Finite Group Databasebeta

← C2×#11730921 #13513486

Subgroups — C2×#11730921 #13513486

Order 1792.

2726 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
1C22×#6442C211yesmaximal, characteristic
2C2×C4×C7×C22⋊C4C211yesmaximal, characteristic
3C2×#89982C211yesmaximal, characteristic
4C2×C4×C22⋊Dic7C211yesmaximal, characteristic
5C2×#89716C211yesmaximal, characteristic
6C2×#89716C211yesmaximal, characteristic
7C2×#89723C211yesmaximal, characteristic
8C2×#89705C211yesmaximal, characteristic, complemented
9C2×#89705C211yesmaximal, characteristic, complemented
10C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
11C2×C4×Dic7⋊C4C211yesmaximal, characteristic, complemented
12#11730921C2116yesmaximal, direct product factor
13C2×#89419C211yesmaximal, characteristic, complemented
14C2×#89425C211yesmaximal, characteristic, complemented
15C2×#89421C211yesmaximal, characteristic, complemented
16C2×#89420C211yesmaximal, characteristic, complemented
17C24×C4×C7C2211yescharacteristic
18C22×C7×C22⋊C4C2211yescharacteristic
19C22×C7×C22⋊C4C2211yescharacteristic
20C22×C42×C7C2211yescharacteristic
21C22×C42×C7C2211yescharacteristic
22C22×C22⋊Dic7C2211yescharacteristic
23C22×C22⋊Dic7C2211yescharacteristic
24C22×C22⋊Dic7C2211yescharacteristic
25C22×C22⋊Dic7C2211yescharacteristic
26C22×C4⋊Dic7C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×Dic7⋊C4C2211yescharacteristic
29C22×Dic7⋊C4C2211yescharacteristic
30C22×Dic7⋊C4C2211yescharacteristic
31C22×Dic7⋊C4C2211yescharacteristic
32C22×Dic7⋊C4C2211yescharacteristic
33C22×Dic7⋊C4C2211yescharacteristic
34C22×C4×Dic7C2211yescharacteristic
35C22×C4×Dic7C2211yescharacteristic
36C22×C4×Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C2×#6442C4116yescomplemented
41C2×#6442C2218yes—
42C4×C7×C22⋊C4C2218yes—
43C2×C7×#95C2211yescharacteristic
44C2×C7×#95C2211yescharacteristic
45#89982C2218yes—
46C4×C22⋊Dic7C2218yes—
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#89723C2218yes—
58#89716C2218yes—
59#89716C2218yes—
60C4×C4⋊Dic7C2218yescomplemented
61#89705C2218yescomplemented
62#89705C2218yescomplemented
63C4×Dic7⋊C4C2218yescomplemented
64#89425C2218yescomplemented
65#89421C2218yescomplemented
66#89420C2218yescomplemented
67#89419C2218yescomplemented
68C2×#2373—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C23×C4×C7—24no—
71C23×C4×C7—24no—
72C23×C4×C7—42no—
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2314yes—
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
87C23×Dic7C2311yescharacteristic
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4C2×C418yes—
90C2×C7×C22⋊C4C2314yes—
91C2×C7×C22⋊C4C2314yes—
92C2×C42×C7—24no—
93C2×C42×C7—42no—
94C2×C42×C7C2314yes—
95C2×C42×C7C2314yes—
96C2×C22⋊Dic7—24no—
97C2×C22⋊Dic7—42no—
98C2×C22⋊Dic7C2×C418yes—
99C2×C22⋊Dic7C2×C418yes—
100C2×C22⋊Dic7C2314yes—
101C2×C22⋊Dic7C2314yes—
102C2×C22⋊Dic7C2314yes—
103C2×C22⋊Dic7C2314yes—
104C2×C4⋊Dic7—24no—
105C2×C4⋊Dic7C2×C418yescomplemented
106C2×C4⋊Dic7C2314yes—
107C2×C4⋊Dic7C2314yes—
108C2×Dic7⋊C4—24no—
109C2×Dic7⋊C4—24no—
110C2×Dic7⋊C4—24no—
111C2×Dic7⋊C4—42no—
112C2×Dic7⋊C4C2×C418yescomplemented
113C2×Dic7⋊C4C2×C418yescomplemented
114C2×Dic7⋊C4C2314yes—
115C2×Dic7⋊C4C2314yes—
116C2×Dic7⋊C4C2314yes—
117C2×Dic7⋊C4C2314yes—
