Finite Group Databasebeta

← #13282230

Subgroups — #13282230

Order 1792.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#388C211yesmaximal, characteristic
2C2×#89757C211yesmaximal, characteristic, complemented
3C2×#89723C211yesmaximal, characteristic
4C2×#89722C211yesmaximal, characteristic
5C2×#89722C211yesmaximal, characteristic
6#11729319C211yesmaximal, characteristic, complemented
7#11729300C211yesmaximal, characteristic
8#11729300C211yesmaximal, characteristic
9#11729298C211yesmaximal, characteristic
10#11729289C211yesmaximal, characteristic, complemented
11#11729289C211yesmaximal, characteristic, complemented
12#11727173C211yesmaximal, characteristic, complemented
13#11727166C211yesmaximal, characteristic, complemented
14#11727166C211yesmaximal, characteristic, complemented
15#11727161C211yesmaximal, 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
33C7×#388C418yescomplemented
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2211yescharacteristic
36C2×C7⋊#95C2211yescharacteristic
37C2×C7⋊#95C2211yescharacteristic
38C2×C7⋊#95C2211yescharacteristic
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52#89757—24no—
53#89723—24no—
54#89722—24no—
55#89722—24no—
56#14442—71nomaximal, Sylow
57C25×C7C2311yescharacteristic
58C23×C4×C7C2311yescharacteristic
59C23×C4×C7C2311yescharacteristic
60C23×C4×C7C2311yescharacteristic
61C23×C4×C7C2311yescharacteristic
62C23×C4×C7C2311yescharacteristic
63C23×C4×C7C2311yescharacteristic
64C23×Dic7—22no—
65C23×Dic7—22no—
66C23×Dic7—22no—
67C23×Dic7—41no—
68C23×Dic7—41no—
69C23×Dic7—41no—
70C23×Dic7—41no—
71C23×Dic7C2311yescharacteristic
72C23×Dic7C2311yescharacteristic
73C23×Dic7C2311yescharacteristic
74C23×Dic7C2311yescharacteristic
75C23×Dic7C2311yescharacteristic
76C23×Dic7C2311yescharacteristic
77C23×Dic7C2311yescharacteristic
78C23×Dic7C2311yescharacteristic
79C2×C7×C4⋊C4—22no—
80C2×C7×C4⋊C4—22no—
81C2×C7×C4⋊C4C2×C414yescomplemented
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—41no—
85C2×C7×C22⋊C4—41no—
86C2×C7×C22⋊C4C2×C414yes—
87C2×C7×C22⋊C4C2×C414yes—
88C2×C7×C22⋊C4C2×C414yes—
89C2×C7×C22⋊C4D414yes—
90C2×C7×C22⋊C4Q814yes—
91C2×C42×C7—41no—
92C2×C42×C7—41no—
93C2×C42×C7C2×C414yescomplemented
94C2×C22⋊Dic7—22no—
95C2×C22⋊Dic7—22no—
96C2×C22⋊Dic7—22no—
97C2×C22⋊Dic7—22no—
98C2×C22⋊Dic7—22no—
99C2×C22⋊Dic7—41no—
100C2×C22⋊Dic7—41no—
101C2×C22⋊Dic7—41no—
102C2×C22⋊Dic7—41no—
103C2×C4⋊Dic7—22no—
104C2×C4⋊Dic7—22no—
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⋊Dic7—22no—
112C2×C4⋊Dic7—22no—
113C2×C4⋊Dic7—41no—
114C2×C4⋊Dic7—41no—
115C2×C4⋊Dic7—41no—
116C2×C4⋊Dic7—41no—
117C2×C4⋊Dic7—41no—
118C2×C4⋊Dic7—41no—
119C2×C4⋊Dic7—41no—
120C2×C4⋊Dic7—41no—
121C2×C4⋊Dic7—41no—
122C2×C4⋊Dic7—41no—
123C2×C4⋊Dic7D414yes—
124C2×C4×Dic7—22no—
125C2×C4×Dic7—22no—
126C2×C4×Dic7—41no—
127C7×#95C2×C414yescomplemented
128C7×#95C2×C414yescomplemented
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—
145C2×#389—71no—
146C2×#388—71no—
147C2×#388D711yescharacteristic
148C2×#385—71no—
149C2×#385—71no—
150#1444—71no—
151#1442—71no—
152#1442—71no—
153#1441—71no—
154#1439—71no—
155#1439—71no—
156#1436—71no—
157C4⋊#95—71no—
158C4⋊#95—71no—
159C22⋊#95—71no—
160C24×C7—21no—
161C24×C7—21no—
162C24×C7—21no—
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×C7C22×C412yes—
173C24×C7C2×D412yes—
174C24×C7C2×Q812yes—
