Finite Group Databasebeta

← C2×#11731837 #13513020

Subgroups — C2×#11731837 #13513020

Order 1792.

3006 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6440C211yesmaximal, characteristic
2C2×C7×#385C211yesmaximal, characteristic
3C2×C4×C22⋊Dic7C211yesmaximal, characteristic
4C22×C7⋊#95C211yesmaximal, characteristic
5C2×#89750C211yesmaximal, characteristic, complemented
6C2×#89750C211yesmaximal, characteristic, complemented
7C2×#89749C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89722C211yesmaximal, characteristic
10C2×#89715C211yesmaximal, characteristic
11C2×C22⋊C4×Dic7C211yesmaximal, characteristic
12#11731837C2116yesmaximal, direct product factor
13C2×#89427C211yesmaximal, characteristic, complemented
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89423C211yesmaximal, characteristic, complemented
16C2×#89420C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C24×Dic7C2211yescharacteristic
19C24×Dic7C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C22⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×C4×Dic7C2211yescharacteristic
31C22×C4×Dic7C2211yescharacteristic
32C22×C4×Dic7C2211yescharacteristic
33C22×C4×Dic7C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C2×#6440C4116yescomplemented
37C2×#6440C2218yes—
38C7×#385C2218yes—
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C4×C22⋊Dic7C2218yes—
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2218yes—
47C2×C7⋊#95C2211yescharacteristic
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
57#89750C2218yescomplemented
58#89750C2218yescomplemented
59#89749C2218yescomplemented
60C4⋊C4×Dic7C2218yescomplemented
61#89722C2218yes—
62#89715C2218yes—
63C22⋊C4×Dic7C2218yes—
64#89427C2218yescomplemented
65#89427C2218yescomplemented
66#89423C2218yescomplemented
67#89420C2218yescomplemented
68C2×#2343—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C23×C4×C7—24no—
71C23×C4×C7—24no—
72C23×C4×C7—42no—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2314yes—
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7—24no—
81C23×Dic7—24no—
82C23×Dic7—24no—
83C23×Dic7—24no—
84C23×Dic7—42no—
85C23×Dic7C2×C418yes—
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2311yescharacteristic
88C23×Dic7C2311yescharacteristic
89C23×Dic7C2314yes—
90C23×Dic7C2314yes—
91C23×Dic7C2311yescharacteristic
92C23×Dic7C2311yescharacteristic
93C23×Dic7C2311yescharacteristic
94C23×Dic7C2311yescharacteristic
95C23×Dic7C2311yescharacteristic
96C2×C7×C4⋊C4—24no—
97C2×C7×C4⋊C4—42no—
98C2×C7×C4⋊C4C2314yes—
99C2×C7×C4⋊C4C2314yes—
100C2×C7×C22⋊C4—24no—
101C2×C7×C22⋊C4C2×C418yes—
102C2×C7×C22⋊C4C2314yes—
103C2×C7×C22⋊C4C2314yes—
104C2×C22⋊Dic7—24no—
105C2×C22⋊Dic7C2×C418yes—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C4⋊Dic7—24no—
109C2×C4⋊Dic7—42no—
110C2×C4⋊Dic7C2314yes—
111C2×C4⋊Dic7C2314yes—
112C2×Dic7⋊C4C2×C418yescomplemented
113C2×Dic7⋊C4C2×C418yescomplemented
114C2×Dic7⋊C4C2314yes—
115C2×Dic7⋊C4C2314yes—
116C2×C4×Dic7—24no—
117C2×C4×Dic7—24no—
118C2×C4×Dic7—42no—
119C2×C4×Dic7—42no—
120C2×C4×Dic7C2×C418yescomplemented
121C2×C4×Dic7C2×C418yescomplemented
122C2×C4×Dic7C2314yes—
123C2×C4×Dic7C2314yes—
124C2×C4×Dic7C2314yes—
125C2×C4×Dic7C2314yes—
126C2×C4×Dic7C2314yes—
127C2×C4×Dic7C2314yes—
128#6440C2×C4164yescomplemented
129C7×#95C2314yes—
130C7×#95C2314yes—
131C7⋊#95C2314yes—
132C7⋊#95C2314yes—
133C7⋊#95C2314yes—
134C7⋊#95C2314yes—
135C7⋊#95C2314yes—
136C7⋊#95C2314yes—
137C7⋊#95C2314yes—
138C7⋊#95C2314yes—
139C7⋊#95C2314yes—
