Finite Group Databasebeta

← C2×#11740519 #13512678

Subgroups — C2×#11740519 #13512678

Order 1792.

2614 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×C7×#126C211yesmaximal, characteristic
2#11740519C2116yesmaximal, direct product factor
3C2×#89757C211yesmaximal, characteristic, complemented
4C2×#89757C211yesmaximal, characteristic, complemented
5C2×#89753C211yesmaximal, characteristic, complemented
6C2×#89753C211yesmaximal, characteristic, complemented
7C2×#89753C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic7C211yesmaximal, characteristic, complemented
9C2×#89723C211yesmaximal, characteristic
10C2×#89723C211yesmaximal, characteristic
11C2×#89723C211yesmaximal, characteristic
12C2×#89722C211yesmaximal, characteristic
13C2×#89722C211yesmaximal, characteristic
14C2×C22⋊C4×Dic7C211yesmaximal, characteristic
15C2×#89708C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊Dic7C211yesmaximal, characteristic, complemented
17C24×Dic7C2211yescharacteristic
18C2×C7×#126C4116yescomplemented
19C2×C7×#126C2218yes—
20C22×C7×C4⋊C4C2211yescharacteristic
21C22×C7×C4⋊C4C2211yescharacteristic
22C22×C7×C4⋊C4C2211yescharacteristic
23C22×C7×C22⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C22×C22⋊Dic7C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C4⋊Dic7C2211yescharacteristic
31C22×C4⋊Dic7C2211yescharacteristic
32C22×C4⋊Dic7C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C22×C4⋊Dic7C2211yescharacteristic
35C22×C4⋊Dic7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C22×C4×Dic7C2211yescharacteristic
38C22×C4×Dic7C2211yescharacteristic
39C22×C4×Dic7C2211yescharacteristic
40C22×C4×Dic7C2211yescharacteristic
41C22×C4×Dic7C2211yescharacteristic
42C2×C7⋊#95C2211yescharacteristic
43C2×C7⋊#95C2211yescharacteristic
44C2×C7⋊#95C2211yescharacteristic
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
54#89757C2218yescomplemented
55#89757C2218yescomplemented
56#89753C2218yescomplemented
57#89753C2218yescomplemented
58#89753C2218yescomplemented
59C4⋊C4×Dic7C2218yescomplemented
60#89723C2218yes—
61#89723C2218yes—
62#89723C2218yes—
63#89722C2218yes—
64#89722C2218yes—
65C22⋊C4×Dic7C2218yes—
66#89708C2218yescomplemented
67C4×C4⋊Dic7C2218yescomplemented
68C2×#2334—71nomaximal, Sylow
69C25×C7C2311yescharacteristic
70C23×C4×C7C2311yescharacteristic
71C23×C4×C7C2311yescharacteristic
72C23×C4×C7C2311yescharacteristic
73C23×C4×C7C2311yescharacteristic
74C23×C4×C7C2311yescharacteristic
75C23×C4×C7C2311yescharacteristic
76C23×Dic7—24no—
77C23×Dic7—42no—
78C23×Dic7—42no—
79C23×Dic7C2311yescharacteristic
80C23×Dic7C2311yescharacteristic
81C23×Dic7C2311yescharacteristic
82C23×Dic7C2311yescharacteristic
83C23×Dic7C2311yescharacteristic
84C23×Dic7C2311yescharacteristic
