Finite Group Databasebeta

← #14261956

Subgroups — #14261956

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
1C7×#3501C211yesmaximal, characteristic, complemented
2#11744003C218yesmaximal, complemented
3#11743998C214yesmaximal, complemented
4#11743992C214yesmaximal, complemented
5#11743990C218yesmaximal, complemented
6#11743816C214yesmaximal, complemented
7#11743812C214yesmaximal, complemented
8#11743652C212yesmaximal, complemented
9#11743651C212yesmaximal, complemented
10#11743641C214yesmaximal, complemented
11#11743640C214yesmaximal, complemented
12#11743328C212yesmaximal, complemented
13#11743325C212yesmaximal, complemented
14#11743039C214yesmaximal, complemented
15C2×#90315C214yesmaximal, complemented
16#11742926C212yesmaximal, complemented
17#11742925C212yesmaximal, complemented
18#11742854C211yesmaximal, characteristic, complemented
19C2×C4×#1159C211yesmaximal, characteristic, complemented
20C2×#6548C2212yes—
21C22×#1159C2211yescharacteristic
22C7×#554C2218yescomplemented
23C7×#554C2214yescomplemented
24C7×D4×Q8C2214yescomplemented
25C7×#544C2212yescomplemented
26C7×#543C2214yescomplemented
27C7×#533C2212yescomplemented
28C2×C7×C22⋊Q8C2214yescomplemented
29C7×#518C2212yes—
30C2×C4×C7×D4C2211yescharacteristic
31#90508C2218yescomplemented
32C2×#6510C2214yescomplemented
33C2×Q8×Dic7C2214yescomplemented
34C2×D4×Dic7C2211yescharacteristic
35C2×#6493C2214yes—
36C2×C4×C22⋊D7C2212yescomplemented
37C22×C4×Dic7C2212yescomplemented
38#90425C2218yescomplemented
39#90424C2218yescomplemented
40#90423C2218yescomplemented
41#90423C2214yescomplemented
42#90421C2214yescomplemented
43#90419C2212yescomplemented
44#90419C2218yescomplemented
45#90419C2212yescomplemented
46#90416C2212yescomplemented
47#90416C2212yescomplemented
48#90388C2218yescomplemented
49#90386C2218yescomplemented
50#90385C2218yescomplemented
51#90385C2218yescomplemented
52#90382C2214yescomplemented
53#90382C2214yescomplemented
54#90382C2218yescomplemented
55#90336C22116yescomplemented
56#90336C2218yescomplemented
57#90336C2218yescomplemented
58#90335C22116yescomplemented
59#90335C2218yescomplemented
60#90333C22116yescomplemented
61#90333C2218yescomplemented
62#90333C22116yescomplemented
63#90328C22116yescomplemented
64#90328C22116yescomplemented
65#90328C22116yescomplemented
66#90321C2218yescomplemented
67#90318C2214yescomplemented
68#90318C2214yescomplemented
69#90318C22116yescomplemented
70#90315C2218yescomplemented
71#90315C2214yescomplemented
72#90315C2218yescomplemented
73#90315C2218yescomplemented
74#90315C2218yescomplemented
75#90315C2218yescomplemented
76#90315C2218yescomplemented
77#90315C2218yescomplemented
78#90315C22116yescomplemented
79#90315C2214yescomplemented
80#90276C2214yescomplemented
81#90275C2218yescomplemented
82#90271C2214yescomplemented
83#90271C2214yescomplemented
84C4×#1161C2214yescomplemented
85C4×#1161C2214yescomplemented
86#90261C2214yescomplemented
87#90246C2218yescomplemented
88#90246C2214yescomplemented
89#90246C2218yescomplemented
90#90245C2218yescomplemented
91#90245C2218yescomplemented
92#90245C2218yescomplemented
93D4×D28C2214yescomplemented
94#90237C2218yescomplemented
95#90236C2218yescomplemented
96C4×D4×D7C2218yescomplemented
