Finite Group Databasebeta

← #13277807

Subgroups — #13277807

Order 1792.

1646 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
2C2×#89440C211yesmaximal, characteristic
3C2×#89438C211yesmaximal, characteristic
4C7×#1442C211yesmaximal, characteristic, complemented
5#11729324C211yesmaximal, characteristic
6#11727181C211yesmaximal, characteristic
7(C2×D7)⋊#95C211yesmaximal, characteristic
8#11727175C211yesmaximal, characteristic, complemented
9#11727162C211yesmaximal, characteristic
10#11727162C211yesmaximal, characteristic
11#11727161C211yesmaximal, characteristic, complemented
12#11727161C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×(C2×D7)⋊C4C2211yescharacteristic
19C22×(C2×D7)⋊C4C2211yescharacteristic
20C22×(C2×D7)⋊C4C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×C4×Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
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⋊C4×Dic7—24no—
52#89440C418yescomplemented
53#89438—24no—
54#14067—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—41no—
73C22×C4×D7—41no—
74C22×C4×D7—41no—
75C22×C4×D7—41no—
76C22×C4×D7C2×C414yes—
77C2×C7×C4⋊C4—22no—
78C2×C7×C4⋊C4—22no—
79C2×C7×C4⋊C4—22no—
80C2×(C2×D7)⋊C4—22no—
81C2×(C2×D7)⋊C4—22no—
82C2×(C2×D7)⋊C4—22no—
83C2×(C2×D7)⋊C4—22no—
84C2×(C2×D7)⋊C4—22no—
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—41no—
92C2×(C2×D7)⋊C4—41no—
93C2×(C2×D7)⋊C4—41no—
94C2×(C2×D7)⋊C4—41no—
95C2×(C2×D7)⋊C4C2×C414yes—
96C2×(C2×D7)⋊C4C2×C414yes—
97C2×(C2×D7)⋊C4Q814yes—
98C2×C4⋊Dic7—22no—
99C2×C4⋊Dic7—22no—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7C2×C414yes—
104C2×Dic7⋊C4—41no—
105C2×Dic7⋊C4—41no—
106C2×Dic7⋊C4C2×C414yes—
107C2×C4×Dic7—22no—
108C2×C4×Dic7—22no—
109C2×C4×Dic7—22no—
110C2×C4×Dic7—22no—
111C2×C4×Dic7—22no—
112C2×C4×Dic7—41no—
113C2×C4×Dic7—41no—
114C2×C4×Dic7—41no—
115C2×C4×Dic7—41no—
116C2×C4×Dic7—41no—
117C2×C4×Dic7—41no—
118C2×C4×Dic7D414yes—
119C7×#95—22no—
120C7×#95—22no—
121C7×#95—22no—
122C7×#95—41no—
123C7×#95—41no—
124C7×#95C2×C414yes—
125C7⋊#95—22no—
126C7⋊#95—22no—
127C7⋊#95—22no—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—41no—
134C7⋊#95—41no—
135C7⋊#95—41no—
136C7⋊#95—41no—
137C7⋊#95—41no—
138C7⋊#95C2×C414yes—
139C2×#385—71no—
140C2×C4×C4⋊C4—71no—
141C2×C4×C22⋊C4—71no—
142#1445—71no—
143#1442D711yescharacteristic, complemented
144#1439—71no—
145#1439—71no—
146#1437—71no—
147#1437—71no—
148#1436—71no—
149#1436—71no—
150#1436—71no—
151#1436—71no—
152#1434—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×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7C22×C412yes—
168C23×D7C2×Q812yes—
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×Dic7C22×C412yes—
259C22×Dic7C22×C412yes—
260C22×Dic7C22×C412yes—
261C22×Dic7C2×D412yes—
262C22×Dic7C2×D412yes—
263C22×Dic7C2×Q812yes—
264C22×Dic7#4112yes—
265C22×Dic7#4112yes—
266C22×Dic7#4112yes—
267C22×Dic7#4112yes—
268C2×C4×D7—28no—
269C2×C4×D7—44no—
270C2×C4×D7—44no—
271C2×C4×D7—44no—
272C2×C4×D7—44no—
273C2×C4×D7—44no—
274C2×C4×D7—44no—
275C7×C4⋊C4—28no—
276(C2×D7)⋊C4—28no—
277(C2×D7)⋊C4—28no—
278(C2×D7)⋊C4—28no—
279(C2×D7)⋊C4—44no—
280(C2×D7)⋊C4—44no—
281(C2×D7)⋊C4—44no—
282C4⋊Dic7—28no—
283C4⋊Dic7—44no—
284Dic7⋊C4—44no—
285C4×Dic7—28no—
286C4×Dic7—44no—
287C4×Dic7—44no—
288C4×Dic7—44no—
289C24×C4—71no—
290C22×C4⋊C4—71no—
291C22×C4⋊C4—71no—
292C22×C4⋊C4—71no—
293C22×C4⋊C4C2×D711yescharacteristic
294C22×C22⋊C4—71no—
295C22×C22⋊C4—71no—
296C22×C22⋊C4—71no—
297C22×C22⋊C4—71no—
298C22×C22⋊C4—71no—
299C22×C22⋊C4—71no—
300C22×C42—71no—
301C22×C42—71no—
302C22×C42—71no—
303C22×C42—71no—
