Finite Group Databasebeta

← #14222285

Subgroups — #14222285

Order 1792.

2078 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#520C211yesmaximal, characteristic, complemented
2#11742806C211yesmaximal, characteristic, complemented
3#11741526C212yesmaximal, complemented
4#11740021C214yesmaximal, complemented
5#11740020C214yesmaximal, complemented
6#11740014C214yesmaximal, complemented
7#11740013C214yesmaximal, complemented
8#11739886C211yesmaximal, characteristic, complemented
9#11739876C211yesmaximal, characteristic, complemented
10C4×#6505C212yesmaximal, complemented
11#11739752C211yesmaximal, characteristic, complemented
12#11739741C211yesmaximal, characteristic, complemented
13C4×#6495C212yesmaximal, complemented
14#11739654C211yesmaximal, characteristic, complemented
15#11739584C212yesmaximal, complemented
16C22×C7×#41C2211yescharacteristic
17C7×#520—22no—
18C7×#520—22no—
19C7×#520C2214yes—
20C7×#520C2214yes—
21C2×C4×C7×Q8C2211yescharacteristic
22C2×C4×C7×Q8C2211yescharacteristic
23C2×C4×C7×D4—21no—
24C2×C4×C7×D4—21no—
25C2×C4×C7×D4C2211yescharacteristic
26C2×C4×C7×D4C2211yescharacteristic
27C2×C7×#117—21no—
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4—21no—
30C22×C7×C4⋊C4C2211yescharacteristic
31C2×#6505C2212yes—
32C2×#6495C2212yes—
33#90482C2212yes—
34#90226C2212yescomplemented
35#90225C2212yescomplemented
36#90225C2212yescomplemented
37#90219—22no—
38#90219—22no—
39#90209C2212yescomplemented
40#90206—21no—
41#90206—21no—
42#90185—21no—
43#90185—21no—
44#90168C2211yescharacteristic
45C4×#1157C2212yes—
46#90161C2211yescharacteristic
47#90011C2214yes—
48#90011C2214yes—
49#90010C2214yes—
50#90010C2214yes—
51#89997C2212yes—
52#89987C2212yes—
53#89979C2212yes—
54#89803C2212yescomplemented
55#89802C2214yescomplemented
56C4×#1144C2214yescomplemented
57#89800C2214yescomplemented
58#89799C2212yescomplemented
59#89798C2214yescomplemented
60C4×#1143C2214yescomplemented
61#89794C2214yescomplemented
62#89793C2212yescomplemented
63#89792C2212yescomplemented
64#89791C2212yescomplemented
65#89790C2214yescomplemented
66C4×#1142C2214yescomplemented
67#89788C2214yescomplemented
68#89787C2212yescomplemented
69#89786C2214yescomplemented
70C4×#1141C2214yescomplemented
71#89781C2214yescomplemented
72#89780C2212yescomplemented
73#89779C2212yescomplemented
74#89772C2214yescomplemented
75#89772C2214yescomplemented
76#89743C2214yescomplemented
77#89742C2214yescomplemented
78#89740C2214yescomplemented
79#89739C2214yescomplemented
80#89738C2212yes—
81#89738C2212yes—
82#89736C2212yes—
83#89736C2212yes—
84#89696C2211yescharacteristic
85#89696C2211yescharacteristic
