Finite Group Databasebeta

← C2×#11733998 #13524093

Subgroups — C2×#11733998 #13524093

Order 1792.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#391C211yesmaximal, characteristic, complemented
2C2×#90003C211yesmaximal, characteristic
3C2×#90002C211yesmaximal, characteristic, complemented
4C2×#89761C211yesmaximal, characteristic
5C2×#89756C211yesmaximal, characteristic, complemented
6C2×#89712C211yesmaximal, characteristic
7C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
8#11733998C2116yesmaximal, direct product factor
9C2×#89449C211yesmaximal, characteristic
10C2×#89440C211yesmaximal, characteristic
11C2×#89431C211yesmaximal, characteristic, complemented
12C2×#89419C211yesmaximal, characteristic, complemented
13C2×#89441C211yesmaximal, characteristic
14C2×#89427C211yesmaximal, characteristic, complemented
15C2×#89426C211yesmaximal, characteristic, complemented
16C2×#89438C211yesmaximal, characteristic
17C23×C7×Q8C2211yescharacteristic
18C23×C4×D7C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×(C2×D7)⋊C4C2211yescharacteristic
22C22×(C2×D7)⋊C4C2211yescharacteristic
23C22×(C2×D7)⋊C4C2211yescharacteristic
24C22×(C2×D7)⋊C4C2211yescharacteristic
25C22×(C2×D7)⋊C4C2211yescharacteristic
26C22×(C2×D7)⋊C4C2211yescharacteristic
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×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C7×#391C2218yescomplemented
39C2×C7×#95C2211yescharacteristic
40C2×C7×#95C2211yescharacteristic
41C2×C7×#95C2211yescharacteristic
42C2×C7×#95C2211yescharacteristic
43#90003C2218yes—
44#90002C2218yescomplemented
45C2×C7⋊#95C2211yescharacteristic
46C2×C7⋊#95C2211yescharacteristic
47C2×C7⋊#95C2211yescharacteristic
48C2×C7⋊#95C2211yescharacteristic
49C2×C7⋊#95C2211yescharacteristic
50C2×C7⋊#95C2211yescharacteristic
51C2×C7⋊#95C2211yescharacteristic
52C2×C7⋊#95C2211yescharacteristic
53C2×C7⋊#95C2211yescharacteristic
54C2×C7⋊#95C2211yescharacteristic
55#89761C2218yes—
56#89756C2218yescomplemented
57#89712C2218yes—
58C4×C4⋊Dic7C2218yescomplemented
59#89449C2218yes—
60#89441C2218yes—
61#89440C2218yes—
62#89438C2218yes—
63#89431C2218yescomplemented
64#89427C2218yescomplemented
65#89426C2218yescomplemented
66#89419C2218yescomplemented
67C2×#2589—71nomaximal, Sylow
68C24×D7C2311yescharacteristic
69C22×C7×Q8—24no—
70C22×C7×Q8—24no—
71C22×C7×Q8—42no—
72C22×C7×Q8C2314yes—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×C4×C7C2311yescharacteristic
77C23×C4×C7C2311yescharacteristic
78C23×C4×C7C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C22×C4×D7—24no—
88C22×C4×D7—42no—
89C22×C4×D7—42no—
90C22×C4×D7C2314yes—
91C2×C7×C4⋊C4—42no—
92C2×C7×C4⋊C4C2314yes—
93C2×C42×C7—24no—
94C2×C42×C7C2314yes—
95C2×(C2×D7)⋊C4—24no—
96C2×(C2×D7)⋊C4—24no—
97C2×(C2×D7)⋊C4—24no—
98C2×(C2×D7)⋊C4—42no—
99C2×(C2×D7)⋊C4—42no—
100C2×(C2×D7)⋊C4Q818yescomplemented
101C2×(C2×D7)⋊C4C2314yes—
102C2×(C2×D7)⋊C4C2314yes—
103C2×(C2×D7)⋊C4C2314yes—
104C2×(C2×D7)⋊C4C2314yes—
105C2×(C2×D7)⋊C4C2314yes—
106C2×(C2×D7)⋊C4C2314yes—
107C2×C4⋊Dic7—24no—
108C2×C4⋊Dic7—24no—
109C2×C4⋊Dic7—24no—
110C2×C4⋊Dic7—42no—
111C2×C4⋊Dic7C2314yes—
112C2×C4⋊Dic7C2314yes—
113C2×C4⋊Dic7C2314yes—
114C2×C4⋊Dic7C2314yes—
115C2×Dic7⋊C4—24no—
116C2×Dic7⋊C4—24no—
117C2×Dic7⋊C4—42no—
118C2×Dic7⋊C4—42no—
119C2×Dic7⋊C4C2314yes—
