Finite Group Databasebeta

← #13277005

Subgroups — #13277005

Order 1792.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic7C211yesmaximal, characteristic
2C22×C7⋊#95C211yesmaximal, characteristic
3C2×#89722C211yesmaximal, characteristic
4C2×#89718C211yesmaximal, characteristic
5C2×#89718C211yesmaximal, characteristic
6C2×#89714C211yesmaximal, characteristic
7C2×#89419C211yesmaximal, characteristic, complemented
8C7×C22⋊#95C211yesmaximal, characteristic
9#11727174C211yesmaximal, characteristic, complemented
10#11727168C211yesmaximal, characteristic, complemented
11#11727164C211yesmaximal, characteristic, complemented
12#11727163C211yesmaximal, characteristic, complemented
13#11727161C211yesmaximal, characteristic, complemented
14#11727160C211yesmaximal, characteristic, complemented
15Dic7⋊#95C211yesmaximal, characteristic, complemented
16C24×C4×C7C2211yescharacteristic
17C24×Dic7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C4⋊Dic7C2211yescharacteristic
24C22×C4⋊Dic7C2211yescharacteristic
25C22×Dic7⋊C4C2211yescharacteristic
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
37C4×C22⋊Dic7—24no—
38C2×C7⋊#95—24no—
39C2×C7⋊#95C2211yescharacteristic
40C2×C7⋊#95C2211yescharacteristic
41C2×C7⋊#95C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53#89722—24no—
54#89718—24no—
55#89718C418yescomplemented
56#89714—24no—
57#89419—24no—
58#14004—71nomaximal, Sylow
59C25×C7C2311yescharacteristic
60C23×C4×C7—22no—
61C23×C4×C7—22no—
62C23×C4×C7—22no—
63C23×C4×C7—22no—
64C23×C4×C7—41no—
65C23×C4×C7—41no—
66C23×C4×C7Q814yes—
67C23×C4×C7C2311yescharacteristic
68C23×C4×C7C2311yescharacteristic
69C23×C4×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×Dic7—22no—
74C23×Dic7—22no—
75C23×Dic7—22no—
76C23×Dic7—22no—
77C23×Dic7—22no—
78C23×Dic7—22no—
79C23×Dic7—22no—
80C23×Dic7—22no—
81C23×Dic7—22no—
82C23×Dic7—41no—
83C23×Dic7—41no—
84C23×Dic7—41no—
85C23×Dic7—41no—
86C23×Dic7C2×C414yes—
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2311yescharacteristic
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C2×C7×C22⋊C4—22no—
96C2×C7×C22⋊C4—22no—
97C2×C7×C22⋊C4—22no—
98C2×C7×C22⋊C4—22no—
99C2×C7×C22⋊C4—22no—
100C2×C7×C22⋊C4C2×C414yes—
101C2×C22⋊Dic7—22no—
102C2×C22⋊Dic7—22no—
103C2×C22⋊Dic7C2×C414yes—
104C2×C22⋊Dic7D414yes—
105C2×C22⋊Dic7D414yes—
106C2×C22⋊Dic7Q814yes—
107C2×C4⋊Dic7—22no—
108C2×C4⋊Dic7—22no—
109C2×C4⋊Dic7—22no—
110C2×C4⋊Dic7—22no—
111C2×C4⋊Dic7—41no—
112C2×C4⋊Dic7—41no—
113C2×Dic7⋊C4—22no—
114C2×Dic7⋊C4—22no—
115C2×Dic7⋊C4—22no—
116C2×Dic7⋊C4—22no—
117C2×Dic7⋊C4—22no—
118C2×Dic7⋊C4—22no—
119C2×Dic7⋊C4—22no—
120C2×Dic7⋊C4—22no—
121C2×Dic7⋊C4—22no—
122C2×Dic7⋊C4—22no—
