Finite Group Databasebeta

← #13282297

Subgroups — #13282297

Order 1792.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6509C211yesmaximal, characteristic
2C2×C7×#391C211yesmaximal, characteristic, complemented
3C2×#90002C211yesmaximal, characteristic, complemented
4#11729324C211yesmaximal, characteristic
5#11729320C211yesmaximal, characteristic, complemented
6#11729291C211yesmaximal, characteristic
7#11729290C211yesmaximal, characteristic, complemented
8#11727181C211yesmaximal, characteristic
9(C2×D7)⋊#95C211yesmaximal, characteristic
10(C2×D7)⋊#95C211yesmaximal, characteristic
11#11727177C211yesmaximal, characteristic, complemented
12#11727176C211yesmaximal, characteristic, complemented
13#11727164C211yesmaximal, characteristic, complemented
14#11727162C211yesmaximal, characteristic
15#11727159C211yesmaximal, characteristic, complemented
16C23×C7×Q8C2211yescharacteristic
17C23×C4×D7C2211yescharacteristic
18C22×C7×C4⋊C4C2211yescharacteristic
19C22×C42×C7C2211yescharacteristic
20C2×#6509—24no—
21C2×#6509—24no—
22C2×#6509C418yescomplemented
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C7×#391—24no—
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2211yescharacteristic
39#90002—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56#14449—71nomaximal, Sylow
57C24×D7C2311yescharacteristic
58C22×C7×Q8—41no—
59C22×C7×Q8—41no—
60C22×C7×Q8—41no—
61C22×C7×Q8—41no—
62C22×C7×Q8C2×C414yes—
63C22×C7×Q8D414yes—
64C22×C7×Q8D414yes—
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
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×D7C2×C414yes—
86C2×C7×C4⋊C4—22no—
87C2×C7×C4⋊C4—41no—
88C2×C7×C4⋊C4—41no—
89C2×C42×C7—22no—
90C2×C42×C7—41no—
91C2×C42×C7—41no—
92#6509—232no—
93C2×(C2×D7)⋊C4—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—41no—
103C2×(C2×D7)⋊C4—41no—
104C2×(C2×D7)⋊C4—41no—
105C2×(C2×D7)⋊C4—41no—
106C2×(C2×D7)⋊C4—41no—
107C2×(C2×D7)⋊C4—41no—
108C2×(C2×D7)⋊C4C2×C414yes—
109C2×(C2×D7)⋊C4C2×C414yes—
110C2×(C2×D7)⋊C4Q814yescomplemented
111C2×C4⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7—22no—
114C2×C4⋊Dic7—41no—
115C2×C4⋊Dic7—41no—
116C2×C4⋊Dic7C2×C414yes—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4C2×C414yes—
122C2×Dic7⋊C4C2×C414yes—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—41no—
125C2×C4×Dic7—41no—
126C7×#95—22no—
127C7×#95—22no—
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—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C22×C22⋊Q8—71no—
147C2×#391—71no—
148C2×#391D711yescharacteristic, complemented
149#1445—71no—
150#1445—71no—
151#1441—71no—
152#1441—71no—
153#1439—71no—
154#1439—71no—
155#1437—71no—
156#1437—71no—
157#1436—71no—
158#1436—71no—
159C22⋊#95—71no—
160C22⋊#95—71no—
161C24×C7C2411yescharacteristic
162C23×D7—21no—
163C23×D7—21no—
164C23×D7—21no—
165C23×D7—21no—
166C23×D7—21no—
167C23×D7—21no—
168C23×D7—21no—
169C23×D7—21no—
170C23×D7—21no—
171C23×D7—21no—
172C23×D7—21no—
173C23×D7—21no—
174C23×D7C22×C412yes—
175C23×D7C2×Q812yes—
176C23×D7#4112yes—
177C2×C7×Q8—44no—
178C2×C7×Q8—44no—
179C2×C7×Q8—44no—
180C2×C7×Q8—44no—
181C2×C7×Q8—44no—
182C2×C7×Q8—44no—
183C2×C7×Q8C22⋊C4116yescomplemented
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×C7C22×C412yes—
223C22×C4×C7C22×C412yes—
224C22×C4×C7C22×C412yes—
225C22×C4×C7C2×D412yes—
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D412yes—
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2×D412yes—
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×Q812yes—
232C22×C4×C7#4112yes—
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×Dic7—21no—
271C22×Dic7—21no—
272C22×Dic7—21no—
273C22×Dic7—21no—
274C22×Dic7—21no—
275C22×Dic7—21no—
276C22×Dic7—21no—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C22×C412yes—
