Finite Group Databasebeta

← C2×#11740594 #14226613

Subgroups — C2×#11740594 #14226613

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#529C211yesmaximal, characteristic, complemented
2C2×#90170C211yesmaximal, characteristic, complemented
3#11740594C2116yesmaximal, direct product factor
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89838C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89829C211yesmaximal, characteristic, complemented
8C2×#89823C211yesmaximal, characteristic, complemented
9C2×#89820C211yesmaximal, characteristic, complemented
10C2×#89810C211yesmaximal, characteristic
11C2×#89813C211yesmaximal, characteristic, complemented
12C2×#89800C211yesmaximal, characteristic, complemented
13C2×#89794C211yesmaximal, characteristic, complemented
14C2×#89788C211yesmaximal, characteristic, complemented
15C2×#89781C211yesmaximal, characteristic, complemented
16C22×C4⋊(C7⋊C8)C211yesmaximal, characteristic, complemented
17C7×#529—24no—
18C7×#529C2218yescomplemented
19C2×C7×#126—21no—
20C2×C7×#125C2211yescharacteristic
21C2×C7×#124C2211yescharacteristic
22C2×C7×#123—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×#121C2211yescharacteristic
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×D4—21no—
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117—21no—
29C22×C42×C7C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×#6492—21no—
36C2×C4×C22⋊D7—21no—
37C2×#6487C2211yescharacteristic
38C23×C7⋊C8C2211yescharacteristic
39C23×C7⋊C8C2211yescharacteristic
40#90170—24no—
41#90170C2218yescomplemented
42C2×#6439—21no—
43C2×#6438C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C2×#6435—21no—
46C2×#6433C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C2×#6409C2211yescharacteristic
49C2×#6409C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89838C2218yescomplemented
53#89835C2218yescomplemented
54#89829C2218yescomplemented
55#89826C2218yescomplemented
56#89823C2218yescomplemented
57#89820C2218yescomplemented
58#89813C2218yescomplemented
59#89810C2218yes—
60#89800C2218yescomplemented
61#89794C2218yescomplemented
62#89788C2218yescomplemented
63#89781C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6383C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4⋊(C7⋊C8)C2218yescomplemented
77C2×#3250—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C23×C4×C7D411yescharacteristic
83C23×C4×C7D411yescharacteristic
84C23×C4×C7C2311yescharacteristic
85C22×C22⋊D7—21no—
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×Dic14C2311yescharacteristic
89C7×#126—28no—
90C7×#125—22no—
91C7×#125C2314yes—
92C7×#124—22no—
93C7×#124C2314yes—
94C7×#123—28no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8C2314yes—
97C7×#121—22no—
98C7×#121C2314yes—
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×D4—28no—
102C4×C7×D4—22no—
103C4×C7×D4C2314yes—
104C7×#117—28no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C42×C7—21no—
117C2×C42×C7D411yescharacteristic
118C2×C42×C7D411yescharacteristic
119C2×C42×C7D414yes—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2314yes—
123C2×C22⋊Dic7—21no—
124C2×#1144—42no—
125C2×#1144C2314yes—
126C2×#1143—42no—
127C2×#1143C2314yes—
128C2×#1142—42no—
129C2×#1142C2314yes—
130C2×#1141—42no—
131C2×#1141C2314yes—
132#6493—22no—
133#6493C2314yes—
134#6492—28no—
135C4×C22⋊D7—28no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×(C2×D7)⋊C4—21no—
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142#6487—22no—
143#6487C2314yes—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×C4×Dic7—21no—
