Finite Group Databasebeta

← #13281736

Subgroups — #13281736

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89712C211yesmaximal, characteristic
2C2×#89440C211yesmaximal, characteristic
3C2×#89440C211yesmaximal, characteristic
4C2×#89442C211yesmaximal, characteristic
5C2×#89422C211yesmaximal, characteristic, complemented
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729324C211yesmaximal, characteristic
8#11729317C211yesmaximal, characteristic, complemented
9#11729289C211yesmaximal, characteristic, complemented
10#11727181C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12#11727174C211yesmaximal, characteristic, complemented
13#11727173C211yesmaximal, characteristic, complemented
14#11727167C211yesmaximal, characteristic, complemented
15#11727165C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
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
51#89712—24no—
52#89442C418yescomplemented
53#89440—24no—
54#89440—24no—
55#89422—24no—
56#14403—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C22×C4×D7—22no—
73C22×C4×D7—22no—
74C22×C4×D7—22no—
75C22×C4×D7—41no—
76C22×C4×D7—41no—
77C22×C4×D7—41no—
78C22×C4×D7—41no—
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4—41no—
82C2×C42×C7—22no—
83C2×C42×C7—22no—
84C2×C42×C7—41no—
85C2×(C2×D7)⋊C4—22no—
86C2×(C2×D7)⋊C4—22no—
87C2×(C2×D7)⋊C4—22no—
88C2×(C2×D7)⋊C4—22no—
89C2×(C2×D7)⋊C4—22no—
90C2×(C2×D7)⋊C4—22no—
91C2×(C2×D7)⋊C4—22no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4—41no—
95C2×(C2×D7)⋊C4—41no—
96C2×(C2×D7)⋊C4—41no—
97C2×(C2×D7)⋊C4—41no—
98C2×(C2×D7)⋊C4C2×C414yes—
99C2×(C2×D7)⋊C4C2×C414yes—
100C2×(C2×D7)⋊C4C2×C414yes—
101C2×(C2×D7)⋊C4D414yes—
102C2×(C2×D7)⋊C4Q814yes—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—41no—
108C2×C4⋊Dic7—41no—
109C2×C4⋊Dic7—41no—
110C2×C4⋊Dic7—41no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7—41no—
114C2×C4⋊Dic7C2×C414yescomplemented
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—41no—
121C2×Dic7⋊C4—41no—
122C2×Dic7⋊C4—41no—
123C2×Dic7⋊C4—41no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7C2×C414yescomplemented
127C7×#95—22no—
128C7×#95—41no—
129C7×#95—41no—
130C7×#95C2×C414yescomplemented
131C7×#95D414yes—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95C2×C414yescomplemented
145C2×#388—71no—
146C2×#388—71no—
147C2×#385—71no—
148C2×#385—71no—
149C2×#382—71no—
150#1444—71no—
151#1444—71no—
152#1442—71no—
153#1441—71no—
154#1439—71no—
155#1439—71no—
156#1436D711yescharacteristic, complemented
157C4⋊#95—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C24×C7C2411yescharacteristic
161C23×D7—21no—
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7C22×C412yes—
174C23×D7C2×D412yes—
175C23×D7C2×Q812yes—
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
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×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7C2×Q812yes—
223C22×C4×C7#4112yes—
224C22×C4×C7#4112yes—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
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—21no—
267C22×Dic7—21no—
268C22×Dic7C22×C412yes—
269C22×Dic7C22×C412yes—
270C22×Dic7C22×C412yes—
271C22×Dic7C2×D412yes—
272C22×Dic7C2×Q812yes—
273C22×Dic7#4112yes—
274C2×C4×D7—44no—
275C2×C4×D7—44no—
276C2×C4×D7—44no—
277C2×C4×D7—44no—
278C2×C4×D7—44no—
279C2×C4×D7—44no—
280C2×C4×D7—44no—
281C7×C4⋊C4—44no—
282C42×C7—44no—
283(C2×D7)⋊C4—28no—
284(C2×D7)⋊C4—44no—
285(C2×D7)⋊C4—44no—
286(C2×D7)⋊C4—44no—
287(C2×D7)⋊C4—44no—
288(C2×D7)⋊C4C4⋊C4116yescomplemented
289C4⋊Dic7—44no—
290C4⋊Dic7—44no—
291C4⋊Dic7—44no—
292C4⋊Dic7—44no—
293Dic7⋊C4—44no—
294Dic7⋊C4—44no—
295Dic7⋊C4—44no—
296C4×Dic7—28no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4C2×D711yescharacteristic