280C22×Dic7C2×Q812yes—
281C22×Dic7#4112yes—
282C2×C4×D7—28no—
283C2×C4×D7—44no—
284C2×C4×D7—44no—
285C2×C4×D7—44no—
286C2×C4×D7—44no—
287C2×C4×D7—44no—
288C2×C4×D7—44no—
289C7×C4⋊C4—44no—
290C42×C7—44no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—44no—
294(C2×D7)⋊C4—44no—
295(C2×D7)⋊C4—44no—
296(C2×D7)⋊C4—44no—
297C4⋊Dic7—28no—
298C4⋊Dic7—44no—
299Dic7⋊C4—28no—
300Dic7⋊C4—28no—
301C4×Dic7—44no—
302C23×Q8C2×D711yescharacteristic
303C24×C4—71no—
304C2×C22⋊Q8—78no—
305C2×C22⋊Q8—144no—
306C2×C22⋊Q8—144no—
307C22×C4⋊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×C22⋊C4—71no—
317C22×C22⋊C4—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#391—24no—
321#391—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×#95C2×D711yescharacteristic
339C2×#95C2×D711yescharacteristic
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7C23×C411yescharacteristic
343C23×C7C22×D411yescharacteristic
344C23×C7C22×D411yescharacteristic
345C23×C7C22×Q811yescharacteristic
346C23×C7C2×#4111yescharacteristic
347C23×C7C2×#4111yescharacteristic
348C23×C7C2×#4111yescharacteristic
349C23×C7H(5,𝔽2)11yescharacteristic
350C23×C7H(5,𝔽2)11yescharacteristic
351C23×C7H(5,𝔽2)11yescharacteristic
352C23×C7H(5,𝔽2)11yescharacteristic
353C23×C7H(5,𝔽2)11yescharacteristic
354C23×C72−1+411yescharacteristic
355C23×C72−1+411yescharacteristic
356C23×C72−1+411yescharacteristic
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—41no—
376C22×D7—41no—
377C22×D7—41no—
378C22×D7—41no—
379C22×D7—41no—
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×D7C4×Q814yes—
392C7×Q8—416no—
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—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—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×C7C2×C22⋊C414yes—
440C2×C4×C7C2×C22⋊C414yes—
441C2×C4×C7C2×C22⋊C414yes—
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—22no—
453C2×Dic7—22no—
454C2×Dic7—22no—
455C2×Dic7—22no—
456C2×Dic7—22no—
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—
483C2×Dic7—41no—
484C2×Dic7—41no—
485C2×Dic7—41no—
486C2×Dic7—41no—
487C2×Dic7—41no—
488C2×Dic7—41no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C4×D7—416no—
492C25—71no—
493C22×Q8—41no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C4×D714yes—
498C22×Q8D2814yes—
499C22×Q8C22⋊D714yes—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—74no—
506C23×C4—71no—
507C23×C4—71no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4—281no—
513C23×C4—281no—
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C23×C4C22×D711yescharacteristic
519C23×C4C22×D711yescharacteristic
520C23×C4C22×D711yescharacteristic
521C22⋊Q8—1432no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—41no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4—74no—
526C2×C4⋊C4—74no—
527C2×C4⋊C4—74no—
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—281no—
536C2×C4⋊C4—281no—
537C2×C22⋊C4—74no—
538C2×C22⋊C4—74no—
539C2×C22⋊C4—74no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—142no—
542C2×C22⋊C4—142no—
543C2×C22⋊C4—142no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—142no—
547C2×C22⋊C4—142no—
548C2×C22⋊C4—142no—
549C2×C22⋊C4—281no—
550C2×C22⋊C4—281no—
551C2×C22⋊C4—281no—
552C2×C22⋊C4—281no—
553C2×C22⋊C4—281no—
554C2×C22⋊C4—281no—
555C2×C42—22no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—142no—
559C2×C42—281no—
560C2×C42—281no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—142no—
569#95—142no—
570#95—142no—
571#95—142no—
572#95—142no—
573#95—281no—
574#95—281no—
575#95—281no—
576#95—281no—
577#95—281no—
578#95—281no—
579#95—281no—
580#95—281no—
581C22×C7C22×C22⋊C411yescharacteristic
582C22×C7C2×C4×Q811yescharacteristic
583C22×C7C4×#4111yescharacteristic
