Finite Group Databasebeta

← #13353611

Subgroups — #13353611

Order 1792.

1374 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90214C211yesmaximal, characteristic
2C2×#89499C211yesmaximal, characteristic
3#11731448C211yesmaximal, characteristic
4C7×#1825C211yesmaximal, characteristic, complemented
5#11729329C211yesmaximal, characteristic, complemented
6#11727679C211yesmaximal, characteristic, complemented
7#11727255C211yesmaximal, characteristic, complemented
8#11726627C211yesmaximal, characteristic, complemented
9#11726626C211yesmaximal, characteristic, complemented
10#11726625C211yesmaximal, characteristic, complemented
11#11726621C211yesmaximal, characteristic, complemented
12#11726621C211yesmaximal, characteristic, complemented
13#11726620C211yesmaximal, characteristic, complemented
14D7×#340C211yesmaximal, characteristic, complemented
15#11726567C211yesmaximal, characteristic, complemented
16C22×#1157C2211yescharacteristic
17C2×C7×#117C2211yescharacteristic
18C22×C4⋊Dic7C2211yescharacteristic
19C22×#1131C2211yescharacteristic
20C22×C8×D7C2211yescharacteristic
21#90214—24no—
22#90214C418yescomplemented
23C2×#6455C2211yescharacteristic
24C2×#6455C2211yescharacteristic
25C2×#6455C2211yescharacteristic
26C2×D7×C4⋊C4C2211yescharacteristic
27C2×D7×C4⋊C4C2211yescharacteristic
28C2×D7×C4⋊C4C2211yescharacteristic
29C2×(C22⋊D7)⋊C4—21no—
30C2×(C22⋊D7)⋊C4—21no—
31C2×C4×D28—21no—
32C2×C4×Dic14—21no—
33C2×C7×C22⋊C8C2211yescharacteristic
34C7×#380C2211yescharacteristic
35#89984C2211yescharacteristic
36C2×C22⋊(C7⋊C8)C2211yescharacteristic
37C2×(C2×D7)⋊C8C2211yescharacteristic
38C2×(C2×D7)⋊C8C2211yescharacteristic
39#89759C2211yescharacteristic
40#89759C2211yescharacteristic
41#89729—21no—
42#89728—21no—
43#89499—24no—
44#89437—21no—
45#89418—21no—
46C7×#340C2211yescharacteristic
47C7×#340C2211yescharacteristic
48C7×#340C2211yescharacteristic
49C7×#340C2211yescharacteristic
50#89346C2211yescharacteristic
51#89346C2211yescharacteristic
52#89346C2211yescharacteristic
53#89346C2211yescharacteristic
54#89324C2211yescharacteristic
55#89324C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#20703—71nomaximal, Sylow
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7D411yescharacteristic
65C22×C22⋊D7D411yescharacteristic
66C23×Dic7—21no—
67C2×#1157—22no—
68C2×#1157—22no—
69C2×#1157—22no—
70C2×#1157—22no—
71C2×#1157C2×C414yes—
72C2×#1157D414yes—
73C22×D28D411yescharacteristic
74C22×C4×D7—21no—
75C22×C4×D7—21no—
76C22×C4×D7—21no—
77C22×C4×D7C2311yescharacteristic
78C22×C4×D7C2311yescharacteristic
79C22×Dic14D411yescharacteristic
80C22×C7×C8C2311yescharacteristic
81C22×C7×C8C2311yescharacteristic
82C7×#117—22no—