175C24×C7C2411yescharacteristic
176C22×C4×C7—21no—
177C22×C4×C7—21no—
178C22×C4×C7—21no—
179C22×C4×C7—21no—
180C22×C4×C7—21no—
181C22×C4×C7—21no—
182C22×C4×C7—21no—
183C22×C4×C7—21no—
184C22×C4×C7—21no—
185C22×C4×C7—21no—
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—21no—
191C22×C4×C7—21no—
192C22×C4×C7—21no—
193C22×C4×C7—21no—
194C22×C4×C7—21no—
195C22×C4×C7—21no—
196C22×C4×C7—21no—
197C22×C4×C7—21no—
198C22×C4×C7—21no—
199C22×C4×C7—21no—
200C22×C4×C7—21no—
201C22×C4×C7—21no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7C22×C412yes—
207C22×C4×C7C22×C412yes—
208C22×C4×C7C22×C412yes—
209C22×C4×C7C22×C412yes—
210C22×C4×C7C22×C412yes—
211C22×C4×C7C22×C412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2×D412yes—
215C22×C4×C7C2×Q812yes—
216C22×C4×C7C2×Q812yes—
217C22×C4×C7#4112yes—
218C22×Dic7—21no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
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—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—44no—
271C22×Dic7—44no—
272C22×Dic7—44no—
273C22×Dic7—44no—
274C22×Dic7—44no—
275C22×Dic7—44no—
276C22×Dic7—44no—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×D412yes—
279C22×Dic7#4112yes—
280C22×Dic7#4112yes—
281C7×C4⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4C4⋊C4116yescomplemented
285C42×C7—44no—
286C22⋊Dic7—44no—
287C22⋊Dic7—44no—
288C22⋊Dic7—44no—
289C4⋊Dic7—44no—
290C4⋊Dic7—44no—
291C4⋊Dic7—44no—
292C4⋊Dic7—44no—
293C4⋊Dic7—44no—
294C4⋊Dic7—44no—
295C4⋊Dic7—44no—
296C4×Dic7—44no—
297C24×C4—71no—
298C22×C4⋊C4—71no—
299C22×C4⋊C4—71no—
300C22×C4⋊C4—71no—
301C22×C4⋊C4—71no—
302C22×C4⋊C4—71no—
303C22×C4⋊C4—71no—
304C22×C4⋊C4—71no—
305C22×C4⋊C4C2×D711yescharacteristic
306C22×C22⋊C4—71no—
307C22×C22⋊C4—71no—
308C22×C22⋊C4—71no—
309C22×C22⋊C4C2×D711yescharacteristic
310C22×C22⋊C4C2×D711yescharacteristic
311C22×C22⋊C4C2×D711yescharacteristic
312C22×C42—71no—
313C22×C42C2×D711yescharacteristic
314#389—144no—
315#388—144no—
316#388Dic718yescomplemented
317#385—144no—
318#385—144no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
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×#95C2×D711yescharacteristic
336C2×#95C2×D711yescharacteristic
337C23×C7—22no—
338C23×C7—22no—
339C23×C7—22no—
340C23×C7—22no—
341C23×C7—22no—
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—41no—
356C23×C7—41no—
357C23×C7—41no—
358C23×C7—41no—
359C23×C7—41no—
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×C7C2×C4⋊C414yes—
372C23×C7C23×C411yescharacteristic
373C23×C7C22×D411yescharacteristic
374C23×C7C22×D411yescharacteristic
375C23×C7C22×Q811yescharacteristic
376C23×C7C2×#4111yescharacteristic
377C23×C7C2×#4111yescharacteristic
378C23×C7C2×#4111yescharacteristic
379C23×C7H(5,𝔽2)11yescharacteristic
380C23×C7H(5,𝔽2)11yescharacteristic
381C23×C7H(5,𝔽2)11yescharacteristic
382C23×C7H(5,𝔽2)11yescharacteristic
383C23×C7H(5,𝔽2)11yescharacteristic
384C23×C72−1+411yescharacteristic
385C23×C72−1+411yescharacteristic
386C23×C72−1+411yescharacteristic
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
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—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
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×C7C2×C4⋊C414yes—
427C2×C4×C7C2×C4⋊C414yes—
428C2×C4×C7C4×D414yes—
429C2×Dic7—22no—
430C2×Dic7—22no—
431C2×Dic7—22no—