140C7⋊#95C2314yes—
141C7⋊#95C2314yes—
142C7⋊#95C2314yes—
143C7⋊#95C2314yes—
144C7⋊#95C2314yes—
145C22×#117—71no—
146#2343—716no—
147C2×#387—71no—
148C2×#387—71no—
149C2×#387—71no—
150C2×#387—71no—
151C2×#385—71no—
152C2×#385D711yescharacteristic
153C2×#383—71no—
154C2×#382—71no—
155C2×#381—71no—
156C2×C4×C4⋊C4—71no—
157C2×C4×C22⋊C4—71no—
158C2×C4×C22⋊C4—71no—
159C2×#376—71no—
160C22×#95—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7C22×C414yes—
166C24×C7#4114yes—
167C24×C7#4114yes—
168C24×C7C2412yes—
169C24×C7C2411yescharacteristic
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7—28no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—22no—
184C22×C4×C7—22no—
185C22×C4×C7—22no—
186C22×C4×C7—28no—
187C22×C4×C7—44no—
188C22×C4×C7—416no—
189C22×C4×C7C22×C414yes—
190C22×C4×C7C22×C414yes—
191C22×C4×C7#4114yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×Dic7—232no—
199C22×Dic7—22no—
200C22×Dic7—22no—
201C22×Dic7—28no—
202C22×Dic7—22no—
203C22×Dic7—22no—
204C22×Dic7—28no—
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—28no—
216C22×Dic7—22no—
217C22×Dic7—22no—
218C22×Dic7—22no—
219C22×Dic7—22no—
220C22×Dic7—22no—
221C22×Dic7—28no—
222C22×Dic7—44no—
223C22×Dic7—416no—
224C22×Dic7C22×C4116yes—
225C22×Dic7C22×C414yes—
226C22×Dic7C22×C414yes—
227C22×Dic7C22×C414yes—
228C22×Dic7C22×C414yes—
229C22×Dic7#4114yes—
230C22×Dic7C2412yes—
231C22×Dic7C2412yes—
232C22×Dic7C2412yes—
233C22×Dic7C2412yes—
234C22×Dic7C2412yes—
235C22×Dic7C2412yes—
236C22×Dic7C2412yes—
237C22×Dic7C2412yes—
238C7×C4⋊C4—28no—
239C7×C4⋊C4—44no—
240C7×C22⋊C4—28no—
241C7×C22⋊C4C22×C4116yes—
242C22⋊Dic7—28no—
243C22⋊Dic7C22×C4116yes—
244C4⋊Dic7—28no—
245C4⋊Dic7—44no—
246Dic7⋊C4C22×C4116yescomplemented
247Dic7⋊C4C22×C4116yescomplemented
248C4×Dic7—28no—
249C4×Dic7—28no—
250C4×Dic7—44no—
251C4×Dic7—44no—
252C4×Dic7C22×C4116yescomplemented
253C4×Dic7C22×C4116yescomplemented
254C24×C4—71no—
255C24×C4—71no—
256C24×C4C2×D711yescharacteristic
257C2×#117—716no—
258C2×#117—78no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C4⋊C4C2×D711yescharacteristic
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4C2×D711yescharacteristic
268C22×C22⋊C4C2×D711yescharacteristic
269C22×C42—71no—
270C22×C42—71no—
271C22×C42—71no—
272C22×C42—71no—
273C22×C42—71no—
274C22×C42—71no—
275#387—78no—
276#387—78no—
277#387—78no—
278#387—78no—
279#385—78no—
280#385C2×D718yes—
281#383—78no—
282#382—78no—
283#381—78no—
284C4×C4⋊C4—78no—
285C4×C22⋊C4—78no—
286C4×C22⋊C4—78no—
287#376—78no—
288C2×#95—78no—
289C2×#95—71no—
290C2×#95—71no—
291C2×#95—71no—
292C2×#95—71no—
293C2×#95—71no—
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
305C23×C7—28no—
306C23×C7—28no—
307C23×C7—28no—
308C23×C7—28no—
309C23×C7—28no—
310C23×C7—28no—
311C23×C7—22no—
312C23×C7—22no—
313C23×C7—22no—
314C23×C7—22no—
315C23×C7#117116yes—
316C23×C7C23×C414yes—
317C23×C7C23×C412yes—
318C23×C7C2×#4114yes—
319C23×C7C2×#4112yes—
320C23×C7C2×#4112yes—
321C23×C7C2×#4114yes—
322C23×C7C2×#4112yes—
323C23×C7C2×#4112yes—
324C23×C7H(5,𝔽2)12yes—
325C23×C72−1+412yes—
326C23×C7C2511yescharacteristic
327C2×C4×C7—28no—
328C2×C4×C7—28no—
329C2×C4×C7—28no—
330C2×C4×C7—22no—
331C2×C4×C7—22no—
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—416no—
346C2×C4×C7—44no—
347C2×C4×C7—44no—
348C2×C4×C7—44no—
349C2×C4×C7C23×C414yes—
350C2×C4×C7C23×C414yes—
351C2×C4×C7C2×#4114yes—
352C2×Dic7—232no—
353C2×Dic7—28no—
354C2×Dic7—28no—
355C2×Dic7—28no—
356C2×Dic7—28no—
357C2×Dic7—28no—
