Finite Group Databasebeta

← #13275437

Subgroups — #13275437

Order 1792.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89985C211yesmaximal, characteristic
2C2×#89728C211yesmaximal, characteristic
3C2×#89729C211yesmaximal, characteristic
4C7×C22⋊#95C211yesmaximal, characteristic, complemented
5#11729881C211yesmaximal, characteristic, complemented
6#11729299C211yesmaximal, characteristic, complemented
7#11729299C211yesmaximal, characteristic, complemented
8(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
9(C2×D7)⋊#95C211yesmaximal, characteristic, complemented
10#11727162C211yesmaximal, characteristic, complemented
11#11727162C211yesmaximal, characteristic, complemented
12#11727160C211yesmaximal, characteristic, complemented
13#11727159C211yesmaximal, characteristic, complemented
14#11727157C211yesmaximal, characteristic, complemented
15#11727156C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C23×C22⋊D7C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
27C22×(C2×D7)⋊C4C2211yescharacteristic
28C22×(C2×D7)⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7×#95C2211yescharacteristic
37#89985C418yescomplemented
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
52#89729C418yescomplemented
53#89728C418yescomplemented
54#13832—71nomaximal, Sylow
55C25×C7C2311yescharacteristic
56C24×D7C2311yescharacteristic
57C23×C4×C7—41no—
58C23×C4×C7—41no—
59C23×C4×C7—41no—
60C23×C4×C7—41no—
61C23×C4×C7—41no—
62C23×C4×C7—41no—
63C23×C4×C7C2×C414yescomplemented
64C23×C4×C7C2311yescharacteristic
65C23×C4×C7C2311yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C22×C22⋊D7—41no—
71C22×C22⋊D7—41no—
72C22×C22⋊D7—41no—
73C22×C22⋊D7—41no—
74C22×C22⋊D7C2×C414yes—
75C22×C22⋊D7C2×C414yes—
76C22×C22⋊D7C2×C414yes—
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C22×C4×D7—41no—
85C22×C4×D7—41no—
86C22×C4×D7—41no—
87C22×C4×D7—41no—
88C22×C4×D7—41no—
89C22×C4×D7—41no—
90C22×C4×D7C2×C414yescomplemented
91C2×C7×C22⋊C4—41no—
92C2×C7×C22⋊C4—41no—
93C2×C7×C22⋊C4—41no—
94C2×C7×C22⋊C4—41no—
95C2×C7×C22⋊C4C2×C414yes—
96C2×C7×C22⋊C4C2×C414yescomplemented
97C2×C22⋊Dic7—41no—
98C2×C22⋊Dic7—41no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7—41no—
102C2×C22⋊Dic7—41no—
103C2×C22⋊Dic7C2×C414yes—
104C2×C22⋊Dic7C2×C414yescomplemented
105C2×C22⋊Dic7C2×C414yescomplemented
106C2×(C2×D7)⋊C4—41no—
107C2×(C2×D7)⋊C4—41no—
108C2×(C2×D7)⋊C4—41no—
109C2×(C2×D7)⋊C4—41no—
110C2×(C2×D7)⋊C4—41no—
111C2×(C2×D7)⋊C4—41no—
112C2×(C2×D7)⋊C4—41no—
113C2×(C2×D7)⋊C4—41no—
114C2×(C2×D7)⋊C4—41no—
115C2×(C2×D7)⋊C4—41no—
116C2×(C2×D7)⋊C4C2×C414yes—
117C2×(C2×D7)⋊C4C2×C414yes—
118C2×(C2×D7)⋊C4C2×C414yescomplemented
119C2×(C2×D7)⋊C4C2×C414yescomplemented
120C2×(C2×D7)⋊C4C2×C414yescomplemented
121C2×Dic7⋊C4—41no—
122C2×Dic7⋊C4—41no—
123C2×Dic7⋊C4C2×C414yescomplemented
124C2×C4×Dic7—41no—
125C2×C4×Dic7—41no—
126C2×C4×Dic7—41no—
127C2×C4×Dic7—41no—
128C2×C4×Dic7—41no—
129C2×C4×Dic7—41no—
130C2×C4×Dic7—41no—
131C2×C4×Dic7—41no—
132C2×C4×Dic7C2×C414yescomplemented