123C2×Dic7⋊C4—41no—
124C2×Dic7⋊C4—41no—
125C2×Dic7⋊C4—41no—
126C2×Dic7⋊C4—41no—
127C2×Dic7⋊C4—41no—
128C2×Dic7⋊C4—41no—
129C2×Dic7⋊C4C2×C414yescomplemented
130C2×Dic7⋊C4C2×C414yescomplemented
131C2×C4×Dic7—22no—
132C2×C4×Dic7—22no—
133C2×C4×Dic7—22no—
134C2×C4×Dic7—22no—
135C2×C4×Dic7—41no—
136C2×C4×Dic7—41no—
137C7×#95—22no—
138C7×#95—22no—
139C7×#95—41no—
140C7×#95—41no—
141C7⋊#95—22no—
142C7⋊#95—22no—
143C7⋊#95—22no—
144C7⋊#95—22no—
145C7⋊#95—22no—
146C7⋊#95—22no—
147C7⋊#95—22no—
148C7⋊#95—22no—
149C7⋊#95—22no—
150C7⋊#95—22no—
151C7⋊#95—22no—
152C7⋊#95C2×C414yescomplemented
153C7⋊#95C2×C414yescomplemented
154C7⋊#95D414yes—
155C2×#389—71no—
156C2×#385—71no—
157C2×#385—71no—
158C2×#385—71no—
159C2×#380—71no—
160C2×C4×C22⋊C4—71no—
161C22×#95—71no—
162#1444—71no—
163#1442—71no—
164#1441—71no—
165#1441—71no—
166#1436—71no—
167#1436—71no—
168C4⋊#95—71no—
169C22⋊#95D711yescharacteristic
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×C7C2×D412yes—
180C24×C7C2×D412yes—
181C24×C7C2×Q812yes—
182C24×C7C2×Q812yes—
183C24×C7#4112yes—
184C24×C7#4112yes—
185C24×C7C2411yescharacteristic
186C22×C4×C7—21no—
187C22×C4×C7—21no—
188C22×C4×C7—21no—
189C22×C4×C7—21no—
190C22×C4×C7—28no—
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—28no—
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—44no—
225C22×C4×C7—44no—
226C22×C4×C7—44no—
227C22×C4×C7—44no—
228C22×C4×C7—44no—
229C22×C4×C7C22×C412yes—
230C22×C4×C7C22×C412yes—
231C22×C4×C7C2×D412yes—
232C22×C4×C7C2×Q812yes—
233C22×C4×C7C2×Q812yes—
234C22×C4×C7#4112yes—
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—28no—
248C22×Dic7—28no—
249C22×Dic7—21no—
250C22×Dic7—21no—
251C22×Dic7—21no—
252C22×Dic7—21no—
253C22×Dic7—21no—
254C22×Dic7—21no—
255C22×Dic7—21no—
256C22×Dic7—21no—
257C22×Dic7—21no—
258C22×Dic7—21no—
259C22×Dic7—21no—
260C22×Dic7—21no—
261C22×Dic7—21no—
262C22×Dic7—21no—
263C22×Dic7—21no—
264C22×Dic7—21no—
265C22×Dic7—21no—
266C22×Dic7—21no—
267C22×Dic7—21no—
268C22×Dic7—21no—
269C22×Dic7—21no—
270C22×Dic7—21no—
271C22×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—28no—
280C22×Dic7—44no—
281C22×Dic7—44no—
282C22×Dic7—44no—
283C22×Dic7—44no—
284C22×Dic7—44no—
285C22×Dic7—44no—
286C22×Dic7—44no—
287C22×Dic7—44no—
288C22×Dic7—44no—
289C22×Dic7—44no—
290C22×Dic7—44no—
291C22×Dic7C22×C412yes—
292C22×Dic7C22×C412yes—
293C22×Dic7C22×C412yes—
294C22×Dic7C22×C412yes—
295C22×Dic7C2×D412yes—
296C22×Dic7C2×D412yes—
297C22×Dic7C2×D412yes—
298C22×Dic7C2×D412yes—
299C22×Dic7C2×D412yes—
300C22×Dic7C2×D412yes—
301C22×Dic7C2×Q812yes—
302C22×Dic7C2×Q812yes—
303C22×Dic7#4112yes—
304C22×Dic7#4112yes—
305C7×C22⋊C4—28no—
306C7×C22⋊C4—44no—
