Finite Group Databasebeta

← #13277892

Subgroups — #13277892

Order 1792.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6440C211yesmaximal, characteristic
2C2×C7×#388C211yesmaximal, characteristic
3C2×#89744C211yesmaximal, characteristic, complemented
4C2×#89750C211yesmaximal, characteristic, complemented
5C2×#89718C211yesmaximal, characteristic
6#11729302C211yesmaximal, characteristic
7#11729301C211yesmaximal, characteristic
8#11729299C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11729290C211yesmaximal, characteristic, complemented
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727163C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15#11727160C211yesmaximal, characteristic, complemented
16C24×Dic7C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×#6440—24no—
34C2×#6440—24no—
35C2×#6440—24no—
36C7×#388—24no—
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
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89750—24no—
56#89744—24no—
57#89718C418yescomplemented
58#14072—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×Dic7—22no—
67C23×Dic7—22no—
68C23×Dic7—22no—
69C23×Dic7—22no—
70C23×Dic7—22no—
71C23×Dic7—22no—
72C23×Dic7C2×C414yes—
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C2×C7×C4⋊C4—22no—
82C2×C7×C4⋊C4—22no—
83C2×C7×C4⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4—22no—
89C2×C7×C22⋊C4—22no—
90C2×C7×C22⋊C4—41no—
91C2×C7×C22⋊C4C2×C414yes—
92C2×C7×C22⋊C4D414yes—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7—41no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—22no—
101C2×C22⋊Dic7—22no—
102C2×C22⋊Dic7—22no—
103C2×C22⋊Dic7—41no—
104C2×C22⋊Dic7C2×C414yes—
105C2×Dic7⋊C4—22no—
106C2×Dic7⋊C4—22no—
107C2×Dic7⋊C4—22no—
108C2×Dic7⋊C4—22no—
109C2×Dic7⋊C4—22no—
110C2×Dic7⋊C4—22no—
111C2×Dic7⋊C4—22no—
112C2×Dic7⋊C4—22no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—41no—
117C2×Dic7⋊C4C2×C414yes—
118C2×Dic7⋊C4C2×C414yes—
119C2×Dic7⋊C4D414yes—
120C2×C4×Dic7—22no—
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—22no—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—22no—
127C2×C4×Dic7—41no—
128C2×C4×Dic7D414yes—
129#6440—232no—
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—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—41no—
146C7⋊#95C2×C414yes—
147C7⋊#95C2×C414yes—
148C22×#117—71no—
149C2×#389—71no—
150C2×#388D711yescharacteristic
151C2×#387—71no—
152C2×#385—71no—
153#1442—71no—
154#1441—71no—
155#1440—71no—
156#1439—71no—
157#1437—71no—
158#1436—71no—
159#1436—71no—
160#1436—71no—
161C22⋊#95—71no—
162C4×#95—71no—
163C24×C7—21no—
164C24×C7—21no—
165C24×C7—21no—
166C24×C7—21no—
167C24×C7—21no—
168C24×C7—21no—
169C24×C7—21no—
170C24×C7—21no—
171C24×C7—21no—
172C24×C7—21no—
173C24×C7—21no—
174C24×C7—21no—
175C24×C7C22×C412yes—
176C24×C7C2×D412yes—
177C24×C7#4112yes—
178C24×C7C2411yescharacteristic
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×C7C22×C412yes—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7#4112yes—
221C22×Dic7—28no—
222C22×Dic7—28no—
223C22×Dic7—28no—
224C22×Dic7—28no—
225C22×Dic7—28no—
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—28no—
239C22×Dic7—28no—
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×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C22×Dic7#4112yes—
282C22×Dic7#4112yes—
283C22×Dic7#4112yes—
284C7×C4⋊C4—44no—
285C7×C22⋊C4—28no—
286C7×C22⋊C4—28no—
287C7×C22⋊C4—44no—
