Finite Group Databasebeta

← C2×#11734234 #13522003

Subgroups — C2×#11734234 #13522003

Order 1792.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic7C211yesmaximal, characteristic, complemented
2C22×#6442C211yesmaximal, characteristic
3C2×C7×#393C211yesmaximal, characteristic
4C2×#90001C211yesmaximal, characteristic, complemented
5C2×#89720C211yesmaximal, characteristic
6C2×#89717C211yesmaximal, characteristic
7C2×#89716C211yesmaximal, characteristic
8C2×#89723C211yesmaximal, characteristic
9C2×#89723C211yesmaximal, characteristic
10#11734234C2116yesmaximal, direct product factor
11C2×#89432C211yesmaximal, characteristic, complemented
12C2×#89419C211yesmaximal, characteristic, complemented
13C2×#89427C211yesmaximal, characteristic, complemented
14C2×#89426C211yesmaximal, characteristic, complemented
15C2×#89425C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×Q8C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C7×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C2×Q8×Dic7—28no—
26C2×Q8×Dic7C2218yescomplemented
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×Dic7⋊C4C2211yescharacteristic
35C22×Dic7⋊C4C2211yescharacteristic
36C22×Dic7⋊C4C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×#6442—28no—
43C2×#6442C2218yes—
44C7×#393C2218yes—
45C2×C7×#95C2211yescharacteristic
46C2×C7×#95C2211yescharacteristic
47C2×C7×#95C2211yescharacteristic
48#90001C2218yescomplemented
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
58#89723C2218yes—
59#89723C2218yes—
60#89720C2218yes—
61#89717C2218yes—
62#89716C2218yes—
63#89432C2218yescomplemented
64#89427C2218yescomplemented
65#89426C2218yescomplemented
66#89425C2218yescomplemented
67#89421C2218yescomplemented
68#89419C2218yescomplemented
69C2×#2469—71nomaximal, Sylow
70C25×C7C2311yescharacteristic
71C22×C7×Q8—24no—
72C22×C7×Q8—24no—
73C22×C7×Q8—24no—
74C22×C7×Q8C2314yes—
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C2×C7×C22⋊C4—24no—
90C2×C7×C22⋊C4—24no—
91C2×C7×C22⋊C4—24no—
92C2×C7×C22⋊C4C2314yes—
93C2×C7×C22⋊C4C2314yes—
94C2×C7×C22⋊C4C2314yes—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7—24no—
97C2×C22⋊Dic7—24no—
98C2×C22⋊Dic7—24no—
99C2×C22⋊Dic7C2314yes—
100C2×C22⋊Dic7C2314yes—
101C2×C22⋊Dic7C2314yes—
102C2×C22⋊Dic7C2314yes—
103Q8×Dic7—232no—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7—24no—
106C2×C4⋊Dic7—24no—
107C2×C4⋊Dic7D418yes—
108C2×C4⋊Dic7C2314yes—
109C2×C4⋊Dic7C2314yes—
110C2×C4⋊Dic7C2314yes—
111C2×C4⋊Dic7C2314yes—
112C2×Dic7⋊C4—24no—
113C2×Dic7⋊C4—24no—
114C2×Dic7⋊C4—24no—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—24no—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×Dic7⋊C4C2314yes—
124C2×C4×Dic7—24no—
125C2×C4×Dic7—24no—
126C2×C4×Dic7—24no—
127C2×C4×Dic7—24no—
128C2×C4×Dic7—24no—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
133C2×C4×Dic7C2314yes—
134#6442—232no—
135C7×#95C2314yes—
136C7×#95C2314yes—
137C7×#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C7⋊#95C2314yes—
146C7⋊#95C2314yes—
147C22×#126—71no—
148C22×C4×Q8—71no—
149#2469—716no—
150C2×#400—71no—
151C2×#396—71no—
152C2×#395—71no—
153C2×#393D711yescharacteristic
154C2×#389—71no—
155C2×#388—71no—
156C2×#388—71no—
157C2×#388—71no—
158C2×#388—71no—
159C2×#387—71no—
160C2×#387—71no—
161C2×#387—71no—
