Finite Group Databasebeta

← #13277010

Subgroups — #13277010

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89761C211yesmaximal, characteristic
2C2×#89761C211yesmaximal, characteristic
3C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
4C2×#89440C211yesmaximal, characteristic
5C2×#89439C211yesmaximal, characteristic
6C2×D7×#95C211yesmaximal, characteristic
7C2×#89419C211yesmaximal, characteristic, complemented
8C7×C4⋊#95C211yesmaximal, characteristic, complemented
9#11729322C211yesmaximal, characteristic, complemented
10#11729319C211yesmaximal, characteristic, complemented
11#11729290C211yesmaximal, characteristic, complemented
12(C2×D7)⋊#95C211yesmaximal, characteristic
13#11727167C211yesmaximal, characteristic, complemented
14#11727163C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
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#89761—24no—
52#89761C418yescomplemented
53C4×(C2×D7)⋊C4—24no—
54#89440—24no—
55#89439—24no—
56D7×#95—24no—
57#89419—24no—
58#14004—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—22no—
78C22×C4×D7—22no—
79C22×C4×D7—22no—
80C22×C4×D7—22no—
81C22×C4×D7—22no—
82C22×C4×D7—22no—
83C22×C4×D7—22no—
84C22×C4×D7—22no—
85C22×C4×D7—22no—
86C22×C4×D7—22no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7—41no—
91C22×C4×D7—41no—
92C22×C4×D7—41no—
93C22×C4×D7C2×C414yes—
94C22×C4×D7Q814yes—
95C2×C7×C4⋊C4—22no—
96C2×C7×C4⋊C4—22no—
97C2×C7×C4⋊C4—41no—
98C2×C7×C4⋊C4—41no—
99C2×C7×C4⋊C4—41no—
100C2×C7×C4⋊C4C2×C414yescomplemented
101C2×C42×C7—22no—
102C2×C42×C7—22no—
103C2×C42×C7—41no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4—22no—
109C2×(C2×D7)⋊C4—22no—
110C2×(C2×D7)⋊C4—22no—
111C2×(C2×D7)⋊C4C2×C414yes—
112C2×(C2×D7)⋊C4C2×C414yes—
113C2×(C2×D7)⋊C4D414yes—
114C2×(C2×D7)⋊C4D414yes—
115C2×(C2×D7)⋊C4Q814yes—
116C2×C4⋊Dic7—22no—
117C2×C4⋊Dic7—22no—
118C2×C4⋊Dic7—41no—
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—22no—
127C2×Dic7⋊C4—22no—
128C2×Dic7⋊C4—22no—
129C2×Dic7⋊C4—41no—
130C2×Dic7⋊C4—41no—
131C2×Dic7⋊C4—41no—
132C2×Dic7⋊C4—41no—
133C2×Dic7⋊C4C2×C414yescomplemented
134C2×C4×Dic7—22no—
135C2×C4×Dic7—22no—
136C2×C4×Dic7—41no—
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—22no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95—22no—
150C7⋊#95—41no—
151C7⋊#95—41no—
152C7⋊#95C2×C414yescomplemented
153C7⋊#95C2×C414yescomplemented
154C7⋊#95D414yes—
155C2×#389—71no—
156C2×#385—71no—
157C2×#385—71no—
158C2×#385—71no—
159C2×#380—71no—
160C2×C4×C22⋊C4—71no—
161C22×#95—71no—
162#1444—71no—
163#1442—71no—
164#1441—71no—
165#1441—71no—
166#1436—71no—
167#1436—71no—
168C4⋊#95D711yescharacteristic, complemented
169C22⋊#95—71no—
170C24×C7C2411yescharacteristic
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×D412yes—
182C23×D7C2×Q812yes—
183C23×D7C2×Q812yes—
184C23×D7#4112yes—
185C23×D7#4112yes—
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×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7C22×C412yes—
226C22×C4×C7C22×C412yes—
227C22×C4×C7C22×C412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×Q812yes—
232C22×C4×C7C2×Q812yes—
233C22×C4×C7#4112yes—
234C22×C4×C7#4112yes—
