Finite Group Databasebeta

← #14261955

Subgroups — #14261955

Order 1792.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×#41C211yesmaximal, characteristic, complemented
2#11744341C212yesmaximal, complemented
3#11742922C218yesmaximal, complemented
4#11742920C214yesmaximal, complemented
5#11742911C214yesmaximal, complemented
6#11742909C218yesmaximal, complemented
7#11742899C214yesmaximal, complemented
8#11742894C214yesmaximal, complemented
9#11742887C212yesmaximal, complemented
10#11742879C212yesmaximal, complemented
11#11742855C214yesmaximal, complemented
12#11742854C211yesmaximal, characteristic, complemented
13#11742844C214yesmaximal, complemented
14#11742834C211yesmaximal, characteristic, complemented
15C4×#6548C212yesmaximal, complemented
16#11742814C212yesmaximal, complemented
17#11742813C214yesmaximal, complemented
18#11742748C212yesmaximal, complemented
19C2×#90170C214yesmaximal, complemented
20C22×C7×#41C2211yescharacteristic
21C2×#6548C2212yes—
22C4×C7×#41C2214yescomplemented
23C4×C7×#41C2214yescomplemented
24C4×C7×#41C2214yescomplemented
25C4×C7×#41C2214yescomplemented
26C2×C4×C7×Q8C2211yescharacteristic, complemented
27C2×C4×C7×Q8C2211yescharacteristic, complemented
28C2×C4×C7×D4C2211yescharacteristic
29C2×C4×C7×D4C2211yescharacteristic
30C2×C4×C7×D4C2212yescomplemented
31C2×C4×C7×D4C2212yescomplemented
32C2×C7×#117C2212yescomplemented
33C2×C7×#117C2211yescharacteristic, complemented
34C22×C42×C7C2212yescomplemented
35C22×C42×C7C2211yescharacteristic, complemented
36#90520C2218yescomplemented
37#90520C2218yescomplemented
38#90515C2218yescomplemented
39#90515C2218yescomplemented
40#90507C2214yescomplemented
41#90495C2218yescomplemented
42#90489C2212yes—
43#90482C2214yescomplemented
44#90482C2214yescomplemented
45#90482C2214yescomplemented
46C2×#6493C2214yes—
47C2×#6492C2218yescomplemented
48C2×C4×C22⋊D7C2218yescomplemented
49C2×#6487C2214yescomplemented
50#90276C2214yescomplemented
51#90275C2214yescomplemented
52#90274C2218yescomplemented
53#90273C2218yescomplemented
54#90272C2218yescomplemented
55#90271C2218yescomplemented
56#90270C2214yescomplemented
57#90269C2218yescomplemented
58#90259C2218yescomplemented
59#90258C2214yescomplemented
60#90256C2218yescomplemented
61#90255C22116yescomplemented
62#90251C22116yescomplemented
63#90247C22116yescomplemented
64#90246C2214yescomplemented
65#90245C2218yescomplemented
66#90243C2218yescomplemented
67#90241C2218yescomplemented
68D4×D28C2214yescomplemented
69#90238C22116yescomplemented
70#90237C2218yescomplemented
71#90236C2218yescomplemented
72C4×D4×D7C2218yescomplemented
73#90234C2214yescomplemented
74#90232C2218yescomplemented
75#90231C22116yescomplemented
76#90230C2218yescomplemented
77#90229C22116yescomplemented
78D4×Dic14C2214yescomplemented
79C4×#1159C2218yescomplemented
80#90224C2218yescomplemented
81#90223C2218yescomplemented
82#90222C22116yescomplemented
83#90222C22116yescomplemented
84#90221C2218yescomplemented
85#90220C2218yescomplemented
86#90218C22116yescomplemented
87#90218C22116yescomplemented
88#90206C2218yescomplemented
89#90206C2218yescomplemented
90#90201C2212yes—
91#90195C2214yescomplemented
92#90191C2212yescomplemented
93#90185C2218yescomplemented
94#90184C2214yes—
95#90177C2218yescomplemented
96#90174C2214yescomplemented
97#90170C2214yescomplemented
98#90170C2218yescomplemented
99#90170C2218yescomplemented
