Finite Group Databasebeta

← #13410853

Subgroups — #13410853

Order 1792.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×D4×C22⋊C4C211yesmaximal, characteristic
2C22×#6406C211yesmaximal, characteristic
3C2×#89779C211yesmaximal, characteristic, complemented
4#11730938C211yesmaximal, characteristic, complemented
5#11729882C211yesmaximal, characteristic
6#11729360C211yesmaximal, characteristic, complemented
7#11729360C211yesmaximal, characteristic, complemented
8#11729358C211yesmaximal, characteristic, complemented
9#11727409C211yesmaximal, characteristic, complemented
10#11727407C211yesmaximal, characteristic, complemented
11#11727407C211yesmaximal, characteristic, complemented
12#11727392C211yesmaximal, characteristic, complemented
13#11727266C211yesmaximal, characteristic, complemented
14#11727258C211yesmaximal, characteristic, complemented
15#11727203C211yesmaximal, characteristic, complemented
16C23×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×C7×C22⋊C4—21no—
20C22×C4⋊Dic7C2211yescharacteristic
21C23×C7⋊C8C2211yescharacteristic
22C2×#6441—21no—
23C2×#6432C2211yescharacteristic, complemented
24C7×#390C2211yescharacteristic
25C7×#390C2211yescharacteristic
26C7×#386—21no—
27C7×#386—21no—
28C7×#380C2211yescharacteristic
29C7×#379—21no—
30C4×C7×C22⋊C4C2211yescharacteristic
31C2×#6406—24no—
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34C2×#6406C2211yescharacteristic
35C2×#6406C2211yescharacteristic
36C2×#6406C2211yescharacteristic
37C2×#6406C2211yescharacteristic
38C2×#6406C2211yescharacteristic
39C2×#6406C2211yescharacteristic
40#89984C2211yescharacteristic
41C2×C22⋊(C7⋊C8)C2211yescharacteristic
42#89779—24no—
43C2×#6381C2211yescharacteristic, complemented
44C2×#6381C2211yescharacteristic, complemented
45C2×#6381C2211yescharacteristic, complemented
46C2×#6381C2211yescharacteristic, complemented
47#89722—21no—
48#89707C2211yescharacteristic, complemented
49#89700C2211yescharacteristic, complemented
50#89700C2211yescharacteristic, complemented
51C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
52C2×C4⋊(C7⋊C8)C2211yescharacteristic, complemented
53#89433—21no—
54#89428—21no—
55#89324C2211yescharacteristic, complemented
56#89324C2211yescharacteristic, complemented
57#89324C2211yescharacteristic, complemented
58#89324C2211yescharacteristic, complemented
59#89319C2211yescharacteristic, complemented
60#89319C2211yescharacteristic, complemented
61#25950—71nomaximal, Sylow
62C25×C7—21no—
63C22×C7×D4—22no—
64C22×C7×D4—22no—
65C22×C7×D4—21no—
66C22×C7×D4—22no—
67C22×C7×D4—41no—
68C22×C7×D4—41no—
69C22×C7×D4Q814yescomplemented
70C22×C7×D4C2311yescharacteristic
71C22×C7×D4C2311yescharacteristic
72C23×C4×C7—21no—
73C23×C4×C7—21no—
74C23×C4×C7C2311yescharacteristic
75C23×Dic7—21no—
76C22×Dic14—21no—
77C4×C7×D4—22no—
78C4×C7×D4—22no—
79C4×C7×D4—41no—
80C4×C7×D4—41no—
81C2×C7×C4⋊C4C2311yescharacteristic
82C2×C7×C4⋊C4C2311yescharacteristic
83C2×C7×C22⋊C4—21no—
84C2×C7×C22⋊C4—21no—
85C2×C7×C22⋊C4—21no—
86C2×C7×C22⋊C4—21no—
87C2×C7×C22⋊C4—21no—
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C7×C22⋊C4—44no—
91C2×C7×C22⋊C4D411yescharacteristic
92C2×C7×C22⋊C4D411yescharacteristic
93C2×C42×C7C2311yescharacteristic
