Finite Group Databasebeta

← #13276712

Subgroups — #13276712

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89759C211yesmaximal, characteristic
2C2×C4×(C2×D7)⋊C4C211yesmaximal, characteristic
3C2×#89440C211yesmaximal, characteristic
4C2×D7×#95C211yesmaximal, characteristic
5C2×#89427C211yesmaximal, characteristic, complemented
6C7×#1436C211yesmaximal, characteristic, complemented
7#11729320C211yesmaximal, characteristic, complemented
8#11729288C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11(C2×D7)⋊#95C211yesmaximal, characteristic
12#11727176C211yesmaximal, characteristic, complemented
13#11727172C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727161C211yesmaximal, characteristic, complemented
16C23×C4×D7C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
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
51#89759—24no—
52C4×(C2×D7)⋊C4—24no—
53#89440C418yescomplemented
54D7×#95—24no—
55#89427—24no—
56#13980—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—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—41no—
86C22×C4×D7—41no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7—41no—
91C22×C4×D7C2×C414yes—
92C22×C4×D7Q814yes—
93C2×C7×C4⋊C4—22no—
94C2×C7×C4⋊C4—22no—
95C2×C7×C4⋊C4—41no—
96C2×C42×C7—22no—
97C2×C42×C7—22no—
98C2×C42×C7—41no—
99C2×(C2×D7)⋊C4—22no—
100C2×(C2×D7)⋊C4—22no—
101C2×(C2×D7)⋊C4—22no—
102C2×(C2×D7)⋊C4—22no—
103C2×(C2×D7)⋊C4—22no—
104C2×(C2×D7)⋊C4—22no—
105C2×(C2×D7)⋊C4—22no—
106C2×(C2×D7)⋊C4—22no—
107C2×(C2×D7)⋊C4—22no—
108C2×(C2×D7)⋊C4C2×C414yes—
109C2×(C2×D7)⋊C4C2×C414yes—
110C2×(C2×D7)⋊C4D414yes—
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7—41no—
114C2×C4⋊Dic7—41no—
115C2×C4⋊Dic7—41no—
116C2×C4⋊Dic7C2×C414yescomplemented
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4C2×C414yescomplemented
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—41no—
123C7×#95—22no—
124C7×#95—41no—
125C7×#95—41no—
126C7×#95C2×C414yescomplemented
127C7×#95D414yes—
128C7⋊#95—22no—
129C7⋊#95—22no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95C2×C414yescomplemented
145C2×#387—71no—
146C2×#385—71no—
147C2×#380—71no—
148C2×C4×C22⋊C4—71no—
149C22×#95—71no—
150#1445—71no—
151#1443—71no—
152#1442—71no—
153#1441—71no—
154#1436—71no—
155#1436D711yescharacteristic, complemented
156#1434—71no—
157C22⋊#95—71no—
158C22⋊#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×D7C22×C412yes—
170C23×D7C2×D412yes—
171C23×D7C2×Q812yes—
172C23×D7#4112yes—
173C23×D7#4112yes—
174C23×D7#4112yes—
175C23×D7#4112yes—
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—28no—
275C2×C4×D7—28no—
276C2×C4×D7—28no—
277C2×C4×D7—28no—
278C2×C4×D7—28no—
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—
289C2×C4×D7—44no—
290C2×C4×D7—44no—
291C2×C4×D7—44no—
292C2×C4×D7—44no—
293C2×C4×D7—44no—
294C2×C4×D7—44no—
295C7×C4⋊C4—44no—
296C42×C7—44no—
297(C2×D7)⋊C4—28no—
298(C2×D7)⋊C4—28no—
299(C2×D7)⋊C4—28no—
300(C2×D7)⋊C4—44no—
301C4⋊Dic7—44no—
302C4⋊Dic7—44no—
303Dic7⋊C4—28no—
304C4×Dic7—44no—
305C24×C4—71no—
306C24×C4—71no—
307C24×C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4—71no—
310C22×C4⋊C4—71no—
311C22×C4⋊C4C2×D711yescharacteristic
312C22×C22⋊C4—71no—
313C22×C22⋊C4—71no—
314C22×C22⋊C4—71no—
315C22×C22⋊C4—71no—
316C22×C42—71no—
317C22×C42C2×D711yescharacteristic
318#387—144no—
319#385—78no—
320#380—144no—
321C4×C22⋊C4—144no—
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×#95—71no—
333C2×#95—71no—
334C2×#95—71no—
335C2×#95—71no—
336C2×#95—71no—
337C2×#95—71no—
338C2×#95—71no—
339C2×#95—144no—