304#385—78no—
305C4×C4⋊C4—144no—
306C4×C22⋊C4—144no—
307C2×#95—71no—
308C2×#95—71no—
309C2×#95—71no—
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×#95C2×D711yescharacteristic
322C2×#95C2×D711yescharacteristic
323C2×#95C2×D711yescharacteristic
324C2×#95C2×D711yescharacteristic
325C2×#95C2×D711yescharacteristic
326C2×#95C2×D711yescharacteristic
327C23×C7C23×C411yescharacteristic
328C23×C7C22×D411yescharacteristic
329C23×C7C22×Q811yescharacteristic
330C23×C7C2×#4111yescharacteristic
331C23×C7C2×#4111yescharacteristic
332C23×C7C2×#4111yescharacteristic
333C23×C7C2×#4111yescharacteristic
334C23×C7C2×#4111yescharacteristic
335C23×C7C2×#4111yescharacteristic
336C23×C7C2×#4111yescharacteristic
337C23×C7C2×#4111yescharacteristic
338C23×C7H(5,𝔽2)11yescharacteristic
339C23×C7H(5,𝔽2)11yescharacteristic
340C23×C7H(5,𝔽2)11yescharacteristic
341C23×C7H(5,𝔽2)11yescharacteristic
342C22×D7—22no—
343C22×D7—22no—
344C22×D7—22no—
345C22×D7—22no—
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—22no—
349C22×D7—22no—
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—41no—
361C22×D7—41no—
362C22×D7—41no—
363C22×D7—41no—
364C22×D7—41no—
365C22×D7—41no—
366C22×D7—41no—
367C22×D7—41no—
368C22×D7—41no—
369C22×D7—41no—
370C22×D7—41no—
371C22×D7—41no—
372C22×D7—41no—
373C22×D7—41no—
374C22×D7—41no—
375C22×D7—41no—
376C22×D7C4×Q814yes—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
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—41no—
399C2×C4×C7—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
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#11714yes—
426C2×Dic7—22no—
427C2×Dic7—22no—
428C2×Dic7—22no—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
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—41no—
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×Dic7C4×D414yes—
474C2×Dic7C22⋊Q814yes—
475C4×D7—416no—
476C25—71no—
477C23×C4—71no—
478C23×C4—71no—
479C23×C4—71no—
480C23×C4—71no—
481C23×C4—71no—
482C23×C4—71no—
483C23×C4—74no—
484C23×C4—71no—
485C23×C4—142no—
486C23×C4—142no—
487C23×C4—281no—
488C23×C4—281no—
489C23×C4—281no—
490C23×C4—281no—
491C23×C4C22×D711yescharacteristic
492C23×C4C22×D711yescharacteristic
493C23×C4C22×D711yescharacteristic
494C23×C4C22×D711yescharacteristic
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—74no—
502C2×C4⋊C4—74no—
503C2×C4⋊C4—142no—
504C2×C4⋊C4—142no—
505C2×C4⋊C4—142no—
506C2×C4⋊C4—142no—
507C2×C4⋊C4—281no—
508C2×C4⋊C4—281no—
509C2×C4⋊C4—281no—
510C2×C22⋊C4—74no—
511C2×C22⋊C4—74no—
512C2×C22⋊C4—74no—
513C2×C22⋊C4—142no—
514C2×C22⋊C4—142no—
515C2×C22⋊C4—142no—
516C2×C22⋊C4—142no—
517C2×C22⋊C4—142no—
518C2×C22⋊C4—142no—
519C2×C22⋊C4—142no—
520C2×C22⋊C4—142no—
521C2×C22⋊C4—142no—
522C2×C22⋊C4—142no—
523C2×C22⋊C4—142no—
524C2×C22⋊C4—281no—
525C2×C22⋊C4—281no—
526C2×C22⋊C4—281no—
527C2×C22⋊C4—281no—
528C2×C42—74no—
529C2×C42—142no—
530C2×C42—142no—
531C2×C42—142no—
532C2×C42—142no—
533C2×C42—142no—
534C2×C42—281no—
535C2×C42—281no—
536C2×C42—281no—
537C2×C42—281no—
538C2×C42—281no—
539C2×C42—281no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—41no—
544#95—41no—
545#95—74no—
546#95—142no—
547#95—142no—
548#95—142no—
549#95—142no—
550#95—142no—
551#95—142no—
552#95—142no—
553#95—142no—
554#95—281no—
555#95—281no—
556#95—281no—
557#95—281no—
558#95—281no—
559#95C4×D714yes—
560C22×C7C2×#11711yescharacteristic
561C22×C7C2×C4×D411yescharacteristic
562C22×C7C2×C4×Q811yescharacteristic
563C22×C7C4×#4111yescharacteristic
564C22×C7C4×#4111yescharacteristic
565C22×C7#51811yescharacteristic