432C2×Dic7—22no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—416no—
442C2×Dic7—41no—
443C2×Dic7—41no—
444C2×Dic7—41no—
445C2×Dic7—41no—
446C2×Dic7—41no—
447C2×Dic7—41no—
448C2×Dic7—41no—
449C2×Dic7—41no—
450C2×Dic7—41no—
451C2×Dic7—41no—
452C2×Dic7—41no—
453C2×Dic7—41no—
454C2×Dic7—41no—
455C2×Dic7—41no—
456C2×Dic7—41no—
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—
486C25C22×D711yescharacteristic
487C23×C4—71no—
488C23×C4—71no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—71no—
493C23×C4—71no—
494C23×C4—71no—
495C23×C4—142no—
496C23×C4—142no—
497C23×C4—142no—
498C23×C4—281no—
499C23×C4—281no—
500C23×C4—281no—
501C23×C4—281no—
502C23×C4C22×D711yescharacteristic
503C23×C4C22×D711yescharacteristic
504C23×C4C22×D711yescharacteristic
505C23×C4C22×D711yescharacteristic
506C23×C4C22×D711yescharacteristic
507C23×C4C22×D711yescharacteristic
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—74no—
511C2×C4⋊C4—142no—
512C2×C4⋊C4—142no—
513C2×C4⋊C4—142no—
514C2×C4⋊C4—142no—
515C2×C4⋊C4—142no—
516C2×C4⋊C4—142no—
517C2×C4⋊C4—142no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—142no—
520C2×C4⋊C4—142no—
521C2×C4⋊C4—281no—
522C2×C4⋊C4—281no—
523C2×C4⋊C4—281no—
524C2×C4⋊C4—281no—
525C2×C4⋊C4—281no—
526C2×C4⋊C4—281no—
527C2×C4⋊C4—281no—
528C2×C4⋊C4—281no—
529C2×C4⋊C4—281no—
530C2×C4⋊C4—281no—
531C2×C4⋊C4C2×Dic714yescomplemented
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—142no—
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⋊C4—281no—
544C2×C22⋊C4—281no—
545C2×C22⋊C4Dic1414yes—
546C2×C22⋊C4D2814yes—
547C2×C22⋊C4C2×Dic714yes—
548C2×C22⋊C4C2×Dic714yes—
549C2×C22⋊C4C2×Dic714yes—
550C2×C42—41no—
551C2×C42—41no—
552C2×C42—142no—
553C2×C42—142no—
554C2×C42—281no—
555C2×C42C2×Dic714yescomplemented
556#95—142no—
557#95—142no—
558#95—142no—
559#95—142no—
560#95—142no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—281no—
566#95—281no—
567#95—281no—
568#95—281no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95C2×Dic714yescomplemented
573#95C2×Dic714yescomplemented
574C22×C7—24no—
575C22×C7—24no—
576C22×C7—24no—
577C22×C7—42no—
578C22×C7—42no—
579C22×C7—42no—
580C22×C7—42no—
581C22×C7—42no—
582C22×C7—42no—
583C22×C7—42no—
584C22×C7—42no—
585C22×C7—42no—
586C22×C7—42no—
587C22×C7—42no—
588C22×C7—42no—
589C22×C7C22×C4⋊C411yescharacteristic
590C22×C7C2×C4×D411yescharacteristic
591C22×C7C4×#4111yescharacteristic
592C22×C7#51811yescharacteristic
593C22×C7#52011yescharacteristic
594C22×C7#52011yescharacteristic
595C22×C7#52011yescharacteristic
596C22×C7#53411yescharacteristic
597C22×C7#53511yescharacteristic
598C22×C7#53611yescharacteristic
599C22×C7#53711yescharacteristic
600C22×C7#53811yescharacteristic
601C22×C7#53811yescharacteristic
602C22×C7#53911yescharacteristic
603C22×C7#53911yescharacteristic
604C22×C7#54111yescharacteristic
605C22×C7#54211yescharacteristic
606C22×C7#54411yescharacteristic
607C22×C7#54411yescharacteristic
608C22×C7D4211yescharacteristic
609C22×C7#54611yescharacteristic
610C22×C7#54611yescharacteristic
611C22×C7#54611yescharacteristic
612C22×C7#54711yescharacteristic
613C22×C7#54811yescharacteristic
614C22×C7D4×Q811yescharacteristic
615C22×C7#55411yescharacteristic
616C22×C7#55411yescharacteristic
617C22×C7#55411yescharacteristic
618C22×C7#55611yescharacteristic
619C22×C7#55911yescharacteristic