94C2×C42×C7C2311yescharacteristic
95C2×C22⋊Dic7—21no—
96C2×C4⋊Dic7—22no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—21no—
99C2×C4⋊Dic7—21no—
100C2×C4⋊Dic7—21no—
101C2×C4⋊Dic7—41no—
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×C4⋊Dic7C2311yescharacteristic
105C2×C4⋊Dic7C2311yescharacteristic
106C2×Dic7⋊C4—21no—
107C2×Dic7⋊C4—21no—
108C22×C7⋊C8—22no—
109C22×C7⋊C8—22no—
110C22×C7⋊C8—41no—
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C22×C7⋊C8C2311yescharacteristic
114C22×C7⋊C8C2311yescharacteristic
115#6441—44no—
116#6432—22no—
117#6432—41no—
118C7×#95—21no—
119C7×#95D411yescharacteristic
120C7×#95D411yescharacteristic
121#6406—22no—
122#6406—22no—
123#6406—22no—
124#6406—22no—
125#6406—22no—
126#6406—41no—
127#6406—41no—
128#6406D414yes—
129C7⋊#95—21no—
130C7⋊#95—21no—
131C7⋊#95—21no—
132C22⋊(C7⋊C8)—22no—
133#6381—22no—
134#6381—22no—
135#6381—41no—
136#6381—41no—
137C4⋊(C7⋊C8)—22no—
138C4⋊(C7⋊C8)—41no—
139C2×#474—71no—
140C22×#102—71no—
141#2440—71no—
142D4×C22⋊C4D711yescharacteristic
143#2093—71no—
144#2067—71no—
145#2067—71no—
146#2023—71no—
147#1862—71no—
148#1862—71no—
149#1852—71no—
150#1850—71no—
151#1808—71no—
152#1802—71no—
153#1786—71no—
154C24×C7—21no—
155C24×C7—21no—
156C24×C7—24no—
157C24×C7—42no—
158C24×C7—42no—
159C24×C7—42no—
160C24×C7—42no—
161C24×C7—81no—
162C24×C7—81no—
163C24×C7C2×D411yescharacteristic
164C2×C7×D4—28no—
165C2×C7×D4—24no—
166C2×C7×D4—21no—
167C2×C7×D4—21no—
168C2×C7×D4—21no—
169C2×C7×D4—21no—
170C2×C7×D4—21no—
171C2×C7×D4—21no—
172C2×C7×D4—21no—
173C2×C7×D4—21no—
174C2×C7×D4—44no—
175C2×C7×D4—44no—
176C2×C7×D4—44no—
177C2×C7×D4—42no—
178C2×C7×D4—42no—
179C2×C7×D4C2×D412yes—
180C2×C7×D4C2×Q812yes—
181C2×C7×D4C2×Q812yes—
182C2×C7×D4#4112yes—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—42no—
190C22×C4×C7—42no—
191C22×C4×C7—42no—
192C22×C4×C7—42no—
193C22×C4×C7—81no—
194C22×C4×C7—81no—
195C22×C4×C7C2×D411yescharacteristic
196C22×C4×C7C2×D411yescharacteristic
197C22×C4×C7C2×D411yescharacteristic
198C22×C4×C7C2×D411yescharacteristic
199C22×C4×C7C2×D411yescharacteristic
200C22×C4×C7C2×Q812yes—
201C22×C4×C7#4112yes—
202C22×C4×C7C2411yescharacteristic
203C22×Dic7—21no—
204C22×Dic7—21no—
205C22×Dic7—21no—
206C22×Dic7—21no—
207C22×Dic7—42no—
208C22×Dic7—42no—
209C22×Dic7—81no—
210C2×Dic14—42no—
211C2×Dic14—42no—
212C2×Dic14—81no—
213C7×C4⋊C4—21no—
214C7×C4⋊C4—21no—
215C7×C4⋊C4—21no—
216C7×C4⋊C4—21no—
217C7×C22⋊C4—22no—
218C7×C22⋊C4—42no—
219C7×C22⋊C4—42no—
220C7×C22⋊C4—42no—
221C7×C22⋊C4—42no—
222C7×C22⋊C4—42no—
223C7×C22⋊C4—81no—
224C7×C22⋊C4—81no—
225C7×C22⋊C4D814yes—
226C42×C7—21no—
227C42×C7—21no—
228C42×C7—21no—
229C42×C7—21no—
230C22⋊Dic7—42no—
231C4⋊Dic7—21no—
232C4⋊Dic7—21no—
233C4⋊Dic7—21no—
234C4⋊Dic7—21no—
235C4⋊Dic7—21no—
236C4⋊Dic7—21no—
237C4⋊Dic7—21no—
238C4⋊Dic7—42no—
239C4⋊Dic7—42no—
240C4⋊Dic7—42no—
241C4⋊Dic7—81no—
242C4⋊Dic7C2×D412yes—
243Dic7⋊C4—42no—
244Dic7⋊C4—42no—
245C2×C7⋊C8—21no—
246C2×C7⋊C8—21no—
247C2×C7⋊C8—21no—
248C2×C7⋊C8—21no—
249C2×C7⋊C8—21no—
250C2×C7⋊C8—21no—
251C2×C7⋊C8—21no—
252C2×C7⋊C8—21no—
253C2×C7⋊C8—21no—
254C2×C7⋊C8—21no—
255C2×C7⋊C8—21no—
256C2×C7⋊C8—44no—
257C2×C7⋊C8C2×D412yes—
258C23×D4C2×D711yescharacteristic