97C4×#1159C2214yescomplemented
98C4×#1159C2214yescomplemented
99C4×#1159C2218yescomplemented
100C4×#1159C2214yescomplemented
101C4×#1159C2214yescomplemented
102#90217C2214yescomplemented
103#90215C2214yescomplemented
104#90214C2214yescomplemented
105#90213C2214yescomplemented
106#90205C22116yescomplemented
107#90205C2218yescomplemented
108C2×#6461C2218yescomplemented
109#90201C2212yes—
110C2×#6456C2214yescomplemented
111C2×#6455C2218yescomplemented
112C2×#6455C2211yescharacteristic, complemented
113C2×#6453C2214yescomplemented
114C2×#6450C2211yescharacteristic, complemented
115#90184C2214yes—
116#90184C2218yescomplemented
117C2×#6449C2218yescomplemented
118#90177C2218yescomplemented
119C2×(C22⋊D7)⋊C4C2218yescomplemented
120C2×(C22⋊D7)⋊C4C2212yescomplemented
121C2×#6440C2212yescomplemented
122#90168C2212yes—
123C2×C42×D7C2211yescharacteristic, complemented
124C2×C4×Dic14C2211yescharacteristic, complemented
125#62781—71nomaximal, Sylow
126C22×C7×Q8C2314yes—
127C22×C7×D4C2311yescharacteristic
128C23×C4×C7C2312yes—
129C22×C22⋊D7C2318yes—
130C22×C22⋊D7C2312yes—
131C23×Dic7C2312yes—
132C23×Dic7C2312yes—
133C2×#1161C2314yes—
134C2×#1161C2314yes—
135#6548—216no—
136C2×#1159—28no—
137C2×#1159C2314yes—
138C2×#1159C2314yes—
139C2×#1159C2318yes—
140C2×D4×D7C2318yes—
141C2×#1157C2314yes—
142C22×D28C2314yes—
143C22×C4×D7C2311yescharacteristic
144C22×C4×D7C2311yescharacteristic
145C22×C4×D7C2311yescharacteristic
146C22×C4×D7C2318yes—
147C22×Dic14C2311yescharacteristic
148C7×C4⋊Q8C2312yes—
149C7×C4⋊Q8C2312yes—
150C7×C4⋊Q8C2318yes—
151C7×#125C2314yes—
152C7×#125C2318yes—
153C7×C22⋊Q8C2314yes—
154C7×C22⋊Q8C2318yes—
155C7×C22⋊Q8C2318yes—
156C7×C22⋊Q8C2318yes—
157C7×C22⋊Q8C2314yes—
158C7×C22⋊Q8C23116yes—
159C7×C22⋊Q8C23116yes—
160C4×C7×Q8C2314yes—
161C4×C7×Q8C2314yes—
162C4×C7×D4C2314yes—
163C4×C7×D4C2314yes—
164C4×C7×D4C2318yes—
165C4×C7×D4C2318yes—
166C7×#117C2314yes—
167C2×C7×C4⋊C4C2311yescharacteristic
168C2×C7×C4⋊C4C2314yes—
169C2×C7×C4⋊C4C2318yes—
170C2×C7×C22⋊C4C2312yes—
171C2×C7×C22⋊C4C2318yes—
172C2×C42×C7C2311yescharacteristic
173C2×C22⋊Dic7C2312yes—
174#6510C2314yes—
175#6510C2314yes—
176#6510C23116yes—
177#6510C2318yes—
178#6510C2318yes—
179#6510C2318yes—
180#6509C23116yes—
181#6509C2314yes—
182#6509C2314yes—
183#6509C23116yes—
184Q8×Dic7C2318yes—
185Q8×Dic7C2314yes—
186Q8×Dic7C2314yes—
187Q8×Dic7C2318yes—
188Q8×Dic7C2318yes—
189D4×Dic7C2314yes—
190D4×Dic7C2314yes—
191#6493C2314yes—
192#6493C2314yes—
193#6493C2318yes—
194#6493C23116yes—
195#6493C23116yes—
196#6493C2318yes—
197#6493C2318yes—
198C4×C22⋊D7C23116yes—
199C4×C22⋊D7C23116yes—
200C4×C22⋊D7C2318yes—
201C4×C22⋊D7C2318yes—
202C2×(C2×D7)⋊C4C2312yes—
203C2×(C2×D7)⋊C4C2318yes—
204C2×(C2×D7)⋊C4C2318yes—
205C2×(C2×D7)⋊C4C2318yes—
206C2×(C2×D7)⋊C4C2318yes—
207C2×C4⋊Dic7C2311yescharacteristic
208C2×C4⋊Dic7C2318yes—
209C2×C4⋊Dic7C2318yes—
210C2×C4⋊Dic7C2314yes—
211C2×Dic7⋊C4C2312yes—
212C2×Dic7⋊C4C2312yes—
213C2×Dic7⋊C4C2318yes—
214C2×C4×Dic7C2312yes—
215C2×C4×Dic7C2311yescharacteristic
216C2×C4×Dic7C2311yescharacteristic
217C2×C4×Dic7C2311yescharacteristic
218C2×C4×Dic7C2312yes—
219C2×C4×Dic7C2312yes—
220C2×C4×Dic7C2318yes—
221C2×C4×Dic7C2314yes—
222C2×C4×Dic7C2314yes—
223C2×C4×Dic7C2314yes—
224C2×C4×Dic7C2314yes—
