Finite Group Databasebeta

← #13371163

Subgroups — #13371163

Order 1792.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2880C211yesmaximal, characteristic
2#11741517C211yesmaximal, characteristic
3#11736029C211yesmaximal, characteristic, complemented
4#11729892C211yesmaximal, characteristic
5#11729771C211yesmaximal, characteristic, complemented
6#11729771C211yesmaximal, characteristic, complemented
7#11729763C211yesmaximal, characteristic, complemented
8#11729762C211yesmaximal, characteristic, complemented
9#11727752C211yesmaximal, characteristic, complemented
10#11727751C211yesmaximal, characteristic, complemented
11#11727750C211yesmaximal, characteristic, complemented
12#11727750C211yesmaximal, characteristic, complemented
13#11727737C211yesmaximal, characteristic, complemented
14#11727729C211yesmaximal, characteristic, complemented
15#11727703C211yesmaximal, characteristic, complemented
16C22×C7×#41C2211yescharacteristic
17C2×C7×#131C2211yescharacteristic
18C2×C7×#131C2211yescharacteristic
19C2×#6489C2211yescharacteristic
20C22×#1136C2211yescharacteristic
21C7×#408—21no—
22C7×#408—21no—
23C7×#408C2211yescharacteristic
24C7×#408C2211yescharacteristic
25C7×#407—21no—
26C7×#407C2211yescharacteristic
27C2×C7×C22⋊C8—21no—
28C2×C7×C22⋊C8C2211yescharacteristic
29C2×#6411C2211yescharacteristic
30C2×#6411C2211yescharacteristic
31C2×#6411C2211yescharacteristic
32C2×#6411C2211yescharacteristic
33#90005C2211yescharacteristic
34#90005C2211yescharacteristic
35#90005C2211yescharacteristic
36#90005C2211yescharacteristic
37#90004C411yescharacteristic, complemented
38#90004C411yescharacteristic, complemented
39#90004C411yescharacteristic, complemented
40#90004C411yescharacteristic, complemented
41#89997C411yescharacteristic, complemented
42#89997C411yescharacteristic, complemented
43#89987C411yescharacteristic, complemented
44#89987C411yescharacteristic, complemented
45C4×C22⋊Dic7C2211yescharacteristic
46#89979C2211yescharacteristic
47C2×#6396C2211yescharacteristic, complemented
48C2×#6396C2211yescharacteristic, complemented
49#89874C2211yescharacteristic, complemented
50#89874C2211yescharacteristic, complemented
51#89873C2211yescharacteristic, complemented
52#89873C2211yescharacteristic, complemented
53C2×#6389C2211yescharacteristic, complemented
54C2×C8×Dic7C2211yescharacteristic, complemented
55#89492—21no—
56#89492—21no—
57#89491—21no—
58#89490—21no—
59#89353C2211yescharacteristic, complemented
60#89353C2211yescharacteristic, complemented
61#89350C2211yescharacteristic, complemented
62#89350C2211yescharacteristic, complemented
63#89350C2211yescharacteristic, complemented
64#89350C2211yescharacteristic, complemented
65#89345C2211yescharacteristic, complemented
66#89345C2211yescharacteristic, complemented
67#22588—71nomaximal, Sylow
68C2×C7×#41—21no—
69C2×C7×#41—21no—
70C2×C7×#41—22no—
71C2×C7×#41—22no—