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—416no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7—44no—
381C2×Dic7C23×C414yes—
382C2×Dic7C23×C414yes—
383C2×Dic7C23×C414yes—
384C2×Dic7C23×C414yes—
385C2×Dic7C2×#4114yes—
386C25C22×D711yescharacteristic
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—42no—
390C23×C4—78no—
391C23×C4—74no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4—71no—
395C23×C4—71no—
396C23×C4—71no—
397C23×C4—71no—
398C23×C4—71no—
399C23×C4—71no—
400C23×C4—74no—
401C23×C4—144no—
402C23×C4—144no—
403C23×C4—144no—
404C23×C4—144no—
405C23×C4—282no—
406C23×C4C22×D711yescharacteristic
407C23×C4C22×D711yescharacteristic
408C23×C4C22×D711yescharacteristic
409C23×C4C22×D714yes—
410C23×C4C22×D711yescharacteristic
411C23×C4C22×D711yescharacteristic
412C23×C4C22×D711yescharacteristic
413#117—764no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—78no—
417C2×C4⋊C4—78no—
418C2×C4⋊C4—74no—
419C2×C4⋊C4—74no—
420C2×C4⋊C4—74no—
421C2×C4⋊C4—74no—
422C2×C4⋊C4—144no—
423C2×C4⋊C4—282no—
424C2×C4⋊C4C22×D714yes—
425C2×C4⋊C4C22×D714yes—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—78no—
428C2×C22⋊C4—74no—
429C2×C22⋊C4—74no—
430C2×C22⋊C4—144no—
431C2×C22⋊C4C4×D718yes—
432C2×C22⋊C4C22×D714yes—
433C2×C22⋊C4C22×D714yes—
434C2×C42—78no—
435C2×C42—78no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—74no—
439C2×C42—74no—
440C2×C42—74no—
441C2×C42—74no—
442C2×C42—144no—
443C2×C42—144no—
444C2×C42—282no—
445C2×C42—282no—
446#95—74no—
447#95—74no—
448#95—74no—
449#95—74no—
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#95—74no—
460#95C22×D714yes—
461#95C22×D714yes—
462C22×C7—232no—
463C22×C7—24no—
464C22×C7—24no—
465C22×C7—24no—
466C22×C7—24no—
467C22×C7—24no—
468C22×C7—24no—
469C22×C7C2×#11718yes—
470C22×C7C2×#11714yes—
471C22×C7C4×#4114yes—
472C22×C7#52014yes—
473C22×C7#55114yes—
474C22×C7#55114yes—
475C22×C7#55214yes—
476C22×C7#55214yes—
477C22×C7C24×C411yescharacteristic
478C22×C7C22×#4111yescharacteristic
479C22×C7C22×#4111yescharacteristic
480C22×C7C22×#4111yescharacteristic
481C22×C7C22×#4111yescharacteristic
482C22×C7C2×H(5,𝔽2)11yescharacteristic
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—24no—
495Dic7—42no—
496Dic7—42no—
497Dic7—42no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24C2×C4×D714yes—
503C24#115914yes—
504C24#116114yes—
505C24C23×D712yes—
506C24C23×D711yescharacteristic
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—44no—
525C22×C4—416no—
526C22×C4—74no—
527C22×C4—74no—
528C22×C4—74no—
529C22×C4—74no—
530C22×C4—716no—
531C22×C4—74no—
532C22×C4—72no—
533C22×C4—72no—
534C22×C4—72no—
535C22×C4—72no—
536C22×C4—72no—
537C22×C4—72no—
538C22×C4—72no—
539C22×C4—72no—
540C22×C4—148no—
541C22×C4—1432no—
542C22×C4—142no—
543C22×C4—148no—
544C22×C4—142no—
545C22×C4—142no—
546C22×C4—142no—
547C22×C4—142no—
548C22×C4—148no—
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×C4—142no—
559C22×C4—148no—
560C22×C4—142no—
561C22×C4—142no—
562C22×C4—142no—
563C22×C4—142no—
564C22×C4—284no—
565C22×C4—2816no—
566C22×C4C2×C4×D714yes—
567C22×C4C2×C4×D714yes—
568C22×C4#115914yes—
569C22×C4C23×D712yes—
570C22×C4C23×D712yes—
571C22×C4C23×D712yes—
572C22×C4C23×D712yes—
573C22×C4C23×D712yes—
574C22×C4C23×D712yes—
575C4⋊C4—28no—
576C4⋊C4—44no—
577C4⋊C4—716no—
578C4⋊C4—716no—
579C4⋊C4—148no—
580C4⋊C4—284no—
581C22⋊C4—28no—
582C22⋊C4—716no—
583C22⋊C4—148no—
584C22⋊C4C2×C4×D7116yes—
585C42—716no—
586C42—716no—
587C42—148no—
588C42—148no—
589C42—284no—