225#6461C23116yes—
226#6461C2318yes—
227#6461C2318yes—
228#6461C23116yes—
229#6461C23116yes—
230#6461C23116yes—
231#6461C23116yes—
232#6461C23116yes—
233#6460C2314yes—
234#6460C2318yes—
235#6460C2314yes—
236#6460C2318yes—
237#6460C2318yes—
238#6458C2314yes—
239#6458C2318yes—
240#6458C2314yes—
241#6458C23116yes—
242#6458C2314yes—
243#6458C2314yes—
244#6457C23116yes—
245#6457C2318yes—
246#6457C2318yes—
247#6457C23116yes—
248#6457C23116yes—
249#6456C2314yes—
250#6456C2318yes—
251#6456C2314yes—
252#6456C2318yes—
253#6456C2318yes—
254#6456C2318yes—
255#6456C2314yes—
256#6456C2314yes—
257#6456C2318yes—
258#6455C23116yes—
259#6455C2318yes—
260#6455C2318yes—
261#6455C2314yes—
262#6455C2318yes—
263#6455C23116yes—
264#6455C23116yes—
265#6455C2314yes—
266#6455C2314yes—
267#6455C2314yes—
268D7×C4⋊C4C2318yes—
269#6453C2318yes—
270#6453C23116yes—
271#6453C2318yes—
272#6453C23116yes—
273#6453C2314yes—
274#6453C2314yes—
275#6453C2318yes—
276#6450C2314yes—
277#6450C2314yes—
278#6450C2314yes—
279#6450C2314yes—
280#6449C2318yes—
281#6449C23116yes—
282#6449C23116yes—
283#6449C23116yes—
284#6449C23116yes—
285#6449C23116yes—
286#6445C23116yes—
287#6445C2318yes—
288#6445C23116yes—
289(C22⋊D7)⋊C4C2318yes—
290(C22⋊D7)⋊C4C23116yes—
291(C22⋊D7)⋊C4C2318yes—
292(C22⋊D7)⋊C4C2318yes—
293(C22⋊D7)⋊C4C23116yes—
294(C22⋊D7)⋊C4C23116yes—
295(C22⋊D7)⋊C4C2318yes—
296D7×C22⋊C4C23116yes—
297#6440C2318yes—
298#6440C2318yes—
299#6440C23116yes—
300#6438C2314yes—
301#6438C2318yes—
302#6437C2312yes—
303C4×D28C2314yes—
304C4×D28C2318yes—
305C4×D28C2318yes—
306C4×D28C2318yes—
307C4×D28C2314yes—
308#6435C2318yes—
309C42×D7C2312yes—
310C42×D7C2312yes—
311C42×D7C2318yes—
312C42×D7C2312yes—
313C42×D7C2312yes—
314#6432C2318yes—
315#6432C2312yes—
316C4×Dic14C2314yes—
317C4×Dic14C2318yes—
318C4×Dic14C2314yes—
319#3521—78no—
320#3515—74no—
321#3514—74no—
322#3507—72no—
323#3505—74no—
324#3501D711yescharacteristic, complemented
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×#41—71no—
338C24×C7C2412yes—
339C23×D7C2418yes—
340C23×D7C2411yescharacteristic
341C2×C7×Q8—48no—
342C2×C7×Q8C2414yes—
343C2×C7×Q8C2418yes—
344C2×C7×Q8C2414yes—
345C2×C7×D4#4118yescomplemented
346C2×C7×D4C2414yes—
347C22×C4×C7—44no—
348C22×C4×C7C2411yescharacteristic
349C22×C4×C7C2414yes—
350C22×C4×C7C2412yes—
351C22×C4×C7C2414yes—
352C22×C4×C7C2411yescharacteristic
353C22×C4×C7C2418yes—
354C22×C4×C7C2418yes—
355C22×C4×C7C2411yescharacteristic
356C2×C22⋊D7—28no—
357C2×C22⋊D7—232no—
358C2×C22⋊D7C2418yes—
359C2×C22⋊D7C2418yes—
360C2×C22⋊D7C24116yes—
361C22×Dic7—28no—
362C22×Dic7—44no—
363C22×Dic7C2414yes—
364C22×Dic7C2414yes—
365C22×Dic7C2418yes—
366C22×Dic7C2411yescharacteristic
367C22×Dic7C2414yes—
368C22×Dic7C2411yescharacteristic
369C22×Dic7C2412yes—
370C22×Dic7C2411yescharacteristic
371C22×Dic7C2412yes—
372C22×Dic7C2414yes—
373#1161—48no—
374#1161—48no—
375#1159—216no—
376#1159—216no—
377#1159—232no—
378D4×D7—232no—
379#1157—216no—
380C2×D28—48no—
381C2×D28C2414yes—
382C2×D28C2414yes—
383C2×D28C2414yes—
384C2×D28C2418yes—
385C2×D28C2418yes—
386C2×D28C2418yes—
387C2×C4×D7—24no—
388C2×C4×D7—416no—
389C2×C4×D7—42no—
390C2×C4×D7—42no—
391C2×C4×D7C2412yes—
392C2×C4×D7C2412yes—
393C2×C4×D7C2412yes—
394C2×C4×D7C2412yes—
