Finite Group Databasebeta

← C2×#11738736 #14232203

Subgroups — C2×#11738736 #14232203

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90302C211yesmaximal, characteristic, complemented
2C2×#90198C211yesmaximal, characteristic, complemented
3C2×C7×#480C211yesmaximal, characteristic, complemented
4C2×#89810C211yesmaximal, characteristic, complemented
5C22×#6381C211yesmaximal, characteristic, complemented
6#11738736C2116yesmaximal, direct product factor
7C2×#89662C211yesmaximal, characteristic, complemented
8C2×#89654C211yesmaximal, characteristic, complemented
9C2×D7×#107C211yesmaximal, characteristic, complemented
10C2×#89646C211yesmaximal, characteristic, complemented
11C2×#89546C211yesmaximal, characteristic, complemented
12C2×#89547C211yesmaximal, characteristic, complemented
13C2×#89531C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×(C22⋊D7)⋊C8C211yesmaximal, characteristic, complemented
16C2×#89508C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×#1157—21no—
19C2×C7×#121C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×#6501C2211yescharacteristic
22C2×#6498—21no—
23C2×D4×Dic7C2211yescharacteristic
24C22×#1141C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6492—21no—
27C2×C4×C22⋊D7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C23×C7⋊C8C2211yescharacteristic
30C22×C8×D7C2211yescharacteristic
31#90302—24no—
32#90302C2218yescomplemented
33C2×#6459—21no—
34#90198—24no—
35#90198C2218yescomplemented
36C2×#6458C2211yescharacteristic
37C2×#6457—21no—
38C2×#6456C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6451C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×#6446—21no—
44C2×#6441—21no—
45C7×#480C2218yescomplemented
46C2×C7×#107C2211yescharacteristic
47C2×C7×#107C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6395C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6392C2211yescharacteristic
56C2×#6392C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89810C2218yescomplemented
60C2×#6383C2211yescharacteristic
61C2×#6381C2211yescharacteristic
62C2×#6381C2211yescharacteristic
63C2×#6381C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2218yescomplemented
67#89662C2218yescomplemented
68#89654C2218yescomplemented
69D7×#107C2218yescomplemented
70#89646C2218yescomplemented
71#89547C2218yescomplemented
72#89546C2218yescomplemented
73#89531C2218yescomplemented
74#89528C2218yescomplemented
75#89508C2218yescomplemented
76(C22⋊D7)⋊C8C2218yescomplemented
77C2×#3334—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7D411yescharacteristic
85C23×Dic7—21no—
86C23×Dic7—21no—
87C2×#1159—28no—
88C2×#1159—48no—
89C2×#1157—28no—
90C2×#1157—48no—
91C22×D28—21no—
92C22×D28C2311yescharacteristic
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7C2311yescharacteristic
97C22×Dic14—21no—
98C22×Dic14—21no—
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C7×#121—22no—
102C7×#121C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—22no—
105C2×C7×C4⋊C4C2314yes—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7D411yescharacteristic
113#6501—22no—
114#6501C2314yes—
115#6498—28no—
116D4×Dic7—22no—
117D4×Dic7C2314yes—
118C2×#1141—24no—
119C2×#1141C2314yes—
120#6493—22no—
121#6493C2314yes—
122#6492—28no—
123C4×C22⋊D7D414yes—
124C4×C22⋊D7C2314yes—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4D411yescharacteristic
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—22no—
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135C2×Dic7⋊C4—21no—
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×Dic7⋊C4D411yescharacteristic
140C2×C4×Dic7C2311yescharacteristic
141C22×C7⋊C8—24no—
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2314yes—
144C22×C7⋊C8C2311yescharacteristic
145C2×C8×D7—24no—
146C2×C8×D7C2314yes—
147#6459—28no—
148#6458—22no—
149#6458C2314yes—
150#6457—28no—
151#6456—22no—
152#6456C2314yes—
153D7×C4⋊C4—22no—
154D7×C4⋊C4—22no—
155D7×C4⋊C4C2314yes—
156D7×C4⋊C4C2314yes—
157#6451—22no—
158#6451—22no—
159#6451C2314yes—
160#6451C2314yes—
161#6446—28no—
162#6441—28no—
163C7×#107C2314yes—
164C7×#107C2314yes—
