Finite Group Databasebeta

← C2×#11740215 #13522227

Subgroups — C2×#11740215 #13522227

Order 1792.

3070 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C7×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#6455C211yesmaximal, characteristic, complemented
3C2×#90003C211yesmaximal, characteristic, complemented
4C2×#90002C211yesmaximal, characteristic, complemented
5C2×#89985C211yesmaximal, characteristic
6C2×C4×C22⋊Dic7C211yesmaximal, characteristic, complemented
7#11740215C2116yesmaximal, direct product factor
8C2×#89761C211yesmaximal, characteristic, complemented
9C2×#89758C211yesmaximal, characteristic, complemented
10C2×#89762C211yesmaximal, characteristic, complemented
11C2×#89750C211yesmaximal, characteristic, complemented
12C2×#89753C211yesmaximal, characteristic, complemented
13C2×#89728C211yesmaximal, characteristic
14C2×#89725C211yesmaximal, characteristic, complemented
15C2×#89733C211yesmaximal, characteristic
16C2×#89716C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C24×C4×C7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C23×C4×D7C2211yescharacteristic
21C2×C7×C22⋊Q8—28no—
22C2×C7×C22⋊Q8C2218yescomplemented
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C4⋊C4C2211yescharacteristic
25C22×C7×C4⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×(C2×D7)⋊C4C2211yescharacteristic
32C22×(C2×D7)⋊C4C2211yescharacteristic
33C22×(C2×D7)⋊C4C2211yescharacteristic
34C22×(C2×D7)⋊C4C2211yescharacteristic
35C22×(C2×D7)⋊C4C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4⋊Dic7C2211yescharacteristic
38C22×Dic7⋊C4C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6455—28no—
43C2×#6455C2218yescomplemented
44#90003C2218yescomplemented
45#90002C2218yescomplemented
46#89985C2218yes—
47C4×C22⋊Dic7C2218yescomplemented
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55C2×C7⋊#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60#89762C2218yescomplemented
61#89761C2218yescomplemented
62#89758C2218yescomplemented
63#89753C2218yescomplemented
64#89750C2218yescomplemented
65#89733C2218yes—
66#89728C2218yes—
67#89725C2218yescomplemented
68#89716C2218yescomplemented
69C2×#2477—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C24×D7C2311yescharacteristic
72C22×C7×Q8—24no—
73C22×C7×Q8—24no—
74C22×C7×Q8—42no—
75C22×C7×Q8C2314yes—
76C23×C4×C7—24no—
77C23×C4×C7—24no—
78C23×C4×C7—42no—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2314yes—
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C23×C4×C7C2311yescharacteristic
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—42no—
89C22×C22⋊D7C2314yes—
90C23×Dic7C2311yescharacteristic
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C22×C4×D7—24no—
98C22×C4×D7—24no—
99C22×C4×D7—24no—
100C22×C4×D7C2314yes—
101C7×C22⋊Q8—232no—
102C2×C7×C4⋊C4—24no—
103C2×C7×C4⋊C4—24no—
104C2×C7×C4⋊C4D418yescomplemented
105C2×C7×C4⋊C4C2314yes—
106C2×C7×C4⋊C4C2314yes—
107C2×C7×C4⋊C4C2314yes—
108C2×C7×C22⋊C4—24no—
109C2×C7×C22⋊C4—24no—
110C2×C7×C22⋊C4C2314yes—
111C2×C7×C22⋊C4C2314yes—
112C2×C22⋊Dic7—24no—
113C2×C22⋊Dic7—24no—
114C2×C22⋊Dic7—24no—
115C2×C22⋊Dic7C2314yes—
116C2×C22⋊Dic7C2314yes—
117C2×C22⋊Dic7C2314yes—
118C2×(C2×D7)⋊C4—24no—