395C2×C4×D7C2418yes—
396C2×C4×D7C2418yes—
397C2×C4×D7C2412yes—
398C2×C4×D7C2412yes—
399C2×C4×D7C2418yes—
400C2×C4×D7C24116yes—
401C2×Dic14—24no—
402C2×Dic14C2414yes—
403C2×Dic14C2414yes—
404C7×C4⋊C4C2414yes—
405C7×C4⋊C4C2414yes—
406C7×C4⋊C4C2414yes—
407C7×C4⋊C4C2414yes—
408C7×C4⋊C4C2418yes—
409C7×C4⋊C4C2418yes—
410C7×C4⋊C4C24116yes—
411C7×C4⋊C4C2414yes—
412C7×C4⋊C4C2418yes—
413C7×C22⋊C4C2418yes—
414C7×C22⋊C4C24116yes—
415C7×C22⋊C4C2418yes—
416C42×C7C2412yes—
417C42×C7C2412yes—
418C42×C7C2418yes—
419C22⋊Dic7C2418yes—
420(C2×D7)⋊C4C2418yes—
421(C2×D7)⋊C4C2418yes—
422(C2×D7)⋊C4C2418yes—
423(C2×D7)⋊C4C2418yes—
424(C2×D7)⋊C4C24116yes—
425(C2×D7)⋊C4C2418yes—
426(C2×D7)⋊C4C2418yes—
427(C2×D7)⋊C4C2418yes—
428(C2×D7)⋊C4C2418yes—
429(C2×D7)⋊C4C24116yes—
430(C2×D7)⋊C4C24116yes—
431(C2×D7)⋊C4C2418yes—
432(C2×D7)⋊C4C24116yes—
433C4⋊Dic7C2414yes—
434C4⋊Dic7C2414yes—
435C4⋊Dic7C2414yes—
436C4⋊Dic7C24116yes—
437C4⋊Dic7C24116yes—
438C4⋊Dic7C2418yes—
439C4⋊Dic7C2418yes—
440C4⋊Dic7C2418yes—
441Dic7⋊C4C2418yes—
442Dic7⋊C4C24116yes—
443Dic7⋊C4C2418yes—
444Dic7⋊C4C2418yes—
445Dic7⋊C4C2418yes—
446C4×Dic7C2414yes—
447C4×Dic7C2414yes—
448C4×Dic7C24116yes—
449C4×Dic7C2412yes—
450C4×Dic7C2412yes—
451C4×Dic7C2412yes—
452C4×Dic7C2412yes—
453C4×Dic7C2411yescharacteristic
454C4×Dic7C2411yescharacteristic
455C4×Dic7C2411yescharacteristic
456C4×Dic7C2411yescharacteristic
457C4×Dic7C2418yes—
458C4×Dic7C2418yes—
459C4×Dic7C2414yes—
460C4×Dic7C2414yes—
461C4×Dic7C2414yes—
462C4×Dic7C2414yes—
463C2×H(5,𝔽2)—72no—
464C22×#41—71no—
465#559—74no—
466#557—74no—
467#556—78no—
468#556—74no—
469#556—78no—
470#555—78no—
471#554—74no—
472#554C2×D718yescomplemented
473#554C2×D714yescomplemented
474#553—78no—
475#553—716no—
476#553—78no—
477#552—78no—
478#552—78no—
479#552—716no—
480#552—716no—
481#552—78no—
482#551—716no—
483#551—716no—
484#551—716no—
485D4×Q8C2×D714yescomplemented
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#544C2×D712yescomplemented
496#543C2×D714yescomplemented
497#542—78no—
498#541—78no—
499#539—78no—
500#539—716no—
501#539—78no—
502#538—78no—
503#538—716no—
504#537—72no—
505#536—74no—
506#534—74no—
507#534—78no—
508#533—72no—
509#533—72no—
510#533—78no—
511#533C2×D712yescomplemented
512#532—72no—
513#532—72no—
514#532—72no—
515#529—74no—
516#529—74no—
517#529—78no—
518#529—74no—
519#529—78no—
520#529—78no—
521#529—78no—
522#529—78no—
523#529—78no—
524#529—78no—
525#529—78no—
526#529—74no—
527#529—716no—
528#529—74no—
529#529—74no—
530C2×#126—78no—
531C2×#125—74no—
532C2×#124—74no—
533#525—74no—
534#525—74no—
535#525—716no—
536#525—74no—
537C2×#123—78no—
538C2×C22⋊Q8C2×D714yescomplemented
539C2×#121—74no—
540#520—78no—
541#520—74no—
542#518—78no—
543#518—78no—
544#518C2×D712yes—
545C4×#41—74no—
546C4×#41—74no—
547C4×#41—74no—
548C4×#41—74no—
549C4×#41—74no—
550C4×#41—74no—
551C4×#41—78no—
552C4×#41—74no—
553C2×C4×Q8—74no—
554C2×C4×Q8—71no—
555C2×C4×Q8—71no—
556C2×C4×D4—71no—
557C2×C4×D4—72no—
558C2×C4×D4—78no—
559C2×C4×D4—74no—
560C2×C4×D4—72no—
561C2×C4×D4—78no—
562C2×C4×D4C2×D711yescharacteristic
563C2×#117—71no—
564C2×#117—78no—
565C2×#117—72no—
566C22×C42—72no—
567C22×C42—71no—
568C23×C7—42no—
569C23×C7—42no—
570C23×C7C2×#4118yes—
571C23×C7C2514yes—
