Finite Group Databasebeta

← #13355339

Subgroups — #13355339

Order 1792.

1708 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11744336C211yesmaximal, characteristic
2C2×#90436C211yesmaximal, characteristic, complemented
3C2×C7×#421C211yesmaximal, characteristic, complemented
4C2×#90008C211yesmaximal, characteristic, complemented
5C2×#89778C211yesmaximal, characteristic, complemented
6#11729736C211yesmaximal, characteristic, complemented
7#11729328C211yesmaximal, characteristic, complemented
8#11728171C218yesmaximal, complemented
9C22×C7×#41C2211yescharacteristic
10C22×#1157C2211yescharacteristic
11C22×C7×M16C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13#90524—22no—
14#90523C2214yes—
15#90521C412yescomplemented
16#90519—22no—
17#90516C412yescomplemented
18#90507C412yescomplemented
19#90496C412yescomplemented
20#90495—22no—
21#90482—22no—
22C2×#6489C2211yescharacteristic
23C2×#6489C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25#90436—22no—
26#90436—22no—
27#90436—22no—
28#90436C2214yescomplemented
29C2×#6470—22no—
30C2×D7×M16—22no—
31C2×#6464—22no—
32C7×#421—22no—
33C7×#421C2214yescomplemented
34C2×C7×#104—22no—
35#90008—22no—
36#90008C2214yescomplemented
37C2×#6411—22no—
38#89778—22no—
39#89778C2214yescomplemented
40C2×#6380—22no—
41#89350C2214yescomplemented
42#89327C2214yescomplemented
43#20947—71nomaximal, Sylow
44C2×C7×#41—21no—
45C2×C7×#41—21no—
46C2×C7×#41—21no—
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41—21no—
54C2×C7×#41C2×C412yes—
55C2×C7×#41C2312yes—
56C22×C7×Q8C2×C411yescharacteristic
57C22×C7×D4—21no—
58C22×C7×D4C2×C411yescharacteristic
59C23×C4×C7—21no—
60C23×C4×C7C2311yescharacteristic
61C22×C22⋊D7D412yes—
62C2×#1157—21no—
63C2×#1157—21no—
64C2×#1157—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157C2×C412yes—
71C2×#1157D412yes—
72C2×#1157D412yes—
73C2×#1157C2312yes—
74C22×D28C2×C411yescharacteristic
75C22×C4×D7D412yes—
76C22×Dic14C2×C411yescharacteristic
77C2×C7×M16—21no—
78C2×C7×M16—21no—
79C2×C7×M16—21no—
80C2×C7×M16D412yescomplemented
81C2×C7×M16D412yescomplemented
82C2×C7×M16C2312yes—
83C22×C7×C8—21no—
84C7×#117—21no—
85C7×#117—21no—
86C7×#117—21no—
87C7×#117C2312yes—
88C2×C7×C4⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C42×C7—21no—
91#6516—24no—
92C2×C22⋊Dic7—21no—
93C2×C22⋊Dic7—21no—
94#6510C2×C414yescomplemented
95#6509—24no—
96#6507C2×C414yescomplemented
97#6503C2×C414yescomplemented
98#6502—28no—
99#6501—24no—
100#6500—24no—
101#6499C2×C414yescomplemented
102#6498—24no—
103#6493—24no—
104#6492—24no—
105C4×C22⋊D7—28no—
106#6489—21no—
107#6489—21no—
108#6489—21no—
109#6489—21no—
110#6489—21no—
111#6489C2×C412yes—
112#6489C2×C412yes—
113#6489C2312yes—
114C2×C4⋊Dic7—21no—
115C2×C4⋊Dic7—21no—
116#6487—24no—
117C2×C4×Dic7—21no—
118C2×C4×Dic7C2312yes—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136D412yescomplemented