100#90170C2218yescomplemented
101#90170C2218yescomplemented
102#90170C2218yescomplemented
103#90170C2218yescomplemented
104#90170C2218yescomplemented
105#90170C2214yescomplemented
106#90170C2214yescomplemented
107#90170C2214yescomplemented
108#90170C2214yescomplemented
109#90170C2214yescomplemented
110C2×#6439C2218yescomplemented
111#90168C2212yes—
112#90168C2212yescomplemented
113#90168C2212yescomplemented
114C2×#6438C2214yescomplemented
115C4×#1157C2214yescomplemented
116C4×#1157C2214yescomplemented
117C4×#1157C2214yescomplemented
118C2×C4×D28C2214yescomplemented
119C2×#6435C2218yescomplemented
120#90161C2212yescomplemented
121#90161C2212yescomplemented
122#90161C2212yescomplemented
123C2×#6433C2214yescomplemented
124C2×C4×Dic14C2214yescomplemented
125#62781—71nomaximal, Sylow
126C2×C7×#41—28no—
127C2×C7×#41C2314yes—
128C2×C7×#41C2314yes—
129C22×C7×Q8C2311yescharacteristic
130C22×C7×D4C2312yes—
131C22×C7×D4C2311yescharacteristic
132C23×C4×C7C2312yes—
133C23×C4×C7C2311yescharacteristic
134C23×C4×C7C2312yes—
135C23×C4×C7C2312yes—
136C23×C4×C7C2311yescharacteristic
137C23×C4×C7C2311yescharacteristic
138C22×C22⋊D7C2318yes—
139#6548—216no—
140C2×#1159C2318yes—
141C2×D4×D7C2318yes—
142C2×#1157C2314yes—
143C2×#1157C2314yes—
144C2×#1157C2314yes—
145C22×D28C2314yes—
146C22×C4×D7C2318yes—
147C22×Dic14C2314yes—
148C4×C7×Q8C2314yes—
149C4×C7×Q8C2314yes—
150C4×C7×Q8C2314yes—
151C4×C7×Q8C2314yes—
152C4×C7×D4C2314yes—
153C4×C7×D4C2314yes—
154C4×C7×D4C2318yes—
155C4×C7×D4C2314yes—
156C4×C7×D4C2318yes—
157C4×C7×D4C2318yes—
158C4×C7×D4C2314yes—
159C4×C7×D4C2318yes—
160C7×#117C2318yes—
161C7×#117C2318yes—
162C7×#117C2314yes—
163C7×#117C2314yes—
164C2×C7×C4⋊C4C2311yescharacteristic
165C2×C7×C4⋊C4C2311yescharacteristic
166C2×C7×C4⋊C4C2312yes—
167C2×C7×C4⋊C4C2312yes—
168C2×C7×C22⋊C4C2312yes—
169C2×C7×C22⋊C4C2312yes—
170C2×C7×C22⋊C4C2312yes—
171C2×C42×C7C2314yes—
172C2×C42×C7C2314yes—
173C2×C42×C7C2311yescharacteristic
174C2×C42×C7C2312yes—
175C2×C42×C7C2312yes—
176C2×C42×C7C2314yes—
177C2×C42×C7C2311yescharacteristic
178C2×C42×C7C2312yes—
179C2×C42×C7C2314yes—
180C2×C42×C7C2311yescharacteristic
181C2×C42×C7C2312yes—
182C2×C42×C7C2311yescharacteristic
183C2×C42×C7C2312yes—
184C2×C42×C7C2312yes—
185C2×C42×C7C2312yes—
186#6516C2318yes—
187C2×C22⋊Dic7C2318yes—
188#6510C2318yes—
189#6509C2318yes—
190#6509C2318yes—
191#6507C2318yes—
192#6502C23116yes—
193#6502C23116yes—
194#6500C23116yes—
195#6498C23116yes—
196D4×Dic7C2318yes—
197D4×Dic7C2318yes—
198#6493C2314yes—
199#6493C2314yes—
200#6493C2314yes—
201#6493C2314yes—
202#6493C2314yes—
203#6493C2314yes—
204#6493C2318yes—
205#6493C2318yes—
206#6493C2318yes—
207#6492C2318yes—
208#6492C23116yes—
209#6492C23116yes—
210#6492C23116yes—
211#6492C2318yes—
212#6492C2318yes—
213C4×C22⋊D7C2318yes—
214C4×C22⋊D7C2318yes—
215C4×C22⋊D7C2318yes—
216C4×C22⋊D7C2318yes—
217C4×C22⋊D7C2318yes—
218C4×C22⋊D7C2318yes—
219C4×C22⋊D7C23116yes—
220C4×C22⋊D7C23116yes—
221C4×C22⋊D7C23116yes—
222C2×(C2×D7)⋊C4C2318yes—
223C2×(C2×D7)⋊C4C2318yes—
224C2×(C2×D7)⋊C4C2318yes—
225C2×(C2×D7)⋊C4C2318yes—
226#6489C2314yes—
227#6489C2314yes—
228#6489C2314yes—
229C2×C4⋊Dic7C2314yes—
230C2×C4⋊Dic7C2314yes—
231#6487C2314yes—
232#6487C2314yes—
233#6487C2314yes—
234#6487C2314yes—
235#6487C2314yes—
236#6487C2314yes—
237#6487C2318yes—
238#6487C2318yes—
239#6487C2318yes—
240C2×Dic7⋊C4C2318yes—