165C7×#102C2314yes—
166C7×#102C2314yes—
167C7×C22⋊C8C2314yes—
168#6406C2314yes—
169#6395C2314yes—
170#6395C2314yes—
171(C2×D7)⋊C8C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174Dic7⋊C8C2314yes—
175C8×Dic7C2314yes—
176#6383C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179#6381C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182C2×#547—71no—
183C2×#547—71no—
184#3334—716no—
185C2×#500—71no—
186C2×#480—71no—
187C2×#480—71no—
188C2×#480—71no—
189C2×#480D711yescharacteristic, complemented
190C2×#474—71no—
191C2×#474—71no—
192C2×#466—71no—
193C2×#466—71no—
194C2×C4×D8—71no—
195C2×C8×D4—71no—
196C22×#107—71no—
197C22×#107—71no—
198C24×C7—21no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C2×C7×D4—24no—
203C2×C7×D4—21no—
204C2×C7×D4—22no—
205C2×C7×D4—22no—
206C2×C7×D4—44no—
207C2×C7×D4C2412yes—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—44no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7D818yescomplemented
224C2×C22⋊D7C2×D414yes—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—24no—
229C22×Dic7—24no—
230C22×Dic7—44no—
231C22×Dic7—44no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235#1159—432no—
236#1157—432no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—24no—
240C2×D28—21no—
241C2×D28—44no—
242C2×D28C2412yes—
243C2×C4×D7—22no—
244C2×C4×D7—22no—
245C2×C4×D7—24no—
246C2×C4×D7—24no—
247C2×C4×D7—24no—
248C2×C4×D7—44no—
249C2×C4×D7—44no—
250C2×C4×D7—44no—
251C2×C4×D7C2×D412yes—
252C2×C4×D7C2412yes—
253C2×Dic14—24no—
254C2×Dic14—24no—
255C2×Dic14—44no—
256C2×Dic14—44no—
257C2×C7×C8—22no—
258C2×C7×C8—22no—
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C7×C4⋊C4—21no—
262C7×C4⋊C4—21no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—24no—
265C7×C4⋊C4C2412yes—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C22⋊C4—24no—
269C22⋊Dic7—24no—
270C22⋊Dic7—24no—
271C22⋊Dic7C2×D414yes—
272#1141—28no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4C2×D414yes—
277C4⋊Dic7—24no—
278C4⋊Dic7—21no—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7C2412yes—
282C4⋊Dic7C2412yes—
283C4⋊Dic7C2412yes—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4C2×D414yes—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—28no—
293C2×C7⋊C8#4114yescomplemented
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296C8×D7—28no—
297C22×#41—141no—
298C22×#41—141no—
299C22×D8—71no—
300C23×C8—71no—
301C23×C8—71no—
302#547—78no—
303#547—78no—
304#547—144no—
305#547—144no—
306C2×C4⋊Q8—71no—
307C2×C4⋊Q8—71no—
308C2×#123—141no—
309C2×#123—141no—
310C2×#123—141no—
311C2×#123—141no—
312C2×C22⋊Q8—141no—
313C2×C22⋊Q8—141no—
314C2×#121—71no—
315C2×#121—71no—
316C2×#121—71no—
317C2×#121C2×D711yescharacteristic
318C2×C4×D4—71no—
319C2×C4×D4—71no—
320C2×C4×D4—71no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—71no—
323C22×C4⋊C4—71no—
324C22×C4⋊C4C2×D711yescharacteristic
325#500—78no—
326#480—78no—
327#480—78no—
328#480—78no—
329#480C2×D718yescomplemented
330#474—78no—
331#474—78no—
332#466—78no—
333#466—78no—
334C4×D8—78no—
335C8×D4—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#107—78no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#107—71no—
343C2×#107—71no—
344C2×#107—78no—
345C2×#107C2×D711yescharacteristic
346C2×#107C2×D711yescharacteristic
347C2×C4⋊C8—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102C2×D711yescharacteristic
353C2×#102C2×D711yescharacteristic
354C2×C22⋊C8—71no—
355C2×C22⋊C8C2×D711yescharacteristic
356C2×C4×C8—71no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7C2×D814yes—
364C23×C7C22×D412yes—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7C2×D814yes—
373C22×D7C22×D412yes—
374C7×D4—22no—
375C7×D4—22no—
376C7×D4—48no—
377C7×D4—42no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7—42no—
388C2×C4×C7—48no—
389C2×C4×C7C22×D412yes—
390C2×C4×C7C22×D411yescharacteristic
391C2×C4×C7C2×#4112yes—
392C2×C4×C72−1+412yes—
393C2×C4×C7C2511yescharacteristic
394C22⋊D7—48no—
395C22⋊D7—48no—
396C22⋊D7C2×D8116yescomplemented
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404C2×Dic7—42no—