86C4×#1136C2212yes—
87#60565—71nomaximal, Sylow
88C2×C7×#41—24no—
89C2×C7×#41—24no—
90C2×C7×#41—22no—
91C2×C7×#41C2314yes—
92C22×C7×Q8C2311yescharacteristic
93C22×C7×D4—21no—
94C22×C7×D4C2311yescharacteristic
95C23×C4×C7—21no—
96C23×C4×C7—21no—
97C23×C4×C7—21no—
98C23×C4×C7—21no—
99C23×C4×C7C2311yescharacteristic
100C2×#1157C2312yes—
101C4×C7×Q8—21no—
102C4×C7×Q8—21no—
103C4×C7×Q8—22no—
104C4×C7×Q8C2312yes—
105C4×C7×Q8C2312yes—
106C4×C7×Q8C2314yes—
107C4×C7×D4—24no—
108C4×C7×D4—24no—
109C4×C7×D4—24no—
110C4×C7×D4—24no—
111C4×C7×D4—21no—
112C4×C7×D4—21no—
113C4×C7×D4—22no—
114C4×C7×D4C2312yes—
115C4×C7×D4C2312yes—
116C4×C7×D4C2314yes—
117C7×#117—24no—
118C7×#117—24no—
119C7×#117D412yes—
120C7×#117D412yes—
121C7×#117C2312yes—
122C7×#117C2312yes—
123C2×C7×C4⋊C4—21no—
124C2×C7×C4⋊C4—21no—
125C2×C7×C4⋊C4—21no—
126C2×C7×C4⋊C4—22no—
127C2×C7×C4⋊C4—24no—
128C2×C7×C4⋊C4—24no—
129C2×C7×C4⋊C4D411yescharacteristic
130C2×C7×C4⋊C4D411yescharacteristic
131C2×C7×C4⋊C4C2311yescharacteristic
132C2×C7×C4⋊C4C2311yescharacteristic
133C2×C7×C4⋊C4C2314yes—
134C2×C7×C22⋊C4—21no—
135C2×C7×C22⋊C4—21no—
136C2×C7×C22⋊C4D411yescharacteristic
137C2×C7×C22⋊C4D411yescharacteristic
138C2×C42×C7—21no—
139C2×C42×C7—21no—
140C2×C42×C7C2311yescharacteristic
141C2×C42×C7C2311yescharacteristic
142#6516—22no—
143C2×#1144C2314yes—
144#6505—28no—
145C2×#1143C2314yes—
146C2×#1142C2314yes—
147#6495—28no—
148C2×#1141C2314yes—
149#6493—21no—
150#6493—21no—
151#6493C2312yes—
152#6493C2312yes—
153#6492—22no—
154C4×C22⋊D7—22no—
155C4×C22⋊D7—22no—
156C4×C22⋊D7—22no—
157C4×C22⋊D7—22no—
158#6489C2312yes—
159#6487—21no—
160#6487—21no—
161#6487C2312yes—
162#6487C2312yes—
163C2×#1136C2312yes—
164C2×#1136C2312yes—
165#6461—22no—
166#6461—22no—
167#6459—22no—
168#6459—22no—
169#6457—22no—
170#6457—22no—
171#6452—22no—
172#6452—22no—
173#6448—22no—
174#6448—22no—
175#6447—22no—
176#6447—22no—
177#6446—22no—
178#6446—22no—
179#6442—22no—
180#6442—22no—
181#6438C2312yes—
182#6437C2311yescharacteristic
183C4×D28—21no—
184C4×D28—21no—
185C4×D28C2312yes—
186C4×D28C2312yes—
187#6435—22no—
188C42×D7—22no—
189#6433C2312yes—
190#6432C2311yescharacteristic
191#6432C2311yescharacteristic
192#6432C2311yescharacteristic
193C4×Dic14—21no—
194C4×Dic14—21no—
195C4×Dic14C2312yes—
196C4×Dic14C2312yes—
197#6409C2314yes—
198#6409C2314yes—
199#6406C2314yes—
200#6406C2314yes—
201C22⋊(C7⋊C8)C2314yes—
202C22⋊(C7⋊C8)C2314yes—
203#6384C2314yes—
204#6384C2314yes—
205#6383C2314yes—
206#6383C2314yes—
207#6382C2314yes—
208#6382C2314yes—
209#6381C2314yes—
210#6381C2314yes—
211C4⋊(C7⋊C8)C2312yes—
212C4⋊(C7⋊C8)C2312yes—
213C4⋊(C7⋊C8)C2312yes—