83C7×#117C2×C414yescomplemented
84C2×C7×C4⋊C4C2311yescharacteristic
85C2×C7×C4⋊C4C2311yescharacteristic
86C2×C7×C4⋊C4C2311yescharacteristic
87C2×C7×C4⋊C4C2311yescharacteristic
88C2×C7×C22⋊C4—21no—
89C2×C7×C22⋊C4—21no—
90C2×C42×C7—21no—
91C2×C22⋊Dic7—21no—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×(C2×D7)⋊C4—21no—
96C2×(C2×D7)⋊C4—21no—
97C2×C4⋊Dic7—21no—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7C2×C414yescomplemented
100C2×C4⋊Dic7C2311yescharacteristic
101C2×C4⋊Dic7C2311yescharacteristic
102C2×C4⋊Dic7C2311yescharacteristic
103C2×C4⋊Dic7C2311yescharacteristic
104C2×Dic7⋊C4—21no—
105C2×Dic7⋊C4—21no—
106C2×Dic7⋊C4—21no—
107C2×C4×Dic7—21no—
108C2×C4×Dic7—21no—
109C2×C4×Dic7—21no—
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C2×#1131—22no—
113C2×#1131—22no—
114C2×#1131—22no—
115C2×C8×D7—22no—
116C2×C8×D7—22no—
117C2×C8×D7—22no—
118#6455—22no—
119#6455—22no—
120#6455—22no—
121#6455—22no—
122#6455C2×C414yes—
123#6455C2×C414yescomplemented
124D7×C4⋊C4—22no—
125D7×C4⋊C4—22no—
126D7×C4⋊C4—22no—
127D7×C4⋊C4—22no—
128D7×C4⋊C4C2×C414yes—
129D7×C4⋊C4C2×C414yescomplemented
130(C22⋊D7)⋊C4—28no—
131(C22⋊D7)⋊C4—28no—
132C4×D28—28no—
133C4×Dic14—28no—
134C7×C22⋊C8—22no—
135C7×#95—21no—
136C7⋊#95—21no—
137C7⋊#95—21no—
138C7⋊#95—21no—
139C22⋊(C7⋊C8)—22no—
140(C2×D7)⋊C8—22no—
141(C2×D7)⋊C8—22no—
142C2×#520—71no—
143C2×#408—71no—
144#2311—71no—
145#1825—71no—
146#1825—71no—
147#1825—71no—
148#1825D711yescharacteristic, complemented
149#1824—71no—
150#1824—71no—
151#1823—71no—
152#1823—71no—
153#1736—71no—
154#1736—71no—
155#1735—71no—
156C2×#340—71no—
157C24×C7C2×D411yescharacteristic
158C23×D7C2×D411yescharacteristic
159C23×D7C2×D411yescharacteristic
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7C22×C412yes—
169C22×C4×C7C2×D411yescharacteristic
170C22×C4×C7C2×D412yes—
171C22×C4×C7C2411yescharacteristic
172C2×C22⋊D7—22no—
173C2×C22⋊D7—22no—
174C2×C22⋊D7—22no—
175C2×C22⋊D7—22no—
176C2×C22⋊D7C22⋊C414yes—
177C2×C22⋊D7C22⋊C414yes—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C22×Dic7—24no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C22×Dic7—81no—
184C22×Dic7—81no—
185C22×Dic7C2×D411yescharacteristic
186C22×Dic7C2×D411yescharacteristic
187#1157—28no—
188#1157—28no—
189#1157—28no—
190#1157—28no—
191C2×D28—22no—
192C2×D28—22no—
193C2×D28C22⋊C414yes—
194C2×C4×D7—21no—
195C2×C4×D7—21no—
196C2×C4×D7—21no—
197C2×C4×D7—21no—
198C2×C4×D7—24no—
199C2×C4×D7—24no—
200C2×C4×D7—42no—
201C2×C4×D7—81no—
202C2×C4×D7—81no—
203C2×C4×D7—81no—
204C2×C4×D7—81no—
205C2×C4×D7—81no—
206C2×C4×D7—81no—
207C2×C4×D7C22×C412yes—
208C2×C4×D7C22×C412yes—
209C2×C4×D7C2×D412yes—
210C2×C4×D7C2×D412yes—
211C2×C4×D7#4112yes—