241C2×Dic7⋊C4C2318yes—
242C2×Dic7⋊C4C2318yes—
243C2×Dic7⋊C4C2318yes—
244C2×C4×Dic7C2318yes—
245#6461C23116yes—
246#6461C23116yes—
247#6460C2318yes—
248#6459C23116yes—
249#6459C23116yes—
250#6458C2318yes—
251#6457C23116yes—
252#6457C23116yes—
253#6456C2318yes—
254#6455C2318yes—
255D7×C4⋊C4C2318yes—
256#6453C2318yes—
257#6452C23116yes—
258#6452C23116yes—
259#6451C2318yes—
260#6450C2318yes—
261#6449C23116yes—
262#6448C23116yes—
263#6447C23116yes—
264#6446C23116yes—
265#6445C23116yes—
266(C22⋊D7)⋊C4C23116yes—
267(C22⋊D7)⋊C4C23116yes—
268D7×C22⋊C4C23116yes—
269#6442C23116yes—
270#6441C23116yes—
271#6441C23116yes—
272#6440C23116yes—
273#6439C2318yes—
274#6439C23116yes—
275#6439C23116yes—
276#6439C23116yes—
277#6439C2318yes—
278#6438C2314yes—
279#6438C2318yes—
280#6438C2318yes—
281#6438C2318yes—
282#6438C2314yes—
283#6438C2314yes—
284#6437C2312yes—
285C4×D28C2314yes—
286C4×D28C2318yes—
287C4×D28C2318yes—
288C4×D28C2318yes—
289C4×D28C2314yes—
290C4×D28C2314yes—
291C4×D28C2314yes—
292C4×D28C2314yes—
293C4×D28C2314yes—
294#6435C2318yes—
295#6435C23116yes—
296#6435C23116yes—
297#6435C23116yes—
298#6435C2318yes—
299#6435C2318yes—
300C42×D7C2318yes—
301#6433C2314yes—
302#6433C2318yes—
303#6433C2318yes—
304#6433C2318yes—
305#6433C2314yes—
306#6433C2314yes—
307#6432C2312yes—
308#6432C2312yes—
309#6432C2312yes—
310C4×Dic14C2314yes—
311C4×Dic14C2318yes—
312C4×Dic14C2318yes—
313C4×Dic14C2318yes—
314C4×Dic14C2314yes—
315C4×Dic14C2314yes—
316C4×Dic14C2314yes—
317C4×Dic14C2314yes—
318C4×Dic14C2314yes—
319#3521—78no—
320#3515—74no—
321#3514—74no—
322#3507—72no—
323#3505—74no—
324#3501—71no—
325#3496—71no—
326#3493—72no—
327#3491—74no—
328#3485—72no—
329#3482—74no—
330#3481—74no—
331#3475—78no—
332#3461—72no—
333#3459—74no—
334#3444—72no—
335C2×#529—74no—
336C4×H(5,𝔽2)—72no—
337C2×C4×#41D711yescharacteristic, complemented
338C24×C7C2411yescharacteristic
339C24×C7C2412yes—
340C23×D7C2418yes—
341C7×#41—216no—
342C7×#41—216no—
343C2×C7×Q8—24no—
344C2×C7×Q8C2414yes—
345C2×C7×D4—28no—
346C2×C7×D4#4118yescomplemented
347C2×C7×D4C2418yes—
348C2×C7×D4C2414yes—
349C22×C4×C7—28no—
350C22×C4×C7—24no—
351C22×C4×C7—44no—
352C22×C4×C7—44no—
353C22×C4×C7—42no—
354C22×C4×C7—42no—
355C22×C4×C7C2414yes—
356C22×C4×C7C2414yes—
357C22×C4×C7C2414yes—
358C22×C4×C7C2411yescharacteristic
359C22×C4×C7C2414yes—
360C22×C4×C7C2412yes—
361C22×C4×C7C2412yes—
362C22×C4×C7C2412yes—
363C22×C4×C7C2412yes—
364C22×C4×C7C2411yescharacteristic
365C22×C4×C7C2411yescharacteristic
366C22×C4×C7C2412yes—
367C22×C4×C7C2414yes—
368C22×C4×C7C2414yes—
369C22×C4×C7C2411yescharacteristic
370C22×C4×C7C2412yes—
371C22×C4×C7C2412yes—
372C22×C4×C7C2411yescharacteristic
373C22×C4×C7C2412yes—
374C22×C4×C7C2412yes—
375C22×C4×C7C2411yescharacteristic
376C2×C22⋊D7—232no—
377C2×C22⋊D7C24116yes—
378C2×C22⋊D7C2418yes—
379C2×C22⋊D7C2418yes—
380C2×C22⋊D7C2418yes—
381C22×Dic7C2418yes—
382C22×Dic7C2418yes—
383C22×Dic7C2418yes—
384#1159—232no—
385D4×D7—232no—
386#1157—216no—
387#1157—48no—
388#1157—48no—
389C2×D28—48no—
390C2×D28C2414yes—
391C2×D28C2414yes—
392C2×D28C2414yes—
393C2×D28C2418yes—
394C2×C4×D7—416no—
395C2×C4×D7C2418yes—
396C2×C4×D7C2418yes—
397C2×C4×D7C2418yes—
398C2×C4×D7C24116yes—
399C2×Dic14—48no—
400C2×Dic14C2414yes—
401C2×Dic14C2414yes—
402C2×Dic14C2414yes—
403C2×Dic14C2418yes—
404C7×C4⋊C4C2414yes—
405C7×C4⋊C4C2414yes—
406C7×C4⋊C4C2418yes—