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4—71no—
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C42—71no—
313C22×C42C2×D711yescharacteristic
314#388—78no—
315#388—144no—
316#385—144no—
317#385—144no—
318#382—144no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C2×#95—71no—
326C2×#95—71no—
327C2×#95—71no—
328C2×#95—71no—
329C2×#95—71no—
330C2×#95—71no—
331C2×#95—71no—
332C2×#95C2×D711yescharacteristic
333C2×#95C2×D711yescharacteristic
334C2×#95C2×D711yescharacteristic
335C2×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7C23×C411yescharacteristic
338C23×C7C22×D411yescharacteristic
339C23×C7C22×D411yescharacteristic
340C23×C7C22×Q811yescharacteristic
341C23×C7C2×#4111yescharacteristic
342C23×C7C2×#4111yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7H(5,𝔽2)11yescharacteristic
345C23×C7H(5,𝔽2)11yescharacteristic
346C23×C7H(5,𝔽2)11yescharacteristic
347C23×C7H(5,𝔽2)11yescharacteristic
348C23×C7H(5,𝔽2)11yescharacteristic
349C23×C72−1+411yescharacteristic
350C23×C72−1+411yescharacteristic
351C23×C72−1+411yescharacteristic
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7C2×C4⋊C414yes—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—22no—
395C2×C4×C7—22no—
396C2×C4×C7—22no—
397C2×C4×C7—22no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—22no—
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—41no—
412C2×C4×C7—41no—
413C2×C4×C7—41no—
414C2×C4×C7—41no—
415C2×C4×C7—41no—
416C2×C4×C7—41no—
417C2×C4×C7—41no—
418C2×C4×C7—41no—
419C2×C4×C7—41no—
420C2×C4×C7—41no—
421C2×C4×C7—41no—
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×C7C2×C4⋊C414yes—
435C2×C4×C7C4×D414yes—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—22no—
449C2×Dic7—22no—
450C2×Dic7—22no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
457C2×Dic7—41no—
458C2×Dic7—41no—
459C2×Dic7—41no—
460C2×Dic7—41no—
461C2×Dic7—41no—
462C2×Dic7—41no—
463C2×Dic7—41no—
464C2×Dic7—41no—
465C2×Dic7—41no—
466C2×Dic7—41no—
467C2×Dic7—41no—
468C2×Dic7—41no—
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×Dic7C2×C4⋊C414yes—
485C4×D7—416no—
486C25—71no—
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—142no—
495C23×C4—142no—
496C23×C4—142no—
497C23×C4—281no—
498C23×C4—281no—
499C23×C4—281no—
500C23×C4—281no—
501C23×C4C22×D711yescharacteristic
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—142no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—281no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4—281no—
526C2×C4⋊C4—281no—
527C2×C4⋊C4—281no—
528C2×C4⋊C4—281no—
529C2×C4⋊C4—281no—
530C2×C4⋊C4—281no—
531C2×C4⋊C4—281no—
532C2×C22⋊C4—74no—
533C2×C22⋊C4—74no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—281no—
545C2×C22⋊C4—281no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4—281no—
548C2×C22⋊C4—281no—
549C2×C22⋊C4—281no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—41no—
553C2×C42—74no—
554C2×C42—142no—
555C2×C42—142no—
556#95—22no—
557#95—41no—
558#95—41no—
559#95—74no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—281no—
568#95—281no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95C4×D714yescomplemented
573#95D2814yes—
574C22×C7C22×C4⋊C411yescharacteristic
575C22×C7C2×C4×D411yescharacteristic
576C22×C7C4×#4111yescharacteristic
577C22×C7#51811yescharacteristic
578C22×C7#52011yescharacteristic
579C22×C7#52011yescharacteristic
580C22×C7#52011yescharacteristic
581C22×C7#53511yescharacteristic
582C22×C7#53511yescharacteristic
583C22×C7#53611yescharacteristic
584C22×C7#53711yescharacteristic
585C22×C7#53811yescharacteristic
586C22×C7#53911yescharacteristic
587C22×C7#54011yescharacteristic
588C22×C7#54111yescharacteristic
589C22×C7#54211yescharacteristic