118C2×Dic7⋊C4C2314yes—
119C2×Dic7⋊C4C2314yes—
120C2×C4×Dic7—24no—
121C2×C4×Dic7—24no—
122C2×C4×Dic7—24no—
123C2×C4×Dic7—42no—
124C2×C4×Dic7—42no—
125C2×C4×Dic7C2×C418yescomplemented
126C2×C4×Dic7C2314yes—
127C2×C4×Dic7C2314yes—
128C2×C4×Dic7C2314yes—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132#6442C2×C4164yescomplemented
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×#126—71no—
146#2373—716no—
147C2×#389—71no—
148C2×#388—71no—
149C2×#388—71no—
150C2×#388—71no—
151C2×#387—71no—
152C2×#387—71no—
153C2×#387—71no—
154C2×#385—71no—
155C2×C4×C4⋊C4—71no—
156C2×C4×C4⋊C4—71no—
157C2×C4×C4⋊C4—71no—
158C2×C4×C22⋊C4—71no—
159C2×C4×C22⋊C4D711yescharacteristic
160C2×#376—71no—
161C24×C7—22no—
162C24×C7—22no—
163C24×C7—22no—
164C24×C7—22no—
165C24×C7—22no—
166C24×C7—22no—
167C24×C7C22×C414yes—
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—22no—
181C22×C4×C7—22no—
182C22×C4×C7—22no—
183C22×C4×C7—28no—
184C22×C4×C7—28no—
185C22×C4×C7—44no—
186C22×C4×C7—416no—
187C22×C4×C7C22×C414yes—
188C22×C4×C7C22×C414yes—
189C22×C4×C7#4114yes—
190C22×C4×C7#4114yes—
191C22×C4×C7#4114yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×C4×C7C2412yes—
195C22×C4×C7C2412yes—
196C22×C4×C7C2412yes—
197C22×C4×C7C2412yes—
198C22×Dic7—22no—
199C22×Dic7—22no—
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×Dic7C22×C414yes—
218C22×Dic7C22×C414yes—
219C22×Dic7C22×C414yes—
220C22×Dic7C22×C414yes—
221C22×Dic7#4114yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C7×C22⋊C4—28no—
231C7×C22⋊C4C22×C4116yes—
232C42×C7—28no—
233C42×C7—44no—
234C22⋊Dic7—28no—
235C22⋊Dic7—44no—
236C22⋊Dic7C22×C4116yes—
237C22⋊Dic7C22×C4116yes—
238C4⋊Dic7—28no—
239C4⋊Dic7C22×C4116yescomplemented
240Dic7⋊C4—28no—
241Dic7⋊C4—28no—
242Dic7⋊C4—28no—
243Dic7⋊C4—44no—
244Dic7⋊C4C22×C4116yescomplemented
245Dic7⋊C4C22×C4116yescomplemented
246C4×Dic7—28no—
247C4×Dic7—28no—
248C4×Dic7—28no—
249C4×Dic7—44no—
250C4×Dic7—44no—
251C4×Dic7C22×C4116yescomplemented
252C24×C4C2×D711yescharacteristic
253C2×#126—716no—
254C2×#126—78no—
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⋊C4—71no—
262C22×C4⋊C4—71no—
263C22×C22⋊C4—71no—
264C22×C22⋊C4—71no—
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—
275C22×C42C2×D711yescharacteristic
276C22×C42C2×D711yescharacteristic
277#389—78no—
278#388—78no—
279#388—78no—
280#388—78no—
281#387—78no—
282#387—78no—
283#387—78no—
284#385—78no—
285C4×C4⋊C4—78no—
286C4×C4⋊C4—78no—
287C4×C4⋊C4—78no—
288C4×C22⋊C4—78no—
289C4×C22⋊C4C2×D718yes—
290#376—78no—
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×#95C2×D711yescharacteristic
302C2×#95C2×D711yescharacteristic
303C23×C7—28no—
304C23×C7—28no—
305C23×C7—28no—
306C23×C7—22no—
307C23×C7—22no—
308C23×C7—22no—
309C23×C7—22no—
310C23×C7—22no—
311C23×C7—22no—
312C23×C7—44no—
313C23×C7—44no—
314C23×C7—44no—
315C23×C7—44no—
316C23×C7C23×C414yes—
317C23×C7C23×C412yes—
318C23×C7C2×#4112yes—
319C23×C7C2×#4112yes—
320C23×C7C2×#4112yes—
321C23×C7C2×#4112yes—
322C23×C7H(5,𝔽2)12yes—
323C23×C72−1+412yes—
324C23×C7C2511yescharacteristic
325C2×C4×C7—28no—
326C2×C4×C7—28no—
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—416no—
344C2×C4×C7—44no—
345C2×C4×C7C23×C414yes—
346C2×C4×C7C23×C414yes—
347C2×C4×C7C2×#4114yes—
348C2×C4×C7C2×#4114yes—