405C2×Dic7—48no—
406C2×Dic7—48no—
407C2×Dic7C2×D814yes—
408C2×Dic7C22×D412yes—
409C2×Dic7C22×D412yes—
410C2×Dic7C22×D412yes—
411D28—22no—
412D28—22no—
413D28—48no—
414D28—42no—
415C4×D7—24no—
416C4×D7—22no—
417C4×D7—22no—
418C4×D7—48no—
419C4×D7—48no—
420C4×D7—48no—
421Dic14—48no—
422Dic14—48no—
423C7×C8—22no—
424C7×C8—22no—
425C7⋊C8—22no—
426C7⋊C8C2×#4114yescomplemented
427C2×#41—148no—
428C2×#41—148no—
429C2×#41—288no—
430C2×#41—288no—
431C22×Q8—141no—
432C22×Q8—141no—
433C22×D4—21no—
434C22×D4—71no—
435C22×D4—71no—
436C22×D4—141no—
437C22×D4—141no—
438C22×D4—141no—
439C22×D4C22×D711yescharacteristic
440C23×C4—21no—
441C23×C4—71no—
442C23×C4—141no—
443C23×C4—141no—
444C23×C4—141no—
445C23×C4—141no—
446C23×C4—141no—
447C23×C4C22×D711yescharacteristic
448C2×D8—74no—
449C2×D8—144no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—74no—
453C22×C8—74no—
454C22×C8—144no—
455C22×C8—144no—
456C22×C8C22×D711yescharacteristic
457C22×C8C22×D711yescharacteristic
458C4⋊Q8—74no—
459C4⋊Q8—74no—
460C4⋊Q8—142no—
461C4⋊Q8—142no—
462#123—148no—
463#123—148no—
464#123—148no—
465#123—148no—
466C22⋊Q8—148no—
467C22⋊Q8—148no—
468#121—22no—
469#121—74no—
470#121—74no—
471#121—74no—
472#121—142no—
473#121—142no—
474#121—142no—
475#121C22×D714yes—
476C4×D4—74no—
477C4×D4—74no—
478C4×D4—74no—
479C4×D4—74no—
480C4×D4—142no—
481C4×D4—142no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—71no—
486C2×C4⋊C4—71no—
487C2×C4⋊C4—71no—
488C2×C4⋊C4—74no—
489C2×C4⋊C4—74no—
490C2×C4⋊C4—74no—
491C2×C4⋊C4—142no—
492C2×C4⋊C4—142no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4C22×D711yescharacteristic
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C4⋊C4C22×D711yescharacteristic
502C2×C4⋊C4C22×D714yes—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—71no—
505C2×C22⋊C4—71no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C42—71no—
512#107—74no—
513#107—74no—
514#107—74no—
515#107—74no—
516#107—74no—
517#107—74no—
518#107—74no—
519#107C22×D714yes—
520#107C22×D714yes—
521C4⋊C8—74no—
522#102—74no—
523#102—74no—
524#102—74no—
525#102—74no—
526#102C22×D714yes—
527#102C22×D714yes—
528C22⋊C8—74no—
529C22⋊C8C22×D714yes—
530C4×C8—74no—
531C22×C7—28no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—84no—
538C22×C7#54712yes—
539C22×C7C22×D814yes—
540C22×C7C22×D812yes—
541C22×C7#57812yes—
542C22×C7C23×D411yescharacteristic
543C2×D7—28no—
544C2×D7—22no—
545C2×D7—22no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—84no—
550C2×D7C22×D814yes—
551C4×C7—22no—
552C4×C7—42no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7#54712yes—
556C4×C7C22×#4111yescharacteristic
557C4×C7C2×2−1+411yescharacteristic
558Dic7—22no—
559Dic7—22no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7C22×D814yes—
564C24—21no—
565C24—71no—
566C24—141no—
567C24D4×D711yescharacteristic
568#41—2832no—
569#41—2832no—
570C2×Q8—144no—
571C2×Q8—144no—
572C2×Q8—284no—
573C2×Q8—284no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—44no—
579C2×D4—78no—
580C2×D4—74no—
581C2×D4—72no—
582C2×D4—144no—
583C2×D4—144no—
584C2×D4—144no—
585C2×D4—141no—
586C2×D4—142no—
587C2×D4—142no—
588C2×D4—284no—
589C2×D4—284no—
590C2×D4—284no—
591C2×D4C23×D712yes—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—44no—
599C22×C4—71no—
600C22×C4—71no—
601C22×C4—71no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—144no—
605C22×C4—144no—
606C22×C4—144no—
607C22×C4—144no—
608C22×C4—142no—
609C22×C4—142no—
610C22×C4—144no—
611C22×C4—141no—
612C22×C4—141no—
613C22×C4—141no—
614C22×C4—284no—
615C22×C4—284no—
616C22×C4—284no—
617C22×C4—284no—
618C22×C4—284no—
619C22×C4D4×D712yes—
620C22×C4D4×D711yescharacteristic
621C22×C4C23×D712yes—
622C22×C4C23×D711yescharacteristic
623D8—148no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—74no—
627C2×C8—72no—
628C2×C8—72no—
629C2×C8—148no—
630C2×C8—148no—
631C2×C8—142no—
632C2×C8C23×D712yes—
633C2×C8C23×D712yes—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—24no—
637C4⋊C4—21no—
638C4⋊C4—74no—
639C4⋊C4—72no—
640C4⋊C4—72no—
641C4⋊C4—72no—
642C4⋊C4—144no—
643C4⋊C4