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C2×#95C2×D711yescharacteristic
343C2×#95C2×D711yescharacteristic
344C2×#95C2×D711yescharacteristic
345C23×C7C23×C411yescharacteristic
346C23×C7C22×D411yescharacteristic
347C23×C7C22×D411yescharacteristic
348C23×C7C22×Q811yescharacteristic
349C23×C7C2×#4111yescharacteristic
350C23×C7C2×#4111yescharacteristic
351C23×C7C2×#4111yescharacteristic
352C23×C7C2×#4111yescharacteristic
353C23×C7C2×#4111yescharacteristic
354C23×C7C2×#4111yescharacteristic
355C23×C7C2×#4111yescharacteristic
356C23×C7H(5,𝔽2)11yescharacteristic
357C23×C7H(5,𝔽2)11yescharacteristic
358C23×C7H(5,𝔽2)11yescharacteristic
359C23×C72−1+411yescharacteristic
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—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#11714yes—
389C22×D7C4×D414yes—
390C22×D7C4×Q814yes—
391C22×D7C22⋊Q814yes—
392C22×D7#12314yes—
393C22×D7#12514yes—
394C22×D7#12614yes—
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—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—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×C7C4×D414yes—
443C2×C4×C7C22⋊Q814yes—
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—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—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×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—
493C4×D7—416no—
494C4×D7—416no—
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—74no—
504C23×C4—74no—
505C23×C4—71no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—142no—
511C23×C4—142no—
512C23×C4—142no—
513C23×C4—142no—
514C23×C4—142no—
515C23×C4—142no—
516C23×C4—142no—
517C23×C4—142no—
518C23×C4—142no—
519C23×C4—281no—
520C23×C4—281no—
521C23×C4—281no—
522C23×C4—281no—
523C23×C4—281no—
524C23×C4—281no—
525C23×C4C22×D711yescharacteristic
526C23×C4C22×D711yescharacteristic
527C23×C4C22×D711yescharacteristic
528C23×C4C22×D711yescharacteristic
529C23×C4C22×D711yescharacteristic
530C23×C4C22×D711yescharacteristic
531C23×C4C22×D711yescharacteristic
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—74no—
536C2×C4⋊C4—74no—
537C2×C4⋊C4—142no—
538C2×C4⋊C4—142no—
539C2×C4⋊C4—142no—
540C2×C4⋊C4—142no—
541C2×C4⋊C4—281no—
542C2×C4⋊C4—281no—
543C2×C4⋊C4—281no—
544C2×C22⋊C4—74no—
545C2×C22⋊C4—74no—
546C2×C22⋊C4—74no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—142no—
550C2×C22⋊C4—142no—
551C2×C22⋊C4—142no—
552C2×C22⋊C4—142no—
553C2×C22⋊C4—142no—
554C2×C22⋊C4—142no—
555C2×C22⋊C4—142no—
556C2×C42—22no—
557C2×C42—22no—
558C2×C42—41no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—281no—
562#95—22no—
563#95—41no—
564#95—41no—
565#95—74no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—142no—
574#95—142no—
575#95—142no—
576#95—142no—
577#95—142no—
578#95—281no—
579#95—281no—
580#95—281no—
581#95—281no—
582#95C4×D714yescomplemented
583#95D2814yes—
584C22×C7C2×#11711yescharacteristic
585C22×C7C2×C4×D411yescharacteristic
586C22×C7C2×C4×D411yescharacteristic
587C22×C7C2×C4×Q811yescharacteristic
588C22×C7C4×#4111yescharacteristic
589C22×C7#51811yescharacteristic
590C22×C7#52011yescharacteristic
591C22×C7C2×C22⋊Q811yescharacteristic
592C22×C7C2×C22⋊Q811yescharacteristic
593C22×C7C2×#12311yescharacteristic
594C22×C7#52511yescharacteristic
595C22×C7C2×#12511yescharacteristic
596C22×C7C2×#12611yescharacteristic
597C22×C7#52911yescharacteristic
598C22×C7#53311yescharacteristic
599C22×C7#53811yescharacteristic
600C22×C7#53911yescharacteristic
601C22×C7#54311yescharacteristic
602C22×C7#54411yescharacteristic
603C22×C7D4211yescharacteristic