72C2×C7×#41—41no—
73C2×C7×#41—41no—
74C2×C7×#41C2×C411yescharacteristic
75C2×C7×#41C2×C411yescharacteristic
76C2×C7×#41C2311yescharacteristic
77C2×C7×#41C2311yescharacteristic
78C22×C7×Q8C2×C411yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2×C411yescharacteristic
81C23×C4×C7—21no—
82C23×C4×C7C2311yescharacteristic
83C7×#131—22no—
84C7×#131—22no—
85C7×#131—41no—
86C7×#131—41no—
87C2×C7×M16—21no—
88C2×C7×M16—21no—
89C2×C7×M16C2311yescharacteristic
90C2×C7×M16C2311yescharacteristic
91C22×C7×C8—21no—
92C22×C7×C8—21no—
93C22×C7×C8C2311yescharacteristic
94C22×C7×C8C2311yescharacteristic
95C2×C22⋊Dic7—21no—
96C2×C22⋊Dic7—21no—
97#6489—21no—
98#6489—21no—
99#6489C2×C411yescharacteristic
100#6489C2×C411yescharacteristic
101#6489C2311yescharacteristic
102#6489C2311yescharacteristic
103C2×C4⋊Dic7C2×C411yescharacteristic
104C2×C4⋊Dic7C2×C411yescharacteristic
105C2×C4×Dic7—21no—
106C2×C4×Dic7C2311yescharacteristic
107C2×C4×Dic7C2311yescharacteristic
108C2×#1136—41no—
109C2×#1136—41no—
110C2×#1136C2×C411yescharacteristic
111C2×#1136C2×C411yescharacteristic
112C2×#1136C2×C411yescharacteristic
113C2×#1136C2×C411yescharacteristic
114C2×#1136C2311yescharacteristic
115C2×#1136C2311yescharacteristic
116C22×C7⋊C8C2311yescharacteristic
117C22×C7⋊C8C2311yescharacteristic
118C7×C22⋊C8—21no—
119C7×C22⋊C8—21no—
120C7×C22⋊C8—21no—
121C7×C22⋊C8—21no—
122C7×C22⋊C8—21no—
123C7×C22⋊C8—21no—
124C7×C22⋊C8D411yescharacteristic
125C7×C22⋊C8D411yescharacteristic
126C7×C22⋊C8D411yescharacteristic
127C7×C22⋊C8D411yescharacteristic
128#6411—22no—
129#6411—22no—
130#6411—41no—
131#6411—41no—
132#6409C2×C411yescharacteristic
133#6409C2×C411yescharacteristic
134#6409C2×C411yescharacteristic
135#6409C2×C411yescharacteristic
136#6409C2×C411yescharacteristic
137#6409C2×C411yescharacteristic
138#6409C2×C411yescharacteristic
139#6409C2×C411yescharacteristic
140#6406C2×C411yescharacteristic
141#6406C2×C411yescharacteristic
142#6406C2×C411yescharacteristic
143#6406C2×C411yescharacteristic
144#6406C2×C411yescharacteristic
145#6406C2×C411yescharacteristic
146#6406C2×C411yescharacteristic
147#6406C2×C411yescharacteristic
148C7⋊#95—21no—
149C22⋊(C7⋊C8)—21no—
150C22⋊(C7⋊C8)—21no—
151#6396—41no—
152#6396—41no—
153#6389—21no—
154#6389—21no—
155#6389—41no—
156Dic7⋊C8—21no—
157Dic7⋊C8—21no—
158Dic7⋊C8—21no—
159Dic7⋊C8—21no—
160C8×Dic7—21no—
161C8×Dic7—21no—
162C8×Dic7—41no—
163#2924—71no—
164#2896—71no—
165#2880D711yescharacteristic
166#1938—71no—
167#1937—71no—
168#1929—71no—
169#1929—71no—
170#1866—71no—
171#1866—71no—
172#1826—71no—
173#1811—71no—
174#1789—71no—
175#1765—71no—
176#1764—71no—
177#1753—71no—
178C24×C7—21no—
179C24×C7#4111yescharacteristic
180C7×#41—21no—
181C7×#41—21no—
182C7×#41—22no—
183C7×#41—22no—
184C7×#41—21no—
185C7×#41—21no—
186C7×#41—21no—
187C7×#41—21no—
188C7×#41—42no—
189C7×#41—42no—
190C7×#41—41no—
191C7×#41—41no—
192C7×#41—42no—