307C22⋊Dic7—28no—
308C22⋊Dic7C4⋊C4116yescomplemented
309C4⋊Dic7—44no—
310C4⋊Dic7—44no—
311Dic7⋊C4—28no—
312Dic7⋊C4—44no—
313Dic7⋊C4—44no—
314Dic7⋊C4—44no—
315Dic7⋊C4—44no—
316Dic7⋊C4—44no—
317C4×Dic7—44no—
318C4×Dic7—44no—
319C24×C4—71no—
320C24×C4—71no—
321C24×C4C2×D711yescharacteristic
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4—71no—
329C22×C4⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4C2×D711yescharacteristic
333C22×C22⋊C4C2×D711yescharacteristic
334C22×C42—71no—
335C22×C42—71no—
336#389—144no—
337#385—78no—
338#385—144no—
339#385—144no—
340#380—144no—
341C4×C22⋊C4—144no—
342C2×#95—71no—
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—144no—
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—22no—
380C23×C7—22no—
381C23×C7—22no—
382C23×C7—22no—
383C23×C7—22no—
384C23×C7—22no—
385C23×C7—22no—
386C23×C7—22no—
387C23×C7—22no—
388C23×C7—22no—
389C23×C7C2×C4⋊C414yes—
390C23×C7C4×D414yes—
391C23×C7C4×Q814yes—
392C23×C7#12114yes—
393C23×C7C22⋊Q814yes—
394C23×C7#12514yes—
395C23×C7C4⋊Q814yes—
396C23×C7C23×C411yescharacteristic
397C23×C7C22×D411yescharacteristic
398C23×C7C22×D411yescharacteristic
399C23×C7C22×D411yescharacteristic
400C23×C7C22×Q811yescharacteristic
401C23×C7C22×Q811yescharacteristic
402C23×C7C2×#4111yescharacteristic
403C23×C7C2×#4111yescharacteristic
404C23×C7C2×#4111yescharacteristic
405C23×C7C2×#4111yescharacteristic
406C23×C7C2×#4111yescharacteristic
407C23×C7H(5,𝔽2)11yescharacteristic
408C23×C7H(5,𝔽2)11yescharacteristic
409C23×C7H(5,𝔽2)11yescharacteristic
410C23×C72−1+411yescharacteristic
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—416no—
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×C7—41no—
436C2×C4×C7—41no—
437C2×C4×C7—41no—
438C2×C4×C7—41no—
439C2×C4×C7—41no—
440C2×C4×C7—41no—
441C2×C4×C7—41no—
442C2×C4×C7—41no—
443C2×C4×C7—41no—
444C2×C4×C7—41no—
445C2×C4×C7—41no—
446C2×C4×C7—41no—
447C2×C4×C7—41no—
448C2×C4×C7—41no—
449C2×C4×C7—41no—
450C2×C4×C7—41no—
451C2×C4×C7—41no—
452C2×C4×C7—41no—
453C2×C4×C7C22⋊Q814yes—
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—22no—
476C2×Dic7—22no—
477C2×Dic7—22no—
478C2×Dic7—22no—
479C2×Dic7—22no—
480C2×Dic7—22no—
481C2×Dic7—22no—
482C2×Dic7—22no—
483C2×Dic7—22no—
484C2×Dic7—22no—
485C2×Dic7—22no—
486C2×Dic7—22no—
487C2×Dic7—416no—
488C2×Dic7—416no—
489C2×Dic7—41no—
490C2×Dic7—41no—
491C2×Dic7—41no—
492C2×Dic7—41no—
493C2×Dic7—41no—
494C2×Dic7—41no—
495C2×Dic7—41no—
496C2×Dic7—41no—
497C2×Dic7—41no—
498C2×Dic7—41no—
499C2×Dic7—41no—
500C2×Dic7—41no—
501C2×Dic7—41no—
502C2×Dic7—41no—
503C2×Dic7—41no—
504C2×Dic7—41no—
505C2×Dic7—41no—
506C2×Dic7—41no—
507C2×Dic7—41no—