119C2×(C2×D7)⋊C4—24no—
120C2×(C2×D7)⋊C4—24no—
121C2×(C2×D7)⋊C4—24no—
122C2×(C2×D7)⋊C4—42no—
123C2×(C2×D7)⋊C4C2314yes—
124C2×(C2×D7)⋊C4C2314yes—
125C2×(C2×D7)⋊C4C2314yes—
126C2×(C2×D7)⋊C4C2314yes—
127C2×(C2×D7)⋊C4C2314yes—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7—42no—
130C2×C4⋊Dic7C2314yes—
131C2×C4⋊Dic7C2314yes—
132C2×Dic7⋊C4—24no—
133C2×Dic7⋊C4C2314yes—
134C2×C4×Dic7—24no—
135C2×C4×Dic7—24no—
136C2×C4×Dic7—42no—
137C2×C4×Dic7C2314yes—
138C2×C4×Dic7C2314yes—
139C2×C4×Dic7C2314yes—
140#6455—232no—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C7⋊#95C2314yes—
148C7⋊#95C2314yes—
149C7⋊#95C2314yes—
150C7⋊#95C2314yes—
151C7⋊#95C2314yes—
152C7⋊#95C2314yes—
153C22×C22⋊Q8D711yescharacteristic, complemented
154C22×#117—71no—
155#2477—716no—
156C2×#400—71no—
157C2×#397—71no—
158C2×#394—71no—
159C2×#393—71no—
160C2×#391—71no—
161C2×#388—71no—
162C2×#388—71no—
163C2×#387—71no—
164C2×#387—71no—
165C2×#386—71no—
166C2×#386—71no—
167C2×#385—71no—
168C2×C4×C22⋊C4—71no—
169C24×C7—22no—
170C24×C7—22no—
171C24×C7—22no—
172C24×C7—22no—
173C24×C7—22no—
174C24×C7—22no—
175C24×C7#4114yes—
176C24×C7C2412yes—
177C24×C7C2411yescharacteristic
178C23×D7—22no—
179C23×D7—22no—
180C23×D7—22no—
181C23×D7—22no—
182C23×D7—22no—
183C23×D7—22no—
184C23×D7#4114yes—
185C23×D7C2412yes—
186C2×C7×Q8—28no—
187C2×C7×Q8—28no—
188C2×C7×Q8—44no—
189C2×C7×Q8—416no—
190C22×C4×C7—22no—
191C22×C4×C7—22no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—22no—
199C22×C4×C7—22no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—22no—
203C22×C4×C7—22no—
204C22×C4×C7—28no—
205C22×C4×C7—28no—
206C22×C4×C7—44no—
207C22×C4×C7—416no—
208C22×C4×C7C2×D414yes—
209C22×C4×C7C2×D414yes—
210C22×C4×C7C2×D414yes—
211C22×C4×C7#4114yes—
212C22×C4×C7C2412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2412yes—
216C22×C4×C7C2412yes—
217C22×C4×C7C2412yes—
218C2×C22⋊D7—28no—
219C2×C22⋊D7—28no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—416no—
222C22×Dic7—22no—
223C22×Dic7—22no—
224C22×Dic7—22no—
225C22×Dic7—22no—
226C22×Dic7—22no—
227C22×Dic7—22no—
228C22×Dic7—22no—
229C22×Dic7—22no—
230C22×Dic7—22no—
231C22×Dic7—22no—
232C22×Dic7—22no—
233C22×Dic7—22no—
234C22×Dic7—22no—
235C22×Dic7—22no—
236C22×Dic7—22no—
237C22×Dic7—22no—
238C22×Dic7—22no—
239C22×Dic7—22no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7#4114yes—
243C22×Dic7C2412yes—
244C22×Dic7C2412yes—
245C22×Dic7C2412yes—
246C22×Dic7C2412yes—
247C22×Dic7C2412yes—
248C22×Dic7C2412yes—
249C22×Dic7C2412yes—
250C2×C4×D7—232no—
251C2×C4×D7—28no—
252C2×C4×D7—28no—
253C2×C4×D7—28no—
254C7×C4⋊C4—28no—
255C7×C4⋊C4—28no—
256C7×C4⋊C4C2×D4116yescomplemented
257C7×C22⋊C4—28no—
258C7×C22⋊C4—28no—
259C22⋊Dic7—28no—
260C22⋊Dic7—28no—
261C22⋊Dic7—28no—
262(C2×D7)⋊C4—28no—
263(C2×D7)⋊C4—28no—
264(C2×D7)⋊C4—28no—
265(C2×D7)⋊C4—28no—
266(C2×D7)⋊C4—44no—
267C4⋊Dic7—28no—
268C4⋊Dic7—44no—
269Dic7⋊C4—28no—
270C4×Dic7—28no—
271C4×Dic7—28no—
272C4×Dic7—44no—
273C23×Q8C2×D711yescharacteristic
274C23×D4—71no—
275C24×C4—71no—
276C24×C4C2×D711yescharacteristic
277C2×C22⋊Q8—28no—
278C2×C22⋊Q8C2×D718yescomplemented
279C2×#117—78no—
280C2×#117—148no—
281C22×C4⋊C4—71no—
282C22×C4⋊C4—71no—
283C22×C4⋊C4—71no—
