Finite Group Databasebeta

← #13277463

Subgroups — #13277463

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
2C2×#89440C211yesmaximal, characteristic
3C2×D7×#95C211yesmaximal, characteristic
4C7×#1434C211yesmaximal, characteristic, complemented
5#11729288C211yesmaximal, characteristic, complemented
6(C2×D7)⋊#95C211yesmaximal, characteristic
7(C2×D7)⋊#95C211yesmaximal, characteristic
8(C2×D7)⋊#95C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10#11727177C211yesmaximal, characteristic, complemented
11#11727175C211yesmaximal, characteristic, complemented
12#11727172C211yesmaximal, characteristic, complemented
13#11727170C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×C4×Dic7C2211yescharacteristic
27C2×C7×#95C2211yescharacteristic
28C2×C7×#95C2211yescharacteristic
29C2×C7×#95C2211yescharacteristic
30C2×C7×#95C2211yescharacteristic
31C2×C7×#95C2211yescharacteristic
32C2×C7×#95C2211yescharacteristic
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
51C4×(C2×D7)⋊C4—24no—
52#89440C418yescomplemented
53D7×#95—24no—
54#14040—71nomaximal, Sylow
55C24×D7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×Dic7C2311yescharacteristic
64C23×Dic7C2311yescharacteristic
65C23×Dic7C2311yescharacteristic
66C23×Dic7C2311yescharacteristic
67C23×Dic7C2311yescharacteristic
68C23×Dic7C2311yescharacteristic
69C23×Dic7C2311yescharacteristic
70C22×C4×D7—22no—
71C22×C4×D7—22no—
72C22×C4×D7—22no—
73C22×C4×D7—22no—
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—41no—
82C22×C4×D7—41no—
83C22×C4×D7—41no—
84C22×C4×D7—41no—
85C22×C4×D7—41no—
86C22×C4×D7—41no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7C2×C414yes—
90C22×C4×D7D414yes—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×(C2×D7)⋊C4—22no—
95C2×(C2×D7)⋊C4—22no—
96C2×(C2×D7)⋊C4—22no—
97C2×(C2×D7)⋊C4—22no—
98C2×(C2×D7)⋊C4—22no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4C2×C414yes—
104C2×(C2×D7)⋊C4C2×C414yes—
105C2×(C2×D7)⋊C4Q814yes—
106C2×C4⋊Dic7—41no—
107C2×C4⋊Dic7—41no—
108C2×C4⋊Dic7C2×C414yescomplemented
109C2×Dic7⋊C4—41no—
110C2×Dic7⋊C4—41no—
111C2×Dic7⋊C4C2×C414yescomplemented
112C2×C4×Dic7—22no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C7×#95—22no—
116C7×#95—22no—
117C7×#95—22no—
118C7×#95—41no—
119C7×#95—41no—
120C7×#95C2×C414yescomplemented
121C7⋊#95—22no—
122C7⋊#95—22no—
123C7⋊#95—22no—
124C7⋊#95—22no—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—41no—
131C7⋊#95—41no—
132C7⋊#95—41no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yescomplemented
139C2×#385—71no—
140C2×C4×C22⋊C4—71no—
141C22×#95—71no—
142#1445—71no—
143#1445—71no—
144#1443—71no—
145#1443—71no—
146#1436—71no—
147#1436—71no—
148#1434—71no—
149#1434D711yescharacteristic, complemented
150C22⋊#95—71no—
151C22⋊#95—71no—
152C22⋊#95—71no—
153C22⋊#95—71no—
154C24×C7C2411yescharacteristic
155C23×D7—21no—
156C23×D7—21no—
157C23×D7—21no—
158C23×D7—21no—
159C23×D7—21no—
160C23×D7—21no—
161C23×D7—21no—
162C23×D7—21no—
163C23×D7C22×C412yes—
164C23×D7C2×D412yes—
165C23×D7C2×Q812yes—
166C23×D7#4112yes—
167C23×D7#4112yes—
168C23×D7#4112yes—
169C23×D7#4112yes—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—21no—
173C22×C4×C7—21no—
174C22×C4×C7—21no—
175C22×C4×C7—21no—
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×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×Q812yes—
216C22×C4×C7#4112yes—
217C22×C4×C7#4112yes—
218C22×C4×C7#4112yes—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—21no—
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×Dic7C22×C412yes—
263C22×Dic7C22×C412yes—
264C22×Dic7C22×C412yes—
265C22×Dic7C2×D412yes—
266C22×Dic7C2×Q812yes—
267C22×Dic7#4112yes—
268C2×C4×D7—28no—