214C4⋊(C7⋊C8)C2312yes—
215#6377C2314yes—
216C4×C7⋊C8C2314yes—
217#3455—71no—
218C2×#520D711yescharacteristic, complemented
219#3125—74no—
220#3124—74no—
221#3120—74no—
222#3119—74no—
223#3092—72no—
224#3078—71no—
225#3077—71no—
226#3037—71no—
227#3036—71no—
228#3005—72no—
229C4×#137—72no—
230C4×AGL(1,ℤ/8)—72no—
231#2921—71no—
232C24×C7—21no—
233C24×C7C2×D411yescharacteristic
234C7×#41—216no—
235C7×#41—28no—
236C7×#41—28no—
237C2×C7×Q8—21no—
238C2×C7×Q8—22no—
239C2×C7×Q8#4114yes—
240C2×C7×Q8C2412yes—
241C2×C7×D4—28no—
242C2×C7×D4—24no—
243C2×C7×D4—21no—
244C2×C7×D4—22no—
245C2×C7×D4#4114yes—
246C2×C7×D4C2412yes—
247C22×C4×C7—28no—
248C22×C4×C7—21no—
249C22×C4×C7—24no—
250C22×C4×C7—22no—
251C22×C4×C7—22no—
252C22×C4×C7—21no—
253C22×C4×C7—21no—
254C22×C4×C7—24no—
255C22×C4×C7—24no—
256C22×C4×C7—22no—
257C22×C4×C7—22no—
258C22×C4×C7—82no—
259C22×C4×C7—82no—
260C22×C4×C7—82no—
261C22×C4×C7C2×D412yes—
262C22×C4×C7C2×D411yescharacteristic
263C22×C4×C7C2×D411yescharacteristic
264C22×C4×C7C2×D411yescharacteristic
265C22×C4×C7C2×D411yescharacteristic
266C22×C4×C7C2×D411yescharacteristic
267C22×C4×C7C2412yes—
268C22×C4×C7C2411yescharacteristic
269C2×C22⋊D7—22no—
270C2×C22⋊D7—22no—
271C2×C22⋊D7—22no—
272#1157—24no—
273#1157—24no—
274C2×D28—21no—
275C2×D28—21no—
276C2×D28C2412yes—
277C2×C4×D7—22no—
278C2×C4×D7—22no—
279C2×C4×D7—22no—
280C2×Dic14—21no—
281C2×Dic14—21no—
282C2×Dic14C2412yes—
283C7×C4⋊C4—24no—
284C7×C4⋊C4—24no—
285C7×C4⋊C4—22no—
286C7×C4⋊C4—22no—
287C7×C4⋊C4—21no—
288C7×C4⋊C4—21no—
289C7×C4⋊C4C2×D412yes—
290C7×C4⋊C4C2×D412yes—
291C7×C4⋊C4C2×D412yes—
292C7×C4⋊C4C2×D412yes—
293C7×C4⋊C4C2412yes—
294C7×C4⋊C4C2412yes—
295C7×C22⋊C4—24no—
296C7×C22⋊C4—22no—
297C7×C22⋊C4—22no—
298C7×C22⋊C4C2×D412yes—
299C7×C22⋊C4C2×D412yes—
300C7×C22⋊C4C2×D412yes—
301C7×C22⋊C4C2×D412yes—
302C42×C7—24no—
303C42×C7—22no—
304C42×C7—22no—
305C42×C7C2×D411yescharacteristic
306C42×C7C2×D411yescharacteristic
307C42×C7C2×D412yes—
308C42×C7C2412yes—
309C42×C7C2411yescharacteristic
310C42×C7C2411yescharacteristic
311C22⋊Dic7—22no—
312C22⋊Dic7—22no—
313C22⋊Dic7—22no—
314#1144—28no—
315#1143—28no—
316#1142—28no—
317#1141—28no—
318(C2×D7)⋊C4—22no—
319(C2×D7)⋊C4—22no—
320(C2×D7)⋊C4—22no—
321(C2×D7)⋊C4—22no—
322(C2×D7)⋊C4—22no—
323(C2×D7)⋊C4—22no—
324C4⋊Dic7—21no—
325C4⋊Dic7—21no—
326C4⋊Dic7—21no—
327C4⋊Dic7—21no—
328C4⋊Dic7C2412yes—
329C4⋊Dic7C2412yes—
330Dic7⋊C4—22no—
331Dic7⋊C4—22no—
332Dic7⋊C4—22no—
333Dic7⋊C4—22no—
334Dic7⋊C4—22no—
335Dic7⋊C4—22no—
336C4×Dic7—22no—
337C4×Dic7—22no—
338C4×Dic7—22no—
339#1136—24no—
340#1136—24no—
341C2×C7⋊C8C2414yes—
342C2×C7⋊C8C2414yes—
343C22×#41C2×D711yescharacteristic