123C2×#1136D412yescomplemented
124C2×#1136C2312yes—
125C22×C7⋊C8—21no—
126#6470—28no—
127#6470—28no—
128D7×M16—28no—
129D7×M16—28no—
130#6464—28no—
131#6464—28no—
132C2×#1131—24no—
133C2×C8×D7—24no—
134C7×#104—28no—
135#6411—28no—
136#6380—28no—
137C2×#568—71no—
138#3449—71no—
139C2×#421—71no—
140C2×#421D711yescharacteristic, complemented
141C2×#410—71no—
142#1884—78no—
143#1733—71no—
144#1733—71no—
145C24×C7—21no—
146C24×C7C2×D411yescharacteristic
147C23×D7C22⋊C412yes—
148C7×#41—22no—
149C7×#41—22no—
150C7×#41—22no—
151C7×#41—22no—
152C7×#41—22no—
153C7×#41—22no—
154C7×#41—22no—
155C7×#41—22no—
156C7×#41—41no—
157C7×#41—41no—
158C7×#41—41no—
159C7×#41—41no—
160C7×#41—41no—
161C7×#41—41no—
162C7×#41—41no—
163C7×#41—41no—
164C2×C7×Q8—21no—
165C2×C7×Q8—21no—
166C2×C7×Q8—21no—
167C2×C7×Q8—21no—
168C2×C7×Q8—21no—
169C2×C7×Q8C22×C412yes—
170C2×C7×D4—22no—
171C2×C7×D4—22no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—21no—
175C2×C7×D4—21no—
176C2×C7×D4—21no—
177C2×C7×D4—41no—
178C2×C7×D4—41no—
179C2×C7×D4—41no—
180C2×C7×D4—41no—
181C2×C7×D4C22×C412yes—
182C22×C4×C7—21no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—41no—
186C22×C4×C7—41no—
187C22×C4×C7—41no—
188C22×C4×C7—41no—
189C22×C4×C7—41no—
190C22×C4×C7C22×C411yescharacteristic
191C22×C4×C7C22×C411yescharacteristic
192C22×C4×C7C2×D411yescharacteristic
193C22×C4×C7C2×D411yescharacteristic
194C22×C4×C7C2×D411yescharacteristic
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7#4111yescharacteristic
200C22×C4×C7#4111yescharacteristic
201C22×C4×C7#4111yescharacteristic
202C22×C4×C7#4111yescharacteristic
203C22×C4×C7C2411yescharacteristic
204C2×C22⋊D7—22no—
205C2×C22⋊D7—22no—
206C2×C22⋊D7—22no—
207C2×C22⋊D7—22no—
208C2×C22⋊D7—28no—
209C2×C22⋊D7C22⋊C414yes—
210C2×C22⋊D7C2×D414yes—
211C22×Dic7—22no—
212C22×Dic7—41no—
213C22×Dic7C22⋊C412yes—
214#1157—22no—
215#1157—22no—
216#1157—22no—
217#1157—22no—
218#1157—22no—
219#1157—22no—
220#1157—22no—
221#1157—22no—
222#1157—22no—
223#1157—22no—
224#1157—22no—
225#1157—22no—
226#1157—22no—
227#1157—22no—
228#1157—22no—
229#1157—22no—
230C2×D28—21no—
231C2×D28—21no—
232C2×D28—21no—
233C2×D28—21no—
234C2×D28C22⋊C412yes—
235C2×D28C22×C412yes—
236C2×C4×D7—22no—
237C2×C4×D7—22no—
238C2×C4×D7—22no—
239C2×C4×D7—22no—
240C2×C4×D7C22⋊C414yes—
241C2×C4×D7C2×D414yes—
242C2×Dic14—21no—
243C2×Dic14—21no—
244C2×Dic14—21no—
245C2×Dic14—21no—
246C2×Dic14C22⋊C412yes—
247C2×Dic14C22×C412yes—
248C7×M16—22no—
249C7×M16—22no—
250C7×M16—22no—
251C7×M16C2×D414yes—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C7×C4⋊C4—22no—
256C7×C4⋊C4—41no—
257C7×C22⋊C4—22no—
258C7×C22⋊C4—41no—
259C42×C7—22no—
260C42×C7—41no—
261C22⋊Dic7—22no—
262C22⋊Dic7—22no—
263C22⋊Dic7—28no—
264C22⋊Dic7—22no—
265C22⋊Dic7—41no—
266(C2×D7)⋊C4—28no—
267C4⋊Dic7—22no—
268C4⋊Dic7—22no—
269C4⋊Dic7—22no—
270C4⋊Dic7—41no—