212C2×C4×D7#4112yes—
213C2×C4×D7#4112yes—
214C2×C4×D7#4112yes—
215C2×Dic14—22no—
216C2×Dic14—22no—
217C2×Dic14C22⋊C414yes—
218C2×C7×C8—21no—
219C2×C7×C8—21no—
220C2×C7×C8—21no—
221C2×C7×C8—21no—
222C2×C7×C8—21no—
223C2×C7×C8—21no—
224C7×C4⋊C4—21no—
225C7×C4⋊C4—21no—
226C7×C4⋊C4—21no—
227C7×C4⋊C4—21no—
228C7×C4⋊C4—21no—
229C7×C4⋊C4—21no—
230C7×C4⋊C4C22×C412yes—
231C7×C4⋊C4C22×C412yes—
232C7×C22⋊C4—24no—
233C7×C22⋊C4—81no—
234C42×C7—24no—
235C22⋊Dic7—81no—
236(C2×D7)⋊C4—24no—
237(C2×D7)⋊C4—24no—
238(C2×D7)⋊C4—42no—
239(C2×D7)⋊C4—81no—
240(C2×D7)⋊C4—81no—
241C4⋊Dic7—24no—
242C4⋊Dic7—21no—
243C4⋊Dic7—21no—
244C4⋊Dic7—21no—
245C4⋊Dic7—21no—
246C4⋊Dic7—21no—
247C4⋊Dic7—21no—
248C4⋊Dic7C22×C412yes—
249C4⋊Dic7C22×C412yes—
250Dic7⋊C4—24no—
251Dic7⋊C4—24no—
252Dic7⋊C4—42no—
253C4×Dic7—24no—
254C4×Dic7—24no—
255C4×Dic7—42no—
256C2×C7⋊C8—21no—
257C2×C7⋊C8—21no—
258C2×C7⋊C8—21no—
259C2×C7⋊C8—21no—
260C2×C7⋊C8—21no—
261C2×C7⋊C8—21no—
262#1131—44no—
263C8×D7—44no—
264C22×#41—71no—
265C22×M16—71no—
266C23×C8—71no—
267#520—78no—
268#520—144no—
269C2×C4×Q8—141no—
270C2×C4×D4—141no—
271C2×C4×D4—141no—
272C2×C4×D4—141no—
273C2×#117—71no—
274C2×#117—71no—
275C2×#117—71no—
276C2×#117C2×D711yescharacteristic
277C22×C4⋊C4—71no—
278C22×C4⋊C4—71no—
279C22×C4⋊C4—71no—
280C22×C4⋊C4—71no—
281#408—144no—
282C2×C22⋊C8—71no—
283C2×C22⋊C8—71no—
284C2×C22⋊C8—71no—
285C2×C22⋊C8C2×D711yescharacteristic
286#391—141no—
287#390—141no—
288#386—141no—
289#386—141no—
290#380—71no—
291#380—71no—
292#380—71no—
293#380C2×D711yescharacteristic
294#340—71no—
295#340—71no—
296#340—71no—
297#340—71no—
298#340—71no—
299#340—71no—
300#340—71no—
301#340—71no—
302#340—71no—
303#340—71no—
304#340—71no—
305#340—71no—
306#340C2×D711yescharacteristic
307#340C2×D711yescharacteristic
308#340C2×D711yescharacteristic
309#340C2×D711yescharacteristic
310C23×C7—21no—
311C23×C7—21no—
312C23×C7—21no—
313C23×C7—21no—
314C23×C7—21no—
315C23×C7—21no—
316C23×C7C2×C22⋊C412yes—
317C23×C7C22×D411yescharacteristic
318C22×D7—21no—
319C22×D7—21no—
320C22×D7—21no—
321C22×D7—21no—
322C22×D7—21no—
323C22×D7—21no—
324C22×D7—21no—
325C22×D7—21no—
326C22×D7—21no—
327C22×D7—21no—
328C22×D7C2×C22⋊C412yes—
329C22×D7C2×C22⋊C412yes—
330C22×D7#12312yes—
331C22×D7#12312yes—
332C2×C4×C7—21no—
333C2×C4×C7—21no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—41no—
341C2×C4×C7—41no—
342C2×C4×C7—41no—
343C2×C4×C7—41no—
344C2×C4×C7—41no—
345C2×C4×C7—41no—
346C2×C4×C7—41no—
347C2×C4×C7—41no—
348C2×C4×C7—41no—
349C2×C4×C7—41no—
350C2×C4×C7C2×C22⋊C412yes—
351C2×C4×C7C23×C411yescharacteristic
352C2×C4×C7C22×D411yescharacteristic
353C2×C4×C7C2×#4111yescharacteristic
354C2×C4×C7C2×#4111yescharacteristic