344C2×#137—72no—
345C2×AGL(1,ℤ/8)—72no—
346#542—72no—
347#542—72no—
348#541—72no—
349#540—72no—
350#539—141no—
351#539—141no—
352#538—141no—
353#538—141no—
354#533—71no—
355#532—71no—
356#529—142no—
357#529—142no—
358#525—72no—
359#520—22no—
360#520—22no—
361#520C2×D714yes—
362#520C2×D714yes—
363C4×#41—72no—
364C2×C4×Q8C2×D711yescharacteristic
365C2×C4×Q8C2×D711yescharacteristic
366C2×C4×D4—21no—
367C2×C4×D4—21no—
368C2×C4×D4C2×D711yescharacteristic
369C2×C4×D4C2×D711yescharacteristic
370C2×#117—21no—
371C2×#117C2×D711yescharacteristic
372C22×C4⋊C4—21no—
373C22×C4⋊C4C2×D711yescharacteristic
374#484—74no—
375#483—74no—
376#481—74no—
377#480—74no—
378#479—74no—
379#478—74no—
380#477—72no—
381#476—72no—
382#475—72no—
383#474—72no—
384#464—74no—
385#463—74no—
386#462—72no—
387#461—72no—
388#460—72no—
389#459—72no—
390#452—74no—
391#452—74no—
392#449—74no—
393#449—74no—
394#442—74no—
395#441—74no—
396#440—74no—
397#440—74no—
398C4×Q16—74no—
399C4×SD16—74no—
400C4×SD16—74no—
401C4×D8—74no—
402#433—74no—
403#433—74no—
404#428—72no—
405#428—72no—
406#423—71no—
407#423—71no—
408#419—72no—
409#418—72no—
410#417—72no—
411#417—72no—
412#407—72no—
413C4×M16—72no—
414C23×C7—22no—
415C23×C7—24no—
416C23×C7—22no—
417C23×C7—41no—
418C23×C7—41no—
419C23×C7—42no—
420C23×C7—42no—
421C23×C7C22×D412yes—
422C23×C7C22×D411yescharacteristic
423C22×D7—22no—
424C7×Q8—24no—
425C7×Q8—22no—
426C7×Q8C2×#4114yes—
427C7×D4—216no—
428C7×D4—24no—
429C7×D4—22no—
430C7×D4C2×#4114yes—
431C2×C4×C7—216no—
432C2×C4×C7—22no—
433C2×C4×C7—24no—
434C2×C4×C7—22no—
435C2×C4×C7—24no—
436C2×C4×C7—22no—
437C2×C4×C7—22no—
438C2×C4×C7—22no—
439C2×C4×C7—22no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—42no—
445C2×C4×C7—42no—
446C2×C4×C7—82no—
447C2×C4×C7—84no—
448C2×C4×C7—82no—
449C2×C4×C7—84no—
450C2×C4×C7C22×D412yes—
451C2×C4×C7C22×D412yes—
452C2×C4×C7C22×D411yescharacteristic
453C2×C4×C7C22×D411yescharacteristic
454C2×C4×C7C22×D412yes—
455C2×C4×C7C22×D411yescharacteristic
456C2×C4×C7C22×D411yescharacteristic
457C2×C4×C7C22×D411yescharacteristic
458C2×C4×C7C2×#4112yes—
459C2×C4×C7C2×#4112yes—
460C2×C4×C7C2511yescharacteristic
461C22⋊D7—44no—
462C22⋊D7—82no—
463C22⋊D7—82no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467D28—22no—
468D28—22no—
469D28—81no—
470D28—81no—
471C4×D7—44no—
472C4×D7—82no—
473C4×D7—82no—
474Dic14—22no—
475Dic14—22no—
476Dic14—81no—
477Dic14—81no—
478C7⋊C8—24no—
479C7⋊C8—24no—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41—22no—
483C2×#41—72no—
484C2×#41C22×D714yes—
485C22×Q8C22×D711yescharacteristic
486C22×D4—21no—