133C7×#95—41no—
134C7×#95—41no—
135C7×#95—41no—
136C7×#95—41no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95—41no—
146C7⋊#95—41no—
147C7⋊#95C2×C414yescomplemented
148C7⋊#95C2×C414yescomplemented
149C7⋊#95C2×C414yescomplemented
150C7⋊#95C2×C414yescomplemented
151C2×#390—71no—
152C2×#386—71no—
153C2×#386—71no—
154#1437—71no—
155#1437—71no—
156#1437—71no—
157#1437—71no—
158#1436—71no—
159#1436—71no—
160#1434—71no—
161#1434—71no—
162C22⋊#95—71no—
163C22⋊#95—71no—
164C22⋊#95—71no—
165C22⋊#95D711yescharacteristic, complemented
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×C7—21no—
176C24×C7—21no—
177C24×C7—21no—
178C24×C7C22×C412yes—
179C24×C7C22×C412yes—
180C24×C7C22×C412yes—
181C24×C7C2411yescharacteristic
182C23×D7—21no—
183C23×D7—21no—
184C23×D7—21no—
185C23×D7—21no—
186C23×D7—21no—
187C23×D7—21no—
188C23×D7—21no—
189C23×D7—21no—
190C23×D7—21no—
191C23×D7—21no—
192C23×D7—21no—
193C23×D7—21no—
194C23×D7C22×C412yes—
195C23×D7C22×C412yes—
196C23×D7C22×C412yes—
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×C7—21no—
223C22×C4×C7—21no—
224C22×C4×C7—21no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—21no—
230C22×C4×C7—21no—
231C22×C4×C7—21no—
232C22×C4×C7—21no—
233C22×C4×C7—44no—
234C22×C4×C7—44no—
235C22×C4×C7—44no—
236C22×C4×C7—44no—
237C22×C4×C7—44no—
238C22×C4×C7—44no—
239C22×C4×C7—44no—
240C22×C4×C7C22×C412yes—
241C22×C4×C7C22×C412yes—
242C22×C4×C7C22×C412yes—
243C22×C4×C7C22×C412yes—
244C22×C4×C7C22×C412yes—
245C22×C4×C7C22×C412yes—
246C2×C22⋊D7—44no—
247C2×C22⋊D7—44no—
248C2×C22⋊D7—44no—
249C2×C22⋊D7—44no—
250C2×C22⋊D7—44no—
251C2×C22⋊D7—44no—
252C2×C22⋊D7C42116yescomplemented
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×Dic7—21no—
278C22×Dic7—21no—
279C22×Dic7—21no—
280C22×Dic7—21no—
281C22×Dic7—21no—
282C22×Dic7—21no—
283C22×Dic7—21no—
284C22×Dic7—21no—
285C22×Dic7—21no—
286C22×Dic7—21no—
287C22×Dic7—21no—
288C22×Dic7—21no—
289C22×Dic7—21no—
290C22×Dic7—21no—
291C22×Dic7—21no—
292C22×Dic7—21no—
293C22×Dic7C22×C412yes—
294C22×Dic7C22×C412yes—
295C22×Dic7C22×C412yes—
296C22×Dic7C22×C412yes—
297C22×Dic7C22×C412yes—
298C22×Dic7C22×C412yes—
299C22×Dic7C22×C412yes—
300C22×Dic7C22×C412yes—
301C22×Dic7C22×C412yes—
302C2×C4×D7—44no—
303C2×C4×D7—44no—
304C2×C4×D7—44no—
305C2×C4×D7—44no—
306C2×C4×D7—44no—
307C2×C4×D7—44no—
308C2×C4×D7—44no—
309C7×C22⋊C4—44no—
310C7×C22⋊C4—44no—
311C22⋊Dic7—44no—
312C22⋊Dic7—44no—
313C22⋊Dic7—44no—
314(C2×D7)⋊C4—44no—
315(C2×D7)⋊C4—44no—
316(C2×D7)⋊C4—44no—
317(C2×D7)⋊C4—44no—
318(C2×D7)⋊C4—44no—
319Dic7⋊C4—44no—
320C4×Dic7—44no—
321C4×Dic7—44no—
322C4×Dic7—44no—
323C23×D4—71no—
324C24×C4—71no—
325C24×C4C2×D711yescharacteristic
326C22×C4⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4—71no—
333C22×C22⋊C4—71no—
334C22×C22⋊C4—71no—
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C22⋊C4C2×D711yescharacteristic
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#390—78no—
341#386—78no—
342#386—78no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95—71no—