407C7×C4⋊C4C2418yes—
408C7×C22⋊C4C2418yes—
409C7×C22⋊C4C2418yes—
410C7×C22⋊C4C2418yes—
411C42×C7C2411yescharacteristic
412C42×C7C2412yes—
413C42×C7C2414yes—
414C42×C7C2412yes—
415C42×C7C2412yes—
416C42×C7C2412yes—
417C42×C7C2414yes—
418C42×C7C2414yes—
419C42×C7C2412yes—
420C42×C7C2411yescharacteristic
421C42×C7C2414yes—
422C42×C7C2412yes—
423C42×C7C2414yes—
424C42×C7C2411yescharacteristic
425C42×C7C2414yes—
426C42×C7C2411yescharacteristic
427C22⋊Dic7C24116yes—
428C22⋊Dic7C2418yes—
429C22⋊Dic7C2418yes—
430C22⋊Dic7C2418yes—
431(C2×D7)⋊C4C2418yes—
432(C2×D7)⋊C4C2418yes—
433(C2×D7)⋊C4C24116yes—
434(C2×D7)⋊C4C24116yes—
435(C2×D7)⋊C4C2418yes—
436(C2×D7)⋊C4C2418yes—
437(C2×D7)⋊C4C2418yes—
438(C2×D7)⋊C4C2418yes—
439(C2×D7)⋊C4C24116yes—
440(C2×D7)⋊C4C24116yes—
441C4⋊Dic7C2414yes—
442C4⋊Dic7C2418yes—
443C4⋊Dic7C2414yes—
444C4⋊Dic7C2414yes—
445C4⋊Dic7C2414yes—
446C4⋊Dic7C2414yes—
447C4⋊Dic7C2414yes—
448C4⋊Dic7C2418yes—
449Dic7⋊C4C2418yes—
450Dic7⋊C4C24116yes—
451Dic7⋊C4C2418yes—
452Dic7⋊C4C2418yes—
453Dic7⋊C4C2418yes—
454Dic7⋊C4C2418yes—
455Dic7⋊C4C2418yes—
456Dic7⋊C4C24116yes—
457Dic7⋊C4C24116yes—
458Dic7⋊C4C24116yes—
459C4×Dic7C2418yes—
460C4×Dic7C2418yes—
461C4×Dic7C2418yes—
462C4×Dic7C24116yes—
463C2×H(5,𝔽2)—72no—
464C22×#41C2×D711yescharacteristic
465#559—74no—
466#557—74no—
467#556—78no—
468#556—74no—
469#556—78no—
470#555—78no—
471#554—74no—
472#554—78no—
473#554—74no—
474#553—716no—
475#553—78no—
476#553—78no—
477#552—78no—
478#552—78no—
479#552—78no—
480#552—716no—
481#552—716no—
482#551—716no—
483#551—716no—
484#551—716no—
485D4×Q8—74no—
486#548—78no—
487#547—78no—
488#547—78no—
489#547—74no—
490#546—78no—
491#546—78no—
492#546—78no—
493#546—78no—
494D42—74no—
495#544—72no—
496#543—74no—
497#542—78no—
498#541—78no—
499#539—716no—
500#539—78no—
501#539—78no—
502#538—716no—
503#538—78no—
504#537—72no—
505#536—74no—
506#534—78no—
507#534—74no—
508#533—78no—
509#533—72no—
510#533—72no—
511#533—72no—
512#532—72no—
513#532—72no—
514#532—72no—
515#529—78no—
516#529—716no—
517#529—74no—
518#529—78no—
519#529—78no—
520#529—78no—
521#529—78no—
522#529—78no—
523#529—78no—
524#529—78no—
525#529—74no—
526#529—74no—
527#529—74no—
528#529—74no—
529#529—74no—
530C2×#126—78no—
531C2×#125—74no—
532C2×#124—74no—
533#525—74no—
534#525—74no—
535#525—74no—
536#525—716no—
537C2×#123—78no—
538C2×C22⋊Q8—74no—
539C2×#121—74no—
540#520—78no—
541#520—74no—
542#518—72no—
543#518—78no—
544#518—78no—
545C4×#41—78no—
546C4×#41—74no—
547C4×#41—74no—
548C4×#41—74no—
549C4×#41C2×D714yescomplemented
550C4×#41C2×D714yescomplemented
551C4×#41C2×D714yescomplemented
552C4×#41C2×D714yescomplemented
553C2×C4×Q8—74no—
554C2×C4×Q8C2×D711yescharacteristic, complemented
555C2×C4×Q8C2×D711yescharacteristic, complemented
556C2×C4×D4—78no—
557C2×C4×D4—78no—
558C2×C4×D4—74no—
559C2×C4×D4C2×D711yescharacteristic
560C2×C4×D4C2×D711yescharacteristic
561C2×C4×D4C2×D712yescomplemented
562C2×C4×D4C2×D712yescomplemented
563C2×#117—78no—
564C2×#117C2×D712yescomplemented
565C2×#117C2×D711yescharacteristic, complemented
566C22×C42C2×D712yescomplemented
567C22×C42C2×D711yescharacteristic, complemented
568C23×C7—22no—
569C23×C7—42no—
570C23×C7—42no—
571C23×C7—41no—
572C23×C7—41no—
573C23×C7C2×#4118yes—
574C23×C7C2512yes—
575C23×C7C2511yescharacteristic
576C23×C7C2514yes—
577C22×D7—216no—
578C22×D7—48no—
579C22×D7—48no—
580C22×D7C2518yes—
581C7×Q8—28no—
