Finite Group Databasebeta

← #13285406

Subgroups — #13285406

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#385C211yesmaximal, characteristic
2C2×#89982C211yesmaximal, characteristic
3C22×C7⋊#95C211yesmaximal, characteristic
4C2×#89756C211yesmaximal, characteristic, complemented
5C2×#89722C211yesmaximal, characteristic
6C2×#89714C211yesmaximal, characteristic
7#11729322C211yesmaximal, characteristic, complemented
8#11729321C211yesmaximal, characteristic, complemented
9#11729319C211yesmaximal, characteristic, complemented
10#11729298C211yesmaximal, characteristic
11#11729298C211yesmaximal, characteristic
12#11727175C211yesmaximal, characteristic, complemented
13#11727168C211yesmaximal, characteristic, complemented
14#11727165C211yesmaximal, characteristic, complemented
15#11727164C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C24×Dic7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C22⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C7×#385—24no—
32C2×C7×#95C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34#89982—24no—
35C2×C7⋊#95—24no—
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54#89756—24no—
55#89722—24no—
56#89714—24no—
57#14736—71nomaximal, Sylow
58C25×C7C2311yescharacteristic
59C23×C4×C7—22no—
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×Dic7—22no—
73C23×Dic7—22no—
74C23×Dic7—22no—
75C23×Dic7—22no—
76C23×Dic7—22no—
77C23×Dic7—22no—
78C23×Dic7—22no—
79C23×Dic7—22no—
80C23×Dic7—22no—
81C23×Dic7—41no—
82C23×Dic7—41no—
83C23×Dic7—41no—
84C23×Dic7—41no—
85C23×Dic7Q814yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—22no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C22⋊C4—22no—
101C2×C7×C22⋊C4—22no—
102C2×C7×C22⋊C4—22no—
103C2×C7×C22⋊C4—22no—
104C2×C7×C22⋊C4D414yes—
105C2×C7×C22⋊C4Q814yes—
106C2×C22⋊Dic7—22no—
107C2×C22⋊Dic7—22no—
108C2×C22⋊Dic7—22no—
109C2×C22⋊Dic7—22no—
110C2×C22⋊Dic7—22no—
111C2×C22⋊Dic7D414yes—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—22no—
115C2×C4⋊Dic7—22no—
116C2×C4⋊Dic7—41no—
117C2×C4⋊Dic7—41no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—22no—
124C2×Dic7⋊C4—22no—
125C2×Dic7⋊C4—22no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4—41no—
129C2×Dic7⋊C4—41no—
130C7×#95—22no—
131C7×#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—41no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95—41no—
149C7⋊#95D414yes—
150C2×#398—71no—
151C2×#385—71no—
152C2×#385—71no—
153C2×#385D711yescharacteristic
154C2×#380—71no—
155C22×#95—71no—
156#1445—71no—
157#1444—71no—
158#1442—71no—
159#1442—71no—
160#1441—71no—
161#1441—71no—
162#1441—71no—
163C22⋊#95—71no—
164C22⋊#95—71no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7C2×D412yes—
174C24×C7C2×D412yes—
175C24×C7C2×Q812yes—
176C24×C7C2×Q812yes—
177C24×C7#4112yes—
178C24×C7#4112yes—
179C24×C7#4112yes—
180C24×C7C2411yescharacteristic
181C22×C4×C7—28no—
182C22×C4×C7—21no—
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—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
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—44no—
219C22×C4×C7—44no—
220C22×C4×C7—44no—
221C22×C4×C7—44no—
222C22×C4×C7—44no—
223C22×C4×C7—44no—
224C22×C4×C7C2×D412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×Q812yes—
228C22×C4×C7C2×Q812yes—
229C22×C4×C7#4112yes—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—28no—
235C22×Dic7—28no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—28no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—21no—
277C22×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7—44no—
282C22×Dic7—44no—
283C22×Dic7—44no—
284C22×Dic7—44no—
285C22×Dic7—44no—
286C22×Dic7—44no—
287C22×Dic7—44no—
288C22×Dic7—44no—
289C22×Dic7—44no—
290C22×Dic7—44no—
291C22×Dic7—44no—
292C22×Dic7C2×D412yes—
293C22×Dic7C2×D412yes—
294C22×Dic7C2×D412yes—
295C22×Dic7C2×D412yes—
296C22×Dic7C2×Q812yes—
297C22×Dic7C2×Q812yes—