346C2×#95—71no—
347C2×#95—71no—
348C2×#95—71no—
349C2×#95—71no—
350C2×#95—71no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95—71no—
357C2×#95C2×D711yescharacteristic
358C2×#95C2×D711yescharacteristic
359C2×#95C2×D711yescharacteristic
360C2×#95C2×D711yescharacteristic
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—22no—
375C23×C7—22no—
376C23×C7—22no—
377C23×C7—22no—
378C23×C7—22no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7—41no—
382C23×C7—41no—
383C23×C7—41no—
384C23×C7—41no—
385C23×C7—41no—
386C23×C7—41no—
387C23×C7—41no—
388C23×C7—41no—
389C23×C7—41no—
390C23×C7—41no—
391C23×C7—41no—
392C23×C7—41no—
393C23×C7—41no—
394C23×C7—41no—
395C23×C7C2×C4214yes—
396C23×C7C23×C411yescharacteristic
397C23×C7C23×C411yescharacteristic
398C23×C7C23×C411yescharacteristic
399C23×C7H(5,𝔽2)11yescharacteristic
400C23×C7H(5,𝔽2)11yescharacteristic
401C23×C7H(5,𝔽2)11yescharacteristic
402C23×C7H(5,𝔽2)11yescharacteristic
403C23×C7H(5,𝔽2)11yescharacteristic
404C23×C7H(5,𝔽2)11yescharacteristic
405C23×C7H(5,𝔽2)11yescharacteristic
406C23×C7H(5,𝔽2)11yescharacteristic
407C23×C7H(5,𝔽2)11yescharacteristic
408C23×C7H(5,𝔽2)11yescharacteristic
409C23×C72−1+411yescharacteristic
410C23×C72−1+411yescharacteristic
411C22×D7—22no—
412C22×D7—22no—
413C22×D7—22no—
414C22×D7—22no—
415C22×D7—22no—
416C22×D7—22no—
417C22×D7—22no—
418C22×D7—22no—
419C22×D7—22no—
420C22×D7—22no—
421C22×D7—22no—
422C22×D7—22no—
423C22×D7—22no—
424C22×D7—22no—
425C22×D7—22no—
426C22×D7—22no—
427C22×D7—22no—
428C22×D7—22no—
429C22×D7—41no—
430C22×D7—41no—
431C22×D7—41no—
432C22×D7—41no—
433C22×D7—41no—
434C22×D7—41no—
435C22×D7—41no—
436C22×D7—41no—
437C22×D7—41no—
438C22×D7—41no—
439C22×D7—41no—
440C22×D7—41no—
441C22×D7—41no—
442C22×D7—41no—
443C22×D7—41no—
444C22×D7—41no—
445C22×D7C2×C4214yes—
446C2×C4×C7—22no—
447C2×C4×C7—22no—
448C2×C4×C7—22no—
449C2×C4×C7—22no—
450C2×C4×C7—22no—
451C2×C4×C7—22no—
452C2×C4×C7—22no—
453C2×C4×C7—22no—
454C2×C4×C7—22no—
455C2×C4×C7—22no—
456C2×C4×C7—22no—
457C2×C4×C7—22no—
458C2×C4×C7—22no—
459C2×C4×C7—22no—
460C2×C4×C7—22no—
461C2×C4×C7—22no—
462C2×C4×C7—22no—
463C2×C4×C7—22no—
464C2×C4×C7—416no—
465C2×C4×C7—41no—
466C2×C4×C7—41no—
467C2×C4×C7—41no—
468C2×C4×C7—41no—
469C2×C4×C7—41no—
470C2×C4×C7—41no—
471C2×C4×C7—41no—
472C2×C4×C7—41no—
473C2×C4×C7—41no—
474C2×C4×C7—41no—
475C2×C4×C7—41no—
476C2×C4×C7—41no—
477C2×C4×C7—41no—
478C2×C4×C7—41no—
479C2×C4×C7—41no—
480C2×C4×C7—41no—
481C2×C4×C7—41no—
482C2×C4×C7—41no—
483C2×C4×C7—41no—
484C2×C4×C7—41no—
485C2×C4×C7—41no—
486C2×C4×C7—41no—
487C2×C4×C7—41no—
488C2×C4×C7—41no—
489C22⋊D7—416no—
490C2×Dic7—22no—
491C2×Dic7—22no—
492C2×Dic7—22no—
493C2×Dic7—22no—
494C2×Dic7—22no—
495C2×Dic7—22no—
496C2×Dic7—22no—
497C2×Dic7—22no—
498C2×Dic7—22no—
499C2×Dic7—22no—
500C2×Dic7—22no—
501C2×Dic7—22no—
502C2×Dic7—22no—
503C2×Dic7—22no—
504C2×Dic7—22no—
505C2×Dic7—22no—
506C2×Dic7—22no—
507C2×Dic7—22no—
508C2×Dic7—22no—
509C2×Dic7—22no—
510C2×Dic7—22no—
511C2×Dic7—22no—
512C2×Dic7—22no—
513C2×Dic7—22no—