193C7×#41—42no—
194C7×#41#4112yes—
195C7×#41#4112yes—
196C2×C7×Q8—21no—
197C2×C7×Q8—22no—
198C2×C7×Q8—41no—
199C2×C7×Q8C22×C411yescharacteristic
200C2×C7×Q8C22×C411yescharacteristic
201C2×C7×D4—21no—
202C2×C7×D4—22no—
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—41no—
208C2×C7×D4—42no—
209C2×C7×D4—42no—
210C2×C7×D4C22×C411yescharacteristic
211C2×C7×D4C22×C411yescharacteristic
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—42no—
222C22×C4×C7—42no—
223C22×C4×C7C22×C411yescharacteristic
224C22×C4×C7C22×C411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7#4111yescharacteristic
228C22×C4×C7C2411yescharacteristic
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C7×M16—21no—
234C7×M16—21no—
235C7×M16—21no—
236C7×M16—21no—
237C7×M16—42no—
238C7×M16—42no—
239C2×C7×C8—21no—
240C2×C7×C8—21no—
241C2×C7×C8—21no—
242C2×C7×C8—21no—
243C2×C7×C8—21no—
244C2×C7×C8—21no—
245C2×C7×C8—42no—
246C2×C7×C8—42no—
247C2×C7×C8C2×D411yescharacteristic
248C2×C7×C8C2×D411yescharacteristic
249C2×C7×C8C2×D411yescharacteristic
250C2×C7×C8C2×D411yescharacteristic
251C22⋊Dic7—21no—
252C22⋊Dic7—21no—
253C22⋊Dic7—21no—
254C22⋊Dic7—21no—
255C22⋊Dic7—42no—
256C4⋊Dic7—21no—
257C4⋊Dic7—21no—
258C4⋊Dic7C22×C411yescharacteristic
259C4⋊Dic7C22×C411yescharacteristic
260C4⋊Dic7C22×C411yescharacteristic
261C4⋊Dic7C22×C411yescharacteristic
262C4×Dic7—21no—
263C4×Dic7—21no—
264C4×Dic7—21no—
265C4×Dic7—21no—
266C4×Dic7—21no—
267C4×Dic7—21no—
268C4×Dic7—21no—
269C4×Dic7—21no—
270#1136—21no—
271#1136—21no—
272#1136—21no—
273#1136—21no—
274#1136—41no—
275#1136—41no—
276#1136—41no—
277#1136—41no—
278C2×C7⋊C8—21no—
279C2×C7⋊C8—21no—
280C2×C7⋊C8—21no—
281C2×C7⋊C8—21no—
282C2×C7⋊C8—21no—
283C2×C7⋊C8—21no—
284C2×C7⋊C8C22×C411yescharacteristic
285C2×C7⋊C8C22×C411yescharacteristic
286C2×C7⋊C8C22×C411yescharacteristic
287C2×C7⋊C8C22×C411yescharacteristic
288C22×#41C2×D711yescharacteristic
289C2×#131C2×D711yescharacteristic
290C2×#131C2×D711yescharacteristic
291C22×M16—71no—
292C2×#117—71no—
293#433—141no—
294#433—141no—
295#432—141no—
296#431—141no—
297C2×#108—71no—
298C2×#108—71no—
299#424—71no—
300#424—71no—
301C2×#104—71no—
302C2×#104—71no—
303C2×#104—71no—
304C2×#104—71no—
305#419—71no—
306#419—71no—
307#418—71no—
308#418—71no—
309#417—71no—
310#417—71no—
311#417—71no—
312#417—71no—
313#416—71no—
314#416—71no—
315#416—71no—
316#416—71no—
317#408—21no—
318#408—21no—
319#408C2×D711yescharacteristic
320#408C2×D711yescharacteristic
321#407—21no—
322#407—71no—
323#407C2×D711yescharacteristic
324C2×C22⋊C8—21no—
325C2×C22⋊C8C2×D711yescharacteristic
326#405—71no—
327#405—71no—
328C2×#97—71no—
329C2×C4×C8—71no—
330C4×C22⋊C4—71no—
331#341—71no—
332#341—71no—
333#339—71no—
334#339—71no—
335#339—71no—
336#339—71no—
337#336—71no—
338#336—71no—
339C23×C7—21no—
340C23×C7—21no—
341C23×C7—21no—
342C23×C7—21no—
343C23×C7—41no—
344C23×C7—41no—
