Finite Group Databasebeta

← #14226137

Subgroups — #14226137

Order 1792.

1686 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#3455C211yesmaximal, characteristic
2C2×#90210C211yesmaximal, characteristic, complemented
3#11740900C214yesmaximal, complemented
4#11740899C214yesmaximal, complemented
5#11740887C214yesmaximal, complemented
6#11740875C214yesmaximal, complemented
7#11740787C211yesmaximal, characteristic, complemented
8#11740786C211yesmaximal, characteristic, complemented
9#11740729C211yesmaximal, characteristic, complemented
10#11740728C211yesmaximal, characteristic, complemented
11#11740360C212yesmaximal, complemented
12#11740359C212yesmaximal, complemented
13#11739954C212yesmaximal, complemented
14#11739953C212yesmaximal, complemented
15#11739654C211yesmaximal, characteristic, complemented
16C7×#542C2212yes—
17C7×#542C2212yes—
18C7×#541C2212yes—
19C7×#540C2212yes—
20C7×#539—21no—
21C7×#539—21no—
22C7×#538—21no—
23C7×#538—21no—
24C7×#533C2211yescharacteristic
25C7×#532C2211yescharacteristic
26C7×#529—22no—
27C7×#529—22no—
28C7×#525C2212yes—
29C4×C7×#41C2212yes—
30C2×C7×#117C2211yescharacteristic
31C2×#6489C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33#90210—22no—
34#90210—22no—
35#90210C2214yes—
36#90210C2214yes—
37C2×#6453—21no—
38C2×#6451—21no—
39C2×#6441—21no—
40C2×#6441—21no—
41C2×#6433C2211yescharacteristic
42C2×#6433C2211yescharacteristic
43C2×#6432C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45#90004C2212yes—
46#90004C2212yes—
47#90004C2212yes—
48#90004C2212yes—
49#89979C2212yes—
50#89854C2212yescomplemented
51#89853C2212yescomplemented
52#89852C2212yescomplemented
53#89852C2212yescomplemented
54#89851C2212yescomplemented
55#89850C2212yescomplemented
56#89843C2212yescomplemented
57#89842C2212yescomplemented
58#89837C2214yescomplemented
59#89836C2214yescomplemented
60#89828C2214yescomplemented
61#89827C2214yescomplemented
62#89817C2214yes—
63#89817C2214yes—
64#89816C2214yes—
65#89815C2214yes—
66#89807C2214yes—
67#89807C2214yes—
68#89806C2214yes—
69#89805C2214yes—
70#89794C2214yescomplemented
71#89794C2214yescomplemented
72#89793C2214yescomplemented
73#89792C2214yescomplemented
74#89781C2214yescomplemented
75#89781C2214yescomplemented
76#89780C2214yescomplemented
77#89779C2214yescomplemented
78#89772C2214yes—
79#89772C2214yes—
80#89767C2212yes—
81#89767C2212yes—
82#89767C2212yes—
83#89767C2212yes—
84#89696C2212yes—
85C4×#1136C2211yescharacteristic
86C4×#1136C2211yescharacteristic
87#60867—71nomaximal, Sylow
88C2×C7×#41C2312yes—
89C23×C4×C7C2311yescharacteristic
90C23×Dic7—21no—
91C22×Dic14—21no—
92C22×Dic14—21no—
93C7×C4⋊Q8C2311yescharacteristic
94C7×C4⋊Q8C2311yescharacteristic
95C7×C4⋊Q8C2311yescharacteristic
96C7×#127C2311yescharacteristic