514C2×Dic7—41no—
515C2×Dic7—41no—
516C2×Dic7—41no—
517C2×Dic7—41no—
518C2×Dic7—41no—
519C2×Dic7—41no—
520C2×Dic7—41no—
521C2×Dic7—41no—
522C2×Dic7—41no—
523C2×Dic7—41no—
524C2×Dic7—41no—
525C2×Dic7—41no—
526C2×Dic7—41no—
527C2×Dic7—41no—
528C2×Dic7—41no—
529C2×Dic7—41no—
530C2×Dic7—41no—
531C2×Dic7—41no—
532C2×Dic7—41no—
533C2×Dic7—41no—
534C2×Dic7—41no—
535C2×Dic7—41no—
536C2×Dic7—41no—
537C2×Dic7—41no—
538C2×Dic7C2×C4214yes—
539C4×D7—416no—
540C25—71no—
541C25C22×D711yescharacteristic
542C22×D4—74no—
543C22×D4—74no—
544C22×D4—74no—
545C22×D4—281no—
546C22×D4—281no—
547C22×D4—281no—
548C22×D4—281no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4—41no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4—41no—
555C23×C4—71no—
556C23×C4—71no—
557C23×C4—71no—
558C23×C4—71no—
559C23×C4—71no—
560C23×C4—71no—
561C23×C4—71no—
562C23×C4—74no—
563C23×C4—281no—
564C23×C4—281no—
565C23×C4—281no—
566C23×C4—281no—
567C23×C4—281no—
568C23×C4—281no—
569C23×C4C4×D714yescomplemented
570C23×C4C22×D711yescharacteristic
571C23×C4C22×D711yescharacteristic
572C23×C4C22×D711yescharacteristic
573C23×C4C22×D711yescharacteristic
574C23×C4C22×D711yescharacteristic
575C23×C4C22×D711yescharacteristic
576C2×C4⋊C4—74no—
577C2×C4⋊C4—281no—
578C2×C4⋊C4—281no—
579C2×C22⋊C4—41no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—74no—
584C2×C22⋊C4—74no—
585C2×C22⋊C4—74no—
586C2×C22⋊C4—74no—
587C2×C22⋊C4—74no—
588C2×C22⋊C4—74no—
589C2×C22⋊C4—74no—
590C2×C22⋊C4—74no—
591C2×C22⋊C4—281no—
592C2×C22⋊C4—281no—
593C2×C22⋊C4—281no—
594C2×C22⋊C4—281no—
595C2×C22⋊C4—281no—
596C2×C22⋊C4—281no—
597C2×C22⋊C4—281no—
598C2×C22⋊C4—281no—
599C2×C22⋊C4—281no—
600C2×C22⋊C4—281no—
601C2×C22⋊C4—281no—
602C2×C22⋊C4—281no—
603C2×C22⋊C4—281no—
604C2×C22⋊C4—281no—
605C2×C22⋊C4—281no—
606C2×C22⋊C4—281no—
607C2×C22⋊C4C4×D714yes—
608C2×C22⋊C4C4×D714yescomplemented
609C2×C42—74no—
610C2×C42—281no—
611C2×C42—281no—
612C2×C42—281no—
613C2×C42—281no—
614C2×C42—281no—
615C2×C42—281no—
616C2×C42—281no—
617C2×C42—281no—
618#95—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—74no—
623#95—74no—
624#95—74no—
625#95—74no—
626#95—281no—
627#95—281no—
628#95—281no—
629#95—281no—
630#95—281no—
631#95—281no—
632#95—281no—
633#95—281no—
634#95—281no—
635#95—281no—
636C22×C7—24no—
637C22×C7—24no—
638C22×C7—24no—
639C22×C7—42no—
640C22×C7—42no—
641C22×C7—42no—
642C22×C7—42no—
643C22×C7—42no—
644C22×C7—42no—
645C22×C7—42no—
646C22×C7—42no—
647C22×C7—42no—
648C22×C7—42no—
649C22×C7—42no—
650C22×C7—42no—
651C22×C7C22×C4211yescharacteristic
652C22×C7#51811yescharacteristic
653C22×C7#51811yescharacteristic
654C22×C7#51811yescharacteristic
655C22×C7#51811yescharacteristic
656C22×C7#51811yescharacteristic
657C22×C7#51811yescharacteristic
658C22×C7#51811yescharacteristic
659C22×C7#51811yescharacteristic
660C22×C7#51811yescharacteristic
661C22×C7#51811yescharacteristic
662C22×C7#51811yescharacteristic
663C22×C7#51811yescharacteristic
664C22×C7#52011yescharacteristic
665C22×C7#52011yescharacteristic