572C23×C7C2511yescharacteristic
573C22×D7—22no—
574C22×D7—216no—
575C22×D7—41no—
576C22×D7—41no—
577C22×D7—48no—
578C22×D7—48no—
579C22×D7C2518yes—
580C22×D7C2512yes—
581C7×Q8—28no—
582C7×Q8—44no—
583C7×Q8—48no—
584C7×D4C2×#41116yes—
585C2×C4×C7—22no—
586C2×C4×C7—28no—
587C2×C4×C7—48no—
588C2×C4×C7—41no—
589C2×C4×C7—44no—
590C2×C4×C7—42no—
591C2×C4×C7—48no—
592C2×C4×C7C2×#4114yes—
593C2×C4×C7C2511yescharacteristic
594C2×C4×C7C2514yes—
595C2×C4×C7C2518yes—
596C2×C4×C7C2512yes—
597C2×C4×C7C2518yes—
598C2×C4×C7C2512yes—
599C2×C4×C7C2511yescharacteristic
600C22⋊D7—216no—
601C22⋊D7—232no—
602C22⋊D7—216no—
603C2×Dic7—24no—
604C2×Dic7—22no—
605C2×Dic7—28no—
606C2×Dic7—28no—
607C2×Dic7—216no—
608C2×Dic7—28no—
609C2×Dic7—22no—
610C2×Dic7—41no—
611C2×Dic7—42no—
612C2×Dic7—44no—
613C2×Dic7C2511yescharacteristic
614C2×Dic7C2512yes—
615C2×Dic7C2514yes—
616C2×Dic7C2511yescharacteristic
617C2×Dic7C2511yescharacteristic
618C2×Dic7C2518yes—
619C2×Dic7C2514yes—
620C2×Dic7C2511yescharacteristic
621D28—28no—
622D28—28no—
623D28—48no—
624D28—48no—
625D28—44no—
626D28—48no—
627C4×D7—24no—
628C4×D7—24no—
629C4×D7—216no—
630C4×D7—24no—
631C4×D7—216no—
632C4×D7—24no—
633C4×D7—42no—
634C4×D7—416no—
635C4×D7—42no—
636C4×D7—48no—
637Dic14—28no—
638Dic14—28no—
639H(5,𝔽2)—1416no—
640C2×#41—74no—
641C2×#41—74no—
642C2×#41—74no—
643C2×#41—74no—
644C2×#41—78no—
645C2×#41—74no—
646C2×#41—148no—
647C22×Q8—71no—
648C22×Q8C22×D714yes—
649C22×D4—72no—
650C22×D4—78no—
651C22×D4—78no—
652C22×D4—74no—
653C22×D4C22×D711yescharacteristic
654C23×C4—72no—
655C23×C4—72no—
656C23×C4—71no—
657C23×C4—78no—
658C23×C4—71no—
659C23×C4—71no—
660C23×C4C22×D712yes—
661C4⋊Q8—72no—
662C4⋊Q8—78no—
663C4⋊Q8C22×D712yes—
664C4⋊Q8C22×D712yes—
665C4⋊Q8C22×D718yes—
666#127—72no—
667#126—78no—
668#126—716no—
669#126—716no—
670#126—716no—
671#126—78no—
672#126—716no—
673#126—716no—
674#126—716no—
675#125—74no—
676#125—78no—
677#125—78no—
678#125—78no—
679#125—74no—
680#125—716no—
681#125—716no—
682#125C22×D714yes—
683#125C22×D718yes—
684#124—74no—
685#124—78no—
686#124—78no—
687#124—78no—
688#124—74no—
689#124—716no—
690#124—74no—
691#124—78no—
692#123—78no—
693#123—78no—
694#123—716no—
695#123—716no—
696#123—716no—
697#123—78no—
698#123—716no—
699#123—716no—
700#123—716no—
701#123—716no—
702#123—716no—
703C22⋊Q8—74no—
704C22⋊Q8—74no—
705C22⋊Q8—716no—
706C22⋊Q8—716no—
707C22⋊Q8—74no—
708C22⋊Q8—74no—
709C22⋊Q8—78no—
710C22⋊Q8—78no—
711C22⋊Q8—78no—
712C22⋊Q8C22×D714yes—
713C22⋊Q8C22×D718yes—
714C22⋊Q8C22×D718yes—
715C22⋊Q8C22×D718yes—
716C22⋊Q8C22×D714yes—
717C22⋊Q8C22×D7116yes—
718C22⋊Q8C22×D7116yes—
719#121—74no—
720#121—78no—
721#121—78no—
722#121—78no—
723#121—74no—
724#121—716no—
725#121—716no—
726#121—74no—
727#121—74no—
728#121—74no—
729#121—74no—
730#121—716no—
731#121—78no—
732#120—78no—
733#120—716no—
734#120—716no—
735C4×Q8—74no—
736C4×Q8—78no—
737C4×Q8—78no—
738C4×Q8—78no—
739C4×Q8—74no—
740C4×Q8—74no—
741C4×Q8—74no—
742C4×Q8—74no—
743C4×Q8—74no—
744C4×Q8—74no—
745C4×Q8—74no—
746C4×Q8—78no—
747C4×Q8C22×D714yes—
748C4×Q8C22×D714yes—
749C4×D4—74no—
750C4×D4—74no—
751C4×D4—78no—
752C4×D4—78no—
753C4×D4—716no—
754C4×D4—716no—
755C4×D4—74no—
756C4×D4—74no—
757C4×D4—78no—
758C4×D4—78no—
759C4×D4—78no—
760C4×D4—74no—