584C22×C7#51811yescharacteristic
585C22×C7#51811yescharacteristic
586C22×C7#51911yescharacteristic
587C22×C7#52011yescharacteristic
588C22×C7#53411yescharacteristic
589C22×C7#53411yescharacteristic
590C22×C7#53411yescharacteristic
591C22×C7#53411yescharacteristic
592C22×C7#53811yescharacteristic
593C22×C7#53911yescharacteristic
594C22×C7#53911yescharacteristic
595C22×C7#53911yescharacteristic
596C22×C7#54211yescharacteristic
597C22×C7#54211yescharacteristic
598C22×C7#54311yescharacteristic
599C22×C7#54411yescharacteristic
600C22×C7#54811yescharacteristic
601C22×C7#54811yescharacteristic
602C22×C7#54811yescharacteristic
603C22×C7#54811yescharacteristic
604C22×C7D4×Q811yescharacteristic
605C22×C7D4×Q811yescharacteristic
606C22×C7#55011yescharacteristic
607C22×C7#55011yescharacteristic
608C22×C7#55111yescharacteristic
609C22×C7#55111yescharacteristic
610C22×C7#55411yescharacteristic
611C22×C7#55411yescharacteristic
612C22×C7#56211yescharacteristic
613C22×C7#56211yescharacteristic
614C22×C7#56311yescharacteristic
615C22×C7#56311yescharacteristic
616C2×D7—24no—
617C2×D7—24no—
618C2×D7—24no—
619C2×D7—42no—
620C2×D7—42no—
621C2×D7—42no—
622C2×D7—42no—
623C2×D7—42no—
624C2×D7—42no—
625C2×D7—42no—
626C2×D7—42no—
627C2×D7—42no—
628C2×D7—42no—
629C2×D7—42no—
630C2×D7—42no—
631C4×C7—24no—
632C4×C7—24no—
633C4×C7—24no—
634C4×C7—42no—
635C4×C7—42no—
636C4×C7—81no—
637C4×C7—81no—
638Dic7—42no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—42no—
643Dic7—81no—
644Dic7—81no—
645C24—72no—
646C24—72no—
647C24—72no—
648C24—141no—
649C24—141no—
650C24—141no—
651C24—141no—
652C24—141no—
653C24—141no—
654C24—141no—
655C24—141no—
656C24—141no—
657C24—141no—
658C24—141no—
659C24—141no—
660C24C23×D711yescharacteristic
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8(C2×D7)⋊C4116yescomplemented
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—72no—
707C22×C4—72no—
708C22×C4—72no—
709C22×C4—72no—
710C22×C4—72no—
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—141no—
737C22×C4—141no—
738C22×C4—141no—
739C22×C4—141no—
740C22×C4—141no—
741C22×C4—148no—
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—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4—284no—
760C22×C4—284no—
761C22×C4—284no—
762C22×C4C2×C4×D712yes—
763C22×C4C2×C4×D712yes—
764C22×C4C2×C4×D712yes—
765C22×C4C2×D2812yes—
766C22×C4C2×D2812yes—
767C22×C4C2×D2812yes—
768C22×C4Q8×D712yes—
769C22×C4#116112yes—
770C22×C4C2×C22⋊D712yes—
771C22×C4C2×C22⋊D712yes—
772C22×C4C2×C22⋊D712yes—
773C4⋊C4—44no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—148no—
777C4⋊C4—284no—
778C22⋊C4—148no—
779C22⋊C4—148no—
780C22⋊C4—284no—
781C22⋊C4—284no—
782C22⋊C4—284no—
783C22⋊C4—284no—
784C42—44no—
785C42—284no—
786C2×C7#230811yescharacteristic
787C2×C7#232911yescharacteristic
788C2×C7#233211yescharacteristic
789C2×C7Q8×C22⋊C411yescharacteristic
790C2×C7#234111yescharacteristic
791C2×C7#236811yescharacteristic
792C2×C7#237811yescharacteristic
793C2×C7#272811yescharacteristic
794C2×C7#272811yescharacteristic
795C2×C7#272911yescharacteristic
796C2×C7#272911yescharacteristic
797C2×C7#273011yescharacteristic
798C2×C7#273011yescharacteristic
799C2×C7#273211yescharacteristic
800C2×C7#273211yescharacteristic
801D7—44no—
802C23—74no—
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—281no—
822C23—281no—
823C23—281no—
824C23—281no—
825C23—281no—
826C23—281no—
827C23—281no—
828C23—281no—
829C23—281no—
830C23—281no—
831C23—281no—
832C23—281no—
833C23—281no—
834C23—281no—
835C23—281no—
836C23—281no—
837C23C22×C4×D711yescharacteristic
838C23C22×D2811yescharacteristic
839C23#654811yescharacteristic
840C23#654811yescharacteristic
841C23#654811yescharacteristic
842C23#654811yescharacteristic
843C23C2×Q8×D711yescharacteristic