345C23×C7—42no—
346C23×C7—42no—
347C23×C7—81no—
348C23×C7C4×D411yescharacteristic
349C23×C7C4×D411yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C7×Q8—21no—
352C7×Q8—21no—
353C7×Q8—21no—
354C7×Q8—42no—
355C7×Q8#11712yes—
356C7×D4—22no—
357C7×D4—22no—
358C7×D4—21no—
359C7×D4—21no—
360C7×D4—21no—
361C7×D4—42no—
362C7×D4—42no—
363C7×D4—42no—
364C7×D4—41no—
365C7×D4—41no—
366C7×D4#11712yes—
367C2×C4×C7—21no—
368C2×C4×C7—21no—
369C2×C4×C7—21no—
370C2×C4×C7—21no—
371C2×C4×C7—21no—
372C2×C4×C7—21no—
373C2×C4×C7—21no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—21no—
377C2×C4×C7—21no—
378C2×C4×C7—21no—
379C2×C4×C7—21no—
380C2×C4×C7—21no—
381C2×C4×C7—42no—
382C2×C4×C7—42no—
383C2×C4×C7—42no—
384C2×C4×C7—41no—
385C2×C4×C7—41no—
386C2×C4×C7C4×D411yescharacteristic
387C2×C4×C7C4×D411yescharacteristic
388C2×C4×C7C23×C411yescharacteristic
389C2×C4×C7C22×D411yescharacteristic
390C2×C4×C7C2×#4111yescharacteristic
391C2×C4×C7C2×#4111yescharacteristic
392C2×C4×C7H(5,𝔽2)11yescharacteristic
393C2×C4×C7H(5,𝔽2)11yescharacteristic
394C2×Dic7—22no—
395C2×Dic7—21no—
396C2×Dic7—21no—
397C2×Dic7—21no—
398C2×Dic7—21no—
399C2×Dic7—41no—
400C2×Dic7—42no—
401C2×Dic7—41no—
402C2×Dic7—41no—
403C2×Dic7—41no—
404C2×Dic7—41no—
405C2×Dic7—81no—
406C7×C8—21no—
407C7×C8—21no—
408C7×C8—21no—
409C7×C8—21no—
410C7×C8—41no—
411C7×C8—41no—
412C7⋊C8—21no—
413C7⋊C8—21no—
414C7⋊C8—21no—
415C7⋊C8—21no—
416C7⋊C8—41no—
417C7⋊C8—41no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41C4×D711yescharacteristic
425C2×#41C4×D711yescharacteristic
426C2×#41C22×D711yescharacteristic
427C2×#41C22×D711yescharacteristic
428C22×Q8C4×D711yescharacteristic
429C22×D4—21no—
430C22×D4C4×D711yescharacteristic
431C23×C4—21no—
432C23×C4C22×D711yescharacteristic
433#131—22no—
434#131—22no—
435#131—41no—
436#131—41no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—71no—
440C2×M16—71no—
441C2×M16—71no—
442C2×M16—71no—
443C2×M16—71no—
444C2×M16—71no—
445C2×M16—281no—
446C2×M16—281no—
447C2×M16C22×D711yescharacteristic
448C2×M16C22×D711yescharacteristic
449C22×C8—21no—
450C22×C8—21no—
451C22×C8—71no—
452C22×C8—71no—
453C22×C8C22×D711yescharacteristic
454C22×C8C22×D711yescharacteristic
455#117—71no—
456#117—71no—
457#117—71no—
458#117—71no—
459#117—141no—
460#117—141no—
461C2×C4⋊C4—71no—
462C2×C4⋊C4—71no—
463C2×C22⋊C4—141no—
464C2×C22⋊C4—141no—
465C2×C42—71no—
466C2×C42—71no—
467C2×C42—141no—
468#108—281no—
469#108—281no—
470C4⋊C8—141no—
471C4⋊C8—141no—
472C4⋊C8—141no—
473C4⋊C8—141no—
474#104—142no—
475#104—142no—
476#104—281no—
477#104—281no—
478#103—71no—
479#103—71no—
480#103—71no—
481#103—71no—
482#103—71no—
483#103—71no—
484#103—71no—
485#103—71no—
486#102—71no—
487#102—71no—
488#102—71no—
489#102—71no—
490#102—71no—
491#102—71no—
492#102—71no—
493#102—71no—
494C22⋊C8—21no—
495C22⋊C8—21no—
496C22⋊C8—21no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499C22⋊C8—21no—