271Dic7⋊C4—28no—
272C4×Dic7—22no—
273C4×Dic7—22no—
274C4×Dic7—41no—
275C4×Dic7C22×C414yes—
276#1136—22no—
277#1136—22no—
278#1136—22no—
279#1136C2×D414yes—
280C2×C7⋊C8—22no—
281C2×C7⋊C8—22no—
282C2×C7⋊C8—22no—
283#1131—216no—
284C8×D7—216no—
285C22×#41—71no—
286C22×#41C2×D711yescharacteristic
287#568—74no—
288#568—142no—
289#568—142no—
290#568—142no—
291C2×#131—142no—
292C2×#131—142no—
293C22×M16—71no—
294C22×M16—142no—
295C22×M16C2×D711yescharacteristic
296#537—142no—
297#536—72no—
298#536—72no—
299#535—72no—
300#535—72no—
301#534—142no—
302#532—74no—
303#525—142no—
304#525—142no—
305C2×#117—71no—
306C2×#117—71no—
307C2×#117C2×D711yescharacteristic
308#421—22no—
309#421—74no—
310#421—142no—
311#421C2×D714yescomplemented
312C2×#104—22no—
313C2×#104—142no—
314#410—74no—
315#410—142no—
316C2×#99—142no—
317#339—74no—
318#339—74no—
319C23×C7—22no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—81no—
323C23×C7—82no—
324C23×C7C2×C22⋊C411yescharacteristic
325C23×C7C2×C22⋊C411yescharacteristic
326C23×C7#12111yescharacteristic
327C23×C7#12111yescharacteristic
328C23×C7#12111yescharacteristic
329C23×C7#12111yescharacteristic
330C23×C7C22×D411yescharacteristic
331C22×D7—22no—
332C22×D7—22no—
333C22×D7—82no—
334C22×D7C2×C22⋊C414yes—
335C7×Q8—22no—
336C7×Q8—22no—
337C7×Q8—41no—
338C7×Q8—41no—
339C7×D4—22no—
340C7×D4—22no—
341C7×D4—42no—
342C7×D4—42no—
343C7×D4—42no—
344C7×D4—42no—
345C7×D4—41no—
346C7×D4—41no—
347C2×C4×C7—22no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7—42no—
351C2×C4×C7—42no—
352C2×C4×C7—42no—
353C2×C4×C7—42no—
354C2×C4×C7—42no—
355C2×C4×C7—82no—
356C2×C4×C7C2×C22⋊C411yescharacteristic
357C2×C4×C7C2×C22⋊C411yescharacteristic
358C2×C4×C7C4×D411yescharacteristic
359C2×C4×C7C4×D411yescharacteristic
360C2×C4×C7C4×D411yescharacteristic
361C2×C4×C7C4×D411yescharacteristic
362C2×C4×C7C4×D411yescharacteristic
363C2×C4×C7C4×D411yescharacteristic
364C2×C4×C7C4×D411yescharacteristic
365C2×C4×C7C4×D411yescharacteristic
366C2×C4×C7#12011yescharacteristic
367C2×C4×C7#12011yescharacteristic
368C2×C4×C7#12011yescharacteristic
369C2×C4×C7#12011yescharacteristic
370C2×C4×C7#12111yescharacteristic
371C2×C4×C7#12111yescharacteristic
372C2×C4×C7#12111yescharacteristic
373C2×C4×C7#12111yescharacteristic
374C2×C4×C7#12311yescharacteristic
375C2×C4×C7#12311yescharacteristic
376C2×C4×C7#12311yescharacteristic
377C2×C4×C7#12311yescharacteristic
378C2×C4×C7C23×C411yescharacteristic
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C22×D411yescharacteristic
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7C2×#4111yescharacteristic
383C2×C4×C7C2×#4111yescharacteristic
384C22⋊D7—24no—
385C22⋊D7—24no—
386C22⋊D7—24no—
387C22⋊D7—24no—
388C22⋊D7—88no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—24no—
392C2×Dic7—42no—
393C2×Dic7—82no—
394C2×Dic7—82no—
395C2×Dic7C2×C22⋊C414yes—
396D28—22no—