120C2×Dic7⋊C4C2314yes—
121C2×Dic7⋊C4C2314yes—
122C2×Dic7⋊C4C2314yes—
123C2×C4×Dic7—42no—
124C2×C4×Dic7—42no—
125C2×C4×Dic7—42no—
126C2×C4×Dic7C2314yes—
127C2×C4×Dic7C2314yes—
128C2×C4×Dic7C2314yes—
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—
143#2589—716no—
144C2×#400—71no—
145C2×#399—71no—
146C2×#398—71no—
147C2×#393—71no—
148C2×#391—71no—
149C2×#391D711yescharacteristic, complemented
150C2×#389—71no—
151C2×#388—71no—
152C2×#388—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#385—71no—
156C2×#385—71no—
157C2×C4×C4⋊C4—71no—
158C2×C4×C22⋊C4—71no—
159C24×C7C2411yescharacteristic
160C23×D7—22no—
161C23×D7—22no—
162C23×D7—22no—
163C23×D7—22no—
164C23×D7—22no—
165C23×D7—22no—
166C23×D7C2×Q814yes—
167C23×D7C2412yes—
168C2×C7×Q8—28no—
169C2×C7×Q8—28no—
170C2×C7×Q8—44no—
171C2×C7×Q8—416no—
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—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×C7C2×Q814yes—
190C22×C4×C7#4114yes—
191C22×C4×C7#4114yes—
192C22×C4×C7#4114yes—
193C22×C4×C7C2412yes—
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×Dic7C2×Q814yes—
220C22×Dic7#4114yes—
221C22×Dic7C2412yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C2×C4×D7—28no—
229C2×C4×D7—44no—
230C2×C4×D7—44no—
231C2×C4×D7—416no—
232C7×C4⋊C4—44no—
233C42×C7—28no—
234(C2×D7)⋊C4—28no—
235(C2×D7)⋊C4—28no—
236(C2×D7)⋊C4—28no—
237(C2×D7)⋊C4—44no—
238(C2×D7)⋊C4—44no—
239(C2×D7)⋊C4C2×Q8116yescomplemented
240C4⋊Dic7—28no—
241C4⋊Dic7—28no—
242C4⋊Dic7—28no—
243C4⋊Dic7—44no—
244Dic7⋊C4—28no—
245Dic7⋊C4—28no—
246Dic7⋊C4—44no—
247Dic7⋊C4—44no—
248C4×Dic7—44no—
249C4×Dic7—44no—
250C4×Dic7—44no—
251C23×Q8C2×D711yescharacteristic
252C24×C4—71no—
253C22×C4⋊C4—71no—
254C22×C4⋊C4—71no—
255C22×C4⋊C4—71no—
256C22×C4⋊C4—71no—
257C22×C4⋊C4—71no—
258C22×C4⋊C4—71no—
259C22×C4⋊C4—71no—
260C22×C4⋊C4—71no—
261C22×C4⋊C4C2×D711yescharacteristic
262C22×C22⋊C4—71no—
263C22×C22⋊C4—71no—
264C22×C22⋊C4—71no—
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C42—71no—
269C22×C42—71no—
270C22×C42—71no—
271C22×C42C2×D711yescharacteristic
272#400—78no—
273#399—78no—
274#398—78no—
275#393—78no—
276#391—78no—
277#391C2×D718yescomplemented
278#389—78no—
279#388—78no—
280#388—78no—
281#387—78no—
282#387—78no—
283#385—78no—
284#385—78no—
285C4×C4⋊C4—78no—
286C4×C22⋊C4—78no—
287C2×#95—71no—
288C2×#95—71no—
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×#95C2×D711yescharacteristic
298C2×#95C2×D711yescharacteristic
299C2×#95C2×D711yescharacteristic
300C2×#95C2×D711yescharacteristic
301C23×C7C22×Q812yes—
302C23×C7C2×#4112yes—
303C23×C7C2×#4112yes—
304C23×C7C2×#4112yes—
305C23×C7C2×#4112yes—
306C23×C7H(5,𝔽2)12yes—
307C23×C7H(5,𝔽2)12yes—
308C23×C7C2511yescharacteristic
309C22×D7—28no—
310C22×D7—28no—
311C22×D7—28no—
312C22×D7—22no—
313C22×D7—22no—
314C22×D7—22no—
315C22×D7—22no—
316C22×D7—22no—
317C22×D7—22no—
318C22×D7—44no—
319C22×D7—44no—
320C22×D7—44no—
321C22×D7—44no—
322C22×D7C22×Q814yes—
323C7×Q8—416no—
324C2×C4×C7—28no—
325C2×C4×C7—28no—
326C2×C4×C7—28no—
327C2×C4×C7—28no—
328C2×C4×C7—22no—
329C2×C4×C7—22no—
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—44no—
346C2×C4×C7—44no—
347C2×C4×C7—44no—
348C2×C4×C7C22×Q814yes—
349C2×C4×C7C2×#4114yes—
350C2×C4×C7C2×#4114yes—
351C2×C4×C7C2×#4114yes—
352C2×Dic7—28no—
353C2×Dic7—28no—