487C22×D4C22×D711yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C22×D711yescharacteristic
493#137—148no—
494AGL(1,ℤ/8)—148no—
495C2×Q16—74no—
496C2×SD16—74no—
497C2×SD16—74no—
498C2×D8—74no—
499C2×M16—72no—
500C2×M16—72no—
501C4⋊Q8—71no—
502C4⋊Q8—71no—
503C4⋊Q8—71no—
504#127—71no—
505#126—142no—
506#126—142no—
507#126—142no—
508#126—142no—
509#125—72no—
510#125—142no—
511#125—142no—
512#124—72no—
513#124—142no—
514#124—142no—
515#123—142no—
516#123—142no—
517#123—142no—
518#123—142no—
519#123—142no—
520C22⋊Q8—72no—
521C22⋊Q8—72no—
522C22⋊Q8—141no—
523C22⋊Q8—141no—
524C22⋊Q8—142no—
525C22⋊Q8—142no—
526#121—72no—
527#121—72no—
528#121—141no—
529#121—141no—
530#121—142no—
531#121—142no—
532#120—142no—
533C4×Q8—22no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—72no—
537C4×Q8—72no—
538C4×Q8—141no—
539C4×Q8—141no—
540C4×Q8C22×D714yes—
541C4×Q8C22×D712yes—
542C4×Q8C22×D712yes—
543C4×D4—24no—
544C4×D4—24no—
545C4×D4—24no—
546C4×D4—24no—
547C4×D4—22no—
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—72no—
551C4×D4—72no—
552C4×D4—142no—
553C4×D4—142no—
554C4×D4—142no—
555C4×D4—142no—
556C4×D4—141no—
557C4×D4—141no—
558C4×D4C22×D714yes—
559C4×D4C22×D712yes—
560C4×D4C22×D712yes—
561#117—24no—
562#117—24no—
563#117—72no—
564#117—142no—
565#117C22⋊D712yes—
566#117C22⋊D712yes—
567#117C22×D712yes—
568#117C22×D712yes—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4C22⋊D711yescharacteristic
576C2×C4⋊C4C22⋊D711yescharacteristic
577C2×C4⋊C4C22×D711yescharacteristic
578C2×C4⋊C4C22×D711yescharacteristic
579C2×C4⋊C4C22×D714yes—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4C22⋊D711yescharacteristic
583C2×C22⋊C4C22⋊D711yescharacteristic
584C2×C42—21no—
585C2×C42—21no—
586C2×C42—142no—
587C2×C42C22×D711yescharacteristic
588C2×C42C22×D711yescharacteristic
589#107—74no—
590#107—74no—
591#106—74no—
592#106—74no—
593C4⋊C8—72no—
594C4⋊C8—72no—
595C4⋊C8—72no—
596C4⋊C8—72no—
597#103—74no—
598#103—74no—
599#103—74no—
600#103—74no—
601#102—74no—
602#102—74no—
603#102—74no—
604#102—74no—
605C22⋊C8—74no—
606C22⋊C8—74no—
607#97—74no—
608C4×C8—74no—
609C22×C7—21no—
610C22×C7—21no—
611C22×C7—22no—
612C22×C7—22no—
613C22×C7—22no—
614C22×C7—24no—
615C22×C7—44no—
616C22×C7—48no—
617C22×C7—42no—
618C22×C7—42no—
619C22×C7#52512yes—
620C22×C7C23×D411yescharacteristic
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C4×C7—21no—
625C4×C7—22no—
626C4×C7—21no—
627C4×C7—21no—
628C4×C7—22no—
629C4×C7—21no—
630C4×C7—22no—
631C4×C7—24no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7#52512yes—
635C4×C7C22×#4111yescharacteristic
636C4×C7C22×#4111yescharacteristic
637Dic7—42no—
638Dic7—42no—
639Dic7—42no—