349C2×C4×C7C2×#4114yes—
350C2×Dic7—28no—
351C2×Dic7—28no—
352C2×Dic7—28no—
353C2×Dic7—28no—
354C2×Dic7—28no—
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—22no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7C23×C414yes—
378C2×Dic7C23×C414yes—
379C2×Dic7C23×C414yes—
380C2×Dic7C23×C414yes—
381C2×Dic7C2×#4114yes—
382C25C22×D711yescharacteristic
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—42no—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—71no—
392C23×C4—71no—
393C23×C4—71no—
394C23×C4C22×D711yescharacteristic
395C23×C4C22×D714yes—
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401#126—764no—
402C2×C4⋊C4—78no—
403C2×C4⋊C4—78no—
404C2×C4⋊C4—78no—
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—282no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—78no—
420C2×C22⋊C4—78no—
421C2×C22⋊C4—74no—
422C2×C22⋊C4—74no—
423C2×C22⋊C4—74no—
424C2×C22⋊C4—74no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—282no—
427C2×C22⋊C4C4×D718yes—
428C2×C22⋊C4C22×D714yes—
429C2×C22⋊C4C22×D714yes—
430C2×C42—24no—
431C2×C42—42no—
432C2×C42—78no—
433C2×C42—74no—
434C2×C42—74no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—74no—
439C2×C42—144no—
440C2×C42—144no—
441C2×C42—144no—
442C2×C42—282no—
443C2×C42—282no—
444C2×C42C22×D714yes—
445C2×C42C22×D714yes—
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#95C22×D714yes—
457#95C22×D714yes—
458C22×C7—24no—
459C22×C7—24no—
460C22×C7—24no—
461C22×C7—416no—
462C22×C7—42no—
463C22×C7—42no—
464C22×C7—42no—
465C22×C7—42no—
466C22×C7C4×#4114yes—
467C22×C7C4×#4114yes—
468C22×C7#52014yes—
469C22×C7#55114yes—
470C22×C7#55214yes—
471C22×C7#55314yes—
472C22×C7#55614yes—
473C22×C7C24×C411yescharacteristic
474C22×C7C22×#4111yescharacteristic
475C22×C7C22×#4111yescharacteristic
476C22×C7C22×#4111yescharacteristic
477C22×C7C22×#4111yescharacteristic
478C22×C7C2×H(5,𝔽2)11yescharacteristic
479C22×C7C2×2−1+411yescharacteristic
480C4×C7—24no—
481C4×C7—24no—
482C4×C7—24no—
483C4×C7—24no—
484C4×C7—24no—
485C4×C7—42no—
486Dic7—24no—
487Dic7—24no—
488Dic7—24no—
489Dic7—24no—
490Dic7—24no—
491Dic7—42no—
492Dic7—42no—
493Dic7—42no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24C2×C4×D714yes—
501C24C23×D712yes—
502C24C23×D711yescharacteristic
503C22×C4—22no—
504C22×C4—22no—
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—28no—
517C22×C4—28no—
518C22×C4—44no—
519C22×C4—416no—
520C22×C4—74no—
521C22×C4—74no—
522C22×C4—74no—
523C22×C4—74no—
524C22×C4—74no—
525C22×C4—72no—
526C22×C4—72no—
527C22×C4—72no—
528C22×C4—72no—
529C22×C4—72no—
530C22×C4—72no—
531C22×C4—72no—
532C22×C4—72no—
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—142no—
552C22×C4C2×C4×D714yes—
553C22×C4C2×C4×D714yes—
554C22×C4#115714yes—
555C22×C4#115714yes—
556C22×C4#115914yes—
557C22×C4C23×D712yes—
558C22×C4C23×D712yes—
559C22×C4C23×D712yes—
560C22×C4C23×D712yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C4⋊C4—716no—
564C4⋊C4—716no—
565C4⋊C4—716no—
566C4⋊C4—148no—
567C4⋊C4—148no—
568C4⋊C4—148no—
569C4⋊C4—148no—
570C4⋊C4—284no—
571C22⋊C4—28no—
572C22⋊C4—716no—
573C22⋊C4—716no—
574C22⋊C4—148no—
575C22⋊C4—284no—
576C22⋊C4C2×C4×D7116yes—
577C42—28no—
578C42—44no—
579C42—716no—
580C42—148no—
581C42—148no—
582C42—148no—
583C42—284no—