604C22×C7#54611yescharacteristic
605C22×C7#54611yescharacteristic
606C22×C7#54611yescharacteristic
607C22×C7#54611yescharacteristic
608C22×C7#54711yescharacteristic
609C22×C7#54811yescharacteristic
610C22×C7#55111yescharacteristic
611C22×C7#55111yescharacteristic
612C22×C7#55111yescharacteristic
613C22×C7#55111yescharacteristic
614C22×C7#55211yescharacteristic
615C22×C7#55211yescharacteristic
616C22×C7#55311yescharacteristic
617C22×C7#55311yescharacteristic
618C22×C7#55311yescharacteristic
619C2×D7—24no—
620C2×D7—24no—
621C2×D7—24no—
622C2×D7—24no—
623C2×D7—24no—
624C2×D7—24no—
625C2×D7—24no—
626C2×D7—24no—
627C2×D7—24no—
628C2×D7—24no—
629C2×D7—24no—
630C2×D7—24no—
631C2×D7—24no—
632C2×D7—24no—
633C2×D7#38718yescomplemented
634C4×C7—24no—
635C4×C7—24no—
636C4×C7—42no—
637C4×C7—42no—
638C4×C7—42no—
639C4×C7—42no—
640C4×C7—81no—
641Dic7—42no—
642Dic7—42no—
643Dic7—42no—
644Dic7—42no—
645Dic7—42no—
646Dic7—42no—
647Dic7—81no—
648C24—72no—
649C24—72no—
650C24—72no—
651C24—72no—
652C24—72no—
653C24—72no—
654C24—72no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24—141no—
661C24—141no—
662C24—141no—
663C24C23×D711yescharacteristic
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—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—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—148no—
710C22×C4—148no—
711C22×C4—148no—
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—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—148no—
749C22×C4—148no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4—284no—
763C22×C4—284no—
764C22×C4—284no—
765C22×C4—284no—
766C22×C4—284no—
767C22×C4—284no—
768C22×C4—284no—
769C22×C4—284no—
770C22×C4—284no—
771C22×C4—284no—
772C22×C4—284no—
773C22×C4C2×C4×D712yes—
774C22×C4C2×C4×D712yes—
775C22×C4C2×C4×D712yes—
776C22×C4C2×D2812yes—
777C22×C4C2×D2812yes—
778C22×C4C2×D2812yes—
779C22×C4#115712yes—
780C22×C4D4×D712yes—
781C22×C4#115912yes—
782C22×C4Q8×D712yes—
783C4⋊C4—44no—
784C4⋊C4—148no—
785C4⋊C4—284no—
786C4⋊C4—284no—
787C22⋊C4—148no—
788C22⋊C4—148no—
789C22⋊C4—148no—
790C22⋊C4—284no—
791C42—44no—
792C42—284no—
793C2×C7C2×#38711yescharacteristic
794C2×C7C4×C22⋊Q811yescharacteristic
795C2×C7#232911yescharacteristic
796C2×C7#235211yescharacteristic
797C2×C7#235311yescharacteristic
798C2×C7#235811yescharacteristic
799C2×C7#235911yescharacteristic
800C2×C7#243711yescharacteristic
801C2×C7#243811yescharacteristic
802C2×C7#244211yescharacteristic
803C2×C7#244311yescharacteristic
804C2×C7#244411yescharacteristic
805C2×C7#248011yescharacteristic
806C2×C7#249311yescharacteristic
807C2×C7#256911yescharacteristic
808D7—28no—
809C23—74no—
810C23—74no—
811C23—74no—
812C23—74no—
813C23—74no—
814C23—74no—
815C23—74no—
816C23—142no—
817C23—142no—
818C23—142no—
819C23—142no—
820C23—142no—
821C23—142no—
822C23—142no—
823C23—142no—
824C23—142no—
825C23—142no—
826C23—142no—
827C23—142no—
828C23—142no—
829C23—142no—
830C23—142no—
831C23—142no—
832C23—142no—
833C23—142no—
834C23—142no—
835C23—142no—
836C23—142no—
837C23—142no—
838C23—142no—
839C23—142no—
840C23—142no—
841C23—142no—
842C23—142no—
843C23—142no—
844C23C22×C4×D711yescharacteristic
845C23C22×D2811yescharacteristic
846C23C2×#115711yescharacteristic
847C23C2×D4×D711yescharacteristic
848C23C2×#115911yescharacteristic
849C23#654811yescharacteristic
850C23#654811yescharacteristic
851C23C2×Q8×D711yescharacteristic
852C23#655111yescharacteristic
853C23D7×#4111yescharacteristic
854C23D7×#4111yescharacteristic
855C23D7×#4111yescharacteristic