620C22×C7#56011yescharacteristic
621C22×C7#56211yescharacteristic
622C22×C7#56211yescharacteristic
623C22×C7#56311yescharacteristic
624C4×C7—24no—
625C4×C7—24no—
626C4×C7—24no—
627C4×C7—42no—
628C4×C7—42no—
629C4×C7—42no—
630Dic7—42no—
631Dic7—42no—
632Dic7—42no—
633Dic7—42no—
634Dic7—81no—
635Dic7—81no—
636Dic7—81no—
637Dic7—81no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24C2×Dic1412yes—
651C24C2×D2812yes—
652C24C22×Dic712yes—
653C24C23×D711yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
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—72no—
685C22×C4—72no—
686C22×C4—72no—
687C22×C4—72no—
688C22×C4—141no—
689C22×C4—141no—
690C22×C4—141no—
691C22×C4—141no—
692C22×C4—141no—
693C22×C4—141no—
694C22×C4—141no—
695C22×C4—141no—
696C22×C4—141no—
697C22×C4—141no—
698C22×C4—141no—
699C22×C4—141no—
700C22×C4—141no—
701C22×C4—141no—
702C22×C4—141no—
703C22×C4—141no—
704C22×C4—141no—
705C22×C4—141no—
706C22×C4—141no—
707C22×C4—141no—
708C22×C4—141no—
709C22×C4—141no—
710C22×C4—141no—
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—284no—
741C22×C4—284no—
742C22×C4—284no—
743C22×C4—284no—
744C22×C4—284no—
745C22×C4—284no—
746C22×C4—284no—
747C22×C4C2×Dic1412yes—
748C22×C4C2×Dic1412yes—
749C22×C4C2×D2812yes—
750C22×C4C2×D2812yes—
751C22×C4D4×D712yes—
752C22×C4#115912yes—
753C22×C4C22×Dic712yes—
754C22×C4C22×Dic712yes—
755C22×C4C22×Dic712yes—
756C22×C4C22×Dic712yes—
757C22×C4C22×Dic712yes—
758C22×C4C22×Dic712yes—
759C4⋊C4—28no—
760C4⋊C4—284no—
761C4⋊C4—284no—
762C4⋊C4—284no—
763C4⋊C4—284no—
764C4⋊C4—284no—
765C4⋊C4—284no—
766C4⋊C4—284no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—284no—
770C22⋊C4—284no—
771C22⋊C4—284no—
772C22⋊C4C4⋊Dic7116yescomplemented
773C42—44no—
774C42—284no—
775C2×C7—44no—
776C2×C7#231711yescharacteristic
777C2×C7#232511yescharacteristic
778C2×C7#233411yescharacteristic
779C2×C7D4×C4⋊C411yescharacteristic
780C2×C7#234911yescharacteristic
781C2×C7#236711yescharacteristic
782C2×C7#237611yescharacteristic
783C2×C7#267811yescharacteristic
784C2×C7#268111yescharacteristic
785C2×C7#268911yescharacteristic
786C2×C7#270411yescharacteristic
787C2×C7#271011yescharacteristic
788C2×C7#272911yescharacteristic
789C2×C7#278811yescharacteristic
790C2×C7#280711yescharacteristic
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
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—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C2×C4⋊Dic714yes—
826C23C22×Dic1411yescharacteristic
827C23C22×D2811yescharacteristic
828C23C2×D4×D711yescharacteristic
829C23C2×#115911yescharacteristic
830C23#654811yescharacteristic
831C23#654811yescharacteristic
832C23D7×#4111yescharacteristic
833C23D7×#4111yescharacteristic
834C23#655311yescharacteristic
835C23#655311yescharacteristic
836C23#655311yescharacteristic
837C23#655411yescharacteristic
838C23#655411yescharacteristic
839C23#655411yescharacteristic
840C23C23×Dic711yescharacteristic
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
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—22no—
866C2×C4—22no—
867C2×C4—22no—
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—142no—
881C2×C4—142no—
882C2×C4—142no—
883C2×C4—142no—
884C2×C4—142no—
885C2×C4—142no—
886C2×C4—142no—
887C2×C4—142no—
888C2×C4—142no—
889C2×C4—142no—
890C2×C4—142no—
891C2×C4—142no—
892C2×C4—2816no—
893C2×C4—281no—