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×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×Q812yes—
282C22×Dic7C2×Q812yes—
283C22×Dic7#4112yes—
284C2×C4×D7—28no—
285C2×C4×D7—28no—
286C2×C4×D7—28no—
287C2×C4×D7—28no—
288C2×C4×D7—28no—
289C2×C4×D7—44no—
290C2×C4×D7—44no—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C2×C4×D7—44no—
296C2×C4×D7—44no—
297C2×C4×D7—44no—
298C2×C4×D7—44no—
299C2×C4×D7—44no—
300C2×C4×D7—44no—
301C2×C4×D7—44no—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C7×C4⋊C4—44no—
306C7×C4⋊C4—44no—
307C42×C7—44no—
308(C2×D7)⋊C4—28no—
309(C2×D7)⋊C4—28no—
310(C2×D7)⋊C4—44no—
311(C2×D7)⋊C4C4⋊C4116yescomplemented
312C4⋊Dic7—44no—
313Dic7⋊C4—28no—
314Dic7⋊C4—44no—
315Dic7⋊C4—44no—
316Dic7⋊C4—44no—
317Dic7⋊C4—44no—
318C4×Dic7—44no—
319C24×C4—71no—
320C24×C4—71no—
321C24×C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4C2×D711yescharacteristic
329C22×C4⋊C4C2×D711yescharacteristic
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C42—71no—
335C22×C42C2×D711yescharacteristic
336#389—144no—
337#385—78no—
338#385—144no—
339#385—144no—
340#380—144no—
341C4×C22⋊C4—144no—
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—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—144no—
357C2×#95C2×D711yescharacteristic
358C2×#95C2×D711yescharacteristic
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C23×C7C23×C411yescharacteristic
362C23×C7C22×D411yescharacteristic
363C23×C7C22×D411yescharacteristic
364C23×C7C22×D411yescharacteristic
365C23×C7C22×Q811yescharacteristic
366C23×C7C22×Q811yescharacteristic
367C23×C7C2×#4111yescharacteristic
368C23×C7C2×#4111yescharacteristic
369C23×C7C2×#4111yescharacteristic
370C23×C7C2×#4111yescharacteristic
371C23×C7C2×#4111yescharacteristic
372C23×C7H(5,𝔽2)11yescharacteristic
373C23×C7H(5,𝔽2)11yescharacteristic
374C23×C7H(5,𝔽2)11yescharacteristic
375C23×C72−1+411yescharacteristic
376C22×D7—22no—
377C22×D7—22no—
378C22×D7—22no—
379C22×D7—22no—
380C22×D7—22no—
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7—22no—
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7—22no—
389C22×D7—22no—
390C22×D7—22no—
391C22×D7—22no—
392C22×D7—22no—
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—22no—
401C22×D7—22no—
402C22×D7—22no—
403C22×D7—22no—
404C22×D7C2×C4⋊C414yes—
405C22×D7C4×D414yes—
406C22×D7C4×Q814yes—
407C22×D7#12114yes—
408C22×D7C22⋊Q814yes—
409C22×D7#12514yes—
410C22×D7C4⋊Q814yes—
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—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
427C2×C4×C7—22no—
428C2×C4×C7—22no—
429C2×C4×C7—22no—
430C2×C4×C7—22no—
431C2×C4×C7—22no—
432C2×C4×C7—22no—
433C2×C4×C7—22no—
434C2×C4×C7—22no—
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×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7—41no—
454C2×C4×C7—41no—
455C2×C4×C7—41no—
456C2×C4×C7—41no—
457C2×C4×C7—41no—
458C2×C4×C7C2×C4⋊C414yes—
459C2×C4×C7C22⋊Q814yes—
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—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
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×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7C2×C4⋊C414yes—
