Finite Group Databasebeta

← #13275390

Subgroups — #13275390

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
3C2×#89723C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×C22⋊C4×Dic7C211yesmaximal, characteristic
6C2×C22⋊C4×Dic7C211yesmaximal, characteristic
7C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
8#11729318C211yesmaximal, characteristic, complemented
9#11729299C211yesmaximal, characteristic
10#11729299C211yesmaximal, characteristic
11C4×C7⋊#95C211yesmaximal, characteristic, complemented
12#11727161C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727161C211yesmaximal, characteristic, complemented
15Dic7×#95C211yesmaximal, 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×C4⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4×Dic7C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C7×#388C418yescomplemented
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
51C2×C7⋊#95C2211yescharacteristic
52C4⋊C4×Dic7—24no—
53#89723C418yescomplemented
54#89722C418yescomplemented
55C22⋊C4×Dic7—24no—
56C22⋊C4×Dic7—24no—
57C4×C4⋊Dic7—24no—
58#13823—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—41no—
71C23×Dic7—41no—
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⋊C4C2×C414yescomplemented
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—22no—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C7×C22⋊C4C2×C414yes—
90C2×C7×C22⋊C4C2×C414yes—
91C2×C7×C22⋊C4C2×C414yes—
92C2×C7×C22⋊C4C2×C414yes—
93C2×C42×C7—22no—
94C2×C42×C7—22no—
95C2×C42×C7C2×C414yescomplemented
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—22no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7—41no—
102C2×C22⋊Dic7C2×C414yes—
103C2×C22⋊Dic7C2×C414yes—
104C2×C22⋊Dic7C2×C414yes—
105C2×C4⋊Dic7—22no—
106C2×C4⋊Dic7—22no—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7C2×C414yes—
112C2×C4⋊Dic7C2×C414yes—
113C2×C4⋊Dic7C2×C414yescomplemented
114C2×C4×Dic7—22no—
115C2×C4×Dic7—22no—
116C2×C4×Dic7—22no—
117C2×C4×Dic7—22no—
118C2×C4×Dic7—22no—
119C2×C4×Dic7—22no—
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—22no—
128C2×C4×Dic7—41no—
129C2×C4×Dic7—41no—
130C2×C4×Dic7—41no—
131C2×C4×Dic7—41no—
132C2×C4×Dic7—41no—
133C2×C4×Dic7—41no—
134C2×C4×Dic7C2×C414yescomplemented
135C7×#95C2×C414yescomplemented
136C7×#95C2×C414yescomplemented
137C7⋊#95—22no—
138C7⋊#95—22no—
139C7⋊#95—22no—
140C7⋊#95—22no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—41no—
144C7⋊#95—41no—
145C7⋊#95C2×C414yes—
146C7⋊#95C2×C414yes—
147C7⋊#95C2×C414yescomplemented
148C7⋊#95C2×C414yescomplemented
149C7⋊#95D414yes—
150C7⋊#95D414yes—
151C2×#388—71no—
152C2×#388D711yescharacteristic
153C2×#385—71no—
154C2×C4×C4⋊C4—71no—
155C2×C4×C4⋊C4—71no—
156C2×C4×C22⋊C4—71no—
157C2×C4×C22⋊C4—71no—
158#1437—71no—
159#1437—71no—
160#1436—71no—
161#1436—71no—
162#1436—71no—
163#1436—71no—
164C4×#95—71no—
165C4×#95—71no—
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
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×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C22×C412yes—
213C22×C4×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C22×C412yes—