149C22×C7⋊C8—42no—
150C22×C7⋊C8—42no—
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2311yescharacteristic
154C22×C7⋊C8C2311yescharacteristic
155C22×C7⋊C8C2314yes—
156C22×C7⋊C8C2314yes—
157#6439—28no—
158#6438—22no—
159#6438C2314yes—
160C4×D28—22no—
161C4×D28C2314yes—
162#6435—28no—
163#6433—22no—
164#6433C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167#6409C2314yes—
168#6409C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6384C2314yes—
172#6384C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#529—71no—
184C2×#529D711yescharacteristic, complemented
185#3250—716no—
186C2×#479—71no—
187C2×#479—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#467—71no—
191C2×#466—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#463—71no—
197C2×#463—71no—
198C22×C4⋊C8—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8C2412yes—
206C2×C7×D4—24no—
207C2×C7×D4—21no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—44no—
211C2×C7×D4C2412yes—
212C22×C4×C7—24no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—21no—
218C22×C4×C7—24no—
219C22×C4×C7—42no—
220C22×C4×C7—44no—
221C22×C4×C7C2×D411yescharacteristic
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D412yes—
227C22×C4×C7C2×D414yes—
228C22×C4×C7C2×D414yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2411yescharacteristic
231C2×C22⋊D7—24no—
232C2×C22⋊D7—44no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C2×D28—22no—
237C2×D28—22no—
238C2×D28—21no—
239C2×D28C2412yes—
240C2×C4×D7—24no—
241C2×C4×D7—44no—
242C2×Dic14—22no—
243C2×Dic14—22no—
244C2×Dic14—21no—
245C2×Dic14C2412yes—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C22⋊C4—24no—
255C7×C22⋊C4—24no—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C42×C7—24no—
260C42×C7C2×D412yes—
261C42×C7C2×D412yes—
262C42×C7C2×D414yes—
263C42×C7C2×D414yes—
264C42×C7C2412yes—
265C42×C7C2412yes—
266C22⋊Dic7—24no—
267#1144—44no—
268#1143—44no—
269#1142—44no—
270#1141—44no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283C4×Dic7—24no—
284C2×C7⋊C8—22no—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—44no—
289C2×C7⋊C8—44no—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292C2×C7⋊C8C2412yes—
293C2×C7⋊C8C2412yes—
294C22×Q16—71no—
295C22×SD16—71no—
296C22×SD16—71no—
297C22×D8—71no—
298C23×C8—71no—
299C23×C8—71no—
300#529—24no—
301#529—78no—
302#529—144no—
303#529C2×D718yescomplemented
304C2×#126—21no—
305C2×#126—141no—
306C2×#125—71no—
307C2×#125C2×D711yescharacteristic
308C2×#124—71no—
309C2×#124C2×D711yescharacteristic
310C2×#123—21no—
311C2×#123—141no—
312C2×C22⋊Q8—71no—
313C2×C22⋊Q8C2×D711yescharacteristic
314C2×#121—71no—
315C2×#121C2×D711yescharacteristic
316C2×C4×Q8—71no—
317C2×C4×Q8C2×D711yescharacteristic
318C2×C4×D4—21no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×C4×D4C2×D711yescharacteristic
322C2×#117—21no—
323C2×#117—141no—
324C22×C42C2×D711yescharacteristic
325#479—78no—
326#479—78no—
327#478—78no—
328#478—78no—
329#467—78no—
330#466—78no—
331#465—78no—
332#465—78no—
333#464—78no—
334#464—78no—
335#463—78no—
336#463—78no—
337C2×#107—71no—
338C2×#107—71no—
339C2×#106—71no—
340C2×#106—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—71no—
345C2×C4⋊C8—78no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—42no—
358C23×C7—42no—
359C23×C7—42no—
360C23×C7#13514yes—
361C23×C7C22×D412yes—
362C23×C7C22×D411yescharacteristic
363C22×D7—22no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×D4—22no—
371C7×D4—22no—
372C7×D4—48no—