508C2×Dic7C4×D414yes—
509C4×D7—416no—
510C4×D7—416no—
511C4×D7—416no—
512C25—71no—
513C23×C4—71no—
514C23×C4—71no—
515C23×C4—71no—
516C23×C4—71no—
517C23×C4—71no—
518C23×C4—71no—
519C23×C4—74no—
520C23×C4—74no—
521C23×C4—71no—
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—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—281no—
536C23×C4—281no—
537C23×C4—281no—
538C23×C4—281no—
539C23×C4—281no—
540C23×C4—281no—
541C23×C4C22×D711yescharacteristic
542C23×C4C22×D711yescharacteristic
543C23×C4C22×D711yescharacteristic
544C23×C4C22×D711yescharacteristic
545C23×C4C22×D711yescharacteristic
546C23×C4C22×D711yescharacteristic
547C23×C4C22×D711yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—74no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4—142no—
562C2×C4⋊C4—142no—
563C2×C4⋊C4—142no—
564C2×C4⋊C4—142no—
565C2×C4⋊C4—142no—
566C2×C4⋊C4—281no—
567C2×C4⋊C4—281no—
568C2×C4⋊C4—281no—
569C2×C4⋊C4—281no—
570C2×C4⋊C4—281no—
571C2×C4⋊C4C4×D714yescomplemented
572C2×C22⋊C4—74no—
573C2×C22⋊C4—74no—
574C2×C22⋊C4—74no—
575C2×C22⋊C4—74no—
576C2×C22⋊C4—74no—
577C2×C22⋊C4—142no—
578C2×C22⋊C4—142no—
579C2×C22⋊C4—142no—
580C2×C22⋊C4—142no—
581C2×C22⋊C4—142no—
582C2×C22⋊C4—142no—
583C2×C22⋊C4—142no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—41no—
587C2×C42—142no—
588C2×C42—142no—
589C2×C42—281no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—74no—
595#95—74no—
596#95—74no—
597#95—142no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—142no—
606#95—281no—
607#95—281no—
608C22×C7C22×C4⋊C411yescharacteristic
609C22×C7C2×C4×D411yescharacteristic
610C22×C7C2×C4×D411yescharacteristic
611C22×C7C2×C4×Q811yescharacteristic
612C22×C7C4×#4111yescharacteristic
613C22×C7#51811yescharacteristic
614C22×C7#52011yescharacteristic
615C22×C7C2×#12111yescharacteristic
616C22×C7C2×C22⋊Q811yescharacteristic
617C22×C7C2×C22⋊Q811yescharacteristic
618C22×C7#52511yescharacteristic
619C22×C7C2×#12511yescharacteristic
620C22×C7#52911yescharacteristic
621C22×C7C2×C4⋊Q811yescharacteristic
622C22×C7#53311yescharacteristic
623C22×C7#53811yescharacteristic
624C22×C7#53911yescharacteristic
625C22×C7#54311yescharacteristic
626C22×C7#54411yescharacteristic
627C22×C7D4211yescharacteristic
628C22×C7D4211yescharacteristic
629C22×C7#54611yescharacteristic
630C22×C7#54611yescharacteristic
631C22×C7#54611yescharacteristic
632C22×C7#54611yescharacteristic
633C22×C7#54611yescharacteristic
634C22×C7#54711yescharacteristic
635C22×C7#54711yescharacteristic
636C22×C7D4×Q811yescharacteristic
637C22×C7#55111yescharacteristic
638C22×C7#55111yescharacteristic
639C22×C7#55211yescharacteristic
640C22×C7#55411yescharacteristic
641C22×C7#55411yescharacteristic
642C22×C7#55411yescharacteristic
643C2×D7—24no—
644C2×D7—24no—
645C2×D7—24no—
646C2×D7—24no—
647C2×D7—24no—
648C2×D7—24no—
649C2×D7—24no—
650C2×D7—24no—
651C2×D7—24no—
652C2×D7—24no—
653C2×D7—24no—
654C2×D7—24no—
655C2×D7—24no—
656C2×D7—24no—
657C2×D7#38918yescomplemented
658C4×C7—24no—
659C4×C7—24no—
660C4×C7—42no—
661C4×C7—42no—
662C4×C7—42no—
663C4×C7—42no—
664C4×C7—81no—
665Dic7—24no—
666Dic7—24no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—81no—