162C2×C4×C4⋊C4—71no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7—22no—
168C24×C7—22no—
169C24×C7—22no—
170C24×C7C2412yes—
171C24×C7C2411yescharacteristic
172C2×C7×Q8—232no—
173C2×C7×Q8—28no—
174C2×C7×Q8—28no—
175C2×C7×Q8—28no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—22no—
187C22×C4×C7—22no—
188C22×C4×C7—22no—
189C22×C4×C7—22no—
190C22×C4×C7—22no—
191C22×C4×C7C2×D414yes—
192C22×C4×C7#4114yes—
193C22×C4×C7#4114yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×C4×C7C2412yes—
199C22×C4×C7C2412yes—
200C22×Dic7—22no—
201C22×Dic7—22no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—22no—
205C22×Dic7—22no—
206C22×Dic7—22no—
207C22×Dic7—22no—
208C22×Dic7—22no—
209C22×Dic7—22no—
210C22×Dic7—22no—
211C22×Dic7—22no—
212C22×Dic7—22no—
213C22×Dic7—22no—
214C22×Dic7—22no—
215C22×Dic7—22no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7C2×D414yes—
221C22×Dic7C2×D414yes—
222C22×Dic7#4114yes—
223C22×Dic7#4114yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C7×C22⋊C4—28no—
233C7×C22⋊C4—28no—
234C7×C22⋊C4—28no—
235C22⋊Dic7—28no—
236C22⋊Dic7—28no—
237C22⋊Dic7—28no—
238C22⋊Dic7—28no—
239C4⋊Dic7—28no—
240C4⋊Dic7—28no—
241C4⋊Dic7—28no—
242C4⋊Dic7C2×D4116yes—
243Dic7⋊C4—28no—
244Dic7⋊C4—28no—
245Dic7⋊C4—28no—
246Dic7⋊C4—28no—
247Dic7⋊C4—28no—
248Dic7⋊C4—28no—
249C4×Dic7—28no—
250C4×Dic7—28no—
251C4×Dic7—28no—
252C4×Dic7—28no—
253C4×Dic7—28no—
254C23×Q8C2×D711yescharacteristic
255C2×#126—78no—
256C2×#126—148no—
257C2×C4×Q8—78no—
258C2×C4×Q8—148no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4—71no—
264C22×C4⋊C4—71no—
265C22×C4⋊C4—71no—
266C22×C4⋊C4—71no—
267C22×C4⋊C4—71no—
268C22×C4⋊C4—71no—
269C22×C22⋊C4—71no—
270C22×C22⋊C4—71no—
271C22×C22⋊C4—71no—
272C22×C22⋊C4—71no—
273C22×C22⋊C4C2×D711yescharacteristic
274C22×C22⋊C4C2×D711yescharacteristic
275C22×C22⋊C4C2×D711yescharacteristic
276C22×C42—71no—
277C22×C42—71no—
278C22×C42—71no—
279C22×C42—71no—
280C22×C42—71no—
281#400—78no—
282#396—78no—
283#395—78no—
284#393C2×D718yes—
285#389—78no—
286#388—78no—
287#388—78no—
288#388—78no—
289#388—78no—
290#387—78no—
291#387—78no—
292#387—78no—
293C4×C4⋊C4—78no—
294C2×#95—71no—
295C2×#95—71no—
296C2×#95—71no—
297C2×#95—71no—
298C2×#95—71no—
299C2×#95—71no—
300C2×#95—71no—
301C2×#95—71no—
302C2×#95—71no—
303C2×#95C2×D711yescharacteristic
304C2×#95C2×D711yescharacteristic
305C2×#95C2×D711yescharacteristic
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—44no—
314C23×C7—44no—
315C23×C7—44no—
316C23×C7—44no—
317C23×C7—44no—
318C23×C7—44no—
319C23×C7—44no—
320C23×C7C22×D412yes—
321C23×C7C2×#4112yes—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7C2×#4112yes—
325C23×C72−1+412yes—
326C23×C72−1+412yes—
327C23×C7C2511yescharacteristic
328C7×Q8—232no—
329C2×C4×C7—28no—
330C2×C4×C7—28no—
331C2×C4×C7—28no—
332C2×C4×C7—22no—
333C2×C4×C7—22no—
334C2×C4×C7—22no—
335C2×C4×C7—22no—
336C2×C4×C7—22no—
337C2×C4×C7—22no—
338C2×C4×C7—22no—
339C2×C4×C7—22no—
340C2×C4×C7—22no—
341C2×C4×C7—22no—
342C2×C4×C7—22no—
343C2×C4×C7—22no—
344C2×C4×C7—22no—
345C2×C4×C7—22no—
346C2×C4×C7—22no—
347C2×C4×C7—44no—
348C2×C4×C7—44no—
349C2×C4×C7—44no—
350C2×C4×C7C22×D414yes—
351C2×C4×C7C2×#4114yes—
352C2×C4×C7C2×#4114yes—
353C2×Dic7—28no—
354C2×Dic7—28no—
355C2×Dic7—28no—
356C2×Dic7—28no—
357C2×Dic7—22no—
358C2×Dic7—22no—