640C24—21no—
641C24C2×C22⋊D711yescharacteristic
642#41—216no—
643#41—28no—
644#41—28no—
645#41—144no—
646#41—144no—
647C2×Q8—22no—
648C2×Q8—21no—
649C2×Q8—72no—
650C2×Q8—141no—
651C2×Q8—141no—
652C2×Q8#115714yes—
653C2×Q8C23×D712yes—
654C2×D4—28no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—72no—
659C2×D4—142no—
660C2×D4—142no—
661C2×D4—142no—
662C2×D4—141no—
663C2×D4—141no—
664C2×D4#115714yes—
665C2×D4C23×D712yes—
666C22×C4—28no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—82no—
678C22×C4—82no—
679C22×C4—82no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4C2×C22⋊D711yescharacteristic
684C22×C4C2×C22⋊D712yes—
685C22×C4C2×C22⋊D711yescharacteristic
686C22×C4C2×C22⋊D711yescharacteristic
687C22×C4C2×C22⋊D711yescharacteristic
688C22×C4C2×C22⋊D711yescharacteristic
689C22×C4C23×D712yes—
690C22×C4C23×D711yescharacteristic
691Q16—148no—
692SD16—148no—
693SD16—148no—
694D8—148no—
695M16—144no—
696M16—144no—
697C2×C8—74no—
698C2×C8—74no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—72no—
706C4⋊C4—72no—
707C4⋊C4—142no—
708C4⋊C4—142no—
709C4⋊C4—142no—
710C4⋊C4—142no—
711C4⋊C4—142no—
712C4⋊C4—142no—
713C4⋊C4—141no—
714C4⋊C4—141no—
715C4⋊C4—141no—
716C4⋊C4—141no—
717C4⋊C4C2×C22⋊D712yes—
718C4⋊C4C2×C22⋊D712yes—
719C4⋊C4C2×C22⋊D712yes—
720C4⋊C4C2×C22⋊D712yes—
721C4⋊C4C23×D712yes—
722C4⋊C4C23×D712yes—
723C22⋊C4—24no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—142no—
727C22⋊C4—142no—
728C22⋊C4—142no—
729C22⋊C4—142no—
730C22⋊C4—142no—
731C22⋊C4—142no—
732C22⋊C4—142no—
733C22⋊C4—142no—
734C22⋊C4—142no—
735C22⋊C4C2×C22⋊D712yes—
736C22⋊C4C2×C22⋊D712yes—
737C22⋊C4C2×C22⋊D712yes—
738C22⋊C4C2×C22⋊D712yes—
739C42—24no—
740C42—22no—
741C42—22no—
742C42—142no—
743C42—142no—
744C42—142no—
745C42C2×C22⋊D712yes—
746C42C2×C22⋊D711yescharacteristic
747C42C2×C22⋊D711yescharacteristic
748C42C23×D712yes—
749C42C23×D711yescharacteristic
750C42C23×D711yescharacteristic
751C2×C7—22no—
752C2×C7—42no—
753C2×C7—44no—
754C2×C7C2×#52511yescharacteristic
755C2×C7#358511yescharacteristic
756C2×C7#358611yescharacteristic
757D7—82no—
758C23—22no—
759C23—24no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—42no—
764C23—42no—
765C23—142no—
766C23C22×C22⋊D712yes—
767C23C22×C22⋊D711yescharacteristic
768Q8—24no—
769Q8—22no—
770Q8—142no—
771Q8—142no—
772Q8—561no—
773Q8—561no—
774Q8C2×#115714yes—
775D4—216no—
776D4—24no—
777D4—22no—
778D4—142no—
779D4—142no—
780D4—284no—
781D4—561no—
782D4—561no—
783D4—562no—
784D4—562no—
785D4C2×#115714yes—
786C2×C4—216no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—84no—
802C2×C4—82no—
803C2×C4—82no—
804C2×C4—84no—