259C23×C8—71no—
260C2×C4⋊Q8—71no—
261C2×C22⋊Q8—141no—
262C2×C4×D4C2×D711yescharacteristic
263C2×C4×D4C2×D711yescharacteristic
264C22×C4⋊C4—71no—
265C22×C22⋊C4—21no—
266#474—144no—
267C2×#107—71no—
268C2×#107—71no—
269C2×#107—71no—
270C2×#107—71no—
271C2×C4⋊C8—71no—
272C2×C4⋊C8—71no—
273C2×#102—71no—
274C2×#102—71no—
275C2×#102—71no—
276C2×#102—71no—
277C2×#102—71no—
278C2×#102—71no—
279C2×#102—71no—
280C2×#102—71no—
281C2×#102—144no—
282C2×C22⋊C8—71no—
283#398—141no—
284#395—141no—
285#390C2×D711yescharacteristic
286#390C2×D711yescharacteristic
287#389—71no—
288#389—71no—
289#386—21no—
290#386—21no—
291#385—141no—
292#384—71no—
293#380—71no—
294#380C2×D711yescharacteristic
295#379—21no—
296C4×C22⋊C4C2×D711yescharacteristic
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301#336—71no—
302#336—71no—
303C23×C7—21no—
304C23×C7—21no—
305C23×C7—21no—
306C23×C7—21no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—48no—
312C23×C7—41no—
313C23×C7—41no—
314C23×C7—41no—
315C23×C7—41no—
316C23×C7—41no—
317C23×C7—41no—
318C23×C7—41no—
319C23×C7—41no—
320C23×C7—41no—
321C23×C7—41no—
322C23×C7—48no—
323C23×C7—84no—
324C23×C7—84no—
325C23×C7—84no—
326C23×C7—84no—
327C23×C7—84no—
328C23×C7C22⋊Q812yes—
329C23×C7C2×D812yes—
330C23×C7#13712yes—
331C23×C7C22×D411yescharacteristic
332C7×D4—22no—
333C7×D4—22no—
334C7×D4—22no—
335C7×D4—22no—
336C7×D4—22no—
337C7×D4—48no—
338C7×D4—41no—
339C7×D4—41no—
340C7×D4C22⋊Q814yescomplemented
341C2×C4×C7—21no—
342C2×C4×C7—21no—
343C2×C4×C7—21no—
344C2×C4×C7—21no—
345C2×C4×C7—21no—
346C2×C4×C7—21no—
347C2×C4×C7—22no—
348C2×C4×C7—22no—
349C2×C4×C7—22no—
350C2×C4×C7—22no—
351C2×C4×C7—21no—
352C2×C4×C7—21no—
353C2×C4×C7—21no—
354C2×C4×C7—21no—
355C2×C4×C7—21no—
356C2×C4×C7—21no—
357C2×C4×C7—41no—
358C2×C4×C7—41no—
359C2×C4×C7—41no—
360C2×C4×C7—41no—
361C2×C4×C7—41no—
362C2×C4×C7—41no—
363C2×C4×C7—84no—
364C2×C4×C7—84no—
365C2×C4×C7C22⋊Q812yes—
366C2×C4×C7C2×D812yes—
367C2×C4×C7C2×D812yes—
368C2×C4×C7C22×D411yescharacteristic
369C2×C4×C7C22×Q811yescharacteristic
370C2×C4×C7C2×#4111yescharacteristic
371C2×C4×C7C2×#4111yescharacteristic
372C2×C4×C7H(5,𝔽2)11yescharacteristic
373C2×C4×C7H(5,𝔽2)11yescharacteristic
374C2×Dic7—22no—
375C2×Dic7—41no—
376C2×Dic7—41no—
377C2×Dic7—41no—
378C2×Dic7—41no—
379C2×Dic7—41no—
380C2×Dic7—41no—
381C2×Dic7—41no—
382C2×Dic7—41no—
383C2×Dic7—41no—
384C2×Dic7—41no—
385C2×Dic7—41no—
386C2×Dic7—84no—
387Dic14—84no—
388C7⋊C8—22no—
389C7⋊C8—41no—
390C7⋊C8—41no—
391C7⋊C8—41no—
392C25—21no—
393C22×Q8—141no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—21no—
398C22×D4—41no—
399C22×D4—41no—
400C22×D4Dic1414yescomplemented
401C22×D4C22×D711yescharacteristic
402C22×D4C22×D711yescharacteristic
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—141no—
406C23×C4C22×D711yescharacteristic
407C22×C8—71no—
408C22×C8—71no—
409C22×C8—71no—
410C22×C8—71no—
411C22×C8—142no—
412C22×C8—142no—
413C22×C8—281no—
414C4⋊Q8—142no—
415C4⋊Q8—281no—
416C22⋊Q8—284no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—41no—
420C4×D4—41no—
421C2×C4⋊C4—71no—
422C2×C4⋊C4—71no—
423C2×C4⋊C4—71no—
424C2×C4⋊C4—71no—
425C2×C4⋊C4—142no—
426C2×C4⋊C4—141no—
427C2×C4⋊C4—141no—
428C2×C4⋊C4—141no—
429C2×C4⋊C4—141no—