354C2×Dic7—22no—
355C2×Dic7—22no—
356C2×Dic7—22no—
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—44no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7C22×Q814yes—
379C2×Dic7C2×#4114yes—
380C4×D7—416no—
381C25—71no—
382C22×Q8—24no—
383C22×Q8—24no—
384C22×Q8—42no—
385C22×Q8C22×D714yes—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—74no—
394C23×C4—144no—
395C23×C4—282no—
396C23×C4—282no—
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401C23×C4C22×D711yescharacteristic
402C23×C4C22×D711yescharacteristic
403C23×C4C22×D711yescharacteristic
404C2×C4⋊C4—42no—
405C2×C4⋊C4—74no—
406C2×C4⋊C4—74no—
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—144no—
414C2×C4⋊C4—144no—
415C2×C4⋊C4—144no—
416C2×C4⋊C4—144no—
417C2×C4⋊C4—144no—
418C2×C4⋊C4—282no—
419C2×C4⋊C4—282no—
420C2×C4⋊C4—282no—
421C2×C4⋊C4C22×D714yes—
422C2×C22⋊C4—78no—
423C2×C22⋊C4—74no—
424C2×C22⋊C4—74no—
425C2×C22⋊C4—74no—
426C2×C22⋊C4—74no—
427C2×C22⋊C4—74no—
428C2×C22⋊C4—74no—
429C2×C22⋊C4—144no—
430C2×C22⋊C4—144no—
431C2×C22⋊C4—144no—
432C2×C22⋊C4—282no—
433C2×C22⋊C4—282no—
434C2×C42—24no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—282no—
439C2×C42—282no—
440C2×C42—282no—
441C2×C42C22×D714yes—
442#95—74no—
443#95—74no—
444#95—74no—
445#95—74no—
446#95—74no—
447#95—74no—
448#95—74no—
449#95—74no—
450#95—74no—
451#95—74no—
452#95C22×D714yes—
453#95C22×D714yes—
454#95C22×D714yes—
455#95C22×D714yes—
456C22×C7#52914yes—
457C22×C7#53314yes—
458C22×C7#53814yes—
459C22×C7#55114yes—
460C22×C7#55414yes—
461C22×C7#55414yes—
462C22×C7#55914yes—
463C22×C7C23×Q811yescharacteristic
464C22×C7C22×#4111yescharacteristic
465C22×C7C22×#4111yescharacteristic
466C22×C7C22×#4111yescharacteristic
467C22×C7C22×#4111yescharacteristic
468C22×C7C2×H(5,𝔽2)11yescharacteristic
469C22×C7C2×H(5,𝔽2)11yescharacteristic
470C2×D7—24no—
471C2×D7—24no—
472C2×D7—24no—
473C2×D7—416no—
474C2×D7—42no—
475C2×D7—42no—
476C2×D7—42no—
477C2×D7—42no—
478C4×C7—24no—
479C4×C7—24no—
480C4×C7—24no—
481C4×C7—24no—
482C4×C7—42no—
483C4×C7—42no—
484C4×C7—42no—
485Dic7—24no—
486Dic7—24no—
487Dic7—42no—
488Dic7—42no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492C24—74no—
493C24—72no—
494C24—142no—
495C24—142no—
496C24—142no—
497C24—142no—
498C24—142no—
499C24—142no—
500C24C23×D711yescharacteristic
501C2×Q8—28no—
502C2×Q8—28no—
503C2×Q8—44no—
504C2×Q8—416no—
505C22×C4—22no—
506C22×C4—22no—
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—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—74no—
523C22×C4—74no—
524C22×C4—72no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—148no—
532C22×C4—142no—
533C22×C4—142no—
534C22×C4—142no—
535C22×C4—142no—
536C22×C4—142no—
537C22×C4—142no—
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—284no—
552C22×C4—284no—
553C22×C4—2816no—
554C22×C4#115714yes—
555C22×C4#115914yes—
556C22×C4Q8×D714yes—
557C22×C4#116114yes—
558C22×C4C23×D712yes—
559C22×C4C23×D712yes—
560C22×C4C23×D712yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C22×C4C23×D712yes—
564C22×C4C23×D712yes—
565C4⋊C4—44no—
566C4⋊C4—148no—
567C4⋊C4—148no—
568C4⋊C4—148no—
569C4⋊C4—148no—
570C4⋊C4—148no—
571C4⋊C4—284no—
572C4⋊C4—284no—
573C4⋊C4—284no—
574C22⋊C4—716no—
575C22⋊C4—148no—
576C22⋊C4—148no—
577C22⋊C4—148no—
578C22⋊C4—284no—
579C22⋊C4—284no—