590C22×C7#54211yescharacteristic
591C22×C7#54411yescharacteristic
592C22×C7#54411yescharacteristic
593C22×C7D4211yescharacteristic
594C22×C7#54611yescharacteristic
595C22×C7#54611yescharacteristic
596C22×C7#54611yescharacteristic
597C22×C7#54711yescharacteristic
598C22×C7#54711yescharacteristic
599C22×C7D4×Q811yescharacteristic
600C22×C7#55111yescharacteristic
601C22×C7#55211yescharacteristic
602C22×C7#55411yescharacteristic
603C22×C7#55411yescharacteristic
604C22×C7#55411yescharacteristic
605C22×C7H(3,𝔽4)11yescharacteristic
606C22×C7#56211yescharacteristic
607C22×C7#56211yescharacteristic
608C22×C7#56311yescharacteristic
609C2×D7—24no—
610C2×D7—24no—
611C2×D7—24no—
612C2×D7—42no—
613C2×D7—42no—
614C2×D7—42no—
615C2×D7—42no—
616C2×D7—42no—
617C2×D7—42no—
618C2×D7—42no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—42no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630C4×C7—81no—
631Dic7—24no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—81no—
636Dic7—81no—
637Dic7—81no—
638C24—72no—
639C24—72no—
640C24—72no—
641C24—141no—
642C24—141no—
643C24—141no—
644C24—141no—
645C24—141no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24C23×D711yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
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—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
711C22×C4—141no—
712C22×C4—141no—
713C22×C4—141no—
714C22×C4—141no—
715C22×C4—141no—
716C22×C4—141no—
717C22×C4—141no—
718C22×C4—141no—
719C22×C4—141no—
720C22×C4—141no—
721C22×C4—141no—
722C22×C4—141no—
723C22×C4—141no—
724C22×C4—141no—
725C22×C4—141no—
726C22×C4—141no—
727C22×C4—141no—
728C22×C4—141no—
729C22×C4—141no—
730C22×C4—141no—
731C22×C4—141no—
732C22×C4—141no—
733C22×C4—141no—
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—284no—
743C22×C4—284no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4—284no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4C2×C4×D712yes—
750C22×C4C2×C4×D712yes—
751C22×C4C2×C4×D712yes—
752C22×C4C2×D2812yes—
753C22×C4C2×D2812yes—
754C22×C4C2×D2812yes—
755C22×C4#115712yes—
756C22×C4D4×D712yes—
757C22×C4#115912yes—
758C22×C4Q8×D712yes—
759C4⋊C4—44no—
760C4⋊C4—284no—
761C4⋊C4—284no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C4⋊C4—284no—
766C4⋊C4—284no—
767C22⋊C4—716no—
768C22⋊C4—148no—
769C22⋊C4—284no—
770C22⋊C4—284no—
771C22⋊C4—284no—
772C22⋊C4—284no—
773C42—44no—
774C42—148no—
775C2×C7#231711yescharacteristic
776C2×C7#232411yescharacteristic
777C2×C7#233411yescharacteristic
778C2×C7D4×C4⋊C411yescharacteristic
779C2×C7#234911yescharacteristic
780C2×C7#235911yescharacteristic
781C2×C7#237911yescharacteristic
782C2×C7#267011yescharacteristic
783C2×C7#267211yescharacteristic
784C2×C7#269811yescharacteristic
785C2×C7#270411yescharacteristic
786C2×C7#270611yescharacteristic
787C2×C7#272011yescharacteristic
788C2×C7#276311yescharacteristic
789C2×C7#276811yescharacteristic
790D7—44no—
791C23—74no—
792C23—142no—
793C23—142no—
794C23—142no—
795C23—142no—
796C23—142no—
797C23—142no—
798C23—142no—
799C23—142no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
808C23—142no—
809C23—142no—
810C23—281no—
811C23—281no—
812C23—281no—
813C23—281no—
814C23—281no—
815C23—281no—
816C23—281no—
817C23—281no—
818C23—281no—
819C23—281no—
820C23—281no—
821C23—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23C22×C4×D711yescharacteristic
827C23C22×D2811yescharacteristic
828C23C2×#115711yescharacteristic
829C23C2×D4×D711yescharacteristic
830C23C2×#115911yescharacteristic
831C23#654811yescharacteristic
832C23#654811yescharacteristic
833C23C2×Q8×D711yescharacteristic
834C23#655111yescharacteristic
835C23D7×#4111yescharacteristic
836C23#655311yescharacteristic