672C24—72no—
673C24—72no—
674C24—72no—
675C24—72no—
676C24—72no—
677C24—72no—
678C24—72no—
679C24—141no—
680C24—141no—
681C24—141no—
682C24—141no—
683C24—141no—
684C24—141no—
685C24—141no—
686C24—141no—
687C24C23×D711yescharacteristic
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—72no—
728C22×C4—72no—
729C22×C4—72no—
730C22×C4—72no—
731C22×C4—72no—
732C22×C4—72no—
733C22×C4—72no—
734C22×C4—72no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—148no—
738C22×C4—148no—
739C22×C4—148no—
740C22×C4—148no—
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—148no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
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×C4—284no—
790C22×C4—284no—
791C22×C4—284no—
792C22×C4—284no—
793C22×C4—284no—
794C22×C4—284no—
795C22×C4—284no—
796C22×C4—284no—
797C22×C4C2×C4×D712yes—
798C22×C4C2×C4×D712yes—
799C22×C4C2×C4×D712yes—
800C22×C4#115712yes—
801C22×C4#115712yes—
802C22×C4D4×D712yes—
803C22×C4D4×D712yes—
804C22×C4D4×D712yes—
805C22×C4Q8×D712yes—
806C22×C4Q8×D712yes—
807C4⋊C4—44no—
808C4⋊C4—44no—
809C4⋊C4—148no—
810C4⋊C4—284no—
811C4⋊C4—284no—
812C4⋊C4—284no—
813C4⋊C4—284no—
814C4⋊C4—284no—
815C22⋊C4—716no—
816C22⋊C4—148no—
817C22⋊C4—148no—
818C22⋊C4—284no—
819C42—44no—
820C42—284no—
821C2×C7C2×#38911yescharacteristic
822C2×C7C4×C22⋊Q811yescharacteristic
823C2×C7#232911yescharacteristic
824C2×C7D4×C4⋊C411yescharacteristic
825C2×C7#234911yescharacteristic
826C2×C7#235811yescharacteristic
827C2×C7#235911yescharacteristic
828C2×C7#242411yescharacteristic
829C2×C7#242511yescharacteristic
830C2×C7#243711yescharacteristic
831C2×C7#243811yescharacteristic
832C2×C7#244011yescharacteristic
833C2×C7#247311yescharacteristic
834C2×C7#250511yescharacteristic
835C2×C7#254911yescharacteristic
836D7—28no—
837C23—74no—
838C23—74no—
839C23—74no—
840C23—74no—
841C23—74no—
842C23—74no—
843C23—74no—
844C23—142no—
845C23—142no—
846C23—142no—
847C23—142no—
848C23—142no—
849C23—142no—
850C23—142no—
851C23—142no—
852C23—142no—
853C23—142no—
854C23—142no—
855C23—142no—
856C23—142no—
857C23—142no—
858C23—142no—
859C23—142no—
860C23—142no—
861C23—142no—
862C23—142no—
863C23—142no—
864C23—142no—
865C23—142no—
866C23—142no—
867C23—142no—
868C23—142no—
869C23—142no—
870C23—142no—
871C23—142no—
872C23C22×C4×D711yescharacteristic
873C23C2×#115711yescharacteristic
874C23C2×#115711yescharacteristic
875C23C2×D4×D711yescharacteristic
876C23C2×D4×D711yescharacteristic
877C23C2×D4×D711yescharacteristic
878C23#654811yescharacteristic
879C23#654811yescharacteristic
880C23C2×Q8×D711yescharacteristic
881C23C2×Q8×D711yescharacteristic
882C23#655111yescharacteristic
883C23D7×#4111yescharacteristic
884C23D7×#4111yescharacteristic
885C23D7×#4111yescharacteristic
886C23#655311yescharacteristic
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—74no—
935C2×C4—74no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—142no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—142no—
960C2×C4—2816no—
961C2×C4—2816no—
962C2×C4—2816no—
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—
974C2×C4—281no—
975C2×C4—281no—
976C2×C4—281no—