805C2×C4—142no—
806C2×C4—142no—
807C2×C4—142no—
808C2×C4—284no—
809C2×C4—562no—
810C2×C4—562no—
811C2×C4C2×#115712yes—
812C2×C4C2×#115712yes—
813C2×C4C22×C22⋊D712yes—
814C2×C4C22×C22⋊D711yescharacteristic
815C2×C4C22×C22⋊D711yescharacteristic
816C2×C4C22×C22⋊D712yes—
817C2×C4C22×C22⋊D711yescharacteristic
818C2×C4C22×C22⋊D711yescharacteristic
819C2×C4C22×C22⋊D712yes—
820C2×C4C22×C22⋊D711yescharacteristic
821C2×C4C24×D711yescharacteristic
822C8—144no—
823C8—144no—
824C7#6056511yescharacteristic, complemented, Sylow
825C22—21no—
826C22—21no—
827C22—22no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—282no—
836C22—282no—
837C22—282no—
838C22#9048212yes—
839C22C23×C22⋊D711yescharacteristic
840C4—22no—
841C4—24no—
842C4—22no—
843C4—21no—
844C4—21no—
845C4—22no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—282no—
851C4—282no—
852C4—282no—
853C4#9048212yes—
854C4C22×#115711yescharacteristic
855C4C22×#115711yescharacteristic
856C2—22no—
857C2—42no—
858C2—44no—
859C2—562no—
860C2C2×#9048211yescharacteristic
861C2#1174434511yescharacteristic
862C2#1174435511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#520C2
socleC22×C7C23×D4
hypercenterC2×#520D7
hypocenterC7#60565
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C7×#520C2semidirect
2. #11742806C2semidirect
3. #11741526C2semidirect
4. #11740021C2semidirect
5. #11740020C2semidirect
6. #11740014C2semidirect
7. #11740013C2semidirect
8. #11739886C2semidirect
9. #11739876C2semidirect
10. C4×#6505C2semidirect
11. #11739752C2semidirect
12. #11739741C2semidirect
13. C4×#6495C2semidirect
14. #11739654C2semidirect
15. #11739584C2semidirect
34. #90226C22semidirect
35. #90225C22semidirect
36. #90225C22semidirect
39. #90209C22semidirect
54. #89803C22semidirect
55. #89802C22semidirect
56. C4×#1144C22semidirect
57. #89800C22semidirect
58. #89799C22semidirect
59. #89798C22semidirect
60. C4×#1143C22semidirect
61. #89794C22semidirect
62. #89793C22semidirect
63. #89792C22semidirect
64. #89791C22semidirect
65. #89790C22semidirect
66. C4×#1142C22semidirect
67. #89788C22semidirect
68. #89787C22semidirect
69. #89786C22semidirect
70. C4×#1141C22semidirect
71. #89781C22semidirect
72. #89780C22semidirect
73. #89779C22semidirect
74. #89772C22semidirect
75. #89772C22semidirect
76. #89743C22semidirect
77. #89742C22semidirect
78. #89740C22semidirect
79. #89739C22semidirect
218. C2×#520D7semidirect
824. C7#60565semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#5202
#117428062
#117415262
#117400212
#117400202
#117400142
#117400132
#117398862
#117398762
C4×#65052
#117397522
#117397412
C4×#64952
#117396542
#117395842
#605657