Finite Group Databasebeta

← #13281773

Subgroups — #13281773

Order 1792.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic, complemented
3C2×#89762C211yesmaximal, characteristic
4C2×#89748C211yesmaximal, characteristic, complemented
5C2×#89440C211yesmaximal, characteristic
6C2×#89440C211yesmaximal, characteristic
7C2×#89441C211yesmaximal, characteristic
8C7×#1441C211yesmaximal, characteristic, complemented
9#11727182C211yesmaximal, characteristic
10#11727181C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727174C211yesmaximal, characteristic, complemented
13#11727168C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727155C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
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×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
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#89762C418yescomplemented
52#89761—24no—
53#89757—24no—
54#89748—24no—
55#89441—24no—
56#89440—24no—
57#89440—24no—
58#14405—71nomaximal, Sylow
59C24×D7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C23×Dic7C2311yescharacteristic
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C22×C4×D7—22no—
75C22×C4×D7—22no—
76C22×C4×D7—22no—
77C22×C4×D7—41no—
78C22×C4×D7—41no—
79C22×C4×D7—41no—
80C22×C4×D7—41no—
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C4⋊C4—22no—
85C2×C7×C4⋊C4—41no—
86C2×C7×C4⋊C4C2×C414yescomplemented
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—22no—
93C2×(C2×D7)⋊C4—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—41no—
97C2×(C2×D7)⋊C4—41no—
98C2×(C2×D7)⋊C4—41no—
99C2×(C2×D7)⋊C4—41no—
100C2×(C2×D7)⋊C4C2×C414yes—
101C2×(C2×D7)⋊C4C2×C414yes—
102C2×(C2×D7)⋊C4C2×C414yes—
103C2×(C2×D7)⋊C4D414yes—
104C2×(C2×D7)⋊C4Q814yes—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7—41no—
113C2×C4⋊Dic7—41no—
114C2×Dic7⋊C4—22no—
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×Dic7⋊C4—41no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4D414yes—
129C2×C4×Dic7—22no—
130C2×C4×Dic7—22no—
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—41no—
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95—22no—
136C7×#95—22no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—41no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—41no—
147C7⋊#95—41no—
148C7⋊#95C2×C414yescomplemented
149C7⋊#95C2×C414yescomplemented
150C7⋊#95D414yes—
151C2×#389—71no—
152C2×#388—71no—
153C2×#388—71no—
154C2×#385—71no—
155C2×#385—71no—
156C2×#385—71no—
157C2×#384—71no—
158#1444—71no—
159#1444—71no—
160#1442—71no—
161#1441D711yescharacteristic, complemented
162#1439—71no—
163#1439—71no—
164#1436—71no—
165#1434—71no—
166C24×C7C2411yescharacteristic
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7—21no—
175C23×D7—21no—
176C23×D7—21no—
177C23×D7—21no—
178C23×D7—21no—
179C23×D7C22×C412yes—
180C23×D7C2×D412yes—
181C23×D7C2×Q812yes—
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—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×Q812yes—
230C22×C4×C7#4112yes—
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×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C2×D412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×Q812yes—
279C22×Dic7#4112yes—
280C2×C4×D7—44no—
281C2×C4×D7—44no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C7×C4⋊C4—28no—
288C7×C4⋊C4—44no—
289(C2×D7)⋊C4—28no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—44no—
292(C2×D7)⋊C4—44no—
293(C2×D7)⋊C4—44no—
294(C2×D7)⋊C4C4⋊C4116yescomplemented
295C4⋊Dic7—44no—
296C4⋊Dic7—44no—
297C4⋊Dic7—44no—
298Dic7⋊C4—44no—
299Dic7⋊C4—44no—
300Dic7⋊C4—44no—
301Dic7⋊C4—44no—
302Dic7⋊C4—44no—
303C4×Dic7—28no—