508C2×Dic7—41no—
509C2×Dic7C2×C4⋊C414yes—
510C2×Dic7C2×C4⋊C414yes—
511C2×Dic7C4×D414yes—
512C25C22×D711yescharacteristic
513C23×C4—22no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—22no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—71no—
520C23×C4—71no—
521C23×C4—71no—
522C23×C4—71no—
523C23×C4—71no—
524C23×C4—71no—
525C23×C4—71no—
526C23×C4—71no—
527C23×C4—74no—
528C23×C4—142no—
529C23×C4—142no—
530C23×C4—142no—
531C23×C4—142no—
532C23×C4—142no—
533C23×C4—142no—
534C23×C4—142no—
535C23×C4—142no—
536C23×C4—142no—
537C23×C4—281no—
538C23×C4—281no—
539C23×C4—281no—
540C23×C4—281no—
541C23×C4Dic1414yes—
542C23×C4C22×D711yescharacteristic
543C23×C4C22×D711yescharacteristic
544C23×C4C22×D711yescharacteristic
545C23×C4C22×D711yescharacteristic
546C23×C4C22×D711yescharacteristic
547C23×C4C22×D711yescharacteristic
548C2×C4⋊C4—74no—
549C2×C4⋊C4—74no—
550C2×C4⋊C4—142no—
551C2×C4⋊C4—142no—
552C2×C4⋊C4—142no—
553C2×C4⋊C4—142no—
554C2×C4⋊C4—142no—
555C2×C4⋊C4—142no—
556C2×C4⋊C4—142no—
557C2×C4⋊C4—142no—
558C2×C4⋊C4—142no—
559C2×C4⋊C4—142no—
560C2×C4⋊C4—142no—
561C2×C4⋊C4—142no—
562C2×C4⋊C4—142no—
563C2×C4⋊C4—142no—
564C2×C4⋊C4—281no—
565C2×C4⋊C4—281no—
566C2×C4⋊C4—281no—
567C2×C4⋊C4—281no—
568C2×C4⋊C4—281no—
569C2×C4⋊C4—281no—
570C2×C4⋊C4—281no—
571C2×C4⋊C4—281no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—74no—
578C2×C22⋊C4—74no—
579C2×C22⋊C4—74no—
580C2×C22⋊C4—74no—
581C2×C22⋊C4—142no—
582C2×C22⋊C4—142no—
583C2×C22⋊C4C4×D714yes—
584C2×C42—142no—
585C2×C42—142no—
586C2×C42—142no—
587C2×C42—142no—
588C2×C42—281no—
589C2×C42—281no—
590#95—22no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95—74no—
595#95—74no—
596#95—74no—
597#95—142no—
598#95—142no—
599#95—142no—
600#95—142no—
601#95—142no—
602#95—142no—
603#95—142no—
604#95—142no—
605#95—142no—
606#95—142no—
607#95—142no—
608C22×C7—24no—
609C22×C7—24no—
610C22×C7—24no—
611C22×C7—24no—
612C22×C7—24no—
613C22×C7—24no—
614C22×C7—24no—
615C22×C7—24no—
616C22×C7—24no—
617C22×C7—24no—
618C22×C7—24no—
619C22×C7—24no—
620C22×C7—24no—
621C22×C7—24no—
622C22×C7#38918yescomplemented
623C22×C7C22×C4⋊C411yescharacteristic
624C22×C7C2×C4×D411yescharacteristic
625C22×C7C2×C4×D411yescharacteristic
626C22×C7C2×C4×Q811yescharacteristic
627C22×C7C4×#4111yescharacteristic
628C22×C7#51811yescharacteristic
629C22×C7#52011yescharacteristic
630C22×C7C2×#12111yescharacteristic
631C22×C7C2×C22⋊Q811yescharacteristic
632C22×C7C2×C22⋊Q811yescharacteristic
633C22×C7#52511yescharacteristic
634C22×C7C2×#12511yescharacteristic
635C22×C7#52911yescharacteristic
636C22×C7C2×C4⋊Q811yescharacteristic
637C22×C7#53311yescharacteristic
638C22×C7#53811yescharacteristic