355C2×C4×C7C2×#4111yescharacteristic
356C2×C4×C7C2×#4111yescharacteristic
357C22⋊D7—28no—
358C22⋊D7—28no—
359C2×Dic7—21no—
360C2×Dic7—21no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—41no—
364C2×Dic7—41no—
365C2×Dic7—41no—
366C2×Dic7—41no—
367C2×Dic7—41no—
368C2×Dic7—41no—
369C2×Dic7—41no—
370C2×Dic7—41no—
371C2×Dic7—41no—
372C2×Dic7—41no—
373C2×Dic7—84no—
374C2×Dic7C2×C22⋊C412yes—
375C2×Dic7C2×C22⋊C412yes—
376C2×Dic7#12312yes—
377C2×Dic7#12312yes—
378D28—28no—
379C4×D7—22no—
380C4×D7—22no—
381C4×D7—22no—
382C4×D7—22no—
383C4×D7—84no—
384C4×D7—84no—
385C4×D7—84no—
386C4×D7#11714yes—
387C4×D7#11714yes—
388C4×D7#12314yes—
389C4×D7#12314yes—
390Dic14—28no—
391C7×C8—41no—
392C7×C8—41no—
393C7⋊C8—41no—
394C7⋊C8—41no—
395C2×#41—74no—
396C2×#41—74no—
397C2×#41—142no—
398C2×#41—142no—
399C2×#41—142no—
400C2×#41—142no—
401C22×Q8—71no—
402C22×D4—71no—
403C22×D4—71no—
404C22×D4—71no—
405C23×C4—71no—
406C23×C4—71no—
407C23×C4—141no—
408C23×C4—141no—
409C23×C4—141no—
410C23×C4—141no—
411C23×C4C22×D711yescharacteristic
412C2×M16—142no—
413C2×M16—142no—
414C2×M16—142no—
415C22×C8—71no—
416C22×C8—71no—
417C22×C8—142no—
418C22×C8—142no—
419C22×C8—142no—
420C22×C8C22×D711yescharacteristic
421C22×C8C22×D711yescharacteristic
422C4×Q8—148no—
423C4×D4—148no—
424C4×D4—148no—
425C4×D4—148no—
426#117—22no—
427#117—74no—
428#117—74no—
429#117—142no—
430#117—142no—
431#117—142no—
432#117—142no—
433#117C4×D714yescomplemented
434C2×C4⋊C4—74no—
435C2×C4⋊C4—71no—
436C2×C4⋊C4—71no—
437C2×C4⋊C4—74no—
438C2×C4⋊C4—74no—
439C2×C4⋊C4—71no—
440C2×C4⋊C4—71no—
441C2×C4⋊C4—142no—
442C2×C4⋊C4—142no—
443C2×C4⋊C4—142no—
444C2×C4⋊C4—142no—
445C2×C4⋊C4—141no—
446C2×C4⋊C4—141no—
447C2×C4⋊C4—141no—
448C2×C4⋊C4—142no—
449C2×C4⋊C4—141no—
450C2×C4⋊C4C22×D711yescharacteristic
451C2×C4⋊C4C22×D711yescharacteristic
452C2×C4⋊C4C22×D711yescharacteristic
453C2×C4⋊C4C22×D711yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—141no—
457C2×C22⋊C4—141no—
458C2×C22⋊C4—141no—
459C2×C22⋊C4—141no—
460C2×C22⋊C4—141no—
461C2×C22⋊C4—141no—
462C2×C42—21no—
463C2×C42—141no—
464C2×C42—141no—
465C2×C42—141no—
466C22⋊C8—22no—
467C22⋊C8—142no—
468C22⋊C8—142no—
469C22⋊C8—142no—
470#95—21no—
471#95—141no—
472#95—141no—
473#95—141no—
474C22×C7—22no—
475C22×C7—22no—
476C22×C7—22no—
477C22×C7—41no—
478C22×C7—41no—
479C22×C7—41no—
480C22×C7—41no—
481C22×C7C22×C22⋊C411yescharacteristic
482C22×C7C2×#12311yescharacteristic
483C22×C7C2×#12311yescharacteristic
484C22×C7#57611yescharacteristic
485C22×C7#57711yescharacteristic
486C22×C7#57711yescharacteristic
487C22×C7#57811yescharacteristic
488C2×D7—22no—
489C2×D7—22no—
490C2×D7—22no—
491C2×D7—22no—
492C2×D7—22no—
493C2×D7—22no—
494C2×D7—22no—