216C22×C4×C7C22×C412yes—
217C22×C4×C7C22×C412yes—
218C22×C4×C7C22×C412yes—
219C22×C4×C7C22×C412yes—
220C22×C4×C7C2×D412yes—
221C22×C4×C7C2×D412yes—
222C22×C4×C7#4112yes—
223C22×C4×C7#4112yes—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—21no—
246C22×Dic7—21no—
247C22×Dic7—21no—
248C22×Dic7—21no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—28no—
265C22×Dic7—28no—
266C22×Dic7—44no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7—44no—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C22×C412yes—
275C22×Dic7C22×C412yes—
276C22×Dic7C22×C412yes—
277C22×Dic7C22×C412yes—
278C22×Dic7C22×C412yes—
279C22×Dic7C2×D412yes—
280C22×Dic7C2×D412yes—
281C22×Dic7C2×D412yes—
282C22×Dic7C2×D412yes—
283C22×Dic7#4112yes—
284C22×Dic7#4112yes—
285C22×Dic7#4112yes—
286C22×Dic7#4112yes—
287C7×C4⋊C4—28no—
288C7×C22⋊C4—28no—
289C7×C22⋊C4—28no—
290C7×C22⋊C4C42116yescomplemented
291C42×C7—28no—
292C22⋊Dic7—28no—
293C22⋊Dic7—28no—
294C22⋊Dic7—44no—
295C4⋊Dic7—28no—
296C4⋊Dic7—28no—
297C4⋊Dic7—28no—
298C4×Dic7—28no—
299C4×Dic7—44no—
300C4×Dic7—44no—
301C4×Dic7—44no—
302C4×Dic7—44no—
303C4×Dic7—44no—
304C4×Dic7—44no—
305C24×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×C42—71no—
320C22×C42—71no—
321C22×C42—71no—
322C22×C42—71no—
323C22×C42C2×D711yescharacteristic
324#388—78no—
325#388Dic718yescomplemented
326#385—78no—
327C4×C4⋊C4—144no—
328C4×C4⋊C4—144no—
329C4×C22⋊C4—144no—
330C4×C22⋊C4—144no—
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×#95—71no—
341C2×#95—71no—
342C2×#95—71no—
343C2×#95—71no—
344C2×#95—71no—
345C2×#95C2×D711yescharacteristic
346C2×#95C2×D711yescharacteristic
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—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
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×C7—41no—
377C23×C7—41no—
378C23×C7—41no—
379C23×C7—41no—
380C23×C7—41no—
381C23×C7C2×C4214yes—
382C23×C7C23×C411yescharacteristic
383C23×C7C23×C411yescharacteristic
384C23×C7C23×C411yescharacteristic
385C23×C7C22×D411yescharacteristic
386C23×C7C22×D411yescharacteristic
387C23×C7C2×#4111yescharacteristic
388C23×C7C2×#4111yescharacteristic
389C23×C7C2×#4111yescharacteristic
390C23×C7C2×#4111yescharacteristic
391C23×C7C2×#4111yescharacteristic
392C23×C7C2×#4111yescharacteristic
393C23×C7H(5,𝔽2)11yescharacteristic
394C23×C7H(5,𝔽2)11yescharacteristic
395C23×C72−1+411yescharacteristic
396C23×C72−1+411yescharacteristic
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—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—22no—
424C2×C4×C7—22no—
425C2×C4×C7—22no—
426C2×C4×C7—22no—
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×C7C2×C4214yes—
436C2×C4×C7C2×C4214yes—
437C2×C4×C7C4×D414yes—
438C2×C4×C7C4×D414yes—
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—22no—
466C2×Dic7—22no—
467C2×Dic7—22no—
468C2×Dic7—22no—
469C2×Dic7—22no—
470C2×Dic7—22no—
471C2×Dic7—22no—
472C2×Dic7—22no—
473C2×Dic7—22no—
474C2×Dic7—22no—
475C2×Dic7—416no—
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×Dic7C4×D414yes—
493C2×Dic7C4×D414yes—
494C2×Dic7C4×D414yes—