304C4×Dic7—44no—
305C24×C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4—71no—
312C22×C4⋊C4—71no—
313C22×C4⋊C4—71no—
314C22×C4⋊C4C2×D711yescharacteristic
315C22×C4⋊C4C2×D711yescharacteristic
316C22×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C22⋊C4—71no—
319C22×C22⋊C4—71no—
320C22×C22⋊C4—71no—
321C22×C22⋊C4—71no—
322C22×C42—71no—
323C22×C42—71no—
324#389—144no—
325#388—78no—
326#388—144no—
327#385—144no—
328#385—144no—
329#385—144no—
330#384—144no—
331C2×#95—71no—
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×#95C2×D711yescharacteristic
343C2×#95C2×D711yescharacteristic
344C2×#95C2×D711yescharacteristic
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
347C23×C7C23×C411yescharacteristic
348C23×C7C22×D411yescharacteristic
349C23×C7C22×D411yescharacteristic
350C23×C7C22×D411yescharacteristic
351C23×C7C22×Q811yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7H(5,𝔽2)11yescharacteristic
355C23×C7H(5,𝔽2)11yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C72−1+411yescharacteristic
359C23×C72−1+411yescharacteristic
360C23×C72−1+411yescharacteristic
361C23×C72−1+411yescharacteristic
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—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—41no—
381C22×D7—41no—
382C22×D7—41no—
383C22×D7—41no—
384C22×D7—41no—
385C22×D7—41no—
386C22×D7—41no—
387C22×D7—41no—
388C22×D7—41no—
389C22×D7—41no—
390C22×D7—41no—
391C22×D7—41no—
392C22×D7—41no—
393C22×D7—41no—
394C22×D7—41no—
395C22×D7—41no—
396C22×D7C2×C4⋊C414yes—
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—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
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×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×C7C2×C4⋊C414yes—
445C2×C4×C7C4×D414yes—
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—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
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×Dic7C2×C4⋊C414yes—
494C2×Dic7C4×D414yes—
495C4×D7—416no—
496C25—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—142no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4—281no—
508C23×C4—281no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4C22×D711yescharacteristic
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—74no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—142no—
532C2×C4⋊C4—142no—
533C2×C4⋊C4—142no—
534C2×C4⋊C4—142no—
535C2×C4⋊C4—142no—
536C2×C4⋊C4—281no—
537C2×C4⋊C4—281no—
538C2×C4⋊C4—281no—
539C2×C4⋊C4—281no—
540C2×C4⋊C4—281no—
541C2×C4⋊C4—281no—
542C2×C4⋊C4—281no—
543C2×C4⋊C4—281no—
544C2×C4⋊C4—281no—
545C2×C4⋊C4—281no—
546C2×C4⋊C4—281no—
547C2×C4⋊C4C4×D714yescomplemented
548C2×C22⋊C4—74no—
549C2×C22⋊C4—74no—
550C2×C22⋊C4—74no—
551C2×C22⋊C4—74no—
552C2×C22⋊C4—74no—
553C2×C22⋊C4—142no—
554C2×C22⋊C4—142no—
555C2×C22⋊C4—142no—
556C2×C22⋊C4—142no—
557C2×C22⋊C4—142no—
558C2×C22⋊C4—142no—
559C2×C22⋊C4—142no—
560C2×C22⋊C4—142no—
561C2×C22⋊C4—142no—
562C2×C22⋊C4—281no—
563C2×C22⋊C4—281no—
564C2×C22⋊C4—281no—
565C2×C22⋊C4—281no—
566C2×C42—74no—
567C2×C42—142no—
568C2×C42—142no—
569C2×C42—142no—
570C2×C42—142no—
571C2×C42—281no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—41no—
577#95—74no—
578#95—74no—
579#95—74no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—142no—
585#95—142no—
586#95—281no—
587#95—281no—
588C22×C7C22×C4⋊C411yescharacteristic
589C22×C7C2×C4×D411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7#52011yescharacteristic
592C22×C7#52011yescharacteristic
593C22×C7#52011yescharacteristic
594C22×C7#52011yescharacteristic
595C22×C7#53411yescharacteristic
596C22×C7#53511yescharacteristic