97C7×#126—22no—
98C7×#126—22no—
99C7×#126—22no—
100C7×#126—22no—
101C7×#125—22no—
102C7×#125—22no—
103C7×#125C2312yes—
104C7×#124—22no—
105C7×#124—22no—
106C7×#124C2312yes—
107C7×#123—22no—
108C7×#123—22no—
109C7×#123—22no—
110C7×#123—22no—
111C7×#123—22no—
112C7×C22⋊Q8—21no—
113C7×C22⋊Q8—21no—
114C7×C22⋊Q8—22no—
115C7×C22⋊Q8—22no—
116C7×C22⋊Q8C2312yes—
117C7×C22⋊Q8C2312yes—
118C7×#121—21no—
119C7×#121—21no—
120C7×#121—22no—
121C7×#121—22no—
122C7×#121C2312yes—
123C7×#121C2312yes—
124C7×#120—22no—
125C4×C7×Q8—21no—
126C4×C7×Q8—21no—
127C4×C7×Q8C2312yes—
128C4×C7×Q8C2312yes—
129C4×C7×D4—22no—
130C4×C7×D4—22no—
131C4×C7×D4—22no—
132C4×C7×D4—22no—
133C4×C7×D4—21no—
134C4×C7×D4—21no—
135C4×C7×D4C2312yes—
136C4×C7×D4C2312yes—
137C7×#117—22no—
138C7×#117D412yes—
139C7×#117D412yes—
140C7×#117C2312yes—
141C7×#117C2312yes—
142C7×#117C2312yes—
143C2×C7×C4⋊C4D411yescharacteristic
144C2×C7×C4⋊C4D411yescharacteristic
145C2×C7×C22⋊C4D411yescharacteristic
146C2×C7×C22⋊C4D411yescharacteristic
147C2×C42×C7—22no—
148C2×C42×C7C2311yescharacteristic
149C2×C42×C7C2311yescharacteristic
150C2×C22⋊Dic7—21no—
151#6489—22no—
152#6489C2314yes—
153C2×C4⋊Dic7—21no—
154C2×C4⋊Dic7—21no—
155C2×C4⋊Dic7—21no—
156C2×C4⋊Dic7—22no—
157C2×C4⋊Dic7C2311yescharacteristic
158C2×C4⋊Dic7C2311yescharacteristic
159C2×C4⋊Dic7C2311yescharacteristic
160C2×C4⋊Dic7C2311yescharacteristic
161C2×C4⋊Dic7C2314yes—
162C2×Dic7⋊C4—21no—
163C2×Dic7⋊C4—21no—
164C2×Dic7⋊C4—21no—
165C2×Dic7⋊C4—21no—
166C2×C4×Dic7—21no—
167C2×#1136C2312yes—
168C2×#1136C2312yes—
169#6453—24no—
170#6453—24no—
171#6451—24no—
172#6451—24no—
173#6441—24no—
174#6441—24no—
175#6441—24no—
176#6441—24no—
177#6433—22no—
178#6433—21no—
179#6433—21no—
180#6433C2314yes—
181#6433C2312yes—
182#6433C2312yes—
183#6432—22no—
184#6432—21no—
185#6432—21no—
186#6432C2314yes—
187#6432C2312yes—
188#6432C2312yes—
189#6409C2314yes—
190#6409C2314yes—
191#6409C2314yes—
192#6409C2314yes—
193#6406C2314yes—
194#6406C2314yes—
195#6406C2314yes—
196#6406C2314yes—
197C22⋊(C7⋊C8)C2314yes—
198C22⋊(C7⋊C8)C2314yes—
199#6382C2314yes—
200#6382C2314yes—
201#6382C2314yes—
202#6382C2314yes—
203#6381C2314yes—
204#6381C2314yes—
205#6381C2314yes—
206#6381C2314yes—
207C4⋊(C7⋊C8)C2314yes—
208C4⋊(C7⋊C8)C2314yes—
209#6377C2312yes—
210#6377C2312yes—
211C4×C7⋊C8C2312yes—
212C4×C7⋊C8C2312yes—
213C2×#544—71no—
214#3455D711yescharacteristic
215#3244—74no—
216#3243—74no—
217#3242—74no—
218#3241—74no—
219#3166—71no—
220#3165—71no—
221#3142—71no—
222#3141—71no—
223#3093—72no—
224#3092—72no—
225#3080—72no—
226#3079—72no—
227#2921—71no—
228C24×C7C2×D411yescharacteristic
229C7×#41—28no—
230C2×C7×Q8—21no—
231C2×C7×Q8—21no—
232C2×C7×Q8C2412yes—
233C2×C7×D4—22no—
234C2×C7×D4—22no—
235C2×C7×D4—22no—
