C22×C4—71no—
973C22×C4—71no—
974C22×C4—74no—
975C22×C4—78no—
976C22×C4—148no—
977C22×C4—144no—
978C22×C4—284no—
979C22×C4—282no—
980C22×C4C23×D714yes—
981C22×C4C23×D712yes—
982C22×C4C23×D711yescharacteristic
983C22×C4C23×D711yescharacteristic
984C22×C4C23×D712yes—
985C22×C4C23×D711yescharacteristic
986C22×C4C23×D712yes—
987C22×C4C23×D711yescharacteristic
988C22×C4C23×D711yescharacteristic
989C22×C4C23×D718yes—
990C22×C4C23×D711yescharacteristic
991C4⋊C4—74no—
992C4⋊C4—78no—
993C4⋊C4—78no—
994C4⋊C4—78no—
995C4⋊C4—74no—
996C4⋊C4—78no—
997C4⋊C4—74no—
998C4⋊C4—78no—
999C4⋊C4—78no—
1000C4⋊C4—78no—
1001C4⋊C4—74no—
1002C4⋊C4—74no—
1003C4⋊C4—78no—
1004C4⋊C4—78no—
1005C4⋊C4—78no—
1006C4⋊C4—78no—
1007C4⋊C4—78no—
1008C4⋊C4—78no—
1009C4⋊C4—74no—
1010C4⋊C4—74no—
1011C4⋊C4—78no—
1012C4⋊C4—78no—
1013C4⋊C4—74no—
1014C4⋊C4—78no—
1015C4⋊C4—78no—
1016C4⋊C4—78no—
1017C4⋊C4—74no—
1018C4⋊C4—74no—
1019C4⋊C4—78no—
1020C4⋊C4—74no—
1021C4⋊C4—74no—
1022C4⋊C4—74no—
1023C4⋊C4—78no—
1024C4⋊C4—74no—
1025C4⋊C4—74no—
1026C4⋊C4—78no—
1027C4⋊C4—78no—
1028C4⋊C4—78no—
1029C4⋊C4—74no—
1030C4⋊C4—78no—
1031C4⋊C4C23×D714yes—
1032C4⋊C4C23×D714yes—
1033C4⋊C4C23×D714yes—
1034C4⋊C4C23×D714yes—
1035C4⋊C4C23×D718yes—
1036C4⋊C4C23×D718yes—
1037C4⋊C4C23×D718yes—
1038C22⋊C4—78no—
1039C22⋊C4—74no—
1040C22⋊C4—78no—
1041C22⋊C4—78no—
1042C22⋊C4—74no—
1043C22⋊C4—78no—
1044C22⋊C4—78no—
1045C22⋊C4—78no—
1046C22⋊C4—78no—
1047C22⋊C4—78no—
1048C22⋊C4C23×D718yes—
1049C22⋊C4C23×D718yes—
1050C22⋊C4C23×D718yes—
1051C22⋊C4C23×D718yes—
1052C22⋊C4C23×D714yes—
1053C22⋊C4C23×D714yes—
1054C22⋊C4C23×D718yes—
1055C42—74no—
1056C42—74no—
1057C42—74no—
1058C42—74no—
1059C42—78no—
1060C42—78no—
1061C42—78no—
1062C42—74no—
1063C42—74no—
1064C42—78no—
1065C42—78no—
1066C42—78no—
1067C42—78no—
1068C42—78no—
1069C42C23×D714yes—
1070C42C23×D714yes—
1071C42C23×D718yes—
1072C2×C7—42no—
1073C2×C7—44no—
1074C2×C7#355514yescomplemented
1075C2×C7C22×2−1+411yescharacteristic
1076C2×C7C22×2−1+411yescharacteristic
1077C2×C7C2×#58511yescharacteristic
1078C23—22no—
1079C23—24no—
1080C23—24no—
1081C23—22no—
1082C23—22no—
1083C23—24no—
1084C23C24×D712yes—
1085C23C24×D714yes—
1086C23C24×D711yescharacteristic
1087Q8—28no—
1088Q8—48no—
1089Q8—148no—
1090Q8—148no—
1091Q8—148no—
1092Q8—148no—
1093Q8—284no—
1094Q8—288no—
1095Q8—288no—
1096Q8—284no—
1097D4—28no—
1098D4—48no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—28no—
1108C2×C4—48no—
1109C2×C4—72no—
1110C2×C4—74no—
1111C2×C4—72no—
1112C2×C4—74no—
1113C2×C4—74no—
1114C2×C4—72no—
1115C2×C4—72no—
1116C2×C4—72no—
1117C2×C4—74no—
1118C2×C4—72no—
1119C2×C4—72no—
1120C2×C4—74no—
1121C2×C4—72no—
1122C2×C4—148no—
1123C2×C4—1416no—
1124C2×C4—144no—
1125C2×C4—144no—
1126C2×C4—142no—