597C22×C7#53511yescharacteristic
598C22×C7#53611yescharacteristic
599C22×C7#53611yescharacteristic
600C22×C7#53611yescharacteristic
601C22×C7#53911yescharacteristic
602C22×C7#53911yescharacteristic
603C22×C7#54211yescharacteristic
604C22×C7#54211yescharacteristic
605C22×C7#54411yescharacteristic
606C22×C7#54411yescharacteristic
607C22×C7D4211yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7D4211yescharacteristic
610C22×C7#54711yescharacteristic
611C22×C7#54711yescharacteristic
612C22×C7#54711yescharacteristic
613C22×C7#54811yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7D4×Q811yescharacteristic
616C22×C7#55311yescharacteristic
617C22×C7#55411yescharacteristic
618C22×C7#55411yescharacteristic
619C22×C7#56011yescharacteristic
620C22×C7#56311yescharacteristic
621C22×C7#56311yescharacteristic
622C22×C7#56311yescharacteristic
623C2×D7—24no—
624C2×D7—24no—
625C2×D7—24no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C2×D7—42no—
631C2×D7—42no—
632C2×D7—42no—
633C2×D7—42no—
634C2×D7—42no—
635C2×D7—42no—
636C2×D7—42no—
637C2×D7—42no—
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—42no—
641C4×C7—42no—
642C4×C7—81no—
643C4×C7—81no—
644C4×C7—81no—
645Dic7—24no—
646Dic7—24no—
647Dic7—42no—
648Dic7—42no—
649Dic7—42no—
650Dic7—42no—
651Dic7—81no—
652C24—72no—
653C24—72no—
654C24—72no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24—141no—
661C24—141no—
662C24—141no—
663C24—141no—
664C24—141no—
665C24—141no—
666C24—141no—
667C24C23×D711yescharacteristic
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—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—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—72no—
713C22×C4—72no—
714C22×C4—72no—
715C22×C4—72no—
716C22×C4—72no—
717C22×C4—72no—
718C22×C4—72no—
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—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—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4—284no—
763C22×C4—284no—
764C22×C4—284no—
765C22×C4C2×C4×D712yes—
766C22×C4C2×C4×D712yes—
767C22×C4C2×C4×D712yes—
768C22×C4D4×D712yes—
769C22×C4D4×D712yes—
770C22×C4D4×D712yes—
771C22×C4#115912yes—
772C22×C4Q8×D712yes—
773C4⋊C4—28no—
774C4⋊C4—44no—
775C4⋊C4—284no—
776C4⋊C4—284no—
777C4⋊C4—284no—
778C4⋊C4—284no—
779C4⋊C4—284no—
780C4⋊C4—284no—
781C4⋊C4—284no—
782C4⋊C4—284no—
783C22⋊C4—716no—
784C22⋊C4—148no—
785C22⋊C4—148no—
786C22⋊C4—284no—
787C22⋊C4—284no—
788C22⋊C4—284no—
789C42—148no—
790C42—284no—
791C2×C7#231711yescharacteristic
792C2×C7#232211yescharacteristic
793C2×C7#232611yescharacteristic
794C2×C7D4×C4⋊C411yescharacteristic
795C2×C7D4×C4⋊C411yescharacteristic
796C2×C7#236111yescharacteristic
797C2×C7#238311yescharacteristic
798C2×C7#266911yescharacteristic
799C2×C7#267411yescharacteristic
800C2×C7#267711yescharacteristic
801C2×C7#268011yescharacteristic
802C2×C7#271811yescharacteristic
803C2×C7#272011yescharacteristic
804C2×C7#272911yescharacteristic
805C2×C7#279011yescharacteristic
806D7—44no—
807C23—74no—
808C23—142no—
809C23—142no—
810C23—142no—
811C23—142no—
812C23—142no—
813C23—142no—
814C23—142no—
815C23—142no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23—281no—
836C23—281no—
837C23—281no—
838C23—281no—
839C23—281no—
840C23—281no—
841C23—281no—
842C23C22×C4×D711yescharacteristic
843C23C2×D4×D711yescharacteristic
844C23C2×D4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×#115911yescharacteristic
847C23#654811yescharacteristic
848C23C2×Q8×D711yescharacteristic
849C23#655111yescharacteristic
850C23#655111yescharacteristic
851C23D7×#4111yescharacteristic
852C23#655311yescharacteristic
853C23#655311yescharacteristic
854C23#655311yescharacteristic