269C2×C4×D7—28no—
270C2×C4×D7—28no—
271C2×C4×D7—28no—
272C2×C4×D7—44no—
273C2×C4×D7—44no—
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—
281C2×C4×D7—44no—
282C2×C4×D7—44no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C2×C4×D7—44no—
288C2×C4×D7—44no—
289C42×C7—44no—
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—44no—
294C4⋊Dic7—44no—
295Dic7⋊C4—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C24×C4—71no—
299C24×C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C22⋊C4—71no—
303C22×C22⋊C4—71no—
304C22×C22⋊C4—71no—
305C22×C22⋊C4—71no—
306C22×C42—71no—
307C22×C42C2×D711yescharacteristic
308#385—78no—
309C4×C22⋊C4—144no—
310C2×#95—71no—
311C2×#95—71no—
312C2×#95—71no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
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—144no—
329C2×#95C2×D711yescharacteristic
330C2×#95C2×D711yescharacteristic
331C2×#95C2×D711yescharacteristic
332C2×#95C2×D711yescharacteristic
333C2×#95C2×D711yescharacteristic
334C2×#95C2×D711yescharacteristic
335C23×C7C23×C411yescharacteristic
336C23×C7C22×D411yescharacteristic
337C23×C7C22×Q811yescharacteristic
338C23×C7C2×#4111yescharacteristic
339C23×C7C2×#4111yescharacteristic
340C23×C7C2×#4111yescharacteristic
341C23×C7C2×#4111yescharacteristic
342C23×C7C2×#4111yescharacteristic
343C23×C7C2×#4111yescharacteristic
344C23×C7C2×#4111yescharacteristic
345C23×C7C2×#4111yescharacteristic
346C23×C7H(5,𝔽2)11yescharacteristic
347C23×C7H(5,𝔽2)11yescharacteristic
348C23×C7H(5,𝔽2)11yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C22×D7—22no—
351C22×D7—22no—
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—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7—22no—
377C22×D7—22no—
378C22×D7#11714yes—
379C22×D7C4×D414yes—
380C22×D7C4×Q814yes—
381C22×D7C22⋊Q814yes—
382C22×D7#12314yes—
383C22×D7#12514yes—
384C22×D7#12614yes—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
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—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
410C2×C4×C7—41no—
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#12314yes—
434C2×Dic7—22no—
435C2×Dic7—22no—
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—22no—
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—
483C4×D7—416no—
484C4×D7—416no—
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—74no—
494C23×C4—74no—
495C23×C4—71no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—142no—
499C23×C4—142no—
500C23×C4—142no—
501C23×C4—142no—
502C23×C4—142no—
503C23×C4—142no—
504C23×C4—142no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4—281no—
508C23×C4—281no—
509C23×C4—281no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4—281no—
513C23×C4—281no—
514C23×C4—281no—
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D711yescharacteristic
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C23×C4C22×D711yescharacteristic
522C2×C4⋊C4—74no—
523C2×C4⋊C4—74no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4—281no—
526C2×C4⋊C4—281no—
527C2×C4⋊C4—281no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—74no—
530C2×C22⋊C4—74no—
531C2×C22⋊C4—142no—
532C2×C22⋊C4—142no—
533C2×C22⋊C4—142no—
534C2×C22⋊C4—142no—
535C2×C22⋊C4—142no—
536C2×C22⋊C4—142no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—142no—
544C2×C42—281no—
545C2×C42—281no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—41no—
550#95—41no—
551#95—74no—
552#95—142no—
553#95—142no—
554#95—142no—
555#95—142no—
556#95—142no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—281no—
562#95—281no—
563#95—281no—
564#95—281no—
565#95—281no—
566#95—281no—
567#95—281no—
568#95—281no—
569#95C4×D714yescomplemented