236C2×C7×D4—21no—
237C2×C7×D4—21no—
238C2×C7×D4C2412yes—
239C22×C4×C7—24no—
240C22×C4×C7—22no—
241C22×C4×C7—22no—
242C22×C4×C7—22no—
243C22×C4×C7C2×D411yescharacteristic
244C22×C4×C7C2×D412yes—
245C22×C4×C7C2×D411yescharacteristic
246C22×C4×C7C2×D411yescharacteristic
247C22×C4×C7C2×D411yescharacteristic
248C22×C4×C7C2×D411yescharacteristic
249C22×C4×C7C2412yes—
250C22×C4×C7C2411yescharacteristic
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—24no—
256C22×Dic7—82no—
257C2×Dic14—24no—
258C2×Dic14—22no—
259C2×Dic14—22no—
260C2×Dic14—82no—
261C2×Dic14—82no—
262C7×C4⋊C4—22no—
263C7×C4⋊C4—22no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—22no—
267C7×C4⋊C4—22no—
268C7×C4⋊C4—22no—
269C7×C4⋊C4—22no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4C2×D412yes—
273C7×C4⋊C4C2×D412yes—
274C7×C4⋊C4C2×D412yes—
275C7×C4⋊C4C2×D412yes—
276C7×C4⋊C4C2412yes—
277C7×C4⋊C4C2412yes—
278C7×C22⋊C4—22no—
279C7×C22⋊C4—22no—
280C7×C22⋊C4—22no—
281C7×C22⋊C4—22no—
282C7×C22⋊C4—22no—
283C7×C22⋊C4—22no—
284C7×C22⋊C4—22no—
285C7×C22⋊C4—22no—
286C7×C22⋊C4—22no—
287C7×C22⋊C4C2×D412yes—
288C7×C22⋊C4C2×D412yes—
289C7×C22⋊C4C2×D412yes—
290C7×C22⋊C4C2×D412yes—
291C42×C7—22no—
292C42×C7—22no—
293C42×C7—22no—
294C42×C7C2×D412yes—
295C42×C7C2×D411yescharacteristic
296C42×C7C2×D411yescharacteristic
297C42×C7C2412yes—
298C42×C7C2411yescharacteristic
299C42×C7C2411yescharacteristic
300C22⋊Dic7—24no—
301C4⋊Dic7—21no—
302C4⋊Dic7—21no—
303C4⋊Dic7—21no—
304C4⋊Dic7—24no—
305C4⋊Dic7—22no—
306C4⋊Dic7—22no—
307C4⋊Dic7—21no—
308C4⋊Dic7—24no—
309C4⋊Dic7C2412yes—
310C4⋊Dic7C2412yes—
311C4⋊Dic7C2412yes—
312C4⋊Dic7C2412yes—
313Dic7⋊C4—24no—
314Dic7⋊C4—22no—
315Dic7⋊C4—22no—
316Dic7⋊C4—24no—
317Dic7⋊C4—22no—
318Dic7⋊C4—22no—
319C4×Dic7—24no—
320#1136—24no—
321#1136—24no—
322C2×C7⋊C8C2414yes—
323C2×C7⋊C8C2414yes—
324#544—74no—
325#544—74no—
326#544—142no—
327#544—142no—
328#542C2×D712yes—
329#542C2×D712yes—
330#541C2×D712yes—
331#540C2×D712yes—
332#539—21no—
333#539—21no—
334#538—21no—
335#538—21no—
336#533C2×D711yescharacteristic
337#532C2×D711yescharacteristic
338C2×C4⋊Q8—71no—
339C2×C4⋊Q8—71no—
340C2×C4⋊Q8—141no—
341#529—22no—
342#529—22no—
343C2×#125—71no—
344C2×#125—71no—
345C2×#125—141no—
346#525C2×D712yes—
347C2×C22⋊Q8—141no—
348C2×C22⋊Q8—141no—
349C4×#41C2×D712yes—
350C2×#117—71no—
351C2×#117C2×D711yescharacteristic
352C22×C4⋊C4—71no—
353#501—72no—
354#501—72no—
355#501—74no—
356#500—72no—
357#499—74no—
358#498—72no—
359#491—72no—
360#490—72no—
361#489—74no—
362#488—74no—
363#487—72no—
364#486—72no—
365#485—74no—
366#485—74no—
367#484—74no—
368#483—74no—
369#482—74no—
370#482—74no—
371#481—74no—
372#480—74no—
373#479—74no—
374#479—74no—
375#478—74no—
376#478—74no—
377#477—74no—
378#476—74no—