495C2×Dic7C4×D414yes—
496C25C22×D711yescharacteristic
497C23×C4—71no—
498C23×C4—71no—
499C23×C4—71no—
500C23×C4—71no—
501C23×C4—71no—
502C23×C4—71no—
503C23×C4—71no—
504C23×C4—71no—
505C23×C4—74no—
506C23×C4—142no—
507C23×C4—142no—
508C23×C4—142no—
509C23×C4—142no—
510C23×C4—281no—
511C23×C4—281no—
512C23×C4C22×D711yescharacteristic
513C23×C4C22×D711yescharacteristic
514C23×C4C22×D711yescharacteristic
515C23×C4C22×D711yescharacteristic
516C23×C4C22×D711yescharacteristic
517C23×C4C22×D711yescharacteristic
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—74no—
521C2×C4⋊C4—74no—
522C2×C4⋊C4—74no—
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⋊C4C2×Dic714yescomplemented
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—74no—
535C2×C22⋊C4—74no—
536C2×C22⋊C4—74no—
537C2×C22⋊C4—142no—
538C2×C22⋊C4—142no—
539C2×C22⋊C4—142no—
540C2×C22⋊C4—142no—
541C2×C22⋊C4—281no—
542C2×C22⋊C4—281no—
543C2×C22⋊C4C4×D714yes—
544C2×C22⋊C4C4×D714yes—
545C2×C22⋊C4C2×Dic714yes—
546C2×C22⋊C4C2×Dic714yes—
547C2×C22⋊C4C2×Dic714yes—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—74no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—142no—
554C2×C42—142no—
555C2×C42—142no—
556C2×C42—142no—
557C2×C42—142no—
558C2×C42—142no—
559C2×C42—142no—
560C2×C42—142no—
561C2×C42—142no—
562C2×C42—142no—
563C2×C42—142no—
564C2×C42—142no—
565C2×C42—281no—
566C2×C42—281no—
567C2×C42—281no—
568C2×C42—281no—
569C2×C42—281no—
570C2×C42—281no—
571C2×C42C2×Dic714yescomplemented
572#95—74no—
573#95—74no—
574#95—74no—
575#95—74no—
576#95—74no—
577#95—74no—
578#95—142no—
579#95—142no—
580#95—142no—
581#95—142no—
582#95—142no—
583#95—142no—
584#95—281no—
585#95—281no—
586#95C2×Dic714yescomplemented
587#95C2×Dic714yescomplemented
588C22×C7—24no—
589C22×C7—24no—
590C22×C7—24no—
591C22×C7—42no—
592C22×C7—42no—
593C22×C7—42no—
594C22×C7—42no—
595C22×C7—42no—
596C22×C7—42no—
597C22×C7—42no—
598C22×C7—42no—
599C22×C7—42no—
600C22×C7—42no—
601C22×C7—42no—
602C22×C7—42no—
603C22×C7C22×C4211yescharacteristic
604C22×C7C2×C4×D411yescharacteristic
605C22×C7C2×C4×D411yescharacteristic
606C22×C7C2×C4×D411yescharacteristic
607C22×C7C2×C4×D411yescharacteristic
608C22×C7C2×C4×D411yescharacteristic
609C22×C7C2×C4×D411yescharacteristic
610C22×C7C4×#4111yescharacteristic
611C22×C7C4×#4111yescharacteristic
612C22×C7C4×#4111yescharacteristic
613C22×C7C4×#4111yescharacteristic
614C22×C7C4×#4111yescharacteristic
615C22×C7C4×#4111yescharacteristic
616C22×C7#51811yescharacteristic
617C22×C7#51911yescharacteristic
618C22×C7#52011yescharacteristic
619C22×C7#52011yescharacteristic
620C22×C7#52011yescharacteristic
621C22×C7#52011yescharacteristic
622C22×C7D4211yescharacteristic
623C22×C7#54611yescharacteristic
624C22×C7#54611yescharacteristic
625C22×C7#54711yescharacteristic
626C22×C7#54711yescharacteristic
627C22×C7#54811yescharacteristic
628C22×C7#54811yescharacteristic
629C22×C7#55111yescharacteristic
630C22×C7#55111yescharacteristic
631C22×C7#55211yescharacteristic
632C22×C7#55211yescharacteristic
633C22×C7#55311yescharacteristic
634C22×C7#55311yescharacteristic