1127C2×C4—144no—
1128C2×C4—142no—
1129C2×C4—142no—
1130C2×C4—142no—
1131C2×C4—142no—
1132C2×C4—144no—
1133C2×C4—142no—
1134C2×C4—142no—
1135C2×C4—288no—
1136C2×C4—284no—
1137C2×C4#655414yes—
1138C2×C4C24×D714yes—
1139C2×C4C24×D712yes—
1140C2×C4C24×D712yes—
1141C2×C4C24×D714yes—
1142C2×C4C24×D712yes—
1143C2×C4C24×D714yes—
1144C2×C4C24×D712yes—
1145C2×C4C24×D712yes—
1146C2×C4C24×D712yes—
1147C7C2×#355511yescharacteristic, complemented, Sylow
1148C22—22no—
1149C22—24no—
1150C22—24no—
1151C22—22no—
1152C22—22no—
1153C22—24no—
1154C22—44no—
1155C22—48no—
1156C22C2×#655412yes—
1157C22#9061812yes—
1158C22D7×2−1+412yes—
1159C22C25×D711yescharacteristic
1160C4—22no—
1161C4—24no—
1162C4—22no—
1163C4—24no—
1164C4—24no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—74no—
1169C4—144no—
1170C4—144no—
1171C4—142no—
1172C4—142no—
1173C4—142no—
1174C4—144no—
1175C4—142no—
1176C4—142no—
1177C4—144no—
1178C4—142no—
1179C4—142no—
1180C4C2×#655414yes—
1181C2—42no—
1182C2—44no—
1183C2#1174360514yesdirect product factor
1184C2C22×#655411yescharacteristic
1185C2C2×#9061811yescharacteristic
1186C2C2×D7×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C7×#542C2
socleC23×C7C25
prime radicalC2×C7×#121C22
hypercenterC2×#542D7
hypocenterC7C2×#3555
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
2. #11743605C2direct (N × H)
3. C2×#90413C2semidirect
4. C2×#90412C2semidirect
5. C2×#90392C2semidirect
6. C2×#90392C2semidirect
7. C2×#90363C2semidirect
8. C2×#90362C2semidirect
9. C2×#90362C2semidirect
10. C2×#90362C2semidirect
11. C2×#90342C2semidirect
12. C2×#90341C2semidirect
13. C2×#90314C2semidirect
14. C2×#90316C2semidirect
15. C2×#90316C2semidirect
16. C2×#90313C2semidirect
19. C2×#90260C2semidirect
20. C2×#90258C2semidirect
21. C2×#90233C2semidirect
22. C2×#90230C2semidirect
23. C2×#90209C2semidirect
24. C2×#90208C2semidirect
61. #90413C22semidirect
62. #90412C22semidirect
63. #90392C22semidirect
64. #90392C22semidirect
65. #90363C22semidirect
66. #90362C22semidirect
67. #90362C22semidirect
68. #90362C22semidirect
69. #90342C22semidirect
70. #90341C22semidirect
71. #90316C22semidirect
72. #90316C22semidirect
73. #90314C22semidirect
74. #90313C22semidirect
77. #90260C22semidirect
78. #90258C22semidirect
79. #90233C22semidirect
80. #90230C22semidirect
81. #90209C22semidirect
82. #90208C22semidirect
1074. C2×C7#3555semidirect
1147. C7C2×#3555semidirect
1183. C2#11743605direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5422
#117436052
C2×#904132
C2×#904122
C2×#903922
C2×#903632
C2×#903622
C2×#903422
C2×#903412
C2×#903142
C2×#903162
C2×#903132
C2×#902942
C2×#902912
C2×#902602
C2×#902582
C2×#902332
C2×#902302
C2×#902092
C2×#902082
C2×#35557