894C2×C4—281no—
895C2×C4—281no—
896C2×C4—281no—
897C2×C4—281no—
898C2×C4—281no—
899C2×C4—281no—
900C2×C4—281no—
901C2×C4—281no—
902C2×C4—281no—
903C2×C4—281no—
904C2×C4—281no—
905C2×C4—281no—
906C2×C4—281no—
907C2×C4—281no—
908C2×C4—281no—
909C2×C4—281no—
910C2×C4—281no—
911C2×C4—281no—
912C2×C4—281no—
913C2×C4—281no—
914C2×C4—281no—
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×C4C2×C4⋊Dic714yes—
938C2×C4C2×C4⋊Dic714yes—
939C2×C4D4×Dic714yes—
940C7#1444211yescharacteristic, complemented, Sylow
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22#9021011yescharacteristic
957C22#9021011yescharacteristic
958C22#9021611yescharacteristic
959C22#9021711yescharacteristic
960C22D4×Dic1411yescharacteristic
961C22#9023011yescharacteristic
962C22#9023011yescharacteristic
963C22#9023411yescharacteristic
964C22D4×D2811yescharacteristic
965C22#9024511yescharacteristic
966C22#9024511yescharacteristic
967C22#9024611yescharacteristic
968C22#9028811yescharacteristic
969C22#9029311yescharacteristic
970C22#9029611yescharacteristic
971C22#9030811yescharacteristic
972C22#9034211yescharacteristic
973C22#9035711yescharacteristic
974C22#9035811yescharacteristic
975C22#9035811yescharacteristic
976C22#9036211yescharacteristic
977C22#9036711yescharacteristic
978C22#9036811yescharacteristic
979C22#9037211yescharacteristic
980C22#9039211yescharacteristic
981C22#9039511yescharacteristic
982C22#9039811yescharacteristic
983C22#9040111yescharacteristic
984C22C22×C4⋊Dic711yescharacteristic
985C22C2×D4×Dic711yescharacteristic
986C22#9048911yescharacteristic
987C22#41×Dic711yescharacteristic
988C22#9051811yescharacteristic
989C22#9051811yescharacteristic
990C22#9051811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—282no—
998C4—282no—
999C4—282no—
1000C4—282no—
1001C4—561no—
1002C4—561no—
1003C4—561no—
1004C4—561no—
1005C2—44no—
1006C2#1173311411yescharacteristic
1007C2#1173311611yescharacteristic
1008C2#1173313011yescharacteristic
1009C2#1173313511yescharacteristic
1010C2#1173315211yescharacteristic
1011C2#1173323111yescharacteristic
1012C2#1173325611yescharacteristic
1013C2#1173336111yescharacteristic
1014C2#1173967811yescharacteristic
1015C2D4×C4⋊Dic711yescharacteristic
1016C2#1173977811yescharacteristic
1017C2#1174007911yescharacteristic
1018C2#1174028511yescharacteristic
1019C2#1174040011yescharacteristic
1020C2#1174051911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC2×C7×#388C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#388D7
hypocenterC7#14442
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#89757C2semidirect
6. #11729319C2semidirect
10. #11729289C2semidirect
11. #11729289C2semidirect
12. #11727173C2semidirect
13. #11727166C2semidirect
14. #11727166C2semidirect
15. #11727161C2semidirect
33. C7×#388C4semidirect
81. C2×C7×C4⋊C4C2×C4semidirect
93. C2×C42×C7C2×C4semidirect
127. C7×#95C2×C4semidirect
128. C7×#95C2×C4semidirect
284. C7×C22⋊C4C4⋊C4semidirect
316. #388Dic7semidirect
531. C2×C4⋊C4C2×Dic7semidirect
555. C2×C42C2×Dic7semidirect
572. #95C2×Dic7semidirect
573. #95C2×Dic7semidirect
772. C22⋊C4C4⋊Dic7semidirect
940. C7#14442semidirect

Maximal subgroups

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

subgroupindex
C2×C7×#3882
C2×#897572
C2×#897232
C2×#897222
#117293192
#117293002
#117292982
#117292892
#117271732
#117271662
#117271612
#144427