500C22⋊C8—141no—
501C22⋊C8—141no—
502C22⋊C8C22⋊D711yescharacteristic
503C22⋊C8C22⋊D711yescharacteristic
504C22⋊C8C22⋊D711yescharacteristic
505C22⋊C8C22⋊D711yescharacteristic
506#97—141no—
507#97—141no—
508#97—281no—
509C4×C8—141no—
510C4×C8—141no—
511C4×C8—281no—
512#95—141no—
513C22×C7—21no—
514C22×C7—21no—
515C22×C7—21no—
516C22×C7—21no—
517C22×C7—22no—
518C22×C7—21no—
519C22×C7—21no—
520C22×C7—21no—
521C22×C7—21no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—81no—
528C22×C7—81no—
529C22×C7—84no—
530C22×C7C2×C4×D411yescharacteristic
531C22×C7#55111yescharacteristic
532C22×C7#55111yescharacteristic
533C4×C7—21no—
534C4×C7—21no—
535C4×C7—22no—
536C4×C7—41no—
537C4×C7C2×#11711yescharacteristic
538C4×C7#51811yescharacteristic
539C4×C7#54611yescharacteristic
540C4×C7#54611yescharacteristic
541Dic7—42no—
542Dic7—41no—
543Dic7—41no—
544Dic7—41no—
545Dic7—41no—
546Dic7—81no—
547C24—21no—
548C24#115711yescharacteristic
549#41—21no—
550#41—21no—
551#41—22no—
552#41—22no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—42no—
558#41—42no—
559#41—41no—
560#41—41no—
561#41—42no—
562#41—42no—
563#41#115912yes—
564#41#115912yes—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—41no—
568C2×Q8C2×C4×D711yescharacteristic
569C2×Q8C2×C4×D711yescharacteristic
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—41no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4C2×C4×D711yescharacteristic
580C2×D4C2×C4×D711yescharacteristic
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4C2×C4×D711yescharacteristic
597C22×C4C2×C4×D711yescharacteristic
598C22×C4#115711yescharacteristic
599C22×C4C2×C22⋊D711yescharacteristic
600C22×C4C2×C22⋊D711yescharacteristic
601C22×C4C23×D711yescharacteristic
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—42no—
607M16—42no—
608M16—141no—
609M16—141no—
610M16—141no—
611M16—141no—
612M16—281no—
613M16—281no—
614M16—281no—
615M16—281no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—42no—
623C2×C8—42no—
624C2×C8—71no—
625C2×C8—71no—
626C2×C8—71no—
627C2×C8—71no—
628C2×C8—141no—
629C2×C8—141no—
630C2×C8—141no—
631C2×C8—141no—
632C2×C8—141no—
633C2×C8—141no—
634C2×C8C2×C22⋊D711yescharacteristic
635C2×C8C2×C22⋊D711yescharacteristic
636C2×C8C2×C22⋊D711yescharacteristic
637C2×C8C2×C22⋊D711yescharacteristic
638C4⋊C4—71no—
639C4⋊C4—71no—
640C4⋊C4—71no—
641C4⋊C4—71no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C22⋊C4—141no—
645C22⋊C4—141no—
646C22⋊C4—141no—
647C22⋊C4—141no—
648C22⋊C4—282no—
649C42—141no—
650C42—141no—
651C42—141no—
652C42—141no—
653C42—141no—
654C42—141no—
655C42—141no—
656C42—141no—
657C2×C7—21no—
658C2×C7—21no—
659C2×C7—41no—
660C2×C7—41no—
661C2×C7—42no—
662C2×C7—81no—
663C2×C7#234211yescharacteristic
664C2×C7#295511yescharacteristic
665C2×C7#295611yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—81no—
675C23C4×C22⋊D711yescharacteristic