379#475—74no—
380#474—74no—
381#433—74no—
382#433—74no—
383#428—72no—
384#428—72no—
385#428—72no—
386#428—72no—
387#423—72no—
388#417—72no—
389#417—72no—
390#417—72no—
391#417—72no—
392#407—72no—
393C4×M16—71no—
394C4×M16—71no—
395C23×C7—22no—
396C23×C7—22no—
397C23×C7—41no—
398C23×C7—41no—
399C23×C7C22×D412yes—
400C23×C7C22×D411yescharacteristic
401C7×Q8—24no—
402C7×Q8—81no—
403C7×Q8—81no—
404C7×D4—24no—
405C7×D4—44no—
406C7×D4—81no—
407C7×D4—81no—
408C7×D4—82no—
409C7×D4—82no—
410C2×C4×C7—22no—
411C2×C4×C7—24no—
412C2×C4×C7—24no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—44no—
421C2×C4×C7—82no—
422C2×C4×C7—82no—
423C2×C4×C7C22×D412yes—
424C2×C4×C7C22×D412yes—
425C2×C4×C7C22×D411yescharacteristic
426C2×C4×C7C22×D411yescharacteristic
427C2×C4×C7C22×D412yes—
428C2×C4×C7C22×D411yescharacteristic
429C2×C4×C7C22×D411yescharacteristic
430C2×C4×C7C22×D411yescharacteristic
431C2×C4×C72−1+414yes—
432C2×C4×C7C2511yescharacteristic
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—42no—
438C2×Dic7—42no—
439C2×Dic7—42no—
440C2×Dic7—42no—
441C2×Dic7—84no—
442Dic14—84no—
443Dic14—82no—
444Dic14—82no—
445C7⋊C8—24no—
446C7⋊C8—24no—
447C2×#41C22×D712yes—
448C22×Q8—141no—
449C22×Q8—141no—
450C23×C4—141no—
451C23×C4C22×D711yescharacteristic
452C2×M16—72no—
453C2×M16—72no—
454C4⋊Q8—74no—
455C4⋊Q8—72no—
456C4⋊Q8—72no—
457C4⋊Q8—144no—
458C4⋊Q8—144no—
459C4⋊Q8—142no—
460C4⋊Q8—141no—
461C4⋊Q8—141no—
462C4⋊Q8C22×D711yescharacteristic
463C4⋊Q8C22×D711yescharacteristic
464C4⋊Q8C22×D711yescharacteristic
465#127C22×D711yescharacteristic
466#126—22no—
467#126—22no—
468#126—22no—
469#126—22no—
470#125—22no—
471#125—22no—
472#125—74no—
473#125—72no—
474#125—72no—
475#125—144no—
476#125—144no—
477#125—142no—
478#125—141no—
479#125—141no—
480#125C22×D712yes—
481#124—22no—
482#124—22no—
483#124C22×D712yes—
484#123—22no—
485#123—22no—
486#123—22no—
487#123—22no—
488#123—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—144no—
494C22⋊Q8—144no—
495C22⋊Q8—144no—
496C22⋊Q8—144no—
497C22⋊Q8C22×D712yes—
498C22⋊Q8C22×D712yes—
499#121—21no—
500#121—21no—
501#121—22no—
502#121—22no—
503#121C22×D712yes—
504#121C22×D712yes—
505#120—22no—
506C4×Q8—21no—
507C4×Q8—21no—
508C4×Q8C22×D712yes—
509C4×Q8C22×D712yes—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4C22×D712yes—
517C4×D4C22×D712yes—
518#117—22no—
519#117—74no—
520#117—142no—
521#117C22⋊D712yes—
522#117C22⋊D712yes—
523#117C22×D712yes—
524#117C22×D712yes—
525#117C22×D712yes—
526C2×C4⋊C4—71no—
527C2×C4⋊C4—71no—
528C2×C4⋊C4—74no—
529C2×C4⋊C4—71no—
530C2×C4⋊C4—71no—
531C2×C4⋊C4—141no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—141no—
534C2×C4⋊C4—141no—
535C2×C4⋊C4—141no—
536C2×C4⋊C4—141no—
537C2×C4⋊C4—141no—
538C2×C4⋊C4—141no—