298C22×Dic7#4112yes—
299C22×Dic7#4112yes—
300C7×C4⋊C4—44no—
301C7×C4⋊C4—44no—
302C7×C22⋊C4—28no—
303C7×C22⋊C4—28no—
304C22⋊Dic7—28no—
305C22⋊Dic7—44no—
306C4⋊Dic7—44no—
307C4⋊Dic7—44no—
308Dic7⋊C4—44no—
309Dic7⋊C4—44no—
310Dic7⋊C4—44no—
311Dic7⋊C4—44no—
312C24×C4—71no—
313C24×C4—71no—
314C24×C4C2×D711yescharacteristic
315C22×C4⋊C4—71no—
316C22×C4⋊C4—71no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4C2×D711yescharacteristic
322C22×C4⋊C4C2×D711yescharacteristic
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4C2×D711yescharacteristic
326C22×C22⋊C4C2×D711yescharacteristic
327#398—144no—
328#385—24no—
329#385—144no—
330#385—144no—
331#380—144no—
332C2×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—71no—
340C2×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—144no—
351C2×#95C2×D711yescharacteristic
352C2×#95C2×D711yescharacteristic
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—22no—
380C23×C7—22no—
381C23×C7#12114yes—
382C23×C7C22⋊Q814yes—
383C23×C7C22⋊Q814yes—
384C23×C7#12314yes—
385C23×C7#12514yes—
386C23×C7#12514yes—
387C23×C7C4⋊Q814yes—
388C23×C7C22×D411yescharacteristic
389C23×C7C22×D411yescharacteristic
390C23×C7C22×D411yescharacteristic
391C23×C7C22×Q811yescharacteristic
392C23×C7C22×Q811yescharacteristic
393C23×C7C2×#4111yescharacteristic
394C23×C7C2×#4111yescharacteristic
395C23×C7C2×#4111yescharacteristic
396C23×C7C2×#4111yescharacteristic
397C23×C7C2×#4111yescharacteristic
398C23×C7C2×#4111yescharacteristic
399C23×C7H(5,𝔽2)11yescharacteristic
400C23×C7H(5,𝔽2)11yescharacteristic
401C23×C7H(5,𝔽2)11yescharacteristic
402C23×C72−1+411yescharacteristic
403C2×C4×C7—22no—
404C2×C4×C7—22no—
405C2×C4×C7—22no—
406C2×C4×C7—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—416no—
422C2×C4×C7—41no—
423C2×C4×C7—41no—
424C2×C4×C7—41no—
425C2×C4×C7—41no—
426C2×C4×C7—41no—
427C2×C4×C7—41no—
428C2×C4×C7—41no—
429C2×C4×C7—41no—
430C2×C4×C7—41no—
431C2×C4×C7—41no—
432C2×C4×C7—41no—
433C2×C4×C7—41no—
434C2×C4×C7—41no—
435C2×C4×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—22no—
452C2×Dic7—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
457C2×Dic7—22no—
458C2×Dic7—22no—
459C2×Dic7—22no—
460C2×Dic7—22no—
461C2×Dic7—22no—
462C2×Dic7—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
465C2×Dic7—22no—
466C2×Dic7—22no—
467C2×Dic7—416no—
468C2×Dic7—416no—
469C2×Dic7—41no—
470C2×Dic7—41no—
471C2×Dic7—41no—
472C2×Dic7—41no—
473C2×Dic7—41no—
474C2×Dic7—41no—
475C2×Dic7—41no—
476C2×Dic7—41no—
477C2×Dic7—41no—
478C2×Dic7—41no—
479C2×Dic7—41no—
480C2×Dic7—41no—
481C2×Dic7—41no—
482C2×Dic7—41no—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7—41no—
503C2×Dic7C22⋊Q814yes—
504C25C22×D711yescharacteristic
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—41no—
511C23×C4—41no—
512C23×C4—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—74no—
519C23×C4—71no—
520C23×C4—71no—
521C23×C4—142no—
522C23×C4—142no—
523C23×C4—142no—
524C23×C4—142no—
525C23×C4—142no—
526C23×C4—142no—
527C23×C4—142no—
528C23×C4—142no—
529C23×C4—142no—
530C23×C4—281no—
531C23×C4—281no—
532C23×C4—281no—
533C23×C4—281no—
534C23×C4C22×D711yescharacteristic
535C23×C4C22×D711yescharacteristic
536C23×C4C22×D711yescharacteristic
537C23×C4C22×D711yescharacteristic
538C23×C4C22×D711yescharacteristic
539C23×C4C22×D711yescharacteristic
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—142no—
547C2×C4⋊C4—142no—
548C2×C4⋊C4—142no—
549C2×C4⋊C4—142no—
550C2×C4⋊C4—142no—
551C2×C4⋊C4—142no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—281no—
559C2×C4⋊C4—281no—
560C2×C4⋊C4—281no—
561C2×C4⋊C4—281no—
562C2×C4⋊C4—281no—
563C2×C4⋊C4—281no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—74no—
569C2×C22⋊C4—142no—
570C2×C22⋊C4—142no—
571C2×C22⋊C4—142no—
572C2×C22⋊C4—142no—
573C2×C22⋊C4—142no—
574C2×C22⋊C4Dic1414yes—
575C2×C22⋊C4C22⋊D714yes—
576#95—22no—