977C2×C4—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4—281no—
986C2×C4D7×C4⋊C414yes—
987C2×C4#645914yes—
988C7#1400411yescharacteristic, complemented, Sylow
989C22—78no—
990C22—144no—
991C22—144no—
992C22—144no—
993C22—144no—
994C22—144no—
995C22—144no—
996C22—144no—
997C22—144no—
998C22—144no—
999C22—144no—
1000C22—144no—
1001C22—144no—
1002C22—144no—
1003C22—144no—
1004C22C4×#115711yescharacteristic
1005C22#9017711yescharacteristic
1006C22#9018111yescharacteristic
1007C22#9018111yescharacteristic
1008C22C2×D7×C4⋊C411yescharacteristic
1009C22#9019811yescharacteristic
1010C22C2×#645911yescharacteristic
1011C22#9020211yescharacteristic
1012C22#9020211yescharacteristic
1013C22#9021811yescharacteristic
1014C22#9021911yescharacteristic
1015C22C4×D4×D711yescharacteristic
1016C22C4×D4×D711yescharacteristic
1017C22#9023811yescharacteristic
1018C22#9024111yescharacteristic
1019C22C4×Q8×D711yescharacteristic
1020C22#9026511yescharacteristic
1021C22#9026911yescharacteristic
1022C22#9027211yescharacteristic
1023C22D7×#12111yescharacteristic
1024C22#9030011yescharacteristic
1025C22#9030111yescharacteristic
1026C22#9030111yescharacteristic
1027C22D7×C22⋊Q811yescharacteristic
1028C22#9032211yescharacteristic
1029C22#9032511yescharacteristic
1030C22#9032911yescharacteristic
1031C22#9036911yescharacteristic
1032C22#9037011yescharacteristic
1033C22D7×#12511yescharacteristic
1034C22#9038111yescharacteristic
1035C22#9040811yescharacteristic
1036C22D7×C4⋊Q811yescharacteristic
1037C22#9041811yescharacteristic
1038C22#9042011yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—81no—
1046C4—144no—
1047C4—144no—
1048C4—282no—
1049C4—282no—
1050C4—282no—
1051C4—282no—
1052C4—561no—
1053C2—148no—
1054C2#1173081411yescharacteristic
1055C2C4×#645911yescharacteristic
1056C2#1173121711yescharacteristic
1057C2#1173134111yescharacteristic
1058C2#1173146711yescharacteristic
1059C2#1173168111yescharacteristic
1060C2#1173177111yescharacteristic
1061C2#1173346811yescharacteristic
1062C2D7×#38911yescharacteristic
1063C2#1173364711yescharacteristic
1064C2#1173368911yescharacteristic
1065C2#1173387711yescharacteristic
1066C2#1173388711yescharacteristic
1067C2#1173405711yescharacteristic
1068C2#1173407211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C4⋊#95C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC4⋊#95D7
hypocenterC7#14004
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
7. C2×#89419C2semidirect
8. C7×C4⋊#95C2semidirect
9. #11729322C2semidirect
10. #11729319C2semidirect
11. #11729290C2semidirect
13. #11727167C2semidirect
14. #11727163C2semidirect
15. #11727160C2semidirect
52. #89761C4semidirect
100. C2×C7×C4⋊C4C2×C4semidirect
133. C2×Dic7⋊C4C2×C4semidirect
152. C7⋊#95C2×C4semidirect
153. C7⋊#95C2×C4semidirect
168. C4⋊#95D7semidirect
311. (C2×D7)⋊C4C4⋊C4semidirect
571. C2×C4⋊C4C4×D7semidirect
657. C2×D7#389semidirect
988. C7#14004semidirect

Maximal subgroups

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

subgroupindex
C2×#897612
C2×C4×(C2×D7)⋊C42
C2×#894402
C2×#894392
C2×D7×#952
C2×#894192
C7×C4⋊#952
#117293222
#117293192
#117292902
(C2×D7)⋊#952
#117271672
#117271632
#117271602
#140047