397D28—22no—
398D28—22no—
399D28—22no—
400C4×D7—24no—
401C4×D7—24no—
402C4×D7—24no—
403C4×D7—24no—
404Dic14—22no—
405Dic14—22no—
406Dic14—22no—
407Dic14—22no—
408C7×C8—24no—
409C7⋊C8—24no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—72no—
421C2×#41—72no—
422C2×#41—72no—
423C2×#41—72no—
424C2×#41—141no—
425C2×#41—141no—
426C2×#41—141no—
427C2×#41—141no—
428C2×#41—141no—
429C2×#41—141no—
430C2×#41—141no—
431C2×#41—141no—
432C2×#41C4×D712yes—
433C2×#41C22×D712yes—
434C22×Q8—71no—
435C22×Q8C4×D711yescharacteristic
436C22×D4—21no—
437C22×D4—72no—
438C22×D4—71no—
439C22×D4C4×D711yescharacteristic
440C23×C4—21no—
441C23×C4—72no—
442C23×C4C22×D711yescharacteristic
443#131—148no—
444#131—148no—
445#131—148no—
446#131—148no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—72no—
451C2×M16—72no—
452C2×M16—72no—
453C2×M16—144no—
454C2×M16—148no—
455C2×M16—148no—
456C2×M16—141no—
457C2×M16—141no—
458C2×M16—141no—
459C2×M16C22⋊D712yescomplemented
460C2×M16C22⋊D712yescomplemented
461C2×M16C22×D712yes—
462C22×C8—21no—
463C22×C8—144no—
464C22×C8—141no—
465C4⋊Q8—74no—
466#127—74no—
467#124—74no—
468#124—74no—
469#123—144no—
470#123—144no—
471C22⋊Q8—144no—
472C22⋊Q8—144no—
473#121—144no—
474#121—144no—
475#121—148no—
476#120—144no—
477#120—144no—
478C4×D4—148no—
479#117—21no—
480#117—21no—
481#117—21no—
482#117—72no—
483#117—72no—
484#117—72no—
485#117—141no—
486#117—141no—
487#117—141no—
488#117—141no—
489#117—141no—
490#117C22×D712yes—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C42—21no—
498C2×C42—72no—
499C2×C42—141no—
500#104—28no—
501#104—148no—
502#99—148no—
503C22×C7—41no—
504C22×C7—41no—
505C22×C7—41no—
506C22×C7—41no—
507C22×C7—41no—
508C22×C7—41no—
509C22×C7—41no—
510C22×C7—44no—
511C22×C7—42no—
512C22×C7—82no—
513C22×C7—82no—
514C22×C7#38611yescharacteristic
515C22×C7#38611yescharacteristic
516C22×C7#38611yescharacteristic
517C22×C7#38611yescharacteristic
518C22×C7C22×C22⋊C411yescharacteristic
519C22×C7C2×#12111yescharacteristic
520C22×C7C2×#12111yescharacteristic
521C2×D7—24no—
522C2×D7—44no—
523C2×D7—44no—
524C2×D7—82no—
525C4×C7—42no—
526C4×C7—82no—
527C4×C7#38611yescharacteristic
528C4×C7#38611yescharacteristic
529C4×C7#38611yescharacteristic
530C4×C7#38611yescharacteristic
531C4×C7C2×C4×D411yescharacteristic
532C4×C7C2×C4×D411yescharacteristic
533C4×C7C2×#12011yescharacteristic
534C4×C7C2×#12311yescharacteristic
535Dic7—24no—
536Dic7—44no—
537Dic7—82no—
538C24—21no—
539C24—72no—
540C24D4×D711yescharacteristic
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—142no—
558#41—142no—
559#41—142no—
560#41—142no—
561#41—142no—
562#41—142no—
563#41—142no—
564#41—142no—
565#41—142no—
566#41—142no—
567#41—142no—
568#41—142no—
569#41—142no—
570#41—142no—
571#41—142no—
572#41—142no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—72no—
579C2×Q8—72no—
580C2×Q8—141no—