635C22×C7#55611yescharacteristic
636C22×C7#55611yescharacteristic
637C22×C7#55911yescharacteristic
638C4×C7—24no—
639C4×C7—24no—
640C4×C7—24no—
641C4×C7—24no—
642C4×C7—42no—
643C4×C7—42no—
644Dic7—24no—
645Dic7—24no—
646Dic7—24no—
647Dic7—24no—
648Dic7—42no—
649Dic7—42no—
650Dic7—42no—
651Dic7—42no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24C2×C4×D712yes—
665C24C2×C4×D712yes—
666C24C22×Dic712yes—
667C24C23×D711yescharacteristic
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—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—72no—
709C22×C4—72no—
710C22×C4—72no—
711C22×C4—72no—
712C22×C4—148no—
713C22×C4—148no—
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—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—284no—
755C22×C4—284no—
756C22×C4—284no—
757C22×C4—284no—
758C22×C4—284no—
759C22×C4C2×C4×D712yes—
760C22×C4C2×C4×D712yes—
761C22×C4C2×C4×D712yes—
762C22×C4C2×C4×D712yes—
763C22×C4D4×D712yes—
764C22×C4D4×D712yes—
765C22×C4#115912yes—
766C22×C4#115912yes—
767C22×C4C22×Dic712yes—
768C22×C4C22×Dic712yes—
769C22×C4C22×Dic712yes—
770C22×C4C22×Dic712yes—
771C22×C4C22×Dic712yes—
772C22×C4C22×Dic712yes—
773C4⋊C4—28no—
774C4⋊C4—148no—
775C4⋊C4—148no—
776C4⋊C4—148no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—148no—
780C22⋊C4—148no—
781C22⋊C4—284no—
782C22⋊C4C4×Dic7116yescomplemented
783C42—28no—
784C42—148no—
785C42—284no—
786C42—284no—
787C42—284no—
788C42—284no—
789C42—284no—
790C42—284no—
791C2×C7—44no—
792C2×C7C42×D411yescharacteristic
793C2×C7C42×D411yescharacteristic
794C2×C7#227411yescharacteristic
795C2×C7#235811yescharacteristic
796C2×C7#235911yescharacteristic
797C2×C7#235911yescharacteristic
798C2×C7#236111yescharacteristic
799C2×C7#236111yescharacteristic
800C2×C7#236211yescharacteristic
801C2×C7#236211yescharacteristic
802C2×C7#236711yescharacteristic
803C2×C7#236711yescharacteristic
804C2×C7#237311yescharacteristic
805C2×C7#237311yescharacteristic
806C2×C7#237411yescharacteristic
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×C4×Dic714yes—
842C23C22×C4×D711yescharacteristic
843C23C22×C4×D711yescharacteristic
844C23C2×D4×D711yescharacteristic
845C23C2×D4×D711yescharacteristic
846C23C2×#115911yescharacteristic
847C23C2×#115911yescharacteristic
848C23D7×#4111yescharacteristic
849C23D7×#4111yescharacteristic
850C23D7×#4111yescharacteristic
851C23D7×#4111yescharacteristic
852C23#655311yescharacteristic
853C23#655311yescharacteristic
854C23#655411yescharacteristic
855C23#655411yescharacteristic
856C23C23×Dic711yescharacteristic
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—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
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—74no—
896C2×C4—74no—
897C2×C4—74no—
898C2×C4—74no—
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—142no—
923C2×C4—142no—
924C2×C4—142no—
925C2×C4—142no—
926C2×C4—142no—
927C2×C4—142no—
928C2×C4—142no—
929C2×C4—142no—
930C2×C4—142no—
931C2×C4—142no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—2816no—
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×C4C2×C4×Dic714yes—