359C2×Dic7—22no—
360C2×Dic7—22no—
361C2×Dic7—22no—
362C2×Dic7—22no—
363C2×Dic7—22no—
364C2×Dic7—22no—
365C2×Dic7—22no—
366C2×Dic7—22no—
367C2×Dic7—22no—
368C2×Dic7—22no—
369C2×Dic7—22no—
370C2×Dic7—22no—
371C2×Dic7—22no—
372C2×Dic7—22no—
373C2×Dic7—22no—
374C2×Dic7—22no—
375C2×Dic7—22no—
376C2×Dic7—22no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7—44no—
381C2×Dic7C22×D414yes—
382C2×Dic7C22×D414yes—
383C2×Dic7C2×#4114yes—
384C2×Dic7C2×#4114yes—
385C25C22×D711yescharacteristic
386C22×Q8—24no—
387C22×Q8—24no—
388C22×Q8—24no—
389C22×Q8C22×D714yes—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—71no—
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404#126—1432no—
405C4×Q8—1432no—
406C2×C4⋊C4—78no—
407C2×C4⋊C4—74no—
408C2×C4⋊C4—74no—
409C2×C4⋊C4—74no—
410C2×C4⋊C4—74no—
411C2×C4⋊C4—74no—
412C2×C4⋊C4—74no—
413C2×C4⋊C4—74no—
414C2×C4⋊C4—74no—
415C2×C4⋊C4—74no—
416C2×C4⋊C4—74no—
417C2×C4⋊C4—144no—
418C2×C4⋊C4—144no—
419C2×C4⋊C4—144no—
420C2×C4⋊C4—144no—
421C2×C4⋊C4—144no—
422C2×C4⋊C4—144no—
423C2×C4⋊C4—144no—
424C2×C4⋊C4—144no—
425C2×C4⋊C4—144no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—74no—
430C2×C22⋊C4—74no—
431C2×C22⋊C4—74no—
432C2×C22⋊C4—74no—
433C2×C22⋊C4—144no—
434C2×C22⋊C4—144no—
435C2×C22⋊C4—144no—
436C2×C22⋊C4—144no—
437C2×C22⋊C4C22×D714yes—
438C2×C22⋊C4C22×D714yes—
439C2×C22⋊C4C22×D714yes—
440C2×C42—74no—
441C2×C42—74no—
442C2×C42—74no—
443C2×C42—74no—
444C2×C42—74no—
445C2×C42—144no—
446C2×C42—144no—
447C2×C42—144no—
448C2×C42—144no—
449C2×C42—144no—
450#95—74no—
451#95—74no—
452#95—74no—
453#95—74no—
454#95—74no—
455#95—74no—
456#95—74no—
457#95—74no—
458#95—74no—
459#95C22×D714yes—
460#95C22×D714yes—
461#95C22×D714yes—
462C22×C7—42no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7—42no—
467C22×C7—42no—
468C22×C7—42no—
469C22×C7—88no—
470C22×C7#52514yes—
471C22×C7#52914yes—
472C22×C7#54114yes—
473C22×C7#54714yes—
474C22×C7#54814yes—
475C22×C7#55614yes—
476C22×C7#55614yes—
477C22×C7C23×D411yescharacteristic
478C22×C7C22×#4111yescharacteristic
479C22×C7C22×#4111yescharacteristic
480C22×C7C22×#4111yescharacteristic
481C22×C7C22×#4111yescharacteristic
482C22×C7C2×2−1+411yescharacteristic
483C22×C7C2×2−1+411yescharacteristic
484C4×C7—24no—
485C4×C7—24no—
486C4×C7—24no—
487C4×C7—42no—
488C4×C7—42no—
489C4×C7—42no—
490Dic7—24no—
491Dic7—24no—
492Dic7—24no—
493Dic7—24no—
494Dic7—42no—
495Dic7—42no—
496Dic7—42no—
497Dic7—42no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24C23×D712yes—
506C24C23×D711yescharacteristic
507C2×Q8—232no—
508C2×Q8—28no—
509C2×Q8—28no—
510C2×Q8—28no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—74no—
527C22×C4—74no—
528C22×C4—74no—
529C22×C4—74no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—142no—
539C22×C4—142no—
540C22×C4—142no—
541C22×C4—142no—
542C22×C4—142no—
543C22×C4—142no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—142no—
549C22×C4—142no—
550C22×C4—142no—
551C22×C4—142no—
552C22×C4—142no—
553C22×C4—142no—
554C22×C4—142no—
555C22×C4—142no—
556C22×C4—142no—
557C22×C4—142no—
558C22×C4D4×D714yes—
559C22×C4#115914yes—
560C22×C4#115914yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C22×C4C23×D712yes—
564C22×C4C23×D712yes—
565C22×C4C23×D712yes—
566C22×C4C23×D712yes—
567C4⋊C4—716no—
568C4⋊C4—148no—