430C2×C4⋊C4—141no—
431C2×C4⋊C4—141no—
432C2×C4⋊C4—281no—
433C2×C4⋊C4C22×D711yescharacteristic
434C2×C4⋊C4C22×D711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—141no—
444C2×C22⋊C4C22⋊D711yescharacteristic
445C2×C22⋊C4C22⋊D711yescharacteristic
446C2×C42C22×D711yescharacteristic
447C2×C42C22×D711yescharacteristic
448#107—142no—
449#107—142no—
450#107—281no—
451#107—281no—
452C4⋊C8—142no—
453C4⋊C8—281no—
454#102—74no—
455#102—142no—
456#102—142no—
457#102—142no—
458#102—142no—
459#102—142no—
460#102—281no—
461#102—281no—
462C22⋊C8—142no—
463#95—21no—
464#95—141no—
465#95—141no—
466#95—141no—
467#95C22⋊D711yescharacteristic
468#95C22⋊D711yescharacteristic
469C22×C7—22no—
470C22×C7—22no—
471C22×C7—22no—
472C22×C7—22no—
473C22×C7—22no—
474C22×C7—22no—
475C22×C7—24no—
476C22×C7—42no—
477C22×C7—42no—
478C22×C7—42no—
479C22×C7—42no—
480C22×C7—42no—
481C22×C7—42no—
482C22×C7—42no—
483C22×C7—42no—
484C22×C7—42no—
485C22×C7—816no—
486C22×C7—81no—
487C22×C7—81no—
488C22×C7—81no—
489C22×C7—81no—
490C22×C7#47414yescomplemented
491C22×C7C2×C22⋊Q811yescharacteristic
492C22×C7D4211yescharacteristic
493C22×C7#54611yescharacteristic
494C22×C7C22×D811yescharacteristic
495C22×C7C2×#13711yescharacteristic
496C22×C7#57611yescharacteristic
497C22×C7#57711yescharacteristic
498C4×C7—22no—
499C4×C7—22no—
500C4×C7—22no—
501C4×C7—41no—
502C4×C7—41no—
503C4×C7—81no—
504C4×C7—81no—
505C4×C7C2×C22⋊Q811yescharacteristic
506C4×C7#54311yescharacteristic
507C4×C7#54611yescharacteristic
508C4×C7#55111yescharacteristic
509Dic7—42no—
510Dic7—81no—
511Dic7—81no—
512Dic7—81no—
513C24—21no—
514C24—21no—
515C24—24no—
516C24—42no—
517C24—42no—
518C24—42no—
519C24—42no—
520C24—81no—
521C24—81no—
522C24C2×C22⋊D711yescharacteristic
523C2×Q8—282no—
524C2×Q8—282no—
525C2×Q8—561no—
526C2×D4—28no—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4C2×Dic1412yes—
542C2×D4C2×Dic1412yes—
543C2×D4D4×D712yes—
544C2×D4#115912yes—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—282no—
562C22×C4—282no—
563C22×C4—561no—
564C22×C4C2×Dic1412yes—
565C22×C4#115712yes—
566C22×C4C2×C22⋊D711yescharacteristic
567C22×C4C2×C22⋊D711yescharacteristic
568C22×C4C2×C22⋊D711yescharacteristic
569C22×C4C2×C22⋊D711yescharacteristic
570C22×C4C2×C22⋊D711yescharacteristic
571C22×C4C23×D711yescharacteristic
572C2×C8—72no—
573C2×C8—141no—
574C2×C8—141no—
575C2×C8—141no—
576C2×C8—141no—
577C2×C8—141no—
578C2×C8—141no—
579C2×C8—141no—
580C2×C8—141no—
581C2×C8—141no—
582C2×C8—141no—
583C2×C8—141no—
584C2×C8—284no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—72no—
590C4⋊C4—141no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—141no—
594C4⋊C4—141no—
595C4⋊C4—141no—
596C4⋊C4—141no—
597C4⋊C4—282no—
598C4⋊C4—282no—
599C4⋊C4—282no—
600C4⋊C4—282no—
601C4⋊C4—282no—
602C4⋊C4—561no—
603C22⋊C4—22no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—282no—
612C22⋊C4#114114yes—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C2×C7—24no—
618C2×C7—44no—
619C2×C7—82no—
620C2×C7#243711yescharacteristic
621C2×C7C2×#47411yescharacteristic
622C2×C7#308111yescharacteristic
623C2×C7#326611yescharacteristic
624C2×C7D4×D811yescharacteristic
625C2×C7#329411yescharacteristic
626C2×C7#331411yescharacteristic