666C22×C7#52011yescharacteristic
667C22×C7#52011yescharacteristic
668C22×C7#52011yescharacteristic
669C22×C7#52011yescharacteristic
670C22×C7#56011yescharacteristic
671C22×C7#56011yescharacteristic
672C22×C7#56011yescharacteristic
673C22×C7#56011yescharacteristic
674C22×C7#56011yescharacteristic
675C22×C7#56011yescharacteristic
676C22×C7#56011yescharacteristic
677C22×C7#56011yescharacteristic
678C22×C7H(3,𝔽4)11yescharacteristic
679C22×C7#56211yescharacteristic
680C22×C7#56211yescharacteristic
681C22×C7#56211yescharacteristic
682C22×C7#56211yescharacteristic
683C22×C7#56211yescharacteristic
684C22×C7#56211yescharacteristic
685C22×C7#56311yescharacteristic
686C2×D7—24no—
687C2×D7—24no—
688C2×D7—24no—
689C2×D7—42no—
690C2×D7—42no—
691C2×D7—42no—
692C2×D7—42no—
693C2×D7—42no—
694C2×D7—42no—
695C2×D7—42no—
696C2×D7—42no—
697C2×D7—42no—
698C2×D7—42no—
699C2×D7—42no—
700C2×D7—42no—
701C4×C7—42no—
702C4×C7—42no—
703C4×C7—42no—
704C4×C7—42no—
705C4×C7—42no—
706C4×C7—42no—
707Dic7—24no—
708Dic7—42no—
709Dic7—42no—
710Dic7—42no—
711Dic7—42no—
712Dic7—42no—
713Dic7—42no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—72no—
727C24—72no—
728C24—72no—
729C24—141no—
730C24—141no—
731C24—141no—
732C24—141no—
733C24—141no—
734C24—141no—
735C24—141no—
736C24—141no—
737C24—141no—
738C24—141no—
739C24—141no—
740C24—141no—
741C24C2×C4×D712yes—
742C24C2×C4×D712yes—
743C24C2×C4×D712yes—
744C24C23×D711yescharacteristic
745C2×D4—716no—
746C2×D4—284no—
747C2×D4—284no—
748C2×D4—284no—
749C2×D4—284no—
750C2×D4—284no—
751C2×D4—284no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—72no—
796C22×C4—72no—
797C22×C4—72no—
798C22×C4—72no—
799C22×C4—72no—
800C22×C4—72no—
801C22×C4—72no—
802C22×C4—72no—
803C22×C4—72no—
804C22×C4—141no—
805C22×C4—141no—
806C22×C4—141no—
807C22×C4—141no—
808C22×C4—141no—
809C22×C4—141no—
810C22×C4—141no—
811C22×C4—141no—
812C22×C4—141no—
813C22×C4—141no—
814C22×C4—141no—
815C22×C4—141no—
816C22×C4—141no—
817C22×C4—141no—
818C22×C4—141no—
819C22×C4—141no—
820C22×C4—141no—
821C22×C4—141no—
822C22×C4—141no—
823C22×C4—141no—
824C22×C4—141no—
825C22×C4—141no—
826C22×C4—141no—
827C22×C4—141no—
828C22×C4—141no—
829C22×C4—141no—
830C22×C4—141no—
831C22×C4—141no—
832C22×C4—141no—
833C22×C4—141no—
834C22×C4—141no—
835C22×C4—141no—
836C22×C4—141no—
837C22×C4—141no—
838C22×C4—141no—
839C22×C4—141no—
840C22×C4—141no—
841C22×C4—141no—
842C22×C4—141no—
843C22×C4—141no—
844C22×C4—284no—
845C22×C4—284no—
846C22×C4—284no—
847C22×C4—284no—
848C22×C4—284no—
849C22×C4—284no—
850C22×C4—284no—
851C22×C4C2×C4×D712yes—
852C22×C4C2×C4×D712yes—
853C22×C4C2×C4×D712yes—
854C22×C4C2×C4×D712yes—
855C22×C4C2×C4×D712yes—
856C22×C4C2×C4×D712yes—
857C4⋊C4—284no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—284no—
861C22⋊C4—284no—
862C22⋊C4—284no—
863C22⋊C4—284no—
864C22⋊C4—284no—
865C22⋊C4—284no—
866C22⋊C4—284no—
867C22⋊C4—284no—
868C42—284no—
869C42—284no—
870C42—284no—
871C2×C7—44no—
872C2×C7#227311yescharacteristic
873C2×C7#227511yescharacteristic