590C42—284no—
591C2×C7—28no—
592C2×C7#234318yescomplemented
593C2×C7C22×#11711yescharacteristic
594C2×C7C2×C4×#4111yescharacteristic
595C2×C7C2×#52011yescharacteristic
596C2×C7C2×#55111yescharacteristic
597C2×C7C2×#55111yescharacteristic
598C2×C7C2×#55211yescharacteristic
599C2×C7C2×#55211yescharacteristic
600C23—28no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—28no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23#6455116yes—
611C23C22×C4×D714yes—
612C23C22×C4×D712yes—
613C23C2×#115914yes—
614C23C2×#115912yes—
615C23C2×#115912yes—
616C23#654812yes—
617C23C2×#116114yes—
618C23C2×#116112yes—
619C23D7×#4112yes—
620C23#655412yes—
621C23C24×D711yescharacteristic
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
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—22no—
640C2×C4—416no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—74no—
645C2×C4—74no—
646C2×C4—74no—
647C2×C4—74no—
648C2×C4—74no—
649C2×C4—1432no—
650C2×C4—148no—
651C2×C4—148no—
652C2×C4—148no—
653C2×C4—148no—
654C2×C4—148no—
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—142no—
671C2×C4—142no—
672C2×C4—142no—
673C2×C4—142no—
674C2×C4—2816no—
675C2×C4—284no—
676C2×C4—284no—
677C2×C4—284no—
678C2×C4C22×C4×D714yes—
679C2×C4C22×C4×D714yes—
680C2×C4C2×#115914yes—
681C7C2×#234311yescharacteristic, complemented, Sylow
682C22—24no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—24no—
688C22—232no—
689C22C2×#645518yes—
690C22C2×#645514yes—
691C22C4×#115914yes—
692C22#9023714yes—
693C22#9027814yes—
694C22#9032814yes—
695C22#9033314yes—
696C22#9034114yes—
697C22C23×C4×D711yescharacteristic
698C22C22×#115911yescharacteristic
699C22C22×#115911yescharacteristic
700C22C2×#654811yescharacteristic
701C22C22×#116111yescharacteristic
702C22C2×D7×#4111yescharacteristic
703C22C2×#655411yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—144no—
711C4—144no—
712C4—144no—
713C4—144no—
714C4—144no—
715C4—282no—
716C4—282no—
717C4—282no—
718C2—28no—
719C2#1173183718yesdirect product factor
720C2C22×#645511yescharacteristic
721C2C2×C4×#115911yescharacteristic
722C2C2×#9023711yescharacteristic
723C2C2×#9027811yescharacteristic
724C2C2×#9033311yescharacteristic
725C2C2×#9032811yescharacteristic
726C2C2×#9034111yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#385C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×#385D7
hypocenterC7C2×#2343
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
5. C2×#89750C2semidirect
6. C2×#89750C2semidirect
7. C2×#89749C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
12. #11731837C2direct (N × H)
13. C2×#89427C2semidirect
14. C2×#89427C2semidirect
15. C2×#89423C2semidirect
16. C2×#89420C2semidirect
36. C2×#6440C4semidirect
57. #89750C22semidirect
58. #89750C22semidirect
59. #89749C22semidirect
60. C4⋊C4×Dic7C22semidirect
64. #89427C22semidirect
65. #89427C22semidirect
66. #89423C22semidirect
67. #89420C22semidirect
112. C2×Dic7⋊C4C2×C4semidirect
113. C2×Dic7⋊C4C2×C4semidirect
120. C2×C4×Dic7C2×C4semidirect
121. C2×C4×Dic7C2×C4semidirect
128. #6440C2×C4semidirect
246. Dic7⋊C4C22×C4semidirect
247. Dic7⋊C4C22×C4semidirect
252. C4×Dic7C22×C4semidirect
253. C4×Dic7C22×C4semidirect
592. C2×C7#2343semidirect
681. C7C2×#2343semidirect
719. C2#11731837direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64402
C2×C7×#3852
C2×C4×C22⋊Dic72
C22×C7⋊#952
C2×#897502
C2×#897492
C2×C4⋊C4×Dic72
C2×#897222
C2×#897152
C2×C22⋊C4×Dic72
#117318372
C2×#894272
C2×#894232
C2×#894202
C2×#23437