373C7×D4—42no—
374C2×C4×C7—22no—
375C2×C4×C7—28no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—24no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—44no—
387C2×C4×C7—48no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7H(5,𝔽2)12yes—
398C2×C4×C72−1+412yes—
399C2×C4×C7C2511yescharacteristic
400C22⋊D7—48no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407D28—22no—
408D28—22no—
409D28—42no—
410C4×D7—48no—
411Dic14—22no—
412Dic14—22no—
413Dic14—42no—
414C7⋊C8—22no—
415C7⋊C8—22no—
416C7⋊C8—22no—
417C7⋊C8—22no—
418C22×Q8—71no—
419C22×Q8C22×D711yescharacteristic
420C22×D4—21no—
421C22×D4—71no—
422C22×D4—141no—
423C22×D4C22×D711yescharacteristic
424C23×C4—21no—
425C23×C4—141no—
426C23×C4C22⋊D711yescharacteristic
427C23×C4C22⋊D711yescharacteristic
428C23×C4C22×D711yescharacteristic
429C2×Q16—74no—
430C2×Q16—282no—
431C2×SD16—74no—
432C2×SD16—74no—
433C2×SD16—282no—
434C2×SD16—282no—
435C2×D8—74no—
436C2×D8—282no—
437C22×C8—71no—
438C22×C8—71no—
439C22×C8—71no—
440C22×C8—71no—
441C22×C8—74no—
442C22×C8—74no—
443C22×C8—282no—
444C22×C8—282no—
445#126—28no—
446#126—148no—
447#125—22no—
448#125—74no—
449#125—142no—
450#125C22×D714yes—
451#124—22no—
452#124—74no—
453#124—142no—
454#124C22×D714yes—
455#123—28no—
456#123—148no—
457C22⋊Q8—22no—
458C22⋊Q8—74no—
459C22⋊Q8—142no—
460C22⋊Q8C22×D714yes—
461#121—22no—
462#121—74no—
463#121—142no—
464#121C22×D714yes—
465C4×Q8—22no—
466C4×Q8—74no—
467C4×Q8—142no—
468C4×Q8C22×D714yes—
469C4×D4—28no—
470C4×D4—22no—
471C4×D4—74no—
472C4×D4—148no—
473C4×D4—142no—
474C4×D4C22×D714yes—
475#117—28no—
476#117—148no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C42—21no—
500C2×C42—141no—
501C2×C42C22⋊D711yescharacteristic
502C2×C42C22⋊D711yescharacteristic
503C2×C42C22⋊D714yes—
504C2×C42C22×D711yescharacteristic
505C2×C42C22×D711yescharacteristic
506C2×C42C22×D714yes—
507#107—74no—
508#107—74no—
509#106—74no—
510#106—74no—
511C4⋊C8—74no—
512C4⋊C8—74no—
513C4⋊C8—74no—
514C4⋊C8—74no—
515#103—74no—
516#103—74no—
517#103—74no—
518#103—74no—
519#102—74no—
520#102—74no—
521#102—74no—
522#102—74no—
523C22×C7—22no—
524C22×C7—28no—
525C22×C7—22no—
526C22×C7—42no—
527C22×C7—42no—
528C22×C7—42no—
529C22×C7—84no—
530C22×C7#53712yes—
531C22×C7C2×#13514yes—
532C22×C7C2×#13512yes—
533C22×C7#57512yes—
534C22×C7C23×D411yescharacteristic
535C2×D7—42no—
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—84no—
539C4×C7—22no—
540C4×C7—22no—
541C4×C7—22no—
542C4×C7—22no—
543C4×C7—22no—
544C4×C7—42no—
545C4×C7—42no—
546C4×C7—42no—
547C4×C7#53712yes—
548C4×C7C2×H(5,𝔽2)11yescharacteristic
549C4×C7C2×2−1+411yescharacteristic
550Dic7—42no—
551Dic7—42no—
552Dic7—42no—
553C24—21no—
554C24—141no—
555C24C2×C22⋊D711yescharacteristic
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—72no—
560C2×Q8—141no—
561C2×Q8—142no—
562C2×Q8—142no—
563C2×Q8C23×D712yes—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—72no—
570C2×D4—144no—
571C2×D4—142no—
572C2×D4—142no—
573C2×D4—141no—
574C2×D4—284no—
575C2×D4C23×D712yes—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—141no—
588C22×C4—144no—
589C22×C4—284no—
590C22×C4C2×C22⋊D712yes—
591C22×C4C2×C22⋊D714yes—
592C22×C4C2×C22⋊D711yescharacteristic
593C22×C4C2×C22⋊D711yescharacteristic
594C22×C4C2×C22⋊D711yescharacteristic
595C22×C4C2×C22⋊D711yescharacteristic
596C22×C4C2×C22⋊D711yescharacteristic
597C22×C4C2×C22⋊D714yes—
598C22×C4C23×D712yes—
599C22×C4C23×D711yescharacteristic
600Q16—284no—
601SD16—284no—
602SD16—284no—
603D8—284no—
604C2×C8—72no—
605C2×C8—72no—