761C4×D4—78no—
762C4×D4—78no—
763C4×D4—74no—
764C4×D4—716no—
765C4×D4—78no—
766C4×D4—78no—
767C4×D4—78no—
768C4×D4—716no—
769C4×D4—716no—
770C4×D4—78no—
771C4×D4—78no—
772C4×D4—78no—
773C4×D4—78no—
774C4×D4—74no—
775C4×D4—74no—
776C4×D4C22×D718yes—
777C4×D4C22×D714yes—
778C4×D4C22×D714yes—
779C4×D4C22×D718yes—
780#117—78no—
781#117—74no—
782#117—74no—
783#117—716no—
784#117—716no—
785#117—716no—
786#117—78no—
787#117—74no—
788#117—74no—
789#117—78no—
790#117—78no—
791#117—78no—
792#117—716no—
793#117—78no—
794#117C22×D714yes—
795C2×C4⋊C4—71no—
796C2×C4⋊C4—72no—
797C2×C4⋊C4—72no—
798C2×C4⋊C4—78no—
799C2×C4⋊C4—78no—
800C2×C4⋊C4—74no—
801C2×C4⋊C4—78no—
802C2×C4⋊C4—78no—
803C2×C4⋊C4C22×D711yescharacteristic
804C2×C4⋊C4C22×D718yes—
805C2×C4⋊C4C22×D714yes—
806C2×C22⋊C4—72no—
807C2×C22⋊C4—72no—
808C2×C22⋊C4—78no—
809C2×C22⋊C4—78no—
810C2×C22⋊C4—78no—
811C2×C22⋊C4—78no—
812C2×C22⋊C4—716no—
813C2×C22⋊C4C22×D712yes—
814C2×C22⋊C4C22×D718yes—
815C2×C42—74no—
816C2×C42—72no—
817C2×C42—71no—
818C2×C42—78no—
819C2×C42—71no—
820C2×C42—74no—
821C2×C42—72no—
822C2×C42—72no—
823C2×C42—74no—
824C2×C42—74no—
825C2×C42—71no—
826C2×C42—78no—
827C2×C42—72no—
828C2×C42—72no—
829C2×C42—72no—
830C2×C42—72no—
831C2×C42C22×D711yescharacteristic
832C22×C7—21no—
833C22×C7—24no—
834C22×C7—21no—
835C22×C7—24no—
836C22×C7—48no—
837C22×C7C22×#4118yes—
838C22×C7C22×#4112yes—
839C22×C7C2611yescharacteristic
840C2×D7—22no—
841C2×D7—28no—
842C2×D7—28no—
843C2×D7—22no—
844C2×D7—22no—
845C2×D7—28no—
846C2×D7—44no—
847C2×D7—816no—
848C4×C7—28no—
849C4×C7—22no—
850C4×C7—21no—
851C4×C7—28no—
852C4×C7—24no—
853C4×C7C22×#4114yes—
854C4×C7#58512yes—
855Dic7—24no—
856Dic7—28no—
857Dic7—21no—
858Dic7—21no—
859Dic7—22no—
860Dic7—24no—
861Dic7—21no—
862Dic7#58512yes—
863C24—78no—
864C24—71no—
865C24C23×D712yes—
866#41—1416no—
867#41—1416no—
868#41—1432no—
869#41—1416no—
870#41—288no—
871#41—288no—
872C2×Q8—48no—
873C2×Q8—74no—
874C2×Q8—74no—
875C2×Q8—144no—
876C2×Q8C23×D714yes—
877C2×Q8C23×D718yes—
878C2×Q8C23×D714yes—
879C2×D4—78no—
880C2×D4—716no—
881C2×D4—78no—
882C2×D4—74no—
883C2×D4—74no—
884C2×D4—74no—
885C2×D4—78no—
886C2×D4—78no—
887C2×D4—78no—
888C2×D4—148no—
889C2×D4—1432no—
890C2×D4—1432no—
891C2×D4—288no—
892C2×D4#116118yescomplemented
893C2×D4C23×D714yes—
894C22×C4—44no—
895C22×C4—74no—
896C22×C4—71no—
897C22×C4—71no—
898C22×C4—74no—
899C22×C4—74no—
900C22×C4—72no—
901C22×C4—78no—
902C22×C4—74no—
903C22×C4—71no—
904C22×C4—72no—
905C22×C4—72no—
906C22×C4—72no—
907C22×C4—72no—
908C22×C4—72no—
909C22×C4—78no—
910C22×C4—78no—
911C22×C4—72no—
912C22×C4—72no—
913C22×C4—78no—
914C22×C4—716no—
915C22×C4—148no—
916C22×C4—144no—
917C22×C4—282no—
918C22×C4—2816no—
919C22×C4—282no—
920C22×C4—284no—
921C22×C4C23×D711yescharacteristic
922C22×C4C23×D714yes—
923C22×C4C23×D714yes—
924C22×C4C23×D712yes—
925C22×C4C23×D711yescharacteristic
926C22×C4C23×D718yes—
927C22×C4C23×D718yes—
928C22×C4C23×D711yescharacteristic
929C4⋊C4—716no—
930C4⋊C4—78no—
931C4⋊C4—78no—
932C4⋊C4—78no—
933C4⋊C4—78no—
934C4⋊C4—74no—
935C4⋊C4—78no—
936C4⋊C4—74no—
937C4⋊C4—78no—
938C4⋊C4—716no—
939C4⋊C4—78no—
940C4⋊C4—716no—
941C4⋊C4—74no—
942C4⋊C4C23×D714yes—
943C4⋊C4C23×D718yes—
944C4⋊C4C23×D714yes—
945C4⋊C4C23×D714yes—