284C22×C4⋊C4C2×D711yescharacteristic
285C22×C4⋊C4C2×D711yescharacteristic
286C22×C4⋊C4C2×D711yescharacteristic
287C22×C22⋊C4—71no—
288C22×C22⋊C4—71no—
289C22×C22⋊C4—71no—
290C22×C22⋊C4—71no—
291C22×C22⋊C4—71no—
292C22×C22⋊C4—71no—
293C22×C22⋊C4—71no—
294C22×C22⋊C4—71no—
295C22×C22⋊C4C2×D711yescharacteristic
296C22×C22⋊C4C2×D711yescharacteristic
297C22×C42—71no—
298C22×C42—71no—
299C22×C42—71no—
300#400—78no—
301#397—78no—
302#394—78no—
303#393—78no—
304#391—78no—
305#388—78no—
306#388—78no—
307#387—78no—
308#387—78no—
309#386—78no—
310#386—78no—
311#385—78no—
312C4×C22⋊C4—78no—
313C2×#95—71no—
314C2×#95—71no—
315C2×#95—71no—
316C2×#95—71no—
317C2×#95—71no—
318C2×#95—71no—
319C2×#95—71no—
320C2×#95—71no—
321C2×#95—71no—
322C2×#95—71no—
323C2×#95—71no—
324C2×#95—71no—
325C23×C7—28no—
326C23×C7—28no—
327C23×C7—28no—
328C23×C7—22no—
329C23×C7—22no—
330C23×C7—22no—
331C23×C7—22no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—44no—
335C23×C7—44no—
336C23×C7—44no—
337C23×C7—44no—
338C23×C7C22×D412yes—
339C23×C7C2×#4112yes—
340C23×C7C2×#4114yes—
341C23×C7C2×#4112yes—
342C23×C7C2×#4112yes—
343C23×C7C2×#4112yes—
344C23×C7H(5,𝔽2)12yes—
345C23×C72−1+412yes—
346C23×C7C2511yescharacteristic
347C22×D7—28no—
348C22×D7—28no—
349C22×D7—28no—
350C22×D7—22no—
351C22×D7—22no—
352C22×D7—22no—
353C22×D7—22no—
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—44no—
357C22×D7—44no—
358C22×D7—44no—
359C22×D7—44no—
360C22×D7C2×#4114yes—
361C7×Q8—416no—
362C2×C4×C7—28no—
363C2×C4×C7—28no—
364C2×C4×C7—28no—
365C2×C4×C7—28no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—416no—
381C2×C4×C7—44no—
382C2×C4×C7—44no—
383C2×C4×C7C22×D414yes—
384C2×C4×C7C22×D414yes—
385C2×C4×C7C22×D414yes—
386C2×C4×C7C2×#4114yes—
387C22⋊D7—416no—
388C2×Dic7—28no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—44no—
410C2×Dic7—44no—
411C2×Dic7—44no—
412C2×Dic7—44no—
413C2×Dic7—44no—
414C2×Dic7—44no—
415C2×Dic7C2×#4114yes—
416C4×D7—232no—
417C25—71no—
418C25C22×D711yescharacteristic
419C22×Q8—24no—
420C22×Q8—24no—
421C22×Q8—42no—
422C22×Q8C22×D714yes—
423C22×D4—74no—
424C22×D4—144no—
425C22×D4—144no—
426C22×D4—282no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—42no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—71no—
433C23×C4—71no—
434C23×C4—71no—
435C23×C4—71no—
436C23×C4—71no—
437C23×C4—74no—
438C23×C4—144no—
439C23×C4—144no—
440C23×C4—144no—
441C23×C4C22×D711yescharacteristic
442C23×C4C22×D711yescharacteristic
443C23×C4C22×D714yes—
444C23×C4C22×D711yescharacteristic
445C23×C4C22×D711yescharacteristic
446C23×C4C22×D711yescharacteristic
447C23×C4C22×D711yescharacteristic
448C22⋊Q8—232no—
449#117—1432no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—74no—
453C2×C4⋊C4—74no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—144no—
456C2×C4⋊C4—144no—
457C2×C4⋊C4—282no—
458C2×C4⋊C4C22⋊D718yescomplemented
459C2×C4⋊C4C22×D714yes—
460C2×C4⋊C4C22×D714yes—
461C2×C4⋊C4C22×D714yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—74no—
465C2×C22⋊C4—74no—
466C2×C22⋊C4—74no—
467C2×C22⋊C4—74no—
468C2×C22⋊C4—74no—
469C2×C22⋊C4—74no—
470C2×C22⋊C4—74no—
471C2×C22⋊C4—74no—
472C2×C22⋊C4—144no—
473C2×C22⋊C4—144no—