566C22×C7#51811yescharacteristic
567C22×C7C2×C22⋊Q811yescharacteristic
568C22×C7#52511yescharacteristic
569C22×C7#52511yescharacteristic
570C22×C7#52511yescharacteristic
571C22×C7#52911yescharacteristic
572C22×C7#52911yescharacteristic
573C22×C7#52911yescharacteristic
574C22×C7#53311yescharacteristic
575C22×C7#53411yescharacteristic
576C22×C7#53511yescharacteristic
577C22×C7#53811yescharacteristic
578C22×C7#53811yescharacteristic
579C22×C7#55111yescharacteristic
580C22×C7#55111yescharacteristic
581C22×C7#55111yescharacteristic
582C22×C7#55311yescharacteristic
583C22×C7#55311yescharacteristic
584C22×C7#55311yescharacteristic
585C22×C7#55311yescharacteristic
586C22×C7#55311yescharacteristic
587C22×C7#55311yescharacteristic
588C22×C7#55411yescharacteristic
589C22×C7#55411yescharacteristic
590C22×C7#55411yescharacteristic
591C22×C7#55411yescharacteristic
592C22×C7#55911yescharacteristic
593C22×C7#55911yescharacteristic
594C22×C7#55911yescharacteristic
595C2×D7—24no—
596C2×D7—24no—
597C2×D7—24no—
598C2×D7—42no—
599C2×D7—42no—
600C2×D7—42no—
601C2×D7—42no—
602C2×D7—42no—
603C2×D7—42no—
604C2×D7—42no—
605C2×D7—42no—
606C2×D7—42no—
607C2×D7—42no—
608C2×D7—42no—
609C2×D7—42no—
610C4×C7—24no—
611C4×C7—42no—
612C4×C7—42no—
613C4×C7—42no—
614C4×C7—42no—
615C4×C7—42no—
616C4×C7—81no—
617Dic7—24no—
618Dic7—24no—
619Dic7—42no—
620Dic7—42no—
621Dic7—42no—
622Dic7—42no—
623Dic7—81no—
624C24—72no—
625C24—72no—
626C24—72no—
627C24—141no—
628C24—141no—
629C24—141no—
630C24—141no—
631C24—141no—
632C24—141no—
633C24—141no—
634C24—141no—
635C24—141no—
636C24—141no—
637C24—141no—
638C24—141no—
639C24C23×D711yescharacteristic
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
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—72no—
682C22×C4—72no—
683C22×C4—72no—
684C22×C4—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—72no—
689C22×C4—72no—
690C22×C4—72no—
691C22×C4—148no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
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—284no—
732C22×C4—284no—
733C22×C4—284no—
734C22×C4—284no—
735C22×C4—284no—
736C22×C4—284no—
737C22×C4C2×C4×D712yes—
738C22×C4C2×C4×D712yes—
739C22×C4C2×C4×D712yes—
740C22×C4D4×D712yes—
741C22×C4#115912yes—
742C22×C4#115912yes—
743C22×C4Q8×D712yes—
744C22×C4#116112yes—
745C4⋊C4—28no—
746C4⋊C4—148no—
747C4⋊C4—284no—
748C4⋊C4—284no—
749C22⋊C4—148no—
750C22⋊C4—148no—
751C22⋊C4—148no—
752C22⋊C4—284no—
753C22⋊C4—284no—
754C22⋊C4—284no—
755C42—148no—
756C42—284no—
757C42—284no—
758C42—284no—
759C2×C7#229011yescharacteristic
760C2×C7C4×C22⋊Q811yescharacteristic
761C2×C7#232111yescharacteristic
762C2×C7#234511yescharacteristic
763C2×C7#235711yescharacteristic
764C2×C7#236811yescharacteristic
765C2×C7#237411yescharacteristic
766C2×C7#257911yescharacteristic
767C2×C7#258011yescharacteristic
768C2×C7#258711yescharacteristic
769C2×C7#258911yescharacteristic
770C2×C7#259511yescharacteristic
771C2×C7#259711yescharacteristic
772C2×C7#259811yescharacteristic
773C2×C7#260011yescharacteristic
774D7—44no—
775C23—74no—
776C23—142no—
777C23—142no—
778C23—142no—
779C23—142no—
780C23—142no—
781C23—142no—
782C23—142no—
783C23—142no—
784C23—142no—
785C23—142no—
786C23—142no—
787C23—142no—
788C23—142no—
789C23—142no—
790C23—142no—
791C23—142no—
792C23—142no—
793C23—142no—
794C23—281no—
795C23—281no—
796C23—281no—
797C23—281no—
798C23—281no—
799C23—281no—
800C23—281no—
801C23—281no—
802C23—281no—
803C23—281no—
804C23—281no—
805C23—281no—
806C23—281no—
807C23—281no—
808C23—281no—
809C23—281no—
810C23C22×C4×D711yescharacteristic
811C23C2×D4×D711yescharacteristic
