Finite Group Databasebeta

← #13282232

Subgroups — #13282232

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×#89717C211yesmaximal, characteristic
2C2×#89717C211yesmaximal, characteristic
3C2×#89722C211yesmaximal, characteristic
4C2×#89718C211yesmaximal, characteristic
5C2×#89419C211yesmaximal, characteristic, complemented
6C7×#1439C211yesmaximal, characteristic
7#11729320C211yesmaximal, characteristic, complemented
8#11729317C211yesmaximal, characteristic, complemented
9#11729301C211yesmaximal, characteristic
10#11729298C211yesmaximal, characteristic
11#11727174C211yesmaximal, characteristic, complemented
12#11727168C211yesmaximal, characteristic, complemented
13#11727167C211yesmaximal, 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×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×C4⋊Dic7C2211yescharacteristic
26C22×Dic7⋊C4C2211yescharacteristic
27C22×Dic7⋊C4C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C2×C7×#95C2211yescharacteristic
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
51#89722—24no—
52#89718—24no—
53#89717—24no—
54#89717C418yescomplemented
55#89419—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—41no—
81C2×C7×C4⋊C4—41no—
82C2×C7×C22⋊C4—22no—
83C2×C7×C22⋊C4—22no—
84C2×C7×C22⋊C4—22no—
85C2×C7×C22⋊C4—22no—
86C2×C7×C22⋊C4—22no—
87C2×C7×C22⋊C4—41no—
88C2×C7×C22⋊C4—41no—
89C2×C7×C22⋊C4—41no—
90C2×C7×C22⋊C4C2×C414yes—
91C2×C22⋊Dic7—22no—
92C2×C22⋊Dic7—22no—
93C2×C22⋊Dic7—41no—
94C2×C22⋊Dic7—41no—
95C2×C22⋊Dic7—41no—
96C2×C22⋊Dic7C2×C414yes—
97C2×C22⋊Dic7C2×C414yes—
98C2×C22⋊Dic7D414yes—
99C2×C22⋊Dic7Q814yes—
100C2×C4⋊Dic7—22no—
101C2×C4⋊Dic7—22no—
102C2×C4⋊Dic7—41no—
103C2×C4⋊Dic7—41no—
104C2×C4⋊Dic7—41no—
105C2×C4⋊Dic7D414yes—
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—41no—
116C2×Dic7⋊C4—41no—
117C2×Dic7⋊C4—41no—
118C2×Dic7⋊C4—41no—
119C2×Dic7⋊C4—41no—
120C2×Dic7⋊C4C2×C414yescomplemented
121C2×C4×Dic7—22no—
122C2×C4×Dic7—22no—
123C2×C4×Dic7—41no—
124C2×C4×Dic7—41no—
125C2×C4×Dic7—41no—
126C2×C4×Dic7C2×C414yescomplemented
127C7×#95—22no—
128C7×#95—22no—
129C7×#95—41no—
130C7⋊#95—22no—
131C7⋊#95—22no—
132C7⋊#95—22no—
133C7⋊#95—22no—
134C7⋊#95—22no—
135C7⋊#95—22no—
136C7⋊#95—22no—
137C7⋊#95—41no—
138C7⋊#95—41no—
139C7⋊#95—41no—
140C7⋊#95—41no—
141C7⋊#95—41no—
142C7⋊#95—41no—
143C7⋊#95C2×C414yescomplemented
144C7⋊#95C2×C414yescomplemented
145C2×#389—71no—
146C2×#388—71no—
147C2×#388—71no—
148C2×#385—71no—
149C2×#385—71no—
150#1444—71no—
151#1442—71no—
152#1442—71no—
153#1441—71no—
154#1439—71no—
155#1439D711yescharacteristic
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×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×C7C22×C412yes—
214C22×C4×C7C22×C412yes—
215C22×C4×C7C2×D412yes—
216C22×C4×C7#4112yes—
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—44no—
264C22×Dic7—44no—
265C22×Dic7—44no—
266C22×Dic7—44no—
267C22×Dic7—44no—
268C22×Dic7—44no—
269C22×Dic7—44no—
270C22×Dic7C22×C412yes—
271C22×Dic7C22×C412yes—
272C22×Dic7C22×C412yes—
273C22×Dic7C22×C412yes—
274C22×Dic7C2×D412yes—
275C22×Dic7C2×D412yes—
276C22×Dic7C2×D412yes—
277C22×Dic7C2×D412yes—
278C22×Dic7C2×Q812yes—
279C22×Dic7C2×Q812yes—
280C22×Dic7#4112yes—
281C7×C4⋊C4—44no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—44no—
284C7×C22⋊C4—44no—
285C22⋊Dic7—44no—
286C22⋊Dic7—44no—