580C42—28no—
581C42—284no—
582C42—284no—
583C42—284no—
584C2×C7#258918yescomplemented
585C2×C7C2×#52911yescharacteristic
586C2×C7C2×#53311yescharacteristic
587C2×C7C2×#53811yescharacteristic
588C2×C7C2×#55111yescharacteristic
589C2×C7C2×#55411yescharacteristic
590C2×C7C2×#55411yescharacteristic
591C2×C7C2×#55911yescharacteristic
592D7—44no—
593C23—74no—
594C23—148no—
595C23—148no—
596C23—148no—
597C23—142no—
598C23—142no—
599C23—142no—
600C23—142no—
601C23—142no—
602C23—142no—
603C23—284no—
604C23—284no—
605C23—284no—
606C23—284no—
607C23C2×#115712yes—
608C23C2×#115912yes—
609C23#654812yes—
610C23C2×Q8×D712yes—
611C23C2×#116112yes—
612C23D7×#4112yes—
613C23#655312yes—
614C23C24×D711yescharacteristic
615Q8—416no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
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—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—74no—
641C2×C4—74no—
642C2×C4—148no—
643C2×C4—148no—
644C2×C4—142no—
645C2×C4—142no—
646C2×C4—142no—
647C2×C4—142no—
648C2×C4—142no—
649C2×C4—142no—
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—2816no—
664C2×C4—284no—
665C2×C4—284no—
666C2×C4—284no—
667C2×C4—284no—
668C2×C4—284no—
669C2×C4C2×#115714yes—
670C2×C4C2×#115914yes—
671C2×C4C2×Q8×D714yes—
672C2×C4C2×#116114yes—
673C7C2×#258911yescharacteristic, complemented, Sylow
674C22—144no—
675C22—144no—
676C22—144no—
677C22—282no—
678C22—282no—
679C22—282no—
680C22—282no—
681C22—2816no—
682C22#9018614yes—
683C22#9026914yes—
684C22#9027614yes—
685C22#9031514yes—
686C22#9032614yes—
687C22#9036914yes—
688C22#9042114yes—
689C22C22×#115711yescharacteristic
690C22C22×#115911yescharacteristic
691C22C2×#654811yescharacteristic
692C22C22×Q8×D711yescharacteristic
693C22C22×#116111yescharacteristic
694C22C2×D7×#4111yescharacteristic
695C22C2×#655311yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—144no—
704C4—144no—
705C4—282no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C2—284no—
711C2#1173399818yesdirect product factor
712C2C2×#9018611yescharacteristic
713C2C2×#9027611yescharacteristic
714C2C2×#9026911yescharacteristic
715C2C2×#9031511yescharacteristic
716C2C2×#9032611yescharacteristic
717C2C2×#9036911yescharacteristic
718C2C2×#9042111yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#391C2
socleC24×C7C24
prime radicalC24×D7C23
hypercenterC2×#391D7
hypocenterC7C2×#2589
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
1. C2×C7×#391C2semidirect
3. C2×#90002C2semidirect
5. C2×#89756C2semidirect
7. C2×C4×C4⋊Dic7C2semidirect
8. #11733998C2direct (N × H)
11. C2×#89431C2semidirect
12. C2×#89419C2semidirect
14. C2×#89427C2semidirect
15. C2×#89426C2semidirect
38. C7×#391C22semidirect
44. #90002C22semidirect
56. #89756C22semidirect
58. C4×C4⋊Dic7C22semidirect
63. #89431C22semidirect
64. #89427C22semidirect
65. #89426C22semidirect
66. #89419C22semidirect
100. C2×(C2×D7)⋊C4Q8semidirect
149. C2×#391D7semidirect
239. (C2×D7)⋊C4C2×Q8semidirect
277. #391C2×D7semidirect
584. C2×C7#2589semidirect
673. C7C2×#2589semidirect
711. C2#11733998direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3912
C2×#900032
C2×#900022
C2×#897612
C2×#897562
C2×#897122
C2×C4×C4⋊Dic72
#117339982
C2×#894492
C2×#894402
C2×#894312
C2×#894192
C2×#894412
C2×#894272
C2×#894262
C2×#894382
C2×#25897