577#95—22no—
578#95—74no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—142no—
587#95—142no—
588#95—142no—
589#95—142no—
590#95—142no—
591#95—142no—
592#95—281no—
593#95—281no—
594#95—281no—
595#95—281no—
596C22×C7—24no—
597C22×C7—24no—
598C22×C7—24no—
599C22×C7—24no—
600C22×C7—24no—
601C22×C7—24no—
602C22×C7—24no—
603C22×C7—24no—
604C22×C7—24no—
605C22×C7—24no—
606C22×C7—24no—
607C22×C7—24no—
608C22×C7—24no—
609C22×C7—24no—
610C22×C7#39818yescomplemented
611C22×C7C2×#12111yescharacteristic
612C22×C7C2×C22⋊Q811yescharacteristic
613C22×C7C2×C22⋊Q811yescharacteristic
614C22×C7C2×C22⋊Q811yescharacteristic
615C22×C7C2×#12311yescharacteristic
616C22×C7#52511yescharacteristic
617C22×C7#52511yescharacteristic
618C22×C7C2×#12511yescharacteristic
619C22×C7C2×#12511yescharacteristic
620C22×C7#52911yescharacteristic
621C22×C7#52911yescharacteristic
622C22×C7C2×C4⋊Q811yescharacteristic
623C22×C7#53311yescharacteristic
624C22×C7#53811yescharacteristic
625C22×C7#53811yescharacteristic
626C22×C7#53911yescharacteristic
627C22×C7#53911yescharacteristic
628C22×C7#54311yescharacteristic
629C22×C7#54411yescharacteristic
630C22×C7D4211yescharacteristic
631C22×C7D4211yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54611yescharacteristic
634C22×C7#54611yescharacteristic
635C22×C7#54611yescharacteristic
636C22×C7#54611yescharacteristic
637C22×C7#54711yescharacteristic
638C22×C7#54711yescharacteristic
639C22×C7D4×Q811yescharacteristic
640C22×C7#55111yescharacteristic
641C22×C7#55111yescharacteristic
642C22×C7#55211yescharacteristic
643C22×C7#55411yescharacteristic
644C22×C7#55411yescharacteristic
645C22×C7#55411yescharacteristic
646C4×C7—42no—
647C4×C7—42no—
648C4×C7—42no—
649C4×C7—42no—
650C4×C7—42no—
651C4×C7—42no—
652Dic7—24no—
653Dic7—42no—
654Dic7—42no—
655Dic7—42no—
656Dic7—42no—
657Dic7—42no—
658Dic7—81no—
659Dic7—81no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24C2×Dic1412yes—
669C24#115712yes—
670C24D4×D712yes—
671C24#115912yes—
672C24Q8×D712yes—
673C24#116112yes—
674C24C2×C22⋊D712yes—
675C24C23×D711yescharacteristic
676C22×C4—28no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—44no—
716C22×C4—44no—
717C22×C4—44no—
718C22×C4—44no—
719C22×C4—72no—
720C22×C4—72no—
721C22×C4—72no—
722C22×C4—72no—
723C22×C4—72no—
724C22×C4—72no—
725C22×C4—72no—
726C22×C4—72no—
727C22×C4—148no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—148no—
733C22×C4—148no—
734C22×C4—141no—
735C22×C4—141no—
736C22×C4—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—141no—
759C22×C4—141no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—284no—
779C22×C4—284no—
780C22×C4—284no—
781C22×C4—284no—
782C22×C4—284no—
783C22×C4—284no—
784C22×C4—284no—
785C22×C4—284no—
786C22×C4—284no—
787C22×C4—284no—
788C22×C4—284no—
789C22×C4C2×Dic1412yes—
790C22×C4C2×Dic1412yes—
791C22×C4D4×D712yes—
792C22×C4#115912yes—
793C22×C4C2×C22⋊D712yes—
794C22×C4C2×C22⋊D712yes—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—284no—
798C4⋊C4—284no—
799C4⋊C4—284no—
800C4⋊C4—284no—
801C4⋊C4—284no—
802C4⋊C4—284no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—148no—
806C22⋊C4—284no—
807C2×C7—28no—
808C2×C7C2×#39811yescharacteristic
809C2×C7#241811yescharacteristic
810C2×C7#241911yescharacteristic
811C2×C7#242411yescharacteristic
812C2×C7#242511yescharacteristic
813C2×C7#243711yescharacteristic
814C2×C7#243811yescharacteristic
815C2×C7#244011yescharacteristic
816C2×C7#244911yescharacteristic
817C2×C7#245011yescharacteristic
818C2×C7#247311yescharacteristic
819C2×C7#250511yescharacteristic
820C2×C7#254911yescharacteristic
821C2×C7#264611yescharacteristic
822C2×C7#285111yescharacteristic
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23#645114yes—
852C23#645214yes—
853C23#645314yes—
854C23#645714yes—
855C23#648714yes—
856C23#650214yes—
857C23#650914yes—
858C23C22×Dic1411yescharacteristic