287C22⋊Dic7C4⋊C4116yescomplemented
288C4⋊Dic7—44no—
289C4⋊Dic7—44no—
290Dic7⋊C4—28no—
291Dic7⋊C4—44no—
292Dic7⋊C4—44no—
293Dic7⋊C4—44no—
294Dic7⋊C4—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×C42—71no—
314#389—144no—
315#388—78no—
316#388—144no—
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×#95C2×D711yescharacteristic
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—41no—
400C2×C4×C7—41no—
401C2×C4×C7—41no—
402C2×C4×C7—41no—
403C2×C4×C7—41no—
404C2×C4×C7—41no—
405C2×C4×C7—41no—
406C2×C4×C7—41no—
407C2×C4×C7—41no—
408C2×C4×C7—41no—
409C2×C4×C7—41no—
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×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—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—416no—
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×Dic7C2×C4⋊C414yes—
485C2×Dic7C2×C4⋊C414yes—
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—41no—
510C2×C4⋊C4—41no—
511C2×C4⋊C4—74no—
512C2×C4⋊C4—74no—
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—142no—
522C2×C4⋊C4—142no—
523C2×C4⋊C4—142no—
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⋊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—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—74no—
541C2×C22⋊C4—74no—
542C2×C22⋊C4—74no—
543C2×C22⋊C4—74no—
544C2×C22⋊C4—142no—
545C2×C22⋊C4—142no—
546C2×C22⋊C4—281no—
547C2×C22⋊C4—281no—
548C2×C22⋊C4—281no—
549C2×C22⋊C4C4×D714yes—
550C2×C42—74no—
551C2×C42—142no—
552C2×C42—142no—
553C2×C42—281no—
554C2×C42—281no—
555C2×C42—281no—
556#95—22no—
557#95—22no—
558#95—41no—
559#95—74no—
560#95—74no—
561#95—142no—
562#95—142no—
563#95—142no—
564#95—142no—
565#95—142no—
566#95—142no—
567#95—142no—
568#95—281no—
569#95—281no—
570#95—281no—
571#95—281no—
572#95—281no—
573#95—281no—
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—42no—
626C4×C7—42no—
627C4×C7—81no—
628C4×C7—81no—
629C4×C7—81no—
630Dic7—24no—
631Dic7—24no—
632Dic7—42no—
633Dic7—42no—
634Dic7—42no—
635Dic7—42no—
636Dic7—42no—
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×C4×D712yes—
651C24D4×D712yes—
652C24Q8×D712yes—
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—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—72no—
692C22×C4—72no—
693C22×C4—72no—
694C22×C4—72no—
695C22×C4—72no—
696C22×C4—72no—
697C22×C4—72no—
698C22×C4—72no—
699C22×C4—72no—
700C22×C4—72no—
701C22×C4—72no—
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—141no—
741C22×C4—141no—
742C22×C4—141no—
743C22×C4—141no—
744C22×C4—141no—
745C22×C4—141no—
746C22×C4—141no—
747C22×C4—284no—
748C22×C4—284no—
749C22×C4—284no—
750C22×C4—284no—
751C22×C4—284no—
752C22×C4—284no—
753C22×C4—284no—
754C22×C4C2×C4×D712yes—
755C22×C4C2×C4×D712yes—
756C22×C4D4×D712yes—
757C22×C4#115912yes—
758C22×C4#115912yes—
759C4⋊C4—44no—
760C4⋊C4—148no—
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—44no—
770C22⋊C4—716no—
771C22⋊C4—284no—
772C22⋊C4—284no—
773C42—284no—
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—
825C23D7×C4⋊C414yes—
826C23C22×C4×D711yescharacteristic
827C23C2×D4×D711yescharacteristic
828C23C2×D4×D711yescharacteristic
829C23C2×#115911yescharacteristic
830C23C2×#115911yescharacteristic
831C23#654811yescharacteristic
832C23#654811yescharacteristic
833C23#654811yescharacteristic
834C23C2×Q8×D711yescharacteristic
835C23D7×#4111yescharacteristic