288C42×C7—44no—
289C22⋊Dic7—28no—
290C22⋊Dic7—28no—
291C22⋊Dic7—44no—
292Dic7⋊C4—28no—
293Dic7⋊C4—28no—
294Dic7⋊C4—28no—
295Dic7⋊C4—28no—
296Dic7⋊C4—44no—
297C4×Dic7—28no—
298C4×Dic7—28no—
299C4×Dic7—44no—
300C24×C4—71no—
301C2×#117—144no—
302C2×#117—144no—
303C2×#117—144no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4—71no—
306C22×C4⋊C4—71no—
307C22×C4⋊C4—71no—
308C22×C4⋊C4—71no—
309C22×C4⋊C4C2×D711yescharacteristic
310C22×C22⋊C4—71no—
311C22×C22⋊C4—71no—
312C22×C22⋊C4—71no—
313C22×C22⋊C4C2×D711yescharacteristic
314C22×C22⋊C4C2×D711yescharacteristic
315C22×C22⋊C4C2×D711yescharacteristic
316C22×C42—71no—
317C22×C42—71no—
318C22×C42—71no—
319C22×C42C2×D711yescharacteristic
320#389—144no—
321#388—24no—
322#387—144no—
323#385—78no—
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—71no—
340C2×#95C2×D711yescharacteristic
341C2×#95C2×D711yescharacteristic
342C23×C7—22no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7—22no—
350C23×C7—22no—
351C23×C7—22no—
352C23×C7—22no—
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—41no—
361C23×C7—41no—
362C23×C7—41no—
363C23×C7—41no—
364C23×C7—41no—
365C23×C7—41no—
366C23×C7—41no—
367C23×C7—41no—
368C23×C7—41no—
369C23×C7—41no—
370C23×C7—41no—
371C23×C7—41no—
372C23×C7—41no—
373C23×C7—41no—
374C23×C7—41no—
375C23×C7—41no—
376C23×C7C4×D414yes—
377C23×C7C23×C411yescharacteristic
378C23×C7C22×D411yescharacteristic
379C23×C7C22×D411yescharacteristic
380C23×C7C22×D411yescharacteristic
381C23×C7C2×#4111yescharacteristic
382C23×C7C2×#4111yescharacteristic
383C23×C7C2×#4111yescharacteristic
384C23×C7C2×#4111yescharacteristic
385C23×C7C2×#4111yescharacteristic
386C23×C7C2×#4111yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7H(5,𝔽2)11yescharacteristic
389C23×C72−1+411yescharacteristic
390C23×C72−1+411yescharacteristic
391C23×C72−1+411yescharacteristic
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—22no—
407C2×C4×C7—22no—
408C2×C4×C7—22no—
409C2×C4×C7—22no—
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#12014yes—
434C2×Dic7—232no—
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—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—22no—
463C2×Dic7—22no—
464C2×Dic7—22no—
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#11714yescomplemented
489C2×Dic7C4×D414yes—
490C2×Dic7C4×D414yes—
491C25C22×D711yescharacteristic
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—74no—
496C23×C4—71no—
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—142no—
502C23×C4—142no—
503C23×C4—142no—
504C23×C4—142no—
505C23×C4—142no—
506C23×C4—142no—
507C23×C4C22×D711yescharacteristic
508C23×C4C22×D711yescharacteristic
509C23×C4C22×D711yescharacteristic
510C23×C4C22×D711yescharacteristic
511C23×C4C22×D711yescharacteristic
512C23×C4C22×D711yescharacteristic
513#117—1432no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—74no—
518C2×C4⋊C4—74no—
519C2×C4⋊C4—74no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—142no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
524C2×C4⋊C4—142no—
525C2×C4⋊C4—142no—
526C2×C4⋊C4—142no—
527C2×C4⋊C4—142no—
528C2×C4⋊C4—142no—
529C2×C4⋊C4—142no—
530C2×C4⋊C4—142no—
531C2×C4⋊C4—281no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—41no—
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—281no—
548C2×C22⋊C4C4×D714yes—
549C2×C22⋊C4C22⋊D714yes—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—41no—