639C22×C7#53911yescharacteristic
640C22×C7#54311yescharacteristic
641C22×C7#54411yescharacteristic
642C22×C7D4211yescharacteristic
643C22×C7D4211yescharacteristic
644C22×C7#54611yescharacteristic
645C22×C7#54611yescharacteristic
646C22×C7#54611yescharacteristic
647C22×C7#54611yescharacteristic
648C22×C7#54611yescharacteristic
649C22×C7#54711yescharacteristic
650C22×C7#54711yescharacteristic
651C22×C7D4×Q811yescharacteristic
652C22×C7#55111yescharacteristic
653C22×C7#55111yescharacteristic
654C22×C7#55211yescharacteristic
655C22×C7#55411yescharacteristic
656C22×C7#55411yescharacteristic
657C22×C7#55411yescharacteristic
658C4×C7—24no—
659C4×C7—42no—
660C4×C7—42no—
661C4×C7—42no—
662C4×C7—81no—
663C4×C7—81no—
664Dic7—24no—
665Dic7—24no—
666Dic7—24no—
667Dic7—42no—
668Dic7—42no—
669Dic7—42no—
670Dic7—42no—
671Dic7—42no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Dic1412yes—
681C24C2×C4×D712yes—
682C24#115712yes—
683C24D4×D712yes—
684C24D4×D712yes—
685C24#115912yes—
686C24Q8×D712yes—
687C24C23×D711yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—28no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—28no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—72no—
732C22×C4—72no—
733C22×C4—72no—
734C22×C4—72no—
735C22×C4—72no—
736C22×C4—72no—
737C22×C4—72no—
738C22×C4—72no—
739C22×C4—72no—
740C22×C4—72no—
741C22×C4—72no—
742C22×C4—72no—
743C22×C4—72no—
744C22×C4—72no—
745C22×C4—148no—
746C22×C4—141no—
747C22×C4—141no—
748C22×C4—141no—
749C22×C4—141no—
750C22×C4—141no—
751C22×C4—141no—
752C22×C4—141no—
753C22×C4—141no—
754C22×C4—141no—
755C22×C4—141no—
756C22×C4—141no—
757C22×C4—141no—
758C22×C4—148no—
759C22×C4—148no—
760C22×C4—141no—
761C22×C4—141no—
762C22×C4—141no—
763C22×C4—141no—
764C22×C4—141no—
765C22×C4—141no—
766C22×C4—141no—
767C22×C4—141no—
768C22×C4—141no—
769C22×C4—141no—
770C22×C4—141no—
771C22×C4—141no—
772C22×C4—141no—
773C22×C4—141no—
774C22×C4—141no—
775C22×C4—141no—
776C22×C4—141no—
777C22×C4—141no—
778C22×C4—141no—
779C22×C4—141no—
780C22×C4—141no—
781C22×C4—141no—
782C22×C4—141no—
783C22×C4—141no—
784C22×C4—141no—
785C22×C4—141no—
786C22×C4—141no—
787C22×C4—141no—
788C22×C4—141no—
789C22×C4—141no—
790C22×C4—284no—
791C22×C4—284no—
792C22×C4—284no—
793C22×C4—284no—
794C22×C4—284no—
795C22×C4—284no—
796C22×C4—284no—
797C22×C4—284no—
798C22×C4—284no—
799C22×C4—284no—
800C22×C4—284no—
801C22×C4C2×Dic1412yes—
802C22×C4C2×Dic1412yes—
803C22×C4C2×C4×D712yes—
804C22×C4C2×C4×D712yes—
805C22×C4D4×D712yes—
806C22×C4#115912yes—
807C4⋊C4—148no—
808C4⋊C4—284no—
809C4⋊C4—284no—
810C4⋊C4—284no—
811C4⋊C4—284no—
812C4⋊C4—284no—
813C4⋊C4—284no—
814C4⋊C4—284no—