539C2×C4⋊C4C22⋊D711yescharacteristic
540C2×C4⋊C4C22⋊D711yescharacteristic
541C2×C22⋊C4—141no—
542C2×C22⋊C4C22⋊D711yescharacteristic
543C2×C22⋊C4C22⋊D711yescharacteristic
544C2×C42—22no—
545C2×C42—141no—
546C2×C42C22×D711yescharacteristic
547C2×C42C22×D711yescharacteristic
548#107—74no—
549#107—74no—
550#107—74no—
551#107—74no—
552#106—74no—
553#106—74no—
554#106—74no—
555#106—74no—
556C4⋊C8—74no—
557C4⋊C8—74no—
558#103—74no—
559#103—74no—
560#103—74no—
561#103—74no—
562#102—74no—
563#102—74no—
564#102—74no—
565#102—74no—
566C22⋊C8—74no—
567C22⋊C8—74no—
568#97—72no—
569#97—72no—
570C4×C8—72no—
571C4×C8—72no—
572C22×C7—21no—
573C22×C7—21no—
574C22×C7—22no—
575C22×C7—22no—
576C22×C7—22no—
577C22×C7—44no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7#53612yes—
582C22×C7C23×D411yescharacteristic
583C4×C7—22no—
584C4×C7—21no—
585C4×C7—21no—
586C4×C7—22no—
587C4×C7—21no—
588C4×C7—21no—
589C4×C7—22no—
590C4×C7—42no—
591C4×C7—42no—
592C4×C7—42no—
593C4×C7#53612yes—
594C4×C7C2×2−1+412yes—
595Dic7—42no—
596Dic7—42no—
597Dic7—42no—
598Dic7—42no—
599C24C2×C22⋊D711yescharacteristic
600#41—28no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—144no—
604C2×Q8—142no—
605C2×Q8—142no—
606C2×Q8—562no—
607C2×Q8—562no—
608C2×Q8C23×D712yes—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4C23×D712yes—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—141no—
623C22×C4—144no—
624C22×C4—562no—
625C22×C4C2×C22⋊D711yescharacteristic
626C22×C4C2×C22⋊D712yes—
627C22×C4C2×C22⋊D711yescharacteristic
628C22×C4C2×C22⋊D711yescharacteristic
629C22×C4C2×C22⋊D711yescharacteristic
630C22×C4C2×C22⋊D711yescharacteristic
631C22×C4C23×D712yes—
632C22×C4C23×D711yescharacteristic
633M16—144no—
634M16—144no—
635C2×C8—74no—
636C2×C8—74no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—72no—
648C4⋊C4—72no—
649C4⋊C4—72no—
650C4⋊C4—72no—
651C4⋊C4—144no—
652C4⋊C4—142no—
653C4⋊C4—142no—
654C4⋊C4—144no—
655C4⋊C4—142no—
656C4⋊C4—142no—
657C4⋊C4—144no—
658C4⋊C4—141no—
659C4⋊C4—141no—
660C4⋊C4—141no—
661C4⋊C4—141no—
662C4⋊C4—144no—
663C4⋊C4—142no—
664C4⋊C4—142no—
665C4⋊C4C2×C22⋊D712yes—
666C4⋊C4C2×C22⋊D712yes—
667C4⋊C4C2×C22⋊D712yes—
668C4⋊C4C2×C22⋊D712yes—
669C4⋊C4C23×D712yes—
670C4⋊C4C23×D712yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—144no—
681C22⋊C4C2×C22⋊D712yes—
682C22⋊C4C2×C22⋊D712yes—
683C22⋊C4C2×C22⋊D712yes—
684C22⋊C4C2×C22⋊D712yes—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—144no—
689C42C2×C22⋊D712yes—
690C42C2×C22⋊D711yescharacteristic
691C42C2×C22⋊D711yescharacteristic
692C42C23×D711yescharacteristic
693C42C23×D711yescharacteristic
694C42C23×D712yes—
695C2×C7—22no—
696C2×C7—42no—
697C2×C7—82no—
698C2×C7C2×#53611yescharacteristic
699C2×C7#358511yescharacteristic