676C23C4×C22⋊D711yescharacteristic
677C23C2×#115711yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—42no—
682Q8#644012yes—
683D4—22no—
684D4—22no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—41no—
692D4—41no—
693D4#644012yes—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—142no—
714C2×C4—141no—
715C2×C4—141no—
716C2×C4—141no—
717C2×C4—141no—
718C2×C4—281no—
719C2×C4—282no—
720C2×C4—281no—
721C2×C4—281no—
722C2×C4—281no—
723C2×C4—281no—
724C2×C4—561no—
725C2×C4C4×C22⋊D711yescharacteristic
726C2×C4C4×C22⋊D711yescharacteristic
727C2×C4C22×C4×D711yescharacteristic
728C2×C4C2×#115911yescharacteristic
729C2×C4C2×#115911yescharacteristic
730C2×C4#654811yescharacteristic
731C2×C4#654811yescharacteristic
732C2×C4C22×C22⋊D711yescharacteristic
733C8—21no—
734C8—21no—
735C8—21no—
736C8—21no—
737C8—41no—
738C8—41no—
739C8—141no—
740C8—141no—
741C8—141no—
742C8—141no—
743C8—281no—
744C8—281no—
745C7#2258811yescharacteristic, complemented, Sylow
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22#9018611yescharacteristic
764C22#9018611yescharacteristic
765C22C2×C4×C22⋊D711yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—41no—
770C4—282no—
771C4—281no—
772C4—281no—
773C4—281no—
774C4—281no—
775C4—561no—
776C4C2×#644011yescharacteristic
777C4#9017711yescharacteristic
778C4#9049711yescharacteristic
779C4#9049711yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2#1173954311yescharacteristic
787C2#1174123711yescharacteristic
788C2#1174125611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2880C2
socleC22×C7C2×C4×D4
prime radicalC22×C7×#41C22
cosocleC22×C4×C7C24
hypercenter#2880D7
hypocenterC7#22588
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
3. #11736029C2semidirect
5. #11729771C2semidirect
6. #11729771C2semidirect
7. #11729763C2semidirect
8. #11729762C2semidirect
9. #11727752C2semidirect
10. #11727751C2semidirect
11. #11727750C2semidirect
12. #11727750C2semidirect
13. #11727737C2semidirect
14. #11727729C2semidirect
15. #11727703C2semidirect
37. #90004C4semidirect
38. #90004C4semidirect
39. #90004C4semidirect
40. #90004C4semidirect
41. #89997C4semidirect
42. #89997C4semidirect
43. #89987C4semidirect
44. #89987C4semidirect
47. C2×#6396C22semidirect
48. C2×#6396C22semidirect
49. #89874C22semidirect
50. #89874C22semidirect
51. #89873C22semidirect
52. #89873C22semidirect
53. C2×#6389C22semidirect
54. C2×C8×Dic7C22semidirect
59. #89353C22semidirect
60. #89353C22semidirect
61. #89350C22semidirect
62. #89350C22semidirect
63. #89350C22semidirect
64. #89350C22semidirect
65. #89345C22semidirect
66. #89345C22semidirect
745. C7#22588semidirect

Maximal subgroups

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

subgroupindex
C7×#28802
#117415172
#117360292
#117298922
#117297712
#117297632
#117297622
#117277522
#117277512
#117277502
#117277372
#117277292
#117277032
#225887