570C22×C7C2×#11711yescharacteristic
571C22×C7C2×C4×D411yescharacteristic
572C22×C7C2×C4×Q811yescharacteristic
573C22×C7C4×#4111yescharacteristic
574C22×C7C4×#4111yescharacteristic
575C22×C7#51811yescharacteristic
576C22×C7#51811yescharacteristic
577C22×C7C2×C22⋊Q811yescharacteristic
578C22×C7C2×#12311yescharacteristic
579C22×C7C2×#12311yescharacteristic
580C22×C7#52511yescharacteristic
581C22×C7C2×#12511yescharacteristic
582C22×C7C2×#12611yescharacteristic
583C22×C7#52911yescharacteristic
584C22×C7#52911yescharacteristic
585C22×C7#53411yescharacteristic
586C22×C7#53511yescharacteristic
587C22×C7#53811yescharacteristic
588C22×C7#53811yescharacteristic
589C22×C7#55111yescharacteristic
590C22×C7#55111yescharacteristic
591C22×C7#55111yescharacteristic
592C22×C7#55111yescharacteristic
593C22×C7#55111yescharacteristic
594C22×C7#55111yescharacteristic
595C22×C7#55111yescharacteristic
596C22×C7#55111yescharacteristic
597C22×C7#55311yescharacteristic
598C22×C7#55311yescharacteristic
599C22×C7#55311yescharacteristic
600C22×C7#55311yescharacteristic
601C22×C7#55411yescharacteristic
602C22×C7#55411yescharacteristic
603C22×C7#55411yescharacteristic
604C22×C7#55411yescharacteristic
605C2×D7—24no—
606C2×D7—24no—
607C2×D7—24no—
608C2×D7—24no—
609C2×D7—24no—
610C2×D7—24no—
611C2×D7—24no—
612C2×D7—24no—
613C2×D7—24no—
614C2×D7—24no—
615C2×D7—24no—
616C2×D7—24no—
617C2×D7—24no—
618C2×D7—24no—
619C2×D7#38718yes—
620C4×C7—24no—
621C4×C7—42no—
622C4×C7—42no—
623C4×C7—42no—
624C4×C7—42no—
625C4×C7—42no—
626C4×C7—81no—
627Dic7—42no—
628Dic7—42no—
629Dic7—42no—
630Dic7—42no—
631Dic7—42no—
632Dic7—42no—
633Dic7—81no—
634C24—72no—
635C24—72no—
636C24—72no—
637C24—72no—
638C24—72no—
639C24—72no—
640C24—72no—
641C24—141no—
642C24—141no—
643C24—141no—
644C24—141no—
645C24—141no—
646C24—141no—
647C24—141no—
648C24—141no—
649C24C23×D711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
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—72no—
692C22×C4—72no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—148no—
698C22×C4—148no—
699C22×C4—148no—
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—148no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4—284no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4—284no—
750C22×C4—284no—
751C22×C4—284no—
752C22×C4—284no—
753C22×C4—284no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4C2×C4×D712yes—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4#115712yes—
765C22×C4#115712yes—
766C22×C4D4×D712yes—
767C22×C4#115912yes—
768C22×C4Q8×D712yes—
769C4⋊C4—284no—
770C4⋊C4—284no—
771C22⋊C4—148no—
772C22⋊C4—148no—
773C22⋊C4—148no—
774C22⋊C4—284no—
775C42—44no—
776C42—284no—
777C2×C7C2×#38711yescharacteristic
778C2×C7C4×#12311yescharacteristic
779C2×C7#232111yescharacteristic
780C2×C7#235311yescharacteristic
781C2×C7#235311yescharacteristic
782C2×C7#236811yescharacteristic
783C2×C7#236811yescharacteristic
784C2×C7#248211yescharacteristic
785C2×C7#248311yescharacteristic
786C2×C7#248711yescharacteristic
787C2×C7#250511yescharacteristic
788C2×C7#250511yescharacteristic
789C2×C7#251011yescharacteristic
790C2×C7#251011yescharacteristic
791C2×C7#257911yescharacteristic
792D7—28no—
793C23—74no—
794C23—74no—
795C23—74no—
796C23—74no—
797C23—74no—
798C23—74no—
799C23—74no—
800C23—142no—
801C23—142no—
802C23—142no—
803C23—142no—
804C23—142no—
805C23—142no—
806C23—142no—
807C23—142no—
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—142no—
827C23—142no—
828C23C22×C4×D711yescharacteristic
829C23C2×#115711yescharacteristic
830C23C2×#115711yescharacteristic
831C23C2×D4×D711yescharacteristic
832C23C2×#115911yescharacteristic