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—48no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—48no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23#648712yes—
653C23C2×#114112yes—
654C23#651412yes—
655C23C22×C22⋊D711yescharacteristic
656Q8—564no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—48no—
663D4—41no—
664D4—41no—
665D4#644114yescomplemented
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—142no—
691C2×C4—281no—
692C2×C4—281no—
693C2×C4—281no—
694C2×C4—281no—
695C2×C4—281no—
696C2×C4—281no—
697C2×C4—281no—
698C2×C4—281no—
699C2×C4—281no—
700C2×C4—281no—
701C2×C4—281no—
702C2×C4—564no—
703C2×C4#648712yes—
704C2×C4C2×#114112yes—
705C2×C4C2×#114112yes—
706C2×C4C22×Dic1411yescharacteristic
707C2×C4C2×#115711yescharacteristic
708C2×C4C2×D4×D711yescharacteristic
709C2×C4C2×#115911yescharacteristic
710C2×C4#654811yescharacteristic
711C2×C4#654811yescharacteristic
712C8—142no—
713C8—281no—
714C8—281no—
715C8—281no—
716C7#2595011yescharacteristic, complemented, Sylow
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#8977914yescomplemented
739C22C2×#648711yescharacteristic
740C22C22×#114111yescharacteristic
741C22D4×C22⋊D711yescharacteristic
742C22#9049711yescharacteristic
743C22C2×#651411yescharacteristic
744C22#9052611yescharacteristic
745C22#9052711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—282no—
754C4—561no—
755C4—561no—
756C4—561no—
757C4C2×#644111yescharacteristic
758C4#9017411yescharacteristic
759C4#9018111yescharacteristic
760C4#9018611yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1173955511yescharacteristic
765C2C2×#8977911yescharacteristic
766C2#1173998411yescharacteristic
767C2#1174092711yescharacteristic
768C2D4×#114111yescharacteristic
769C2#1174094311yescharacteristic
770C2#1174095111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC22×C4×C7C24
FrattiniC22×C4C23×D7
FittingC7×D4×C22⋊C4C2
socleC23×C7C22×D4
prime radicalC23×C7×D4C22
hypercenterD4×C22⋊C4D7
hypocenterC7#25950
LCSG ▷ C22×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#89779C2semidirect
4. #11730938C2semidirect
6. #11729360C2semidirect
7. #11729360C2semidirect
8. #11729358C2semidirect
9. #11727409C2semidirect
10. #11727407C2semidirect
11. #11727407C2semidirect
12. #11727392C2semidirect
13. #11727266C2semidirect
14. #11727258C2semidirect
15. #11727203C2semidirect
23. C2×#6432C22semidirect
43. C2×#6381C22semidirect
44. C2×#6381C22semidirect
45. C2×#6381C22semidirect
46. C2×#6381C22semidirect
48. #89707C22semidirect
49. #89700C22semidirect
50. #89700C22semidirect
51. C2×C4⋊(C7⋊C8)C22semidirect
52. C2×C4⋊(C7⋊C8)C22semidirect
55. #89324C22semidirect
56. #89324C22semidirect
57. #89324C22semidirect
58. #89324C22semidirect
59. #89319C22semidirect
60. #89319C22semidirect
69. C22×C7×D4Q8semidirect
340. C7×D4C22⋊Q8semidirect
400. C22×D4Dic14semidirect
490. C22×C7#474semidirect
665. D4#6441semidirect
716. C7#25950semidirect
738. C22#89779semidirect

Maximal subgroups

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

subgroupindex
C7×D4×C22⋊C42
C22×#64062
C2×#897792
#117309382
#117298822
#117293602
#117293582
#117274092
#117274072
#117273922
#117272662
#117272582
#117272032
#259507