553C2×C42—74no—
554C2×C42—142no—
555C2×C42—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—281no—
562#95—22no—
563#95—22no—
564#95—74no—
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—142no—
579#95—281no—
580C22×C7—24no—
581C22×C7—24no—
582C22×C7—24no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7—42no—
590C22×C7—42no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7C2×#11711yescharacteristic
596C22×C7C2×C4×D411yescharacteristic
597C22×C7C2×C4×D411yescharacteristic
598C22×C7C2×C4×D411yescharacteristic
599C22×C7C4×#4111yescharacteristic
600C22×C7#51911yescharacteristic
601C22×C7#52011yescharacteristic
602C22×C7C2×#12011yescharacteristic
603C22×C7#52511yescharacteristic
604C22×C7#52511yescharacteristic
605C22×C7#52511yescharacteristic
606C22×C7#52911yescharacteristic
607C22×C7#52911yescharacteristic
608C22×C7#53211yescharacteristic
609C22×C7#53211yescharacteristic
610C22×C7#53611yescharacteristic
611C22×C7#53711yescharacteristic
612C22×C7#54111yescharacteristic
613C22×C7#54211yescharacteristic
614C22×C7#54611yescharacteristic
615C22×C7#54611yescharacteristic
616C22×C7#54711yescharacteristic
617C22×C7#54711yescharacteristic
618C22×C7#54711yescharacteristic
619C22×C7#54711yescharacteristic
620C22×C7#54811yescharacteristic
621C22×C7#54811yescharacteristic
622C22×C7#55111yescharacteristic
623C22×C7#55211yescharacteristic
624C22×C7#55211yescharacteristic
625C22×C7#55211yescharacteristic
626C22×C7#55211yescharacteristic
627C22×C7#55211yescharacteristic
628C22×C7#55311yescharacteristic
629C22×C7#55611yescharacteristic
630C4×C7—24no—
631C4×C7—42no—
632C4×C7—42no—
633C4×C7—42no—
634C4×C7—42no—
635C4×C7—81no—
636Dic7—24no—
637Dic7—24no—
638Dic7—24no—
639Dic7—42no—
640Dic7—42no—
641Dic7—42no—
642Dic7—42no—
643Dic7—81no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D712yes—
657C24#115712yes—
658C24C2×C22⋊D712yes—
659C24C23×D711yescharacteristic
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—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—72no—
702C22×C4—72no—
703C22×C4—72no—
704C22×C4—72no—
705C22×C4—72no—
706C22×C4—72no—
707C22×C4—72no—
708C22×C4—148no—
709C22×C4—148no—
710C22×C4—148no—
711C22×C4—148no—
712C22×C4—148no—
713C22×C4—148no—
714C22×C4—148no—
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—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×C4C2×C4×D712yes—
759C22×C4C2×C4×D712yes—
760C22×C4D4×D712yes—
761C22×C4D4×D712yes—
762C22×C4#115912yes—
763C22×C4C2×C22⋊D712yes—
764C22×C4C2×C22⋊D712yes—
765C4⋊C4—44no—
766C4⋊C4—148no—
767C4⋊C4—148no—
768C4⋊C4—148no—
769C4⋊C4—148no—
770C4⋊C4—284no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—44no—
774C22⋊C4—148no—
775C22⋊C4—148no—
776C22⋊C4—284no—
777C42—44no—
778C42—148no—
779C42—148no—
780C42—284no—
781C2×C7—44no—
782C2×C7#229311yescharacteristic
783C2×C7C4×#12011yescharacteristic
784C2×C7#232311yescharacteristic
785C2×C7#234411yescharacteristic
786C2×C7#235211yescharacteristic
787C2×C7#235911yescharacteristic
788C2×C7#236211yescharacteristic
789C2×C7#243011yescharacteristic
790C2×C7#243211yescharacteristic
791C2×C7#247011yescharacteristic
792C2×C7#247511yescharacteristic
793C2×C7#247711yescharacteristic
794C2×C7#247811yescharacteristic
795C2×C7#260111yescharacteristic
796C2×C7#261111yescharacteristic
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23C4×C22⋊D714yes—
832C23C22×C4×D711yescharacteristic