833C23#654811yescharacteristic
834C23C2×Q8×D711yescharacteristic
835C23D7×#4111yescharacteristic
836C23D7×#4111yescharacteristic
837C23D7×#4111yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23#655311yescharacteristic
841C23#655311yescharacteristic
842C23#655311yescharacteristic
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—41no—
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—41no—
889C2×C4—41no—
890C2×C4—41no—
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—142no—
905C2×C4—142no—
906C2×C4—142no—
907C2×C4—142no—
908C2×C4—142no—
909C2×C4—2816no—
910C2×C4—2816no—
911C2×C4—2816no—
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×C4—281no—
939C2×C4—281no—
940C2×C4—281no—
941C2×C4—281no—
942C2×C4—281no—
943C2×C4#644614yes—
944C7#1404011yescharacteristic, complemented, Sylow
945C22—78no—
946C22—144no—
947C22—144no—
948C22—144no—
949C22—144no—
950C22—144no—
951C22—144no—
952C22—144no—
953C22—144no—
954C22—144no—
955C22—144no—
956C22—144no—
957C22—144no—
958C22—144no—
959C22—144no—
960C22C4×#115711yescharacteristic
961C22C2×#644611yescharacteristic
962C22#9020211yescharacteristic
963C22D7×#11711yescharacteristic
964C22#9021211yescharacteristic
965C22#9021811yescharacteristic
966C22#9021811yescharacteristic
967C22#9021811yescharacteristic
968C22#9021911yescharacteristic
969C22#9022111yescharacteristic
970C22#9022111yescharacteristic
971C22C4×#115911yescharacteristic
972C22C4×D4×D711yescharacteristic
973C22#9023611yescharacteristic
974C22#9023811yescharacteristic
975C22#9024711yescharacteristic
976C22#9024811yescharacteristic
977C22C4×Q8×D711yescharacteristic
978C22#9027011yescharacteristic
979C22#9029811yescharacteristic
980C22#9030511yescharacteristic
981C22D7×C22⋊Q811yescharacteristic
982C22#9032611yescharacteristic
983C22D7×#12311yescharacteristic
984C22#9034411yescharacteristic
985C22#9034911yescharacteristic
986C22#9034911yescharacteristic
987C22#9036911yescharacteristic
988C22#9037011yescharacteristic
989C22D7×#12511yescharacteristic
990C22#9038111yescharacteristic
991C22D7×#12611yescharacteristic
992C22#9039511yescharacteristic
993C22#9039611yescharacteristic
994C22#9040011yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—282no—
1003C4—282no—
1004C4—282no—
1005C4—282no—
1006C4—282no—
1007C4—282no—
1008C4—561no—
1009C2—148no—
1010C2#1173086211yescharacteristic
1011C2C4×#644611yescharacteristic
1012C2#1173122011yescharacteristic
1013C2#1173135711yescharacteristic
1014C2#1173157511yescharacteristic
1015C2#1173168111yescharacteristic
1016C2#1173174611yescharacteristic
1017C2D7×#38711yescharacteristic
1018C2#1173275611yescharacteristic
1019C2#1173278511yescharacteristic
1020C2#1173281511yescharacteristic
1021C2#1173327211yescharacteristic
1022C2#1173328011yescharacteristic
1023C2#1173331111yescharacteristic
1024C2#1173331511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1434C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1434D7
hypocenterC7#14040
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. C7×#1434C2semidirect
5. #11729288C2semidirect
10. #11727177C2semidirect
11. #11727175C2semidirect
12. #11727172C2semidirect
13. #11727170C2semidirect
14. #11727161C2semidirect
15. #11727160C2semidirect
52. #89440C4semidirect
108. C2×C4⋊Dic7C2×C4semidirect
111. C2×Dic7⋊C4C2×C4semidirect
120. C7×#95C2×C4semidirect
138. C7⋊#95C2×C4semidirect
149. #1434D7semidirect
569. #95C4×D7semidirect
944. C7#14040semidirect

Maximal subgroups

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

subgroupindex
C2×C4×(C2×D7)⋊C42
C2×#894402
C2×D7×#952
C7×#14342
#117292882
(C2×D7)⋊#952
#117271772
#117271752
#117271722
#117271702
#117271612
#117271602
#140407