474C2×C22⋊C4—144no—
475C2×C22⋊C4—144no—
476C2×C22⋊C4—144no—
477C2×C22⋊C4—144no—
478C2×C22⋊C4—144no—
479C2×C22⋊C4—282no—
480C2×C22⋊C4C22×D714yes—
481C2×C22⋊C4C22×D714yes—
482C2×C42—74no—
483C2×C42—74no—
484C2×C42—74no—
485C2×C42—144no—
486C2×C42—144no—
487C2×C42—282no—
488#95—74no—
489#95—74no—
490#95—74no—
491#95—74no—
492#95—74no—
493#95—74no—
494#95—74no—
495#95—74no—
496#95—74no—
497#95—74no—
498#95—74no—
499#95—74no—
500C22×C7—24no—
501C22×C7—24no—
502C22×C7—24no—
503C22×C7—42no—
504C22×C7—42no—
505C22×C7—42no—
506C22×C7—42no—
507C22×C7—416no—
508C22×C7#52514yes—
509C22×C7#52914yes—
510C22×C7#54214yes—
511C22×C7#54614yes—
512C22×C7#54814yes—
513C22×C7#55114yes—
514C22×C7#55214yes—
515C22×C7C23×D411yescharacteristic
516C22×C7C22×#4111yescharacteristic
517C22×C7C22×#4111yescharacteristic
518C22×C7C22×#4111yescharacteristic
519C22×C7C22×#4111yescharacteristic
520C22×C7C2×H(5,𝔽2)11yescharacteristic
521C22×C7C2×2−1+411yescharacteristic
522C2×D7—24no—
523C2×D7—24no—
524C2×D7—24no—
525C2×D7—42no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—416no—
530C4×C7—24no—
531C4×C7—24no—
532C4×C7—24no—
533C4×C7—24no—
534C4×C7—42no—
535C4×C7—42no—
536Dic7—24no—
537Dic7—42no—
538Dic7—42no—
539Dic7—42no—
540Dic7—42no—
541Dic7—42no—
542Dic7—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—74no—
550C24—72no—
551C24—142no—
552C24—142no—
553C24—142no—
554C24—142no—
555C24—142no—
556C24—142no—
557C24#116114yes—
558C24C23×D712yes—
559C24C23×D711yescharacteristic
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—44no—
563C2×Q8—416no—
564C2×D4—148no—
565C2×D4—148no—
566C2×D4—284no—
567C2×D4—2816no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—416no—
586C22×C4—74no—
587C22×C4—72no—
588C22×C4—72no—
589C22×C4—72no—
590C22×C4—72no—
591C22×C4—72no—
592C22×C4—72no—
593C22×C4—72no—
594C22×C4—148no—
595C22×C4—148no—
596C22×C4—1432no—
597C22×C4—142no—
598C22×C4—142no—
599C22×C4—148no—
600C22×C4—142no—
601C22×C4—142no—
602C22×C4—142no—
603C22×C4—142no—
604C22×C4—142no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—142no—
611C22×C4—142no—
612C22×C4—142no—
613C22×C4—142no—
614C22×C4—142no—
615C22×C4—142no—
616C22×C4—142no—
617C22×C4—142no—
618C22×C4#115914yes—
619C22×C4C2×C22⋊D714yes—
620C22×C4C2×C22⋊D714yes—
621C22×C4C2×C22⋊D714yes—
622C22×C4C23×D712yes—
623C22×C4C23×D712yes—
624C22×C4C23×D712yes—
625C22×C4C23×D712yes—
626C22×C4C23×D712yes—
627C22×C4C23×D712yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—148no—
631C4⋊C4—148no—
632C4⋊C4—284no—
633C4⋊C4C2×C22⋊D7116yescomplemented
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—148no—
637C22⋊C4—148no—
638C22⋊C4—148no—
639C22⋊C4—148no—
640C22⋊C4—148no—
641C22⋊C4—148no—
642C22⋊C4—148no—
643C22⋊C4—284no—
644C42—148no—
645C42—148no—
646C42—284no—
647C2×C7—44no—
648C2×C7#247718yescomplemented
649C2×C7C2×#52511yescharacteristic
650C2×C7C2×#52911yescharacteristic
651C2×C7C2×#54211yescharacteristic
652C2×C7C2×#54611yescharacteristic
653C2×C7C2×#54811yescharacteristic
654C2×C7C2×#55111yescharacteristic
655C2×C7C2×#55211yescharacteristic
656D7—44no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—74no—
671C23—148no—
672C23—148no—