581C2×Q8—141no—
582C2×Q8—141no—
583C2×Q8—141no—
584C2×Q8C2×C4×D712yes—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—74no—
597C2×D4—74no—
598C2×D4—72no—
599C2×D4—72no—
600C2×D4—142no—
601C2×D4—142no—
602C2×D4—142no—
603C2×D4—142no—
604C2×D4—148no—
605C2×D4—141no—
606C2×D4—141no—
607C2×D4—141no—
608C2×D4—141no—
609C2×D4C2×C4×D712yes—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—72no—
619C22×C4—74no—
620C22×C4—74no—
621C22×C4—142no—
622C22×C4—142no—
623C22×C4—142no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—281no—
627C22×C4C2×C4×D711yescharacteristic
628C22×C4C2×C4×D711yescharacteristic
629C22×C4#115711yescharacteristic
630C22×C4#115711yescharacteristic
631C22×C4D4×D711yescharacteristic
632C22×C4D4×D711yescharacteristic
633C22×C4D4×D711yescharacteristic
634C22×C4D4×D711yescharacteristic
635C22×C4D4×D711yescharacteristic
636C22×C4#115911yescharacteristic
637C22×C4#115911yescharacteristic
638C22×C4C2×C22⋊D711yescharacteristic
639C22×C4C2×C22⋊D711yescharacteristic
640C22×C4C23×D711yescharacteristic
641M16—22no—
642M16—22no—
643M16—22no—
644M16—74no—
645M16—1416no—
646M16—142no—
647M16—142no—
648M16—142no—
649M16C2×C22⋊D714yes—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—1416no—
654C2×C8—142no—
655C2×C8—142no—
656C2×C8—142no—
657C4⋊C4—22no—
658C4⋊C4—41no—
659C4⋊C4—148no—
660C4⋊C4—142no—
661C4⋊C4—142no—
662C4⋊C4—142no—
663C4⋊C4—281no—
664C22⋊C4—22no—
665C22⋊C4—41no—
666C22⋊C4—148no—
667C22⋊C4—148no—
668C22⋊C4—142no—
669C22⋊C4—142no—
670C22⋊C4—142no—
671C22⋊C4—281no—
672C42—22no—
673C42—41no—
674C42—74no—
675C42—142no—
676C42—142no—
677C42—281no—
678C2×C7—21no—
679C2×C7—21no—
680C2×C7—21no—
681C2×C7—21no—
682C2×C7—21no—
683C2×C7—21no—
684C2×C7—21no—
685C2×C7—82no—
686C2×C7C2×#38611yescharacteristic
687D7—44no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—74no—
692C23—81no—
693C23—82no—
694C23—142no—
695C23—142no—
696C23—562no—
697C23D7×C22⋊C411yescharacteristic
698C23D7×C22⋊C411yescharacteristic
699C23#644711yescharacteristic
700C23#644711yescharacteristic
701C23#650111yescharacteristic
702C23#650111yescharacteristic
703C23C2×D4×D711yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—41no—
707Q8—41no—
708Q8—142no—
709Q8—142no—
710Q8—142no—
711Q8—142no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—144no—
721D4—144no—
722D4—144no—
723D4—144no—
724D4—142no—
725D4—142no—
726D4—142no—
727D4—142no—
728D4—568no—
729C2×C4—22no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—74no—
738C2×C4—82no—
739C2×C4—142no—
740C2×C4—142no—
741C2×C4—144no—
742C2×C4—144no—
743C2×C4—144no—
744C2×C4—144no—
745C2×C4—144no—
746C2×C4—282no—
747C2×C4—562no—
748C2×C4—562no—
749C2×C4D7×C22⋊C411yescharacteristic
750C2×C4D7×C22⋊C411yescharacteristic
751C2×C4(C22⋊D7)⋊C411yescharacteristic
752C2×C4(C22⋊D7)⋊C411yescharacteristic
753C2×C4(C22⋊D7)⋊C411yescharacteristic