85C23×Dic7C2311yescharacteristic
86C23×Dic7C2311yescharacteristic
87C23×Dic7C2314yes—
88C7×#126C2×C4164yescomplemented
89C2×C7×C4⋊C4C2×C418yescomplemented
90C2×C7×C4⋊C4C2×C418yescomplemented
91C2×C7×C4⋊C4C2×C418yescomplemented
92C2×C7×C4⋊C4C2314yes—
93C2×C7×C4⋊C4C2314yes—
94C2×C7×C4⋊C4C2314yes—
95C2×C7×C22⋊C4C2×C418yes—
96C2×C7×C22⋊C4C2×C418yes—
97C2×C7×C22⋊C4C2×C418yes—
98C2×C7×C22⋊C4C2314yes—
99C2×C7×C22⋊C4C2314yes—
100C2×C7×C22⋊C4C2314yes—
101C2×C42×C7C2×C418yescomplemented
102C2×C42×C7C2314yes—
103C2×C22⋊Dic7—24no—
104C2×C22⋊Dic7—42no—
105C2×C22⋊Dic7—42no—
106C2×C22⋊Dic7C2314yes—
107C2×C22⋊Dic7C2314yes—
108C2×C22⋊Dic7C2314yes—
109C2×C4⋊Dic7—24no—
110C2×C4⋊Dic7—24no—
111C2×C4⋊Dic7—24no—
112C2×C4⋊Dic7—42no—
113C2×C4⋊Dic7—42no—
114C2×C4⋊Dic7—42no—
115C2×C4⋊Dic7—42no—
116C2×C4⋊Dic7C2314yes—
117C2×C4⋊Dic7C2314yes—
118C2×C4⋊Dic7C2314yes—
119C2×C4⋊Dic7C2314yes—
120C2×C4⋊Dic7C2314yes—
121C2×C4⋊Dic7C2314yes—
122C2×C4⋊Dic7C2314yes—
123C2×C4×Dic7—24no—
124C2×C4×Dic7—42no—
125C2×C4×Dic7—42no—
126C2×C4×Dic7—42no—
127C2×C4×Dic7—42no—
128C2×C4×Dic7C2314yes—
129C2×C4×Dic7C2314yes—
130C2×C4×Dic7C2314yes—
131C2×C4×Dic7C2314yes—
132C2×C4×Dic7C2314yes—
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×#126D711yescharacteristic
146#2334—716no—
147C2×#389—71no—
148C2×#389—71no—
149C2×#388—71no—
150C2×#388—71no—
151C2×#388—71no—
152C2×#387—71no—
153C2×#387—71no—
154C2×#387—71no—
155C2×#385—71no—
156C2×#385—71no—
157C2×#382—71no—
158C2×C4×C4⋊C4—71no—
159C2×C4×C4⋊C4—71no—
160C2×C4×C22⋊C4—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×C7C22×C414yes—
183C22×C4×C7C22×C414yes—
184C22×C4×C7C22×C414yes—
185C22×C4×C7C22×C414yes—
186C22×C4×C7C22×C414yes—
187C22×C4×C7C22×C414yes—
188C22×C4×C7C2412yes—
189C22×C4×C7C2412yes—
190C22×C4×C7C2412yes—
191C22×C4×C7C2412yes—
192C22×C4×C7C2412yes—
193C22×C4×C7C2412yes—
194C22×Dic7—22no—
195C22×Dic7—22no—
196C22×Dic7—22no—
197C22×Dic7—22no—
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—28no—
217C22×Dic7—44no—
218C22×Dic7—44no—
219C22×Dic7—416no—
220C22×Dic7#4114yes—
221C22×Dic7#4114yes—
222C22×Dic7C2412yes—
223C22×Dic7C2412yes—
224C22×Dic7C2412yes—
225C22×Dic7C2412yes—
226C22×Dic7C2412yes—
227C22×Dic7C2412yes—
228C22×Dic7C2412yes—
229C22×Dic7C2412yes—
230C7×C4⋊C4C22×C4116yescomplemented
231C7×C4⋊C4C22×C4116yescomplemented
232C7×C4⋊C4C22×C4116yescomplemented
233C7×C22⋊C4C22×C4116yes—
234C7×C22⋊C4C22×C4116yes—
235C7×C22⋊C4C22×C4116yes—
236C42×C7C22×C4116yescomplemented
237C22⋊Dic7—28no—
238C22⋊Dic7—44no—
239C22⋊Dic7—44no—
240C4⋊Dic7—28no—
241C4⋊Dic7—28no—
242C4⋊Dic7—28no—
243C4⋊Dic7—44no—
244C4⋊Dic7—44no—
245C4⋊Dic7—44no—
246C4⋊Dic7—44no—
247C4×Dic7—28no—
248C4×Dic7—44no—
249C4×Dic7—44no—
250C4×Dic7—44no—
251C4×Dic7—44no—
252C24×C4—71no—
253C2×#126Dic7116yescomplemented