812C23C2×#115911yescharacteristic
813C23C2×#115911yescharacteristic
814C23#654811yescharacteristic
815C23C2×Q8×D711yescharacteristic
816C23C2×#116111yescharacteristic
817C23D7×#4111yescharacteristic
818C23D7×#4111yescharacteristic
819C23D7×#4111yescharacteristic
820C23D7×#4111yescharacteristic
821C23D7×#4111yescharacteristic
822C23#655311yescharacteristic
823C23#655311yescharacteristic
824C23#655311yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
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—74no—
874C2×C4—74no—
875C2×C4—142no—
876C2×C4—142no—
877C2×C4—142no—
878C2×C4—142no—
879C2×C4—142no—
880C2×C4—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
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—2816no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
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#645514yes—
924C7#1406711yescharacteristic, complemented, Sylow
925C22—144no—
926C22—144no—
927C22—144no—
928C22—282no—
929C22—282no—
930C22—282no—
931C22—282no—
932C22—282no—
933C22—282no—
934C22—282no—
935C22—282no—
936C22—282no—
937C22—282no—
938C22—282no—
939C22—282no—
940C22C2×#645511yescharacteristic
941C22#9021211yescharacteristic
942C22#9021311yescharacteristic
943C22C4×#115911yescharacteristic
944C22C4×D4×D711yescharacteristic
945C22#9023611yescharacteristic
946C22C4×Q8×D711yescharacteristic
947C22#9027711yescharacteristic
948C22#9029211yescharacteristic
949C22#9029611yescharacteristic
950C22#9030511yescharacteristic
951C22#9031511yescharacteristic
952C22D7×C22⋊Q811yescharacteristic
953C22#9031811yescharacteristic
954C22#9032611yescharacteristic
955C22#9032611yescharacteristic
956C22#9034011yescharacteristic
957C22#9034711yescharacteristic
958C22#9034811yescharacteristic
959C22#9034911yescharacteristic
960C22#9035211yescharacteristic
961C22#9036511yescharacteristic
962C22#9037211yescharacteristic
963C22#9037211yescharacteristic
964C22#9037211yescharacteristic
965C22#9037911yescharacteristic
966C22#9038111yescharacteristic
967C22#9038611yescharacteristic
968C22#9038611yescharacteristic
969C22#9038611yescharacteristic
970C22#9039511yescharacteristic
971C22#9039611yescharacteristic
972C22#9039611yescharacteristic
973C22#9039711yescharacteristic
974C22#9042111yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—144no—
983C4—144no—
984C4—282no—
985C4—282no—
986C4—282no—
987C4—282no—
988C4—561no—
989C2—284no—
990C2#1173160511yescharacteristic
991C2#1173182211yescharacteristic
992C2#1173238611yescharacteristic
993C2#1173275611yescharacteristic
994C2#1173293211yescharacteristic
995C2#1173327111yescharacteristic
996C2#1173364611yescharacteristic
997C2#1173424711yescharacteristic
998C2#1173440811yescharacteristic
999C2#1173497611yescharacteristic
1000C2#1173524711yescharacteristic
1001C2#1173540511yescharacteristic
1002C2#1173564111yescharacteristic
1003C2#1173564411yescharacteristic
1004C2#1173564811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1442C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1442D7
hypocenterC7#14067
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×Dic7C2semidirect
4. C7×#1442C2semidirect
8. #11727175C2semidirect
11. #11727161C2semidirect
12. #11727161C2semidirect
13. #11727161C2semidirect
14. #11727160C2semidirect
15. #11727156C2semidirect
52. #89440C4semidirect
143. #1442D7semidirect
924. C7#14067semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×Dic72
C2×#894402
C2×#894382
C7×#14422
#117293242
#117271812
(C2×D7)⋊#952
#117271752
#117271622
#117271612
#117271602
#117271562
#140677