855C23#655411yescharacteristic
856C23#655411yescharacteristic
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—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
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—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
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—74no—
905C2×C4—74no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—142no—
915C2×C4—142no—
916C2×C4—142no—
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—2816no—
931C2×C4—281no—
932C2×C4—281no—
933C2×C4—281no—
934C2×C4—281no—
935C2×C4—281no—
936C2×C4—281no—
937C2×C4—281no—
938C2×C4—281no—
939C2×C4—281no—
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(C22⋊D7)⋊C414yes—
955C2×C4D7×C4⋊C414yes—
956C7#1440511yescharacteristic, complemented, Sylow
957C22—144no—
958C22—144no—
959C22—144no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22—282no—
967C22—282no—
968C22—282no—
969C22—282no—
970C22—282no—
971C22—282no—
972C22C2×(C22⋊D7)⋊C411yescharacteristic
973C22C2×D7×C4⋊C411yescharacteristic
974C22#9021411yescharacteristic
975C22C4×D4×D711yescharacteristic
976C22#9023711yescharacteristic
977C22#9026511yescharacteristic
978C22#9026511yescharacteristic
979C22#9028111yescharacteristic
980C22#9028911yescharacteristic
981C22#9029211yescharacteristic
982C22#9029811yescharacteristic
983C22#9030011yescharacteristic
984C22#9030011yescharacteristic
985C22#9030211yescharacteristic
986C22#9031911yescharacteristic
987C22#9031911yescharacteristic
988C22#9032211yescharacteristic
989C22#9032311yescharacteristic
990C22#9032611yescharacteristic
991C22#9033411yescharacteristic
992C22#9033411yescharacteristic
993C22#9033711yescharacteristic
994C22#9034411yescharacteristic
995C22#9034611yescharacteristic
996C22#9035711yescharacteristic
997C22#9036511yescharacteristic
998C22#9038011yescharacteristic
999C22#9038111yescharacteristic
1000C22#9038311yescharacteristic
1001C22#9039011yescharacteristic
1002C22#9039811yescharacteristic
1003C22#9040311yescharacteristic
1004C22#9041511yescharacteristic
1005C22#9041811yescharacteristic
1006C22#9042011yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—81no—
1014C4—144no—
1015C4—144no—
1016C4—282no—
1017C4—282no—
1018C4—282no—
1019C4—282no—
1020C4—561no—
1021C2—284no—
1022C2#1173145511yescharacteristic
1023C2#1173212111yescharacteristic
1024C2#1173242511yescharacteristic
1025C2#1173274211yescharacteristic
1026C2#1173341311yescharacteristic
1027C2#1173364711yescharacteristic
1028C2#1173392911yescharacteristic
1029C2#1173457311yescharacteristic
1030C2#1173470611yescharacteristic
1031C2#1173487211yescharacteristic
1032C2#1173488611yescharacteristic
1033C2#1173535011yescharacteristic
1034C2#1173541411yescharacteristic
1035C2#1173543011yescharacteristic
1036C2#1173569311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1441C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1441D7
hypocenterC7#14405
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#89757C2semidirect
4. C2×#89748C2semidirect
8. C7×#1441C2semidirect
11. #11727174C2semidirect
12. #11727174C2semidirect
13. #11727168C2semidirect
14. #11727160C2semidirect
15. #11727155C2semidirect
51. #89762C4semidirect
86. C2×C7×C4⋊C4C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
148. C7⋊#95C2×C4semidirect
149. C7⋊#95C2×C4semidirect
161. #1441D7semidirect
294. (C2×D7)⋊C4C4⋊C4semidirect
547. C2×C4⋊C4C4×D7semidirect
956. C7#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#897612
C2×#897572
C2×#897622
C2×#897482
C2×#894402
C2×#894412
C7×#14412
#117271822
#117271812
#117271742
#117271682
#117271602
#117271552
#144057