582C7×D4—216no—
583C7×D4C2×#41116yes—
584C2×C4×C7—22no—
585C2×C4×C7—24no—
586C2×C4×C7—28no—
587C2×C4×C7—28no—
588C2×C4×C7—24no—
589C2×C4×C7—24no—
590C2×C4×C7—28no—
591C2×C4×C7—28no—
592C2×C4×C7—24no—
593C2×C4×C7—24no—
594C2×C4×C7—22no—
595C2×C4×C7—22no—
596C2×C4×C7—42no—
597C2×C4×C7—41no—
598C2×C4×C7—44no—
599C2×C4×C7—42no—
600C2×C4×C7—42no—
601C2×C4×C7—41no—
602C2×C4×C7—44no—
603C2×C4×C7—42no—
604C2×C4×C7C2×#4114yes—
605C2×C4×C7C2512yes—
606C2×C4×C7C2514yes—
607C2×C4×C7C2511yescharacteristic
608C2×C4×C7C2511yescharacteristic
609C2×C4×C7C2511yescharacteristic
610C2×C4×C7C2511yescharacteristic
611C2×C4×C7C2514yes—
612C2×C4×C7C2512yes—
613C2×C4×C7C2514yes—
614C2×C4×C7C2512yes—
615C2×C4×C7C2511yescharacteristic
616C2×C4×C7C2511yescharacteristic
617C22⋊D7—216no—
618C22⋊D7—232no—
619C22⋊D7—48no—
620C22⋊D7—48no—
621C2×Dic7—216no—
622C2×Dic7—48no—
623C2×Dic7—48no—
624C2×Dic7C2518yes—
625C2×Dic7C2518yes—
626C2×Dic7C2518yes—
627D28—28no—
628D28—28no—
629D28—48no—
630D28—44no—
631C4×D7—216no—
632C4×D7—216no—
633C4×D7—416no—
634C4×D7—48no—
635Dic14—28no—
636Dic14—28no—
637Dic14—48no—
638Dic14—44no—
639H(5,𝔽2)—1416no—
640C2×#41—28no—
641C2×#41—78no—
642C2×#41—74no—
643C2×#41—74no—
644C2×#41—74no—
645C2×#41C22×D714yes—
646C2×#41C22×D714yes—
647C22×Q8—74no—
648C22×Q8C22×D711yescharacteristic
649C22×D4—78no—
650C22×D4—78no—
651C22×D4—74no—
652C22×D4C22×D712yes—
653C22×D4C22×D711yescharacteristic
654C23×C4—78no—
655C23×C4C22×D712yes—
656C23×C4C22×D711yescharacteristic
657C23×C4C22×D712yes—
658C23×C4C22×D712yes—
659C23×C4C22×D711yescharacteristic
660C23×C4C22×D711yescharacteristic
661C4⋊Q8—78no—
662C4⋊Q8—78no—
663C4⋊Q8—72no—
664C4⋊Q8—72no—
665C4⋊Q8—72no—
666#127—72no—
667#126—716no—
668#126—716no—
669#126—716no—
670#126—78no—
671#126—716no—
672#126—716no—
673#126—716no—
674#126—78no—
675#125—716no—
676#125—78no—
677#125—716no—
678#125—74no—
679#125—78no—
680#125—78no—
681#125—78no—
682#125—74no—
683#125—74no—
684#124—78no—
685#124—716no—
686#124—74no—
687#124—78no—
688#124—78no—
689#124—78no—
690#124—74no—
691#124—74no—
692#123—716no—
693#123—78no—
694#123—716no—
695#123—716no—
696#123—716no—
697#123—78no—
698#123—78no—
699#123—716no—
700#123—716no—
701#123—716no—
702#123—716no—
703C22⋊Q8—78no—
704C22⋊Q8—78no—
705C22⋊Q8—74no—
706C22⋊Q8—78no—
707C22⋊Q8—78no—
708C22⋊Q8—78no—
709C22⋊Q8—74no—
710C22⋊Q8—74no—
711C22⋊Q8—74no—
712C22⋊Q8—74no—
713C22⋊Q8—74no—
714C22⋊Q8—716no—
715C22⋊Q8—78no—
716C22⋊Q8—716no—
717C22⋊Q8—716no—
718C22⋊Q8—716no—
719#121—716no—
720#121—716no—
721#121—74no—
722#121—78no—
723#121—78no—
724#121—78no—
725#121—74no—
726#121—74no—
727#121—74no—
728#121—74no—
729#121—74no—
730#121—78no—
731#121—716no—
732#120—78no—
733#120—716no—
734#120—716no—
735C4×Q8—78no—
736C4×Q8—74no—
737C4×Q8—78no—
738C4×Q8—78no—
739C4×Q8—78no—
740C4×Q8—74no—
741C4×Q8—74no—
742C4×Q8—74no—
743C4×Q8—74no—
744C4×Q8—74no—
745C4×Q8C22×D714yes—
746C4×Q8C22×D714yes—
747C4×Q8C22×D714yes—
748C4×Q8C22×D714yes—
749C4×D4—78no—
750C4×D4—78no—
751C4×D4—716no—
752C4×D4—78no—
753C4×D4—716no—
754C4×D4—716no—
755C4×D4—78no—
756C4×D4—78no—
757C4×D4—78no—
758C4×D4—78no—
759C4×D4—78no—
760C4×D4—78no—
761C4×D4—716no—
762C4×D4—716no—
763C4×D4—74no—
764C4×D4—74no—
765C4×D4—78no—
766C4×D4—78no—
767C4×D4—78no—
768C4×D4—74no—
769C4×D4—74no—
770C4×D4—74no—
771C4×D4—74no—
772C4×D4C22×D714yes—
773C4×D4C22×D714yes—
774C4×D4C22×D714yes—