700C2×C7#358611yescharacteristic
701C23—22no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23C22×C22⋊D712yes—
706C23C22×C22⋊D711yescharacteristic
707Q8—24no—
708Q8—81no—
709Q8—81no—
710Q8—564no—
711Q8—562no—
712Q8—562no—
713D4—24no—
714D4—44no—
715D4—81no—
716D4—81no—
717D4—82no—
718D4—82no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—44no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—282no—
737C2×C4—282no—
738C2×C4—282no—
739C2×C4—282no—
740C2×C4—564no—
741C2×C4#655414yes—
742C2×C4C22×C22⋊D712yes—
743C2×C4C22×C22⋊D712yes—
744C2×C4C22×C22⋊D712yes—
745C2×C4C22×C22⋊D711yescharacteristic
746C2×C4C22×C22⋊D711yescharacteristic
747C2×C4C22×C22⋊D711yescharacteristic
748C2×C4C22×C22⋊D711yescharacteristic
749C2×C4C22×C22⋊D711yescharacteristic
750C2×C4C24×D711yescharacteristic
751C8—144no—
752C8—144no—
753C7#6086711yescharacteristic, complemented, Sylow
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22#9051612yes—
764C22C23×C22⋊D711yescharacteristic
765C4—22no—
766C4—22no—
767C4—21no—
768C4—21no—
769C4—22no—
770C4—21no—
771C4—21no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—282no—
776C4—282no—
777C4—282no—
778C4—282no—
779C4#9051612yes—
780C4C2×#655412yes—
781C2—22no—
782C2—42no—
783C2—82no—
784C2C2×#9051611yescharacteristic
785C2#1174436611yescharacteristic
786C2#1174436711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
Fitting, prime radicalC7×#3455C2
socleC22×C7C23×D4
hypercenter#3455D7
hypocenterC7#60867
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3455

Complements

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

NH ≅ G/Ntype
2. C2×#90210C2semidirect
3. #11740900C2semidirect
4. #11740899C2semidirect
5. #11740887C2semidirect
6. #11740875C2semidirect
7. #11740787C2semidirect
8. #11740786C2semidirect
9. #11740729C2semidirect
10. #11740728C2semidirect
11. #11740360C2semidirect
12. #11740359C2semidirect
13. #11739954C2semidirect
14. #11739953C2semidirect
15. #11739654C2semidirect
50. #89854C22semidirect
51. #89853C22semidirect
52. #89852C22semidirect
53. #89852C22semidirect
54. #89851C22semidirect
55. #89850C22semidirect
56. #89843C22semidirect
57. #89842C22semidirect
58. #89837C22semidirect
59. #89836C22semidirect
60. #89828C22semidirect
61. #89827C22semidirect
70. #89794C22semidirect
71. #89794C22semidirect
72. #89793C22semidirect
73. #89792C22semidirect
74. #89781C22semidirect
75. #89781C22semidirect
76. #89780C22semidirect
77. #89779C22semidirect
753. C7#60867semidirect

Maximal subgroups

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

subgroupindex
C7×#34552
C2×#902102
#117409002
#117408992
#117408872
#117408752
#117407872
#117407862
#117407292
#117407282
#117403602
#117403592
#117399542
#117399532
#117396542
#608677