254C2×#126C2×D718yes—
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⋊C4C2×D711yescharacteristic
263C22×C4⋊C4C2×D711yescharacteristic
264C22×C4⋊C4C2×D711yescharacteristic
265C22×C22⋊C4—71no—
266C22×C22⋊C4—71no—
267C22×C22⋊C4—71no—
268C22×C22⋊C4C2×D711yescharacteristic
269C22×C22⋊C4C2×D711yescharacteristic
270C22×C22⋊C4C2×D711yescharacteristic
271C22×C42—71no—
272C22×C42—71no—
273C22×C42—71no—
274C22×C42—71no—
275C22×C42—71no—
276C22×C42C2×D711yescharacteristic
277#389—78no—
278#389—78no—
279#388—78no—
280#388—78no—
281#388—78no—
282#387—78no—
283#387—78no—
284#387—78no—
285#385—78no—
286#385—78no—
287#382—78no—
288C4×C4⋊C4—78no—
289C4×C4⋊C4—78no—
290C4×C22⋊C4—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×#95—71no—
302C2×#95—71no—
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×C7H(5,𝔽2)12yes—
321C23×C7H(5,𝔽2)12yes—
322C23×C72−1+412yes—
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—28no—
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×C7C23×C414yes—
344C2×C4×C7C23×C414yes—
345C2×C4×C7C23×C414yes—
346C2×C4×C7C23×C414yes—
347C2×C4×C7C23×C414yes—
348C2×C4×C7C23×C414yes—
349C2×Dic7—28no—
350C2×Dic7—28no—
351C2×Dic7—22no—
352C2×Dic7—22no—
353C2×Dic7—22no—
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—416no—
374C2×Dic7—44no—
375C2×Dic7—44no—
376C2×Dic7—44no—
377C2×Dic7—44no—
378C2×Dic7—44no—
379C2×Dic7—44no—
380C2×Dic7C2×#4114yes—
381C2×Dic7C2×#4114yes—
382C25C22×D711yescharacteristic
383C23×C4—71no—
384C23×C4—71no—
385C23×C4—71no—
386C23×C4—71no—
387C23×C4—71no—
388C23×C4—71no—
389C23×C4—71no—
390C23×C4—71no—
391C23×C4—74no—
392C23×C4—144no—
393C23×C4—282no—
394C23×C4—282no—
395C23×C4C22×D711yescharacteristic
396C23×C4C22×D711yescharacteristic
397C23×C4C22×D711yescharacteristic
398C23×C4C22×D711yescharacteristic
399C23×C4C22×D711yescharacteristic
400C23×C4C22×D711yescharacteristic
401#126C2×Dic7164yescomplemented
402C2×C4⋊C4—74no—
403C2×C4⋊C4—74no—
404C2×C4⋊C4—74no—
405C2×C4⋊C4—74no—
406C2×C4⋊C4—74no—
407C2×C4⋊C4—74no—
408C2×C4⋊C4—74no—
409C2×C4⋊C4—144no—
410C2×C4⋊C4—144no—
411C2×C4⋊C4—144no—
412C2×C4⋊C4—282no—
413C2×C4⋊C4—282no—
414C2×C4⋊C4—282no—
415C2×C4⋊C4—282no—
416C2×C4⋊C4C2×Dic718yescomplemented
417C2×C4⋊C4C2×Dic718yescomplemented
418C2×C4⋊C4C2×Dic718yescomplemented
419C2×C4⋊C4C22×D714yes—
420C2×C4⋊C4C22×D714yes—
421C2×C4⋊C4C22×D714yes—
422C2×C22⋊C4—74no—
423C2×C22⋊C4—74no—
424C2×C22⋊C4—74no—
425C2×C22⋊C4—144no—
426C2×C22⋊C4—282no—
427C2×C22⋊C4—282no—
428C2×C22⋊C4C2×Dic718yes—
429C2×C22⋊C4C2×Dic718yes—
430C2×C22⋊C4C2×Dic718yes—
431C2×C22⋊C4C22×D714yes—
432C2×C22⋊C4C22×D714yes—
433C2×C22⋊C4C22×D714yes—
434C2×C42—74no—
435C2×C42—74no—
436C2×C42—74no—
437C2×C42—74no—
438C2×C42—74no—
439C2×C42—144no—
440C2×C42—282no—
441C2×C42—282no—
442C2×C42—282no—