775C4×D4C22×D714yes—
776C4×D4C22×D718yes—
777C4×D4C22×D718yes—
778C4×D4C22×D718yes—
779C4×D4C22×D718yes—
780#117—74no—
781#117—74no—
782#117—74no—
783#117—78no—
784#117—716no—
785#117—78no—
786#117—716no—
787#117—716no—
788#117—716no—
789#117—78no—
790#117—78no—
791#117C22×D718yes—
792#117C22×D718yes—
793#117C22×D714yes—
794#117C22×D714yes—
795C2×C4⋊C4—78no—
796C2×C4⋊C4—78no—
797C2×C4⋊C4—78no—
798C2×C4⋊C4—74no—
799C2×C4⋊C4—74no—
800C2×C4⋊C4—78no—
801C2×C4⋊C4—78no—
802C2×C4⋊C4C22×D711yescharacteristic
803C2×C4⋊C4C22×D711yescharacteristic
804C2×C4⋊C4C22×D712yes—
805C2×C4⋊C4C22×D712yes—
806C2×C22⋊C4—78no—
807C2×C22⋊C4—78no—
808C2×C22⋊C4—78no—
809C2×C22⋊C4—78no—
810C2×C22⋊C4—78no—
811C2×C22⋊C4—716no—
812C2×C22⋊C4C22×D712yes—
813C2×C22⋊C4C22×D712yes—
814C2×C22⋊C4C22×D712yes—
815C2×C42—78no—
816C2×C42—78no—
817C2×C42C22×D714yes—
818C2×C42C22×D711yescharacteristic
819C2×C42C22×D712yes—
820C2×C42C22×D714yes—
821C2×C42C22×D711yescharacteristic
822C2×C42C22×D711yescharacteristic
823C2×C42C22×D712yes—
824C2×C42C22×D712yes—
825C2×C42C22×D712yes—
826C2×C42C22×D712yes—
827C2×C42C22×D714yes—
828C2×C42C22×D714yes—
829C2×C42C22×D712yes—
830C2×C42C22×D712yes—
831C2×C42C22×D711yescharacteristic
832C22×C7—24no—
833C22×C7—24no—
834C22×C7—21no—
835C22×C7—21no—
836C22×C7—22no—
837C22×C7—22no—
838C22×C7—22no—
839C22×C7—48no—
840C22×C7—44no—
841C22×C7C22×#4118yes—
842C22×C7C22×#4112yes—
843C22×C7C2611yescharacteristic
844C2×D7—28no—
845C2×D7—28no—
846C2×D7—28no—
847C2×D7—816no—
848C4×C7—21no—
849C4×C7—21no—
850C4×C7—24no—
851C4×C7—24no—
852C4×C7—22no—
853C4×C7—24no—
854C4×C7—22no—
855C4×C7—21no—
856C4×C7—21no—
857C4×C7C22×#4114yes—
858C4×C7#58512yes—
859C4×C7#58512yes—
860Dic7—28no—
861Dic7—28no—
862Dic7—28no—
863C24—78no—
864C24C23×D711yescharacteristic
865C24C23×D712yes—
866#41—216no—
867#41—216no—
868#41—1432no—
869#41—1416no—
870#41—288no—
871#41—288no—
872C2×Q8—24no—
873C2×Q8—74no—
874C2×Q8—74no—
875C2×Q8—74no—
876C2×Q8—78no—
877C2×Q8—288no—
878C2×Q8C23×D714yes—
879C2×D4—28no—
880C2×D4—78no—
881C2×D4—716no—
882C2×D4—78no—
883C2×D4—78no—
884C2×D4—74no—
885C2×D4—74no—
886C2×D4—74no—
887C2×D4—78no—
888C2×D4—1432no—
889C2×D4—1432no—
890C2×D4—288no—
891C2×D4#115718yescomplemented
892C2×D4C23×D718yes—
893C2×D4C23×D714yes—
894C22×C4—28no—
895C22×C4—24no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—78no—
901C22×C4—78no—
902C22×C4—78no—
903C22×C4—78no—
904C22×C4—78no—
905C22×C4—78no—
906C22×C4—716no—
907C22×C4—2816no—
908C22×C4C23×D711yescharacteristic
909C22×C4C23×D711yescharacteristic
910C22×C4C23×D714yes—
911C22×C4C23×D714yes—
912C22×C4C23×D714yes—
913C22×C4C23×D712yes—
914C22×C4C23×D712yes—
915C22×C4C23×D712yes—
916C22×C4C23×D712yes—
917C22×C4C23×D714yes—
918C22×C4C23×D711yescharacteristic
919C22×C4C23×D712yes—
920C22×C4C23×D714yes—
921C22×C4C23×D714yes—
922C22×C4C23×D711yescharacteristic
923C22×C4C23×D712yes—
924C22×C4C23×D711yescharacteristic
925C22×C4C23×D712yes—
926C22×C4C23×D712yes—
927C22×C4C23×D712yes—
928C22×C4C23×D711yescharacteristic
929C4⋊C4—78no—
930C4⋊C4—78no—
931C4⋊C4—716no—
932C4⋊C4—78no—
933C4⋊C4—78no—
934C4⋊C4—716no—
935C4⋊C4—716no—
936C4⋊C4—716no—
937C4⋊C4—78no—
938C4⋊C4—78no—
939C4⋊C4—74no—
940C4⋊C4—74no—
941C4⋊C4—74no—
942C4⋊C4—78no—
943C4⋊C4—78no—
944C4⋊C4—74no—
945C4⋊C4—74no—
946C4⋊C4—74no—
947C4⋊C4C23×D714yes—
948C4⋊C4C23×D714yes—
949C4⋊C4C23×D718yes—
950C4⋊C4C23×D718yes—