946C4⋊C4C23×D7116yes—
947C4⋊C4C23×D718yes—
948C4⋊C4C23×D714yes—
949C4⋊C4C23×D714yes—
950C4⋊C4C23×D718yes—
951C22⋊C4—78no—
952C22⋊C4—78no—
953C22⋊C4—78no—
954C22⋊C4—78no—
955C22⋊C4—78no—
956C22⋊C4—78no—
957C22⋊C4—716no—
958C22⋊C4—78no—
959C22⋊C4—716no—
960C22⋊C4—716no—
961C22⋊C4—716no—
962C22⋊C4—78no—
963C22⋊C4—78no—
964C22⋊C4—78no—
965C22⋊C4C23×D7116yes—
966C22⋊C4C23×D718yes—
967C22⋊C4C23×D718yes—
968C42—71no—
969C42—72no—
970C42—71no—
971C42—71no—
972C42—71no—
973C42—74no—
974C42—72no—
975C42—74no—
976C42—78no—
977C42—72no—
978C42—74no—
979C42—72no—
980C42—74no—
981C42—74no—
982C42—74no—
983C42—78no—
984C42—716no—
985C42C23×D712yes—
986C42C23×D712yes—
987C42C23×D718yes—
988C2×C7—22no—
989C2×C7—28no—
990C2×C7C23×#4111yescharacteristic
991C2×C7C2×#58511yescharacteristic
992C2×C7C2×#58511yescharacteristic
993D7—42no—
994D7—48no—
995C23—42no—
996C23—42no—
997C23—78no—
998C23—72no—
999C23—142no—
1000C23—1416no—
1001C23—281no—
1002C23—281no—
1003C23—288no—
1004C23—288no—
1005C23C2×#116118yes—
1006C23C24×D714yes—
1007C23C24×D711yescharacteristic
1008Q8—28no—
1009Q8—48no—
1010Q8—44no—
1011Q8—148no—
1012Q8—148no—
1013D4—1432no—
1014D4—1416no—
1015D4—1416no—
1016D4—148no—
1017D4—148no—
1018D4—288no—
1019D4—288no—
1020D4—288no—
1021D4—284no—
1022D4C2×#1161116yes—
1023C2×C4—22no—
1024C2×C4—28no—
1025C2×C4—44no—
1026C2×C4—42no—
1027C2×C4—48no—
1028C2×C4—41no—
1029C2×C4—48no—
1030C2×C4—71no—
1031C2×C4—71no—
1032C2×C4—71no—
1033C2×C4—72no—
1034C2×C4—71no—
1035C2×C4—74no—
1036C2×C4—74no—
1037C2×C4—78no—
1038C2×C4—1416no—
1039C2×C4—144no—
1040C2×C4—148no—
1041C2×C4—142no—
1042C2×C4—142no—
1043C2×C4—144no—
1044C2×C4—148no—
1045C2×C4—148no—
1046C2×C4—1416no—
1047C2×C4—144no—
1048C2×C4—144no—
1049C2×C4—1416no—
1050C2×C4—144no—
1051C2×C4—282no—
1052C2×C4—2816no—
1053C2×C4—282no—
1054C2×C4—288no—
1055C2×C4—281no—
1056C2×C4—284no—
1057C2×C4—282no—
1058C2×C4C2×#116114yes—
1059C2×C4C24×D711yescharacteristic
1060C2×C4C24×D714yes—
1061C2×C4C24×D718yes—
1062C2×C4C24×D712yes—
1063C2×C4C24×D718yes—
1064C2×C4C24×D712yes—
1065C2×C4C24×D711yescharacteristic
1066C7#6278111yescharacteristic, complemented, Sylow
1067C22—24no—
1068C22—21no—
1069C22—24no—
1070C22—21no—
1071C22—48no—
1072C22—142no—
1073C22—148no—
1074C22—142no—
1075C22—148no—
1076C22—148no—
1077C22—142no—
1078C22—284no—
1079C22—5616no—
1080C22C22×#116118yes—
1081C22C22×#116112yes—
1082C22C25×D711yescharacteristic
1083C4—21no—
1084C4—24no—
1085C4—28no—
1086C4—28no—
1087C4—22no—
1088C4—72no—
1089C4—141no—
1090C4—141no—
1091C4—148no—
1092C4—144no—
1093C4—142no—
1094C4—144no—
1095C4—141no—
1096C4C22×#116114yes—
1097C4#9061812yes—
1098C2—22no—
1099C2—28no—
1100C2—282no—
1101C2—288no—
1102C2C23×#116111yescharacteristic
1103C2C2×#9061811yescharacteristic
1104C2D7×#58511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D7
commutator, socle, cosocleC22×C7C26
FittingC7×#3501C2
hypercenter#3501D7
hypocenterC7#62781
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. #11744003C2semidirect
3. #11743998C2semidirect
4. #11743992C2semidirect
5. #11743990C2semidirect
6. #11743816C2semidirect
7. #11743812C2semidirect
8. #11743652C2semidirect
9. #11743651C2semidirect
10. #11743641C2semidirect
11. #11743640C2semidirect