856C23D7×#4111yescharacteristic
857C23D7×#4111yescharacteristic
858C23#655311yescharacteristic
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—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
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—41no—
905C2×C4—41no—
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—2816no—
925C2×C4—2816no—
926C2×C4—2816no—
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—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—281no—
955C2×C4—281no—
956C2×C4—281no—
957C2×C4—281no—
958C2×C4C4×D2814yes—
959C2×C4#646014yes—
960C7#1398011yescharacteristic, complemented, Sylow
961C22—78no—
962C22—144no—
963C22—144no—
964C22—144no—
965C22—144no—
966C22—144no—
967C22—144no—
968C22—144no—
969C22—144no—
970C22—144no—
971C22—144no—
972C22—144no—
973C22—144no—
974C22—144no—
975C22—144no—
976C22C2×C4×D2811yescharacteristic
977C22#9018111yescharacteristic
978C22#9019511yescharacteristic
979C22C2×#646011yescharacteristic
980C22D7×#11711yescharacteristic
981C22#9021511yescharacteristic
982C22#9021811yescharacteristic
983C22C4×#115911yescharacteristic
984C22C4×D4×D711yescharacteristic
985C22#9023611yescharacteristic
986C22D4×D2811yescharacteristic
987C22#9024511yescharacteristic
988C22#9024511yescharacteristic
989C22#9024811yescharacteristic
990C22#9024911yescharacteristic
991C22C4×Q8×D711yescharacteristic
992C22#9026711yescharacteristic
993C22#9026911yescharacteristic
994C22#9027211yescharacteristic
995C22#9028211yescharacteristic
996C22#9030411yescharacteristic
997C22#9030511yescharacteristic
998C22D7×C22⋊Q811yescharacteristic
999C22#9032211yescharacteristic
1000C22#9032511yescharacteristic
1001C22#9033011yescharacteristic
1002C22D7×#12311yescharacteristic
1003C22#9034911yescharacteristic
1004C22#9035011yescharacteristic
1005C22#9037011yescharacteristic
1006C22D7×#12511yescharacteristic
1007C22#9038311yescharacteristic
1008C22D7×#12611yescharacteristic
1009C22#9040011yescharacteristic
1010C22#9042011yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—282no—
1019C4—282no—
1020C4—282no—
1021C4—282no—
1022C4—282no—
1023C4—282no—
1024C4—561no—
1025C2—148no—
1026C2#1173102211yescharacteristic
1027C2C4×#646011yescharacteristic
1028C2#1173121611yescharacteristic
1029C2#1173185811yescharacteristic
1030C2#1173204211yescharacteristic
1031C2#1173234211yescharacteristic
1032C2D7×#38711yescharacteristic
1033C2#1173276411yescharacteristic
1034C2#1173278211yescharacteristic
1035C2#1173280611yescharacteristic
1036C2#1173298511yescharacteristic
1037C2#1173328011yescharacteristic
1038C2#1173344811yescharacteristic
1039C2#1173364411yescharacteristic
1040C2#1173407211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1436C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenter#1436D7
hypocenterC7#13980
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
5. C2×#89427C2semidirect
6. C7×#1436C2semidirect
7. #11729320C2semidirect
8. #11729288C2semidirect
12. #11727176C2semidirect
13. #11727172C2semidirect
14. #11727166C2semidirect
15. #11727161C2semidirect
53. #89440C4semidirect
116. C2×C4⋊Dic7C2×C4semidirect
119. C2×Dic7⋊C4C2×C4semidirect
126. C7×#95C2×C4semidirect
144. C7⋊#95C2×C4semidirect
155. #1436D7semidirect
582. #95C4×D7semidirect
633. C2×D7#387semidirect
960. C7#13980semidirect

Maximal subgroups

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

subgroupindex
C2×#897592
C2×C4×(C2×D7)⋊C42
C2×#894402
C2×D7×#952
C2×#894272
C7×#14362
#117293202
#117292882
(C2×D7)⋊#952
#117271762
#117271722
#117271662
#117271612
#139807