815C22⋊C4—28no—
816C22⋊C4—44no—
817C22⋊C4—716no—
818C22⋊C4—148no—
819C42—284no—
820C42—284no—
821C2×C7—28no—
822C2×C7C2×#38911yescharacteristic
823C2×C7C4×C22⋊Q811yescharacteristic
824C2×C7#232911yescharacteristic
825C2×C7D4×C4⋊C411yescharacteristic
826C2×C7#234911yescharacteristic
827C2×C7#235811yescharacteristic
828C2×C7#235911yescharacteristic
829C2×C7#242411yescharacteristic
830C2×C7#242511yescharacteristic
831C2×C7#243711yescharacteristic
832C2×C7#243811yescharacteristic
833C2×C7#244011yescharacteristic
834C2×C7#247311yescharacteristic
835C2×C7#250511yescharacteristic
836C2×C7#254911yescharacteristic
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23C4×Dic1414yes—
866C23#644114yes—
867C23(C22⋊D7)⋊C414yes—
868C23#644714yes—
869C23#645114yes—
870C23#645214yes—
871C23D7×C4⋊C414yes—
872C23C22×Dic1411yescharacteristic
873C23C22×C4×D711yescharacteristic
874C23C2×#115711yescharacteristic
875C23C2×D4×D711yescharacteristic
876C23C2×D4×D711yescharacteristic
877C23C2×D4×D711yescharacteristic
878C23C2×#115911yescharacteristic
879C23C2×#115911yescharacteristic
880C23#654811yescharacteristic
881C23#654811yescharacteristic
882C23C2×Q8×D711yescharacteristic
883C23D7×#4111yescharacteristic
884C23D7×#4111yescharacteristic
885C23#655311yescharacteristic
886C23#655411yescharacteristic
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—416no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—74no—
930C2×C4—74no—
931C2×C4—74no—
932C2×C4—142no—
933C2×C4—142no—
934C2×C4—142no—
935C2×C4—142no—
936C2×C4—142no—
937C2×C4—142no—
938C2×C4—142no—
939C2×C4—142no—
940C2×C4—142no—
941C2×C4—142no—
942C2×C4—142no—
943C2×C4—142no—
944C2×C4—142no—
945C2×C4—142no—
946C2×C4—142no—
947C2×C4—142no—
948C2×C4—142no—
949C2×C4—142no—
950C2×C4—142no—
951C2×C4—142no—
952C2×C4—142no—
953C2×C4—142no—
954C2×C4—142no—
955C2×C4—142no—
956C2×C4—142no—
957C2×C4—142no—
958C2×C4—142no—
959C2×C4—142no—
960C2×C4—142no—
961C2×C4—142no—
962C2×C4—142no—
963C2×C4—142no—
964C2×C4—142no—
965C2×C4—2816no—
966C2×C4—2816no—
967C2×C4—281no—
968C2×C4—281no—
969C2×C4—281no—
970C2×C4—281no—
971C2×C4—281no—
972C2×C4—281no—
973C2×C4—281no—
974C2×C4—281no—
975C2×C4—281no—
976C2×C4—281no—
977C2×C4—281no—
978C2×C4—281no—
979C2×C4—281no—
980C2×C4—281no—
981C2×C4—281no—
982C2×C4—281no—
983C2×C4—281no—
984C2×C4—281no—
985C2×C4—281no—
986C2×C4—281no—
987C2×C4#644114yes—
988C7#1400411yescharacteristic, complemented, Sylow
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#8941918yescomplemented
1004C22C2×C4×Dic1411yescharacteristic
1005C22C2×#644111yescharacteristic
1006C22C2×#644111yescharacteristic
1007C22#9017411yescharacteristic