495C2×D7—22no—
496C2×D7—22no—
497C2×D7—41no—
498C2×D7—41no—
499C2×D7—41no—
500C2×D7—41no—
501C2×D7#38114yes—
502C4×C7—22no—
503C4×C7—42no—
504C4×C7—42no—
505C4×C7—81no—
506C4×C7—81no—
507C4×C7C2×#11711yescharacteristic
508C4×C7C2×#11711yescharacteristic
509C4×C7C2×#12311yescharacteristic
510C4×C7C2×#12311yescharacteristic
511Dic7—22no—
512Dic7—42no—
513Dic7—42no—
514Dic7—81no—
515Dic7—81no—
516Dic7#38114yes—
517C24—71no—
518C24—71no—
519C24D4×D711yescharacteristic
520#41—148no—
521#41—148no—
522#41—148no—
523#41—148no—
524C2×Q8—74no—
525C2×Q8—142no—
526C2×Q8—142no—
527C2×D4—74no—
528C2×D4—74no—
529C2×D4—74no—
530C2×D4—142no—
531C2×D4—142no—
532C2×D4—142no—
533C2×D4—142no—
534C2×D4—142no—
535C2×D4—142no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—71no—
545C22×C4—72no—
546C22×C4—72no—
547C22×C4—72no—
548C22×C4—72no—
549C22×C4—72no—
550C22×C4—72no—
551C22×C4—71no—
552C22×C4—72no—
553C22×C4—72no—
554C22×C4—144no—
555C22×C4—144no—
556C22×C4—141no—
557C22×C4—141no—
558C22×C4—141no—
559C22×C4—141no—
560C22×C4—141no—
561C22×C4—141no—
562C22×C4—144no—
563C22×C4—141no—
564C22×C4—141no—
565C22×C4—282no—
566C22×C4—561no—
567C22×C4—561no—
568C22×C4—561no—
569C22×C4—561no—
570C22×C4—561no—
571C22×C4—561no—
572C22×C4—561no—
573C22×C4—561no—
574C22×C4C2×C4×D712yes—
575C22×C4D4×D711yescharacteristic
576C22×C4D4×D712yes—
577C22×C4C23×D711yescharacteristic
578M16—284no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—141no—
586C2×C8—141no—
587C2×C8—141no—
588C2×C8—141no—
589C2×C8—141no—
590C2×C8—141no—
591C2×C8—284no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—72no—
599C4⋊C4—72no—
600C4⋊C4—144no—
601C4⋊C4—144no—
602C4⋊C4—144no—
603C4⋊C4—141no—
604C4⋊C4—141no—
605C4⋊C4—141no—
606C4⋊C4—141no—
607C4⋊C4—141no—
608C4⋊C4—141no—
609C4⋊C4—282no—
610C4⋊C4C2×C4×D712yes—
611C4⋊C4C2×C4×D712yes—
612C22⋊C4—24no—
613C22⋊C4—81no—
614C22⋊C4—144no—
615C22⋊C4—144no—
616C22⋊C4—282no—
617C22⋊C4—561no—
618C22⋊C4—561no—
619C22⋊C4—561no—
620C42—24no—
621C42—144no—
622C42—144no—
623C42—282no—
624C2×C7—42no—
625C2×C7C2×#38111yescharacteristic
626C2×C7#289711yescharacteristic
627C2×C7#289811yescharacteristic
628C2×C7#309611yescharacteristic
629C2×C7#309711yescharacteristic
630C2×C7#309811yescharacteristic
631C2×C7#309911yescharacteristic
632D7—24no—
633D7—42no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—72no—
641C23—72no—
642C23—72no—
643C23—72no—
644C23—141no—
645C23—141no—
646C23—141no—
647C23—141no—
648C23—141no—
649C23—141no—
650C23—141no—
651C23—141no—
652C23—141no—
653C23—141no—
654C23D7×C22⋊C412yes—
655C23C2×D4×D711yescharacteristic
656Q8—148no—
657D4—148no—
658D4—148no—
659D4—148no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—72no—