859C23C2×#115711yescharacteristic
860C23C2×D4×D711yescharacteristic
861C23C2×D4×D711yescharacteristic
862C23C2×#115911yescharacteristic
863C23C2×#115911yescharacteristic
864C23#654811yescharacteristic
865C23#654811yescharacteristic
866C23C2×Q8×D711yescharacteristic
867C23C2×#116111yescharacteristic
868C23D7×#4111yescharacteristic
869C23D7×#4111yescharacteristic
870C23#655311yescharacteristic
871C23#655411yescharacteristic
872C23C22×C22⋊D711yescharacteristic
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—416no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—74no—
917C2×C4—142no—
918C2×C4—142no—
919C2×C4—142no—
920C2×C4—142no—
921C2×C4—142no—
922C2×C4—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—2816no—
939C2×C4—2816no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4—281no—
950C2×C4—281no—
951C2×C4—281no—
952C2×C4—281no—
953C2×C4—281no—
954C2×C4—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4—281no—
959C2×C4—281no—
960C2×C4—281no—
961C2×C4—281no—
962C2×C4—281no—
963C2×C4—281no—
964C2×C4—281no—
965C2×C4—281no—
966C2×C4—281no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4—281no—
972C2×C4—281no—
973C2×C4—281no—
974C7#1473611yescharacteristic, complemented, Sylow
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22#8975618yescomplemented
990C22C2×#645111yescharacteristic
991C22C2×#645211yescharacteristic
992C22C2×#645311yescharacteristic
993C22C2×#645711yescharacteristic
994C22D4×Dic1411yescharacteristic
995C22#9022911yescharacteristic
996C22#9023011yescharacteristic
997C22#9023011yescharacteristic
998C22#9023411yescharacteristic
999C22#9023811yescharacteristic
1000C22#9025111yescharacteristic
1001C22#9025511yescharacteristic
1002C22#9027711yescharacteristic
1003C22#9028111yescharacteristic
1004C22#9028211yescharacteristic
1005C22#9028411yescharacteristic
1006C22#9031311yescharacteristic
1007C22#9031411yescharacteristic
1008C22D7×C22⋊Q811yescharacteristic
1009C22#9032111yescharacteristic
1010C22#9032511yescharacteristic
1011C22#9032811yescharacteristic
1012C22#9032811yescharacteristic
1013C22#9033311yescharacteristic
1014C22#9034011yescharacteristic
1015C22#9034511yescharacteristic
1016C22#9034611yescharacteristic
1017C22#9035611yescharacteristic
1018C22C2×#648711yescharacteristic
1019C22D4×C22⋊D711yescharacteristic
1020C22C2×#650211yescharacteristic
1021C22#9049711yescharacteristic
1022C22C2×#650911yescharacteristic
1023C22#9051511yescharacteristic
1024C22#9052011yescharacteristic
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—144no—
1032C4—282no—
1033C4—282no—
1034C4—282no—
1035C4—282no—
1036C4—282no—
1037C4—561no—
1038C4—561no—
1039C2—28no—
1040C2#1173185311yescharacteristic
1041C2#1173186111yescharacteristic
1042C2#1173188711yescharacteristic
1043C2#1173190911yescharacteristic
1044C2#1173191711yescharacteristic
1045C2#1173194911yescharacteristic
1046C2#1173203111yescharacteristic
1047C2#1173204811yescharacteristic
1048C2C2×#8975611yescharacteristic
1049C2#1173980511yescharacteristic
1050C2#1173980611yescharacteristic
1051C2#1174003211yescharacteristic
1052C2#1174020711yescharacteristic
1053C2#1174026111yescharacteristic
1054C2#1174029211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutator, socle, cosocleC24×C7C24
FittingC2×C7×#385C2
prime radicalC25×C7C23
hypercenterC2×#385D7
hypocenterC7#14736
LCSG ▷ C24×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#89756C2semidirect
7. #11729322C2semidirect
8. #11729321C2semidirect
9. #11729319C2semidirect
12. #11727175C2semidirect
13. #11727168C2semidirect
14. #11727165C2semidirect
15. #11727164C2semidirect
610. C22×C7#398semidirect
974. C7#14736semidirect
989. C22#89756semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3852
C2×#899822
C22×C7⋊#952
C2×#897562
C2×#897222
C2×#897142
#117293222
#117293212
#117293192
#117292982
#117271752
#117271682
#117271652
#117271642
#147367