584C42—284no—
585C2×C7—44no—
586C2×C7#237318yescomplemented
587C2×C7C2×C4×#4111yescharacteristic
588C2×C7C2×C4×#4111yescharacteristic
589C2×C7C2×#52011yescharacteristic
590C2×C7C2×#55111yescharacteristic
591C2×C7C2×#55211yescharacteristic
592C2×C7C2×#55311yescharacteristic
593C2×C7C2×#55611yescharacteristic
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C22×C4×D714yes—
608C23C22×C4×D712yes—
609C23C2×#115712yes—
610C23C2×#115712yes—
611C23C2×#115912yes—
612C23#654812yes—
613C23D7×#4112yes—
614C23#655412yes—
615C23C24×D711yescharacteristic
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
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—416no—
635C2×C4—44no—
636C2×C4—74no—
637C2×C4—74no—
638C2×C4—74no—
639C2×C4—74no—
640C2×C4—74no—
641C2×C4—148no—
642C2×C4—148no—
643C2×C4—148no—
644C2×C4—148no—
645C2×C4—148no—
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—142no—
664C2×C4—142no—
665C2×C4—284no—
666C2×C4—284no—
667C2×C4—284no—
668C2×C4C22×C4×D714yes—
669C2×C4C22×C4×D714yes—
670C2×C4C2×#115714yes—
671C2×C4C2×#115714yes—
672C2×C4C2×#115914yes—
673C7C2×#237311yescharacteristic, complemented, Sylow
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—416no—
682C22C4×#115714yes—
683C22#9018614yes—
684C22#9022414yes—
685C22C4×#115914yes—
686C22#9023214yes—
687C22#9023714yes—
688C22#9024914yes—
689C22C23×C4×D711yescharacteristic
690C22C22×#115711yescharacteristic
691C22C22×#115711yescharacteristic
692C22C22×#115911yescharacteristic
693C22C2×#654811yescharacteristic
694C22C2×D7×#4111yescharacteristic
695C22C2×#655411yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—42no—
702C4—144no—
703C4—144no—
704C4—144no—
705C4—144no—
706C4—144no—
707C4—282no—
708C4—282no—
709C4—282no—
710C2—44no—
711C2#1173092118yesdirect product factor
712C2C2×C4×#115711yescharacteristic
713C2C2×#9018611yescharacteristic
714C2C2×#9022411yescharacteristic
715C2C2×C4×#115911yescharacteristic
716C2C2×#9023711yescharacteristic
717C2C2×#9023211yescharacteristic
718C2C2×#9024911yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C4×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC2×C4×C22⋊C4D7
hypocenterC7C2×#2373
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C2×#89705C2semidirect
9. C2×#89705C2semidirect
10. C2×C4×C4⋊Dic7C2semidirect
11. C2×C4×Dic7⋊C4C2semidirect
12. #11730921C2direct (N × H)
13. C2×#89419C2semidirect
14. C2×#89425C2semidirect
15. C2×#89421C2semidirect
16. C2×#89420C2semidirect
40. C2×#6442C4semidirect
60. C4×C4⋊Dic7C22semidirect
61. #89705C22semidirect
62. #89705C22semidirect
63. C4×Dic7⋊C4C22semidirect
64. #89425C22semidirect
65. #89421C22semidirect
66. #89420C22semidirect
67. #89419C22semidirect
105. C2×C4⋊Dic7C2×C4semidirect
112. C2×Dic7⋊C4C2×C4semidirect
113. C2×Dic7⋊C4C2×C4semidirect
125. C2×C4×Dic7C2×C4semidirect
132. #6442C2×C4semidirect
239. C4⋊Dic7C22×C4semidirect
244. Dic7⋊C4C22×C4semidirect
245. Dic7⋊C4C22×C4semidirect
251. C4×Dic7C22×C4semidirect
586. C2×C7#2373semidirect
673. C7C2×#2373semidirect
711. C2#11730921direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64422
C2×C4×C7×C22⋊C42
C2×#899822
C2×C4×C22⋊Dic72
C2×#897162
C2×#897232
C2×#897052
C2×C4×C4⋊Dic72
C2×C4×Dic7⋊C42
#117309212
C2×#894192
C2×#894252
C2×#894212
C2×#894202
C2×#23737