754C2×C4(C22⋊D7)⋊C411yescharacteristic
755C2×C4#644611yescharacteristic
756C2×C4#644611yescharacteristic
757C2×C4#644611yescharacteristic
758C2×C4#644611yescharacteristic
759C2×C4#644711yescharacteristic
760C2×C4#644711yescharacteristic
761C2×C4C4×C22⋊D711yescharacteristic
762C2×C4C4×C22⋊D711yescharacteristic
763C2×C4C4×C22⋊D711yescharacteristic
764C2×C4C4×C22⋊D711yescharacteristic
765C2×C4#650011yescharacteristic
766C2×C4#650011yescharacteristic
767C2×C4#650011yescharacteristic
768C2×C4#650011yescharacteristic
769C2×C4#650111yescharacteristic
770C2×C4#650111yescharacteristic
771C2×C4C22×C4×D711yescharacteristic
772C2×C4C2×#115711yescharacteristic
773C2×C4C2×D4×D711yescharacteristic
774C2×C4C2×D4×D711yescharacteristic
775C2×C4C2×#115911yescharacteristic
776C2×C4C22×C22⋊D711yescharacteristic
777C8—24no—
778C8—144no—
779C7#2094711yescharacteristic, complemented, Sylow
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—44no—
788C22—42no—
789C22—82no—
790C22—82no—
791C22—144no—
792C22—284no—
793C22—284no—
794C22—562no—
795C22#8972811yescharacteristic
796C22#8972811yescharacteristic
797C22#8972811yescharacteristic
798C22#8972811yescharacteristic
799C22C2×D7×C22⋊C411yescharacteristic
800C22C2×#644711yescharacteristic
801C22C2×#650111yescharacteristic
802C4—42no—
803C4—82no—
804C4—144no—
805C4—284no—
806C4—562no—
807C4#8972811yescharacteristic
808C4#8972811yescharacteristic
809C4#8972811yescharacteristic
810C4#8972811yescharacteristic
811C4C2×(C22⋊D7)⋊C411yescharacteristic
812C4C2×#644611yescharacteristic
813C4C2×C4×C22⋊D711yescharacteristic
814C4C2×#650011yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—284no—
824C2C2×#8972811yescharacteristic
subgroupG/H
centerC4C2×#6500
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#421C2
socleC2×C7C2×#386
prime radical#11744336C2
cosocleC22×C4×C7C24
hypercenterC2×#421D7
hypocenterC7#20947
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#90436C2semidirect
3. C2×C7×#421C2semidirect
4. C2×#90008C2semidirect
5. C2×#89778C2semidirect
6. #11729736C2semidirect
7. #11729328C2semidirect
8. #11728171C2semidirect
15. #90521C4semidirect
17. #90516C4semidirect
18. #90507C4semidirect
19. #90496C4semidirect
28. #90436C22semidirect
33. C7×#421C22semidirect
36. #90008C22semidirect
39. #89778C22semidirect
41. #89350C22semidirect
42. #89327C22semidirect
80. C2×C7×M16D4semidirect
81. C2×C7×M16D4semidirect
94. #6510C2×C4semidirect
96. #6507C2×C4semidirect
97. #6503C2×C4semidirect
101. #6499C2×C4semidirect
122. C2×#1136D4semidirect
123. C2×#1136D4semidirect
140. C2×#421D7semidirect
311. #421C2×D7semidirect
459. C2×M16C22⋊D7semidirect
460. C2×M16C22⋊D7semidirect
779. C7#20947semidirect

Maximal subgroups

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

subgroupindex
#117443362
C2×#904362
C2×C7×#4212
C2×#900082
C2×#897782
#117297362
#117293282
#117281712
#209477