874C2×C7#227511yescharacteristic
875C2×C7#237511yescharacteristic
876C2×C7#237511yescharacteristic
877C2×C7#237611yescharacteristic
878C2×C7#237611yescharacteristic
879C2×C7#237711yescharacteristic
880C2×C7#237711yescharacteristic
881C2×C7#237711yescharacteristic
882C2×C7#237711yescharacteristic
883C2×C7#237711yescharacteristic
884C2×C7#237711yescharacteristic
885C2×C7#237911yescharacteristic
886C2×C7#238011yescharacteristic
887D7—44no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—74no—
923C23—142no—
924C23—142no—
925C23—142no—
926C23—142no—
927C23—142no—
928C23—142no—
929C23—142no—
930C23—142no—
931C23—142no—
932C23—142no—
933C23—142no—
934C23—142no—
935C23—142no—
936C23—142no—
937C23—142no—
938C23—142no—
939C23—142no—
940C23—142no—
941C23—281no—
942C23—281no—
943C23—281no—
944C23—281no—
945C23—281no—
946C23—281no—
947C23—281no—
948C23—281no—
949C23—281no—
950C23—281no—
951C23—281no—
952C23—281no—
953C23—281no—
954C23—281no—
955C23—281no—
956C23—281no—
957C23C42×D714yes—
958C23C22×C4×D711yescharacteristic
959C23C22×C4×D711yescharacteristic
960C23C22×C4×D711yescharacteristic
961C23#654811yescharacteristic
962C23#654811yescharacteristic
963C23#654811yescharacteristic
964C23#654811yescharacteristic
965C23#654811yescharacteristic
966C23#654811yescharacteristic
967C23#654811yescharacteristic
968C23#655111yescharacteristic
969C23#655311yescharacteristic
970C23#655311yescharacteristic
971C23#655311yescharacteristic
972C23#655411yescharacteristic
973D4—2816no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—416no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—74no—
1018C2×C4—142no—
1019C2×C4—142no—
1020C2×C4—142no—
1021C2×C4—142no—
1022C2×C4—142no—
1023C2×C4—142no—
1024C2×C4—142no—
1025C2×C4—142no—
1026C2×C4—142no—
1027C2×C4—142no—
1028C2×C4—142no—
1029C2×C4—142no—
1030C2×C4—142no—
1031C2×C4—142no—
1032C2×C4—142no—
1033C2×C4—142no—
1034C2×C4—142no—
1035C2×C4—142no—
1036C2×C4—142no—
1037C2×C4—142no—
1038C2×C4—142no—
1039C2×C4—142no—
1040C2×C4—142no—
1041C2×C4—142no—
1042C2×C4—2816no—
1043C2×C4—281no—
1044C2×C4—281no—
1045C2×C4—281no—
1046C2×C4—281no—
1047C2×C4—281no—
1048C2×C4—281no—
1049C2×C4—281no—
1050C2×C4—281no—
1051C2×C4—281no—
1052C2×C4—281no—
1053C2×C4—281no—
1054C2×C4—281no—
1055C2×C4—281no—
1056C2×C4—281no—
1057C2×C4—281no—
1058C2×C4—281no—
1059C2×C4—281no—
1060C2×C4—281no—
1061C2×C4—281no—
1062C2×C4—281no—
1063C2×C4—281no—
1064C2×C4—281no—
1065C2×C4—281no—
1066C2×C4—281no—
1067C7#1383211yescharacteristic, complemented, Sylow
1068C22—24no—
1069C22—24no—
1070C22—24no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—144no—
1084C22—144no—
1085C22—144no—
1086C22—282no—
1087C22—282no—
1088C22—282no—
1089C22—282no—
1090C22—282no—
1091C22—282no—
1092C22—282no—
1093C22—282no—
1094C22—282no—
1095C22—282no—
1096C22—282no—
1097C22—282no—
1098C22C2×C42×D711yescharacteristic
1099C22#9017711yescharacteristic
1100C22#9017711yescharacteristic
1101C22#9017711yescharacteristic
1102C22#9017711yescharacteristic