12. #11743328C2semidirect
13. #11743325C2semidirect
14. #11743039C2semidirect
15. C2×#90315C2semidirect
16. #11742926C2semidirect
17. #11742925C2semidirect
18. #11742854C2semidirect
19. C2×C4×#1159C2semidirect
22. C7×#554C22semidirect
23. C7×#554C22semidirect
24. C7×D4×Q8C22semidirect
25. C7×#544C22semidirect
26. C7×#543C22semidirect
27. C7×#533C22semidirect
28. C2×C7×C22⋊Q8C22semidirect
31. #90508C22semidirect
32. C2×#6510C22semidirect
33. C2×Q8×Dic7C22semidirect
36. C2×C4×C22⋊D7C22semidirect
37. C22×C4×Dic7C22semidirect
38. #90425C22semidirect
39. #90424C22semidirect
40. #90423C22semidirect
41. #90423C22semidirect
42. #90421C22semidirect
43. #90419C22semidirect
44. #90419C22semidirect
45. #90419C22semidirect
46. #90416C22semidirect
47. #90416C22semidirect
48. #90388C22semidirect
49. #90386C22semidirect
50. #90385C22semidirect
51. #90385C22semidirect
52. #90382C22semidirect
53. #90382C22semidirect
54. #90382C22semidirect
55. #90336C22semidirect
56. #90336C22semidirect
57. #90336C22semidirect
58. #90335C22semidirect
59. #90335C22semidirect
60. #90333C22semidirect
61. #90333C22semidirect
62. #90333C22semidirect
63. #90328C22semidirect
64. #90328C22semidirect
65. #90328C22semidirect
66. #90321C22semidirect
67. #90318C22semidirect
68. #90318C22semidirect
69. #90318C22semidirect
70. #90315C22semidirect
71. #90315C22semidirect
72. #90315C22semidirect
73. #90315C22semidirect
74. #90315C22semidirect
75. #90315C22semidirect
76. #90315C22semidirect
77. #90315C22semidirect
78. #90315C22semidirect
79. #90315C22semidirect
80. #90276C22semidirect
81. #90275C22semidirect
82. #90271C22semidirect
83. #90271C22semidirect
84. C4×#1161C22semidirect
85. C4×#1161C22semidirect
86. #90261C22semidirect
87. #90246C22semidirect
88. #90246C22semidirect
89. #90246C22semidirect
90. #90245C22semidirect
91. #90245C22semidirect
92. #90245C22semidirect
93. D4×D28C22semidirect
94. #90237C22semidirect
95. #90236C22semidirect
96. C4×D4×D7C22semidirect
97. C4×#1159C22semidirect
98. C4×#1159C22semidirect
99. C4×#1159C22semidirect
100. C4×#1159C22semidirect
101. C4×#1159C22semidirect
102. #90217C22semidirect
103. #90215C22semidirect
104. #90214C22semidirect
105. #90213C22semidirect
106. #90205C22semidirect
107. #90205C22semidirect
108. C2×#6461C22semidirect
110. C2×#6456C22semidirect
111. C2×#6455C22semidirect
112. C2×#6455C22semidirect
113. C2×#6453C22semidirect
114. C2×#6450C22semidirect
116. #90184C22semidirect
117. C2×#6449C22semidirect
118. #90177C22semidirect
119. C2×(C22⋊D7)⋊C4C22semidirect
120. C2×(C22⋊D7)⋊C4C22semidirect
121. C2×#6440C22semidirect
123. C2×C42×D7C22semidirect
124. C2×C4×Dic14C22semidirect
324. #3501D7semidirect
345. C2×C7×D4#41semidirect
472. #554C2×D7semidirect
473. #554C2×D7semidirect
485. D4×Q8C2×D7semidirect
495. #544C2×D7semidirect
496. #543C2×D7semidirect
511. #533C2×D7semidirect
538. C2×C22⋊Q8C2×D7semidirect
892. C2×D4#1161semidirect
1066. C7#62781semidirect

Maximal subgroups

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

subgroupindex
C7×#35012
#117440032
#117439982
#117439922
#117439902
#117438162
#117438122
#117436522
#117436512
#117436412
#117436402
#117433282
#117433252
#117430392
C2×#903152
#117429262
#117429252
#117428542
C2×C4×#11592
#627817