951C22⋊C4—78no—
952C22⋊C4—716no—
953C22⋊C4—78no—
954C22⋊C4—78no—
955C22⋊C4—78no—
956C22⋊C4—78no—
957C22⋊C4—78no—
958C22⋊C4—78no—
959C22⋊C4—716no—
960C22⋊C4—78no—
961C22⋊C4—716no—
962C22⋊C4—716no—
963C22⋊C4—716no—
964C22⋊C4—78no—
965C22⋊C4C23×D718yes—
966C22⋊C4C23×D718yes—
967C22⋊C4C23×D718yes—
968C42—78no—
969C42—716no—
970C42—78no—
971C42—78no—
972C42C23×D711yescharacteristic
973C42C23×D711yescharacteristic
974C42C23×D714yes—
975C42C23×D712yes—
976C42C23×D712yes—
977C42C23×D714yes—
978C42C23×D714yes—
979C42C23×D712yes—
980C42C23×D714yes—
981C42C23×D712yes—
982C42C23×D712yes—
983C42C23×D714yes—
984C42C23×D712yes—
985C42C23×D711yescharacteristic
986C42C23×D711yescharacteristic
987C42C23×D714yes—
988C2×C7—28no—
989C2×C7—22no—
990C2×C7—42no—
991C2×C7C23×#4111yescharacteristic
992C2×C7C2×#58511yescharacteristic
993C2×C7C2×#58511yescharacteristic
994D7—48no—
995C23—22no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—41no—
1000C23—78no—
1001C23—1416no—
1002C23—288no—
1003C23—288no—
1004C23C2×#115718yes—
1005C23C24×D712yes—
1006C23C24×D711yescharacteristic
1007C23C24×D714yes—
1008Q8—28no—
1009Q8—148no—
1010Q8—148no—
1011Q8—288no—
1012Q8—284no—
1013D4—216no—
1014D4—1416no—
1015D4—1432no—
1016D4—148no—
1017D4—148no—
1018D4—288no—
1019D4—284no—
1020D4—288no—
1021D4—288no—
1022D4C2×#1157116yes—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—28no—
1026C2×C4—28no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—28no—
1032C2×C4—28no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—44no—
1036C2×C4—42no—
1037C2×C4—44no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—41no—
1041C2×C4—42no—
1042C2×C4—41no—
1043C2×C4—78no—
1044C2×C4—78no—
1045C2×C4—78no—
1046C2×C4—1416no—
1047C2×C4—1416no—
1048C2×C4—1416no—
1049C2×C4—2816no—
1050C2×C4—288no—
1051C2×C4—288no—
1052C2×C4—288no—
1053C2×C4C2×#115714yes—
1054C2×C4C24×D712yes—
1055C2×C4C24×D714yes—
1056C2×C4C24×D711yescharacteristic
1057C2×C4C24×D711yescharacteristic
1058C2×C4C24×D711yescharacteristic
1059C2×C4C24×D711yescharacteristic
1060C2×C4C24×D714yes—
1061C2×C4C24×D712yes—
1062C2×C4C24×D714yes—
1063C2×C4C24×D712yes—
1064C2×C4C24×D711yescharacteristic
1065C2×C4C24×D711yescharacteristic
1066C7#6278111yescharacteristic, complemented, Sylow
1067C22—21no—
1068C22—21no—
1069C22—24no—
1070C22—24no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—48no—
1075C22—44no—
1076C22—148no—
1077C22—148no—
1078C22—148no—
1079C22—5616no—
1080C22C22×#115712yes—
1081C22C22×#115718yes—
1082C22C25×D711yescharacteristic
1083C4—21no—
1084C4—21no—
1085C4—24no—
1086C4—21no—
1087C4—21no—
1088C4—24no—
1089C4—22no—
1090C4—24no—
1091C4—22no—
1092C4—148no—
1093C4—148no—
1094C4—148no—
1095C4C22×#115714yes—
1096C4#9061612yes—
1097C4#9061612yes—
1098C2—22no—
1099C2—28no—
1100C2—42no—
1101C2—288no—
1102C2C23×#115711yescharacteristic
1103C2C2×#9061611yescharacteristic
1104C2C2×#9061611yescharacteristic
subgroupG/H
centerC2×C4C24×D7
commutator, socle, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC2×C4×C7×#41C2
hypercenterC2×C4×#41D7
hypocenterC7#62781
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×#41C2semidirect
2. #11744341C2semidirect
3. #11742922C2semidirect
4. #11742920C2semidirect
5. #11742911C2semidirect
6. #11742909C2semidirect
7. #11742899C2semidirect
8. #11742894C2semidirect
9. #11742887C2semidirect
10. #11742879C2semidirect