837C23#655311yescharacteristic
838C23#655311yescharacteristic
839C23#655411yescharacteristic
840C23#655411yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—74no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—142no—
893C2×C4—142no—
894C2×C4—142no—
895C2×C4—142no—
896C2×C4—142no—
897C2×C4—142no—
898C2×C4—142no—
899C2×C4—142no—
900C2×C4—142no—
901C2×C4—142no—
902C2×C4—142no—
903C2×C4—142no—
904C2×C4—2816no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
915C2×C4—281no—
916C2×C4—281no—
917C2×C4—281no—
918C2×C4—281no—
919C2×C4—281no—
920C2×C4—281no—
921C2×C4—281no—
922C2×C4—281no—
923C2×C4—281no—
924C2×C4—281no—
925C2×C4—281no—
926C2×C4—281no—
927C2×C4—281no—
928C2×C4—281no—
929C2×C4—281no—
930C2×C4—281no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4C4×D2814yes—
939C2×C4D7×C4⋊C414yes—
940C7#1440311yescharacteristic, complemented, Sylow
941C22—144no—
942C22—144no—
943C22—144no—
944C22—282no—
945C22—282no—
946C22—282no—
947C22—282no—
948C22—282no—
949C22—282no—
950C22—282no—
951C22—282no—
952C22—282no—
953C22—282no—
954C22—282no—
955C22—282no—
956C22C2×C4×D2811yescharacteristic
957C22#9018611yescharacteristic
958C22C2×D7×C4⋊C411yescharacteristic
959C22#9020111yescharacteristic
960C22#9021411yescharacteristic
961C22#9021611yescharacteristic
962C22#9022211yescharacteristic
963C22C4×#115911yescharacteristic
964C22#9023611yescharacteristic
965C22#9023711yescharacteristic
966C22D4×D2811yescharacteristic
967C22#9024211yescharacteristic
968C22#9024511yescharacteristic
969C22#9024611yescharacteristic
970C22#9025311yescharacteristic
971C22#9026511yescharacteristic
972C22Q8×D2811yescharacteristic
973C22#9027011yescharacteristic
974C22#9027311yescharacteristic
975C22#9028211yescharacteristic
976C22#9029811yescharacteristic
977C22#9031211yescharacteristic
978C22#9031911yescharacteristic
979C22#9032611yescharacteristic
980C22#9032711yescharacteristic
981C22#9033411yescharacteristic
982C22#9034511yescharacteristic
983C22#9035611yescharacteristic
984C22#9035811yescharacteristic
985C22#9037411yescharacteristic
986C22#9038011yescharacteristic
987C22#9038711yescharacteristic
988C22#9039511yescharacteristic
989C22#9040311yescharacteristic
990C22#9042011yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—144no—
999C4—282no—
1000C4—282no—
1001C4—282no—
1002C4—561no—
1003C4—561no—
1004C4—561no—
1005C2—284no—
1006C2#1173090911yescharacteristic
1007C2#1173120811yescharacteristic
1008C2C4⋊C4×D2811yescharacteristic
1009C2#1173183911yescharacteristic
1010C2#1173207411yescharacteristic
1011C2#1173226211yescharacteristic
1012C2#1173239911yescharacteristic
1013C2#1173261411yescharacteristic
1014C2#1173265711yescharacteristic
1015C2#1173284011yescharacteristic
1016C2#1173293811yescharacteristic
1017C2#1173335811yescharacteristic
1018C2#1173341311yescharacteristic
1019C2#1173371211yescharacteristic
1020C2#1173403111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#14403
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
5. C2×#89422C2semidirect
6. C7×#1436C2semidirect
8. #11729317C2semidirect
9. #11729289C2semidirect
12. #11727174C2semidirect
13. #11727173C2semidirect
14. #11727167C2semidirect
15. #11727165C2semidirect
52. #89442C4semidirect
114. C2×C4⋊Dic7C2×C4semidirect
126. C2×C4×Dic7C2×C4semidirect
130. C7×#95C2×C4semidirect
144. C7⋊#95C2×C4semidirect
156. #1436D7semidirect
288. (C2×D7)⋊C4C4⋊C4semidirect
572. #95C4×D7semidirect
940. C7#14403semidirect

Maximal subgroups

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

subgroupindex
C2×#897122
C2×#894402
C2×#894422
C2×#894222
C7×#14362
#117293242
#117293172
#117292892
#117271812
(C2×D7)⋊#952
#117271742
#117271732
#117271672
#117271652
#144037