833C23C2×#115711yescharacteristic
834C23C2×D4×D711yescharacteristic
835C23C2×D4×D711yescharacteristic
836C23C2×#115911yescharacteristic
837C23#654811yescharacteristic
838C23D7×#4111yescharacteristic
839C23D7×#4111yescharacteristic
840C23D7×#4111yescharacteristic
841C23D7×#4111yescharacteristic
842C23D7×#4111yescharacteristic
843C23#655411yescharacteristic
844C23#655411yescharacteristic
845C23#655411yescharacteristic
846C23C22×C22⋊D711yescharacteristic
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—22no—
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—74no—
889C2×C4—74no—
890C2×C4—74no—
891C2×C4—1432no—
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—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—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#650014yes—
946C7#1407211yescharacteristic, complemented, Sylow
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22#9020711yescharacteristic
963C22D7×#11711yescharacteristic
964C22#9022211yescharacteristic
965C22#9022211yescharacteristic
966C22C4×#115911yescharacteristic
967C22#9023211yescharacteristic
968C22C4×D4×D711yescharacteristic
969C22C4×D4×D711yescharacteristic
970C22#9023711yescharacteristic
971C22#9023811yescharacteristic
972C22#9023811yescharacteristic
973C22#9024711yescharacteristic
974C22#9028711yescharacteristic
975C22#9028811yescharacteristic
976C22#9030111yescharacteristic
977C22#9030211yescharacteristic
978C22#9034011yescharacteristic
979C22#9034111yescharacteristic
980C22#9035211yescharacteristic
981C22#9035311yescharacteristic
982C22#9035911yescharacteristic
983C22#9036611yescharacteristic
984C22#9036811yescharacteristic
985C22#9036811yescharacteristic
986C22#9039211yescharacteristic
987C22#9039311yescharacteristic
988C22#9039711yescharacteristic
989C22#9039911yescharacteristic
990C22C2×C4×C22⋊D711yescharacteristic
991C22C2×#650011yescharacteristic
992C22#9049711yescharacteristic
993C22#9051511yescharacteristic
994C22#9051511yescharacteristic
995C22#9051511yescharacteristic
996C22#9051911yescharacteristic
997C4—24no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—81no—
1003C4—144no—
1004C4—144no—
1005C4—144no—
1006C4—282no—
1007C4—282no—
1008C4—282no—
1009C4—282no—
1010C4—561no—
1011C2—44no—
1012C2#1173289511yescharacteristic
1013C2#1173290411yescharacteristic
1014C2#1173292311yescharacteristic
1015C2#1173297811yescharacteristic
1016C2#1173308811yescharacteristic
1017C2#1173309611yescharacteristic
1018C2#1173327911yescharacteristic
1019C2#1173331011yescharacteristic
1020C2#1173968311yescharacteristic
1021C2#1173978411yescharacteristic
1022C2C4×#650011yescharacteristic
1023C2#1174009611yescharacteristic
1024C2#1174029911yescharacteristic
1025C2#1174040411yescharacteristic
1026C2#1174052411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14072
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×#89744C2semidirect
4. C2×#89750C2semidirect
10. #11729290C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727168C2semidirect
13. #11727163C2semidirect
14. #11727160C2semidirect
15. #11727160C2semidirect
57. #89718C4semidirect
488. C2×Dic7#117semidirect
946. C7#14072semidirect

Maximal subgroups

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

subgroupindex
C22×#64402
C2×C7×#3882
C2×#897442
C2×#897502
C2×#897182
#117293022
#117293012
#117292992
#117292982
#117292902
C4×C7⋊#952
#117271682
#117271632
#117271602
#140727