836C23#655311yescharacteristic
837C23#655311yescharacteristic
838C23#655411yescharacteristic
839C23#655411yescharacteristic
840C23#655411yescharacteristic
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—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
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—74no—
883C2×C4—74no—
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—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—2816no—
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×C4—281no—
938C2×C4—281no—
939C2×C4(C22⋊D7)⋊C414yes—
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—
956C22C2×(C22⋊D7)⋊C411yescharacteristic
957C22C2×D7×C4⋊C411yescharacteristic
958C22#9021411yescharacteristic
959C22C4×#115911yescharacteristic
960C22#9023611yescharacteristic
961C22#9023711yescharacteristic
962C22#9023711yescharacteristic
963C22#9028211yescharacteristic
964C22#9028311yescharacteristic
965C22#9028411yescharacteristic
966C22#9028811yescharacteristic
967C22#9028911yescharacteristic
968C22#9029411yescharacteristic
969C22#9029611yescharacteristic
970C22#9030011yescharacteristic
971C22#9030211yescharacteristic
972C22#9030311yescharacteristic
973C22#9031211yescharacteristic
974C22#9031411yescharacteristic
975C22#9031411yescharacteristic
976C22#9032311yescharacteristic
977C22#9032611yescharacteristic
978C22#9032611yescharacteristic
979C22#9032711yescharacteristic
980C22#9033911yescharacteristic
981C22#9034511yescharacteristic
982C22#9035611yescharacteristic
983C22#9035611yescharacteristic
984C22#9035711yescharacteristic
985C22#9036211yescharacteristic
986C22#9036911yescharacteristic
987C22#9037511yescharacteristic
988C22#9039211yescharacteristic
989C22#9040311yescharacteristic
990C22#9040411yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—81no—
995C4—81no—
996C4—81no—
997C4—144no—
998C4—144no—
999C4—282no—
1000C4—282no—
1001C4—282no—
1002C4—282no—
1003C4—282no—
1004C4—561no—
1005C2—44no—
1006C2#1173145511yescharacteristic
1007C2#1173182711yescharacteristic
1008C2#1173183911yescharacteristic
1009C2#1173211111yescharacteristic
1010C2#1173291211yescharacteristic
1011C2#1173328611yescharacteristic
1012C2#1173375211yescharacteristic
1013C2#1173417111yescharacteristic
1014C2#1173429411yescharacteristic
1015C2#1173445111yescharacteristic
1016C2#1173458111yescharacteristic
1017C2#1173479611yescharacteristic
1018C2#1173481411yescharacteristic
1019C2#1173501511yescharacteristic
1020C2#1173553311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×#1439C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenter#1439D7
hypocenterC7#14442
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
5. C2×#89419C2semidirect
7. #11729320C2semidirect
8. #11729317C2semidirect
11. #11727174C2semidirect
12. #11727168C2semidirect
13. #11727167C2semidirect
14. #11727161C2semidirect
15. Dic7⋊#95C2semidirect
54. #89717C4semidirect
120. C2×Dic7⋊C4C2×C4semidirect
126. C2×C4×Dic7C2×C4semidirect
143. C7⋊#95C2×C4semidirect
144. C7⋊#95C2×C4semidirect
287. C22⋊Dic7C4⋊C4semidirect
940. C7#14442semidirect

Maximal subgroups

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

subgroupindex
C2×#897172
C2×#897222
C2×#897182
C2×#894192
C7×#14392
#117293202
#117293172
#117293012
#117292982
#117271742
#117271682
#117271672
#117271612
Dic7⋊#952
#144427