443C2×C42—282no—
444C2×C42C2×Dic718yescomplemented
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#95—74no—
457#95—74no—
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×C7#52014yes—
468C22×C7#52014yes—
469C22×C7#53814yes—
470C22×C7#53914yes—
471C22×C7#54114yes—
472C22×C7#54214yes—
473C22×C7C24×C411yescharacteristic
474C22×C7C22×#4111yescharacteristic
475C22×C7C22×#4111yescharacteristic
476C22×C7C2×H(5,𝔽2)11yescharacteristic
477C22×C7C2×H(5,𝔽2)11yescharacteristic
478C22×C7C2×2−1+411yescharacteristic
479C22×C7C2×2−1+411yescharacteristic
480C4×C7—24no—
481C4×C7—24no—
482C4×C7—24no—
483C4×C7—24no—
484C4×C7—24no—
485C4×C7—24no—
486Dic7—24no—
487Dic7—24no—
488Dic7—42no—
489Dic7—42no—
490Dic7—42no—
491Dic7—42no—
492Dic7—42no—
493Dic7—42no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24C22×Dic714yes—
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—74no—
516C22×C4—74no—
517C22×C4—72no—
518C22×C4—72no—
519C22×C4—72no—
520C22×C4—72no—
521C22×C4—72no—
522C22×C4—72no—
523C22×C4—72no—
524C22×C4—72no—
525C22×C4—148no—
526C22×C4—142no—
527C22×C4—142no—
528C22×C4—142no—
529C22×C4—142no—
530C22×C4—142no—
531C22×C4—142no—
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—284no—
549C22×C4—284no—
550C22×C4—2816no—
551C22×C4C22×Dic714yes—
552C22×C4C22×Dic714yes—
553C22×C4C22×Dic714yes—
554C22×C4C22×Dic714yes—
555C22×C4C22×Dic714yes—
556C22×C4C22×Dic714yes—
557C22×C4C23×D712yes—
558C22×C4C23×D712yes—
559C22×C4C23×D712yes—
560C22×C4C23×D712yes—
561C22×C4C23×D712yes—
562C22×C4C23×D712yes—
563C4⋊C4—148no—
564C4⋊C4—148no—
565C4⋊C4—148no—
566C4⋊C4—284no—
567C4⋊C4—284no—
568C4⋊C4—284no—
569C4⋊C4—284no—
570C4⋊C4C22×Dic7116yescomplemented
571C4⋊C4C22×Dic7116yescomplemented
572C4⋊C4C22×Dic7116yescomplemented
573C22⋊C4—148no—
574C22⋊C4—284no—
575C22⋊C4—284no—
576C22⋊C4C22×Dic7116yes—
577C22⋊C4C22×Dic7116yes—
578C22⋊C4C22×Dic7116yes—
579C42—148no—
580C42—284no—
581C42—284no—
582C42—284no—
583C42—284no—
584C42C22×Dic7116yescomplemented
585C2×C7—44no—
586C2×C7#233418yescomplemented
587C2×C7C2×C4×#4111yescharacteristic
588C2×C7C2×#52011yescharacteristic
589C2×C7C2×#52011yescharacteristic
590C2×C7C2×#53811yescharacteristic
591C2×C7C2×#53911yescharacteristic
592C2×C7C2×#54111yescharacteristic
593C2×C7C2×#54211yescharacteristic
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—
607C23D7×#4112yes—
608C23D7×#4112yes—
609C23#655312yes—
610C23#655312yes—
611C23#655412yes—
612C23#655412yes—
613C23C23×Dic714yes—
614C23C23×Dic712yes—
615C23C24×D711yescharacteristic
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
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—74no—
635C2×C4—74no—
636C2×C4—148no—
637C2×C4—148no—
638C2×C4—142no—
639C2×C4—142no—
640C2×C4—142no—
641C2×C4—142no—