673C23—148no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23—142no—
680C23—284no—
681C23—284no—
682C23—284no—
683C23—284no—
684C23C2×#115912yes—
685C23#654812yes—
686C23C2×#116114yes—
687C23C2×#116112yes—
688C23#655112yes—
689C23D7×#4112yes—
690C23D7×#4112yes—
691C23C22×C22⋊D712yes—
692C23C24×D711yescharacteristic
693Q8—416no—
694D4—2816no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—74no—
717C2×C4—1432no—
718C2×C4—148no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—142no—
725C2×C4—142no—
726C2×C4—142no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—142no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—284no—
740C2×C4—284no—
741C2×C4—284no—
742C2×C4—284no—
743C2×C4—284no—
744C2×C4—284no—
745C2×C4C2×#115914yes—
746C2×C4C22×C22⋊D714yes—
747C2×C4C22×C22⋊D714yes—
748C2×C4C22×C22⋊D714yes—
749C7C2×#247711yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—416no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—144no—
759C22—144no—
760C22—144no—
761C22—282no—
762C22—282no—
763C22—2816no—
764C22—282no—
765C22—282no—
766C22#9031514yes—
767C22#9032814yes—
768C22#9033014yes—
769C22#9033114yes—
770C22#9049714yes—
771C22#9050814yes—
772C22#9051914yes—
773C22C22×#115911yescharacteristic
774C22C2×#654811yescharacteristic
775C22C22×#116111yescharacteristic
776C22C2×#655111yescharacteristic
777C22C2×D7×#4111yescharacteristic
778C22C2×D7×#4111yescharacteristic
779C22C23×C22⋊D711yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—144no—
787C4—282no—
788C4—282no—
789C4—282no—
790C4—282no—
791C4—282no—
792C4—282no—
793C2—44no—
794C2—284no—
795C2#1174021518yesdirect product factor
796C2C2×#9031511yescharacteristic
797C2C2×#9033111yescharacteristic
798C2C2×#9032811yescharacteristic
799C2C2×#9033011yescharacteristic
800C2C2×#9049711yescharacteristic
801C2C2×#9050811yescharacteristic
802C2C2×#9051911yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC22×C7×C22⋊Q8C2
socleC24×C7C24
prime radicalC23×C22⋊D7C22
hypercenterC22×C22⋊Q8D7
hypocenterC7C2×#2477
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C7×C22⋊Q8C2semidirect
2. C22×#6455C2semidirect
3. C2×#90003C2semidirect
4. C2×#90002C2semidirect
6. C2×C4×C22⋊Dic7C2semidirect
7. #11740215C2direct (N × H)
8. C2×#89761C2semidirect
9. C2×#89758C2semidirect
10. C2×#89762C2semidirect
11. C2×#89750C2semidirect
12. C2×#89753C2semidirect
14. C2×#89725C2semidirect
16. C2×#89716C2semidirect
22. C2×C7×C22⋊Q8C22semidirect
43. C2×#6455C22semidirect
44. #90003C22semidirect
45. #90002C22semidirect
47. C4×C22⋊Dic7C22semidirect
60. #89762C22semidirect
61. #89761C22semidirect
62. #89758C22semidirect
63. #89753C22semidirect
64. #89750C22semidirect
67. #89725C22semidirect
68. #89716C22semidirect
104. C2×C7×C4⋊C4D4semidirect
153. C22×C22⋊Q8D7semidirect
256. C7×C4⋊C4C2×D4semidirect
278. C2×C22⋊Q8C2×D7semidirect
458. C2×C4⋊C4C22⋊D7semidirect
633. C4⋊C4C2×C22⋊D7semidirect
648. C2×C7#2477semidirect
749. C7C2×#2477semidirect
795. C2#11740215direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×C22⋊Q82
C22×#64552
C2×#900032
C2×#900022
C2×#899852
C2×C4×C22⋊Dic72
#117402152
C2×#897612
C2×#897582
C2×#897622
C2×#897502
C2×#897532
C2×#897282
C2×#897252
C2×#897332
C2×#897162
C2×#24777