569C4⋊C4—148no—
570C4⋊C4—148no—
571C4⋊C4—148no—
572C4⋊C4—148no—
573C4⋊C4—148no—
574C4⋊C4—148no—
575C4⋊C4—148no—
576C4⋊C4—148no—
577C22⋊C4—28no—
578C22⋊C4—28no—
579C22⋊C4—28no—
580C22⋊C4—148no—
581C22⋊C4—148no—
582C22⋊C4—148no—
583C22⋊C4—148no—
584C42—148no—
585C42—148no—
586C42—148no—
587C42—148no—
588C42—148no—
589C2×C7—82no—
590C2×C7#246918yescomplemented
591C2×C7C2×#52511yescharacteristic
592C2×C7C2×#52911yescharacteristic
593C2×C7C2×#54111yescharacteristic
594C2×C7C2×#54711yescharacteristic
595C2×C7C2×#54811yescharacteristic
596C2×C7C2×#55611yescharacteristic
597C2×C7C2×#55611yescharacteristic
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C2×D4×D712yes—
613C23C2×#115912yes—
614C23C2×#115912yes—
615C23#655112yes—
616C23D7×#4112yes—
617C23D7×#4112yes—
618C23#655412yes—
619C23C24×D711yescharacteristic
620Q8—232no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—74no—
643C2×C4—74no—
644C2×C4—74no—
645C2×C4—74no—
646C2×C4—148no—
647C2×C4—148no—
648C2×C4—148no—
649C2×C4—148no—
650C2×C4—142no—
651C2×C4—142no—
652C2×C4—142no—
653C2×C4—142no—
654C2×C4—142no—
655C2×C4—142no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—142no—
661C2×C4—142no—
662C2×C4—142no—
663C2×C4—142no—
664C2×C4—142no—
665C2×C4—142no—
666C2×C4—142no—
667C2×C4—142no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—284no—
671C2×C4—284no—
672C2×C4—284no—
673C2×C4—284no—
674C2×C4C2×D4×D714yes—
675C2×C4C2×#115914yes—
676C2×C4C2×#115914yes—
677C7C2×#246911yescharacteristic, complemented, Sylow
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—88no—
686C22#9027714yes—
687C22#9031614yes—
688C22#9032214yes—
689C22#9033214yes—
690C22#9036214yes—
691C22#9036814yes—
692C22#9037114yes—
693C22C22×D4×D711yescharacteristic
694C22C22×#115911yescharacteristic
695C22C22×#115911yescharacteristic
696C22C2×#655111yescharacteristic
697C22C2×D7×#4111yescharacteristic
698C22C2×D7×#4111yescharacteristic
699C22C2×#655411yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—144no—
707C4—144no—
708C4—144no—
709C4—144no—
710C4—282no—
711C4—282no—
712C4—282no—
713C4—282no—
714C2—82no—
715C2#1173423418yesdirect product factor
716C2C2×#9027711yescharacteristic
717C2C2×#9031611yescharacteristic
718C2C2×#9033211yescharacteristic
719C2C2×#9032211yescharacteristic
720C2C2×#9037111yescharacteristic
721C2C2×#9036211yescharacteristic
722C2C2×#9036811yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#393C2
socleC24×C7C24
prime radicalC25×C7C23
hypercenterC2×#393D7
hypocenterC7C2×#2469
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic7C2semidirect
4. C2×#90001C2semidirect
10. #11734234C2direct (N × H)
11. C2×#89432C2semidirect
12. C2×#89419C2semidirect
13. C2×#89427C2semidirect
14. C2×#89426C2semidirect
15. C2×#89425C2semidirect
16. C2×#89421C2semidirect
26. C2×Q8×Dic7C22semidirect
48. #90001C22semidirect
63. #89432C22semidirect
64. #89427C22semidirect
65. #89426C22semidirect
66. #89425C22semidirect
67. #89421C22semidirect
68. #89419C22semidirect
590. C2×C7#2469semidirect
677. C7C2×#2469semidirect
715. C2#11734234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic72
C22×#64422
C2×C7×#3932
C2×#900012
C2×#897202
C2×#897172
C2×#897162
C2×#897232
#117342342
C2×#894322
C2×#894192
C2×#894272
C2×#894262
C2×#894252
C2×#894212
C2×#24697