642C2×C4—142no—
643C2×C4—142no—
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—2816no—
661C2×C4—284no—
662C2×C4—284no—
663C2×C4—284no—
664C2×C4—284no—
665C2×C4—284no—
666C2×C4—284no—
667C2×C4C23×Dic714yes—
668C2×C4C23×Dic714yes—
669C2×C4C23×Dic714yes—
670C2×C4C23×Dic714yes—
671C2×C4C23×Dic714yes—
672C2×C4C23×Dic714yes—
673C7C2×#233411yescharacteristic, complemented, Sylow
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#9039214yes—
683C22#9039514yes—
684C22#9039814yes—
685C22#9040114yes—
686C22#41×Dic714yes—
687C22#9051814yes—
688C22#9051814yes—
689C22C2×D7×#4111yescharacteristic
690C22C2×D7×#4111yescharacteristic
691C22C2×#655311yescharacteristic
692C22C2×#655311yescharacteristic
693C22C2×#655411yescharacteristic
694C22C2×#655411yescharacteristic
695C22C24×Dic711yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—144no—
703C4—144no—
704C4—282no—
705C4—282no—
706C4—282no—
707C4—282no—
708C4—282no—
709C4—282no—
710C2—44no—
711C2#1174051918yesdirect product factor
712C2C2×#9039211yescharacteristic
713C2C2×#9040111yescharacteristic
714C2C2×#9039511yescharacteristic
715C2C2×#9039811yescharacteristic
716C2C2×#41×Dic711yescharacteristic
717C2C2×#9051811yescharacteristic
718C2C2×#9051811yescharacteristic
subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC22×C7×#126C2
socleC24×C7C24
prime radicalC25×C7C23
cosocleC23×C7C25
hypercenterC22×#126D7
hypocenterC7C2×#2334
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
2. #11740519C2direct (N × H)
3. C2×#89757C2semidirect
4. C2×#89757C2semidirect
5. C2×#89753C2semidirect
6. C2×#89753C2semidirect
7. C2×#89753C2semidirect
8. C2×C4⋊C4×Dic7C2semidirect
15. C2×#89708C2semidirect
16. C2×C4×C4⋊Dic7C2semidirect
18. C2×C7×#126C4semidirect
54. #89757C22semidirect
55. #89757C22semidirect
56. #89753C22semidirect
57. #89753C22semidirect
58. #89753C22semidirect
59. C4⋊C4×Dic7C22semidirect
66. #89708C22semidirect
67. C4×C4⋊Dic7C22semidirect
88. C7×#126C2×C4semidirect
89. C2×C7×C4⋊C4C2×C4semidirect
90. C2×C7×C4⋊C4C2×C4semidirect
91. C2×C7×C4⋊C4C2×C4semidirect
101. C2×C42×C7C2×C4semidirect
230. C7×C4⋊C4C22×C4semidirect
231. C7×C4⋊C4C22×C4semidirect
232. C7×C4⋊C4C22×C4semidirect
236. C42×C7C22×C4semidirect
253. C2×#126Dic7semidirect
401. #126C2×Dic7semidirect
416. C2×C4⋊C4C2×Dic7semidirect
417. C2×C4⋊C4C2×Dic7semidirect
418. C2×C4⋊C4C2×Dic7semidirect
444. C2×C42C2×Dic7semidirect
570. C4⋊C4C22×Dic7semidirect
571. C4⋊C4C22×Dic7semidirect
572. C4⋊C4C22×Dic7semidirect
584. C42C22×Dic7semidirect
586. C2×C7#2334semidirect
673. C7C2×#2334semidirect
711. C2#11740519direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C7×#1262
#117405192
C2×#897572
C2×#897532
C2×C4⋊C4×Dic72
C2×#897232
C2×#897222
C2×C22⋊C4×Dic72
C2×#897082
C2×C4×C4⋊Dic72
C2×#23347