1008C22C2×(C22⋊D7)⋊C411yescharacteristic
1009C22C2×#644711yescharacteristic
1010C22C2×#645111yescharacteristic
1011C22C2×#645211yescharacteristic
1012C22C2×D7×C4⋊C411yescharacteristic
1013C22#9020811yescharacteristic
1014C22#9021011yescharacteristic
1015C22C4×#115911yescharacteristic
1016C22#9022911yescharacteristic
1017C22C4×D4×D711yescharacteristic
1018C22#9023611yescharacteristic
1019C22#9023711yescharacteristic
1020C22#9023811yescharacteristic
1021C22#9025111yescharacteristic
1022C22#9025511yescharacteristic
1023C22#9027811yescharacteristic
1024C22#9028111yescharacteristic
1025C22#9028211yescharacteristic
1026C22#9028211yescharacteristic
1027C22#9030011yescharacteristic
1028C22#9030111yescharacteristic
1029C22#9030111yescharacteristic
1030C22#9030211yescharacteristic
1031C22#9032311yescharacteristic
1032C22#9032611yescharacteristic
1033C22#9032711yescharacteristic
1034C22#9032711yescharacteristic
1035C22#9034111yescharacteristic
1036C22#9034511yescharacteristic
1037C22#9034611yescharacteristic
1038C22#9034911yescharacteristic
1039C4—24no—
1040C4—42no—
1041C4—42no—
1042C4—42no—
1043C4—81no—
1044C4—81no—
1045C4—144no—
1046C4—144no—
1047C4—144no—
1048C4—282no—
1049C4—282no—
1050C4—282no—
1051C4—282no—
1052C4—282no—
1053C2—28no—
1054C2C2×#8941911yescharacteristic
1055C2C4×#644111yescharacteristic
1056C2#1173089211yescharacteristic
1057C2#1173127311yescharacteristic
1058C2#1173134411yescharacteristic
1059C2#1173138311yescharacteristic
1060C2#1173151211yescharacteristic
1061C2#1173183811yescharacteristic
1062C2#1173183911yescharacteristic
1063C2#1173188511yescharacteristic
1064C2#1173190711yescharacteristic
1065C2#1173212011yescharacteristic
1066C2#1173214111yescharacteristic
1067C2#1173232411yescharacteristic
1068C2#1173233811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D7
commutatorC23×C7C23×C4
FittingC7×C22⋊#95C2
socle, cosocleC24×C7C24
prime radicalC25×C7C23
hypercenterC22⋊#95D7
hypocenterC7#14004
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
7. C2×#89419C2semidirect
9. #11727174C2semidirect
10. #11727168C2semidirect
11. #11727164C2semidirect
12. #11727163C2semidirect
13. #11727161C2semidirect
14. #11727160C2semidirect
15. Dic7⋊#95C2semidirect
55. #89718C4semidirect
129. C2×Dic7⋊C4C2×C4semidirect
130. C2×Dic7⋊C4C2×C4semidirect
152. C7⋊#95C2×C4semidirect
153. C7⋊#95C2×C4semidirect
308. C22⋊Dic7C4⋊C4semidirect
622. C22×C7#389semidirect
988. C7#14004semidirect
1003. C22#89419semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic72
C22×C7⋊#952
C2×#897222
C2×#897182
C2×#897142
C2×#894192
C7×C22⋊#952
#117271742
#117271682
#117271642
#117271632
#117271612
#117271602
Dic7⋊#952
#140047