679C2×C4—72no—
680C2×C4—72no—
681C2×C4—74no—
682C2×C4—74no—
683C2×C4—74no—
684C2×C4—74no—
685C2×C4—72no—
686C2×C4—141no—
687C2×C4—141no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
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—281no—
703C2×C4—281no—
704C2×C4—564no—
705C2×C4—564no—
706C2×C4—564no—
707C2×C4—564no—
708C2×C4D7×C22⋊C412yes—
709C2×C4C22×C4×D711yescharacteristic
710C2×C4C2×D4×D711yescharacteristic
711C2×C4D7×#4111yescharacteristic
712C2×C4D7×#4111yescharacteristic
713C2×C4D7×#4111yescharacteristic
714C2×C4D7×#4111yescharacteristic
715C8—41no—
716C8—41no—
717C8—281no—
718C8—281no—
719C7#2070311yescharacteristic, complemented, Sylow
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—74no—
728C22—142no—
729C22—142no—
730C22—142no—
731C22—142no—
732C22—142no—
733C22—142no—
734C22—142no—
735C22—142no—
736C22—142no—
737C22—281no—
738C22—281no—
739C22—281no—
740C22—281no—
741C22C2×D7×C22⋊C411yescharacteristic
742C22D7×#12311yescharacteristic
743C22D7×#12311yescharacteristic
744C22#9046111yescharacteristic
745C22#9046211yescharacteristic
746C22#9046511yescharacteristic
747C22#9046911yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—74no—
752C4—81no—
753C4—81no—
754C4—142no—
755C4—282no—
756C4—282no—
757C4—561no—
758C4—561no—
759C4D7×#11711yescharacteristic
760C4D7×#11711yescharacteristic
761C4D7×#12311yescharacteristic
762C4D7×#12311yescharacteristic
763C2—42no—
764C2—144no—
765C2—282no—
766C2D7×#38111yescharacteristic
767C2#1173627711yescharacteristic
768C2#1173632711yescharacteristic
769C2#1173882011yescharacteristic
770C2#1173882111yescharacteristic
771C2#1173896411yescharacteristic
772C2#1173896611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#1825C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
cosocleC22×C4×C7C24
hypercenter#1825D7
hypocenterC7#20703
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. C7×#1825C2semidirect
5. #11729329C2semidirect
6. #11727679C2semidirect
7. #11727255C2semidirect
8. #11726627C2semidirect
9. #11726626C2semidirect
10. #11726625C2semidirect
11. #11726621C2semidirect
12. #11726621C2semidirect
13. #11726620C2semidirect
14. D7×#340C2semidirect
15. #11726567C2semidirect
22. #90214C4semidirect
83. C7×#117C2×C4semidirect
99. C2×C4⋊Dic7C2×C4semidirect
123. #6455C2×C4semidirect
129. D7×C4⋊C4C2×C4semidirect
148. #1825D7semidirect
433. #117C4×D7semidirect
719. C7#20703semidirect

Maximal subgroups

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

subgroupindex
C2×#902142
C2×#894992
#117314482
C7×#18252
#117293292
#117276792
#117272552
#117266272
#117266262
#117266252
#117266212
#117266202
D7×#3402
#117265672
#207037