1103C22#9017711yescharacteristic
1104C22#9019511yescharacteristic
1105C22#9019511yescharacteristic
1106C22#9019511yescharacteristic
1107C22#9021211yescharacteristic
1108C22#9021411yescharacteristic
1109C22#9023611yescharacteristic
1110C22#9023611yescharacteristic
1111C22#9023611yescharacteristic
1112C22#9023611yescharacteristic
1113C22#9023611yescharacteristic
1114C22#9023611yescharacteristic
1115C22#9023711yescharacteristic
1116C22#9023711yescharacteristic
1117C22#9028511yescharacteristic
1118C22#9028611yescharacteristic
1119C22#9028611yescharacteristic
1120C22#9028611yescharacteristic
1121C22#9031111yescharacteristic
1122C22#9031111yescharacteristic
1123C22#9031111yescharacteristic
1124C22#9031211yescharacteristic
1125C22#9033711yescharacteristic
1126C22#9033811yescharacteristic
1127C22#9033811yescharacteristic
1128C22#9033811yescharacteristic
1129C22#9035711yescharacteristic
1130C22#9035711yescharacteristic
1131C22#9035811yescharacteristic
1132C22#9035811yescharacteristic
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—42no—
1139C4—144no—
1140C4—282no—
1141C4—282no—
1142C4—282no—
1143C4—282no—
1144C4—282no—
1145C4—282no—
1146C2—44no—
1147C2—284no—
1148C2#1173076711yescharacteristic
1149C2#1173088111yescharacteristic
1150C2#1173100511yescharacteristic
1151C2#1173129611yescharacteristic
1152C2#1173145811yescharacteristic
1153C2#1173145911yescharacteristic
1154C2#1173156911yescharacteristic
1155C2#1173184611yescharacteristic
1156C2#1173184611yescharacteristic
1157C2#1173184711yescharacteristic
1158C2#1173204311yescharacteristic
1159C2#1173212811yescharacteristic
1160C2#1173213011yescharacteristic
1161C2#1173232711yescharacteristic
1162C2#1173232811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22⋊#95D7
hypocenterC7#13832
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C7×C22⋊#95C2semidirect
5. #11729881C2semidirect
6. #11729299C2semidirect
7. #11729299C2semidirect
8. (C2×D7)⋊#95C2semidirect
9. (C2×D7)⋊#95C2semidirect
10. #11727162C2semidirect
11. #11727162C2semidirect
12. #11727160C2semidirect
13. #11727159C2semidirect
14. #11727157C2semidirect
15. #11727156C2semidirect
37. #89985C4semidirect
52. #89729C4semidirect
53. #89728C4semidirect
63. C23×C4×C7C2×C4semidirect
90. C22×C4×D7C2×C4semidirect
96. C2×C7×C22⋊C4C2×C4semidirect
104. C2×C22⋊Dic7C2×C4semidirect
105. C2×C22⋊Dic7C2×C4semidirect
118. C2×(C2×D7)⋊C4C2×C4semidirect
119. C2×(C2×D7)⋊C4C2×C4semidirect
120. C2×(C2×D7)⋊C4C2×C4semidirect
123. C2×Dic7⋊C4C2×C4semidirect
132. C2×C4×Dic7C2×C4semidirect
147. C7⋊#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
149. C7⋊#95C2×C4semidirect
150. C7⋊#95C2×C4semidirect
165. C22⋊#95D7semidirect
252. C2×C22⋊D7C42semidirect
569. C23×C4C4×D7semidirect
608. C2×C22⋊C4C4×D7semidirect
1067. C7#13832semidirect

Maximal subgroups

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

subgroupindex
C2×#899852
C2×#897282
C2×#897292
C7×C22⋊#952
#117298812
#117292992
(C2×D7)⋊#952
#117271622
#117271602
#117271592
#117271572
#117271562
#138327