11. #11742855C2semidirect
12. #11742854C2semidirect
13. #11742844C2semidirect
14. #11742834C2semidirect
15. C4×#6548C2semidirect
16. #11742814C2semidirect
17. #11742813C2semidirect
18. #11742748C2semidirect
19. C2×#90170C2semidirect
22. C4×C7×#41C22semidirect
23. C4×C7×#41C22semidirect
24. C4×C7×#41C22semidirect
25. C4×C7×#41C22semidirect
26. C2×C4×C7×Q8C22semidirect
27. C2×C4×C7×Q8C22semidirect
30. C2×C4×C7×D4C22semidirect
31. C2×C4×C7×D4C22semidirect
32. C2×C7×#117C22semidirect
33. C2×C7×#117C22semidirect
34. C22×C42×C7C22semidirect
35. C22×C42×C7C22semidirect
36. #90520C22semidirect
37. #90520C22semidirect
38. #90515C22semidirect
39. #90515C22semidirect
40. #90507C22semidirect
41. #90495C22semidirect
43. #90482C22semidirect
44. #90482C22semidirect
45. #90482C22semidirect
47. C2×#6492C22semidirect
48. C2×C4×C22⋊D7C22semidirect
49. C2×#6487C22semidirect
50. #90276C22semidirect
51. #90275C22semidirect
52. #90274C22semidirect
53. #90273C22semidirect
54. #90272C22semidirect
55. #90271C22semidirect
56. #90270C22semidirect
57. #90269C22semidirect
58. #90259C22semidirect
59. #90258C22semidirect
60. #90256C22semidirect
61. #90255C22semidirect
62. #90251C22semidirect
63. #90247C22semidirect
64. #90246C22semidirect
65. #90245C22semidirect
66. #90243C22semidirect
67. #90241C22semidirect
68. D4×D28C22semidirect
69. #90238C22semidirect
70. #90237C22semidirect
71. #90236C22semidirect
72. C4×D4×D7C22semidirect
73. #90234C22semidirect
74. #90232C22semidirect
75. #90231C22semidirect
76. #90230C22semidirect
77. #90229C22semidirect
78. D4×Dic14C22semidirect
79. C4×#1159C22semidirect
80. #90224C22semidirect
81. #90223C22semidirect
82. #90222C22semidirect
83. #90222C22semidirect
84. #90221C22semidirect
85. #90220C22semidirect
86. #90218C22semidirect
87. #90218C22semidirect
88. #90206C22semidirect
89. #90206C22semidirect
91. #90195C22semidirect
92. #90191C22semidirect
93. #90185C22semidirect
95. #90177C22semidirect
96. #90174C22semidirect
97. #90170C22semidirect
98. #90170C22semidirect
99. #90170C22semidirect
100. #90170C22semidirect
101. #90170C22semidirect
102. #90170C22semidirect
103. #90170C22semidirect
104. #90170C22semidirect
105. #90170C22semidirect
106. #90170C22semidirect
107. #90170C22semidirect
108. #90170C22semidirect
109. #90170C22semidirect
110. C2×#6439C22semidirect
112. #90168C22semidirect
113. #90168C22semidirect
114. C2×#6438C22semidirect
115. C4×#1157C22semidirect
116. C4×#1157C22semidirect
117. C4×#1157C22semidirect
118. C2×C4×D28C22semidirect
119. C2×#6435C22semidirect
120. #90161C22semidirect
121. #90161C22semidirect
122. #90161C22semidirect
123. C2×#6433C22semidirect
124. C2×C4×Dic14C22semidirect
337. C2×C4×#41D7semidirect
346. C2×C7×D4#41semidirect
549. C4×#41C2×D7semidirect
550. C4×#41C2×D7semidirect
551. C4×#41C2×D7semidirect
552. C4×#41C2×D7semidirect
554. C2×C4×Q8C2×D7semidirect
555. C2×C4×Q8C2×D7semidirect
561. C2×C4×D4C2×D7semidirect
562. C2×C4×D4C2×D7semidirect
564. C2×#117C2×D7semidirect
565. C2×#117C2×D7semidirect
566. C22×C42C2×D7semidirect
567. C22×C42C2×D7semidirect
891. C2×D4#1157semidirect
1066. C7#62781semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×#412
#117443412
#117429222
#117429202
#117429112
#117429092
#117428992
#117428942
#117428872
#117428792
#117428552
#117428542
#117428442
#117428342
C4×#65482
#117428142
#117428132
#117427482
C2×#901702
#627817