953C2×C4C2×C4×Dic714yes—
954C2×C4D4×Dic714yes—
955C2×C4D4×Dic714yes—
956C7#1382311yescharacteristic, complemented, Sylow
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#9020711yescharacteristic
973C22#9021211yescharacteristic
974C22#9021411yescharacteristic
975C22#9021411yescharacteristic
976C22C4×#115911yescharacteristic
977C22C4×#115911yescharacteristic
978C22C4×#115911yescharacteristic
979C22C4×#115911yescharacteristic
980C22C4×D4×D711yescharacteristic
981C22C4×D4×D711yescharacteristic
982C22C4×D4×D711yescharacteristic
983C22C4×D4×D711yescharacteristic
984C22#9028911yescharacteristic
985C22#9030011yescharacteristic
986C22#9030211yescharacteristic
987C22#9030911yescharacteristic
988C22#9034111yescharacteristic
989C22#9034511yescharacteristic
990C22#9034611yescharacteristic
991C22#9034911yescharacteristic
992C22#9036211yescharacteristic
993C22#9036711yescharacteristic
994C22#9036811yescharacteristic
995C22#9037211yescharacteristic
996C22#9039311yescharacteristic
997C22#9039611yescharacteristic
998C22#9039911yescharacteristic
999C22#9040011yescharacteristic
1000C22C22×C4×Dic711yescharacteristic
1001C22C2×D4×Dic711yescharacteristic
1002C22C2×D4×Dic711yescharacteristic
1003C22#41×Dic711yescharacteristic
1004C22#41×Dic711yescharacteristic
1005C22#9051811yescharacteristic
1006C22#9051811yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—144no—
1014C4—144no—
1015C4—144no—
1016C4—144no—
1017C4—282no—
1018C4—282no—
1019C4—282no—
1020C4—282no—
1021C2—44no—
1022C2#1173292211yescharacteristic
1023C2#1173292311yescharacteristic
1024C2#1173292411yescharacteristic
1025C2#1173292711yescharacteristic
1026C2#1173293111yescharacteristic
1027C2#1173293311yescharacteristic
1028C2#1173328111yescharacteristic
1029C2#1173328311yescharacteristic
1030C2#1173966811yescharacteristic
1031C2C4×D4×Dic711yescharacteristic
1032C2C4×D4×Dic711yescharacteristic
1033C2#1174008111yescharacteristic
1034C2#1174028311yescharacteristic
1035C2#1174040011yescharacteristic
1036C2#1174052011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC22×C7C22×C42
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#13823
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic7C2semidirect
7. C2×C4×C4⋊Dic7C2semidirect
8. #11729318C2semidirect
11. C4×C7⋊#95C2semidirect
12. #11727161C2semidirect
13. #11727161C2semidirect
14. #11727161C2semidirect
15. Dic7×#95C2semidirect
35. C7×#388C4semidirect
53. #89723C4semidirect
54. #89722C4semidirect
83. C2×C7×C4⋊C4C2×C4semidirect
95. C2×C42×C7C2×C4semidirect
113. C2×C4⋊Dic7C2×C4semidirect
134. C2×C4×Dic7C2×C4semidirect
135. C7×#95C2×C4semidirect
136. C7×#95C2×C4semidirect
147. C7⋊#95C2×C4semidirect
148. C7⋊#95C2×C4semidirect
290. C7×C22⋊C4C42semidirect
325. #388Dic7semidirect
529. C2×C4⋊C4C2×Dic7semidirect
571. C2×C42C2×Dic7semidirect
586. #95C2×Dic7semidirect
587. #95C2×Dic7semidirect
782. C22⋊C4C4×Dic7semidirect
956. C7#13823semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×C4⋊C4×Dic72
C2×#897232
C2×#897222
C2×C22⋊C4×Dic72
C2×C4×C4⋊Dic72
#117293182
#117292992
C4×C7⋊#952
#117271612
Dic7×#952
#138237