606C2×C8—72no—
607C2×C8—72no—
608C2×C8—142no—
609C2×C8—142no—
610C2×C8—142no—
611C2×C8—142no—
612C2×C8—284no—
613C2×C8—284no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—72no—
621C4⋊C4—72no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—141no—
627C4⋊C4—141no—
628C4⋊C4C23×D712yes—
629C4⋊C4C23×D712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C22⋊C4—144no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C42—24no—
641C42—144no—
642C42C2×C22⋊D714yes—
643C42C2×C22⋊D714yes—
644C42C2×C22⋊D712yes—
645C42C2×C22⋊D712yes—
646C42C23×D712yes—
647C42C23×D712yes—
648C2×C7—24no—
649C2×C7—82no—
650C2×C7#325014yescomplemented
651C2×C7C2×#53711yescharacteristic
652C2×C7C22×#13511yescharacteristic
653C2×C7C2×#57511yescharacteristic
654D7—82no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—142no—
662C23—282no—
663C23—282no—
664C23—282no—
665C23#651314yes—
666C23C22×C22⋊D712yes—
667C23C22×C22⋊D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—142no—
672Q8—142no—
673Q8—282no—
674D4—22no—
675D4—22no—
676D4—48no—
677D4—42no—
678D4—142no—
679D4—142no—
680D4—288no—
681D4—282no—
682C2×C4—28no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—48no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—288no—
703C2×C4—282no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4#655312yes—
707C2×C4#655412yes—
708C2×C4C22×C22⋊D712yes—
709C2×C4C22×C22⋊D712yes—
710C2×C4C22×C22⋊D712yes—
711C2×C4C22×C22⋊D712yes—
712C2×C4C22×C22⋊D712yes—
713C2×C4C22×C22⋊D711yescharacteristic
714C2×C4C24×D711yescharacteristic
715C8—142no—
716C8—142no—
717C8—142no—
718C8—142no—
719C7C2×#325011yescharacteristic, complemented, Sylow
720C22—22no—
721C22—22no—
722C22—28no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—282no—
728C22—282no—
729C22—282no—
730C22—564no—
731C22C2×#651314yes—
732C22C2×#651312yes—
733C22#9051312yes—
734C22#9052412yes—
735C22C23×C22⋊D711yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—282no—
745C4—282no—
746C4—282no—
747C4#9052412yes—
748C4C2×#655311yescharacteristic
749C4C2×#655411yescharacteristic
750C2—24no—
751C2—82no—
752C2—562no—
753C2#1174059414yesdirect product factor
754C2C22×#651311yescharacteristic
755C2C2×#9051311yescharacteristic
756C2C2×#9052411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#529C2
socleC23×C7C22×D4
prime radicalC2×#89810C2
hypercenterC2×#529D7
hypocenterC7C2×#3250
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C7×#529C2semidirect
2. C2×#90170C2semidirect
3. #11740594C2direct (N × H)
4. C2×#89835C2semidirect
5. C2×#89838C2semidirect
6. C2×#89826C2semidirect
7. C2×#89829C2semidirect
8. C2×#89823C2semidirect
9. C2×#89820C2semidirect
11. C2×#89813C2semidirect
12. C2×#89800C2semidirect
13. C2×#89794C2semidirect
14. C2×#89788C2semidirect
15. C2×#89781C2semidirect
16. C22×C4⋊(C7⋊C8)C2semidirect
18. C7×#529C22semidirect
41. #90170C22semidirect
52. #89838C22semidirect
53. #89835C22semidirect
54. #89829C22semidirect
55. #89826C22semidirect
56. #89823C22semidirect
57. #89820C22semidirect
58. #89813C22semidirect
60. #89800C22semidirect
61. #89794C22semidirect
62. #89788C22semidirect
63. #89781C22semidirect
76. C2×C4⋊(C7⋊C8)C22semidirect
184. C2×#529D7semidirect
303. #529C2×D7semidirect
650. C2×C7#3250semidirect
719. C7C2×#3250semidirect
753. C2#11740594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5292
C2×#901702
#117405942
C2×#898352
C2×#898382
C2×#898262
C2×#898292
C2×#898232
C2×#898202
C2×#898102
C2×#898132
C2×#898002
C2×#897942
C2×#897882
C2×#897812
C22×C4⋊(C7⋊C8)2
C2×#32507