844C23C2×#116111yescharacteristic
845C23#655111yescharacteristic
846C23#655111yescharacteristic
847C23D7×#4111yescharacteristic
848C23D7×#4111yescharacteristic
849C23#655311yescharacteristic
850C23#655411yescharacteristic
851C23C22×C22⋊D711yescharacteristic
852Q8—416no—
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—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—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—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—142no—
910C2×C4—142no—
911C2×C4—142no—
912C2×C4—142no—
913C2×C4—142no—
914C2×C4—2816no—
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—281no—
944C2×C4—281no—
945C2×C4—281no—
946C2×C4—281no—
947C2×C4—281no—
948C2×C4—281no—
949C2×C4C2×(C2×D7)⋊C414yes—
950C2×C4C2×(C2×D7)⋊C414yes—
951C2×C4C2×(C2×D7)⋊C414yes—
952C7#1444911yescharacteristic, complemented, Sylow
953C22—144no—
954C22—144no—
955C22—144no—
956C22—282no—
957C22—282no—
958C22—282no—
959C22—282no—
960C22—282no—
961C22—282no—
962C22—282no—
963C22—282no—
964C22—282no—
965C22—282no—
966C22—282no—
967C22—282no—
968C22#9017711yescharacteristic
969C22#9017711yescharacteristic
970C22#9018411yescharacteristic
971C22#9018411yescharacteristic
972C22C4×Q8×D711yescharacteristic
973C22#9026311yescharacteristic
974C22C4×#116111yescharacteristic
975C22#9026511yescharacteristic
976C22Q8×D2811yescharacteristic
977C22#9026711yescharacteristic
978C22#9026711yescharacteristic
979C22#9026811yescharacteristic
980C22#9032511yescharacteristic
981C22#9032711yescharacteristic
982C22#9032811yescharacteristic
983C22#9032911yescharacteristic
984C22#9032911yescharacteristic
985C22#9033611yescharacteristic
986C22#9033711yescharacteristic
987C22#9033811yescharacteristic
988C22#9036011yescharacteristic
989C22#9036911yescharacteristic
990C22#9037011yescharacteristic
991C22#9037511yescharacteristic
992C22#9042011yescharacteristic
993C22#9042111yescharacteristic
994C22#9042411yescharacteristic
995C22#9042611yescharacteristic
996C22C22×(C2×D7)⋊C411yescharacteristic
997C22#9049511yescharacteristic
998C22#9049511yescharacteristic
999C22Q8×C22⋊D711yescharacteristic
1000C22#9050811yescharacteristic
1001C22#9052211yescharacteristic
1002C22#9052511yescharacteristic
1003C4—24no—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4—282no—
1011C4—282no—
1012C4—282no—
1013C4—282no—
1014C4—282no—
1015C4—561no—
1016C4—561no—
1017C2—284no—
1018C2#1173393211yescharacteristic
1019C2#1173401611yescharacteristic
1020C2#1173405711yescharacteristic
1021C2#1173406111yescharacteristic
1022C2#1173406211yescharacteristic
1023C2#1173409911yescharacteristic
1024C2#1173410011yescharacteristic
1025C2#1173410111yescharacteristic
1026C2#1173956611yescharacteristic
1027C2#1173990211yescharacteristic
1028C2Q8×(C2×D7)⋊C411yescharacteristic
1029C2#1174025211yescharacteristic
1030C2#1174027611yescharacteristic
1031C2#1174045111yescharacteristic
1032C2#1174071211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#391C2
socle, cosocleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7#14449
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×C7×#391C2semidirect
3. C2×#90002C2semidirect
5. #11729320C2semidirect
7. #11729290C2semidirect
11. #11727177C2semidirect
12. #11727176C2semidirect
13. #11727164C2semidirect
15. #11727159C2semidirect
22. C2×#6509C4semidirect
110. C2×(C2×D7)⋊C4Q8semidirect
148. C2×#391D7semidirect
183. C2×C7×Q8C22⋊C4semidirect
667. C2×Q8(C2×D7)⋊C4semidirect
952. C7#14449semidirect

Maximal subgroups

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

subgroupindex
C22×#65092
C2×C7×#3912
C2×#900022
#117293242
#117293202
#117292912
#117292902
#117271812
(C2×D7)⋊#952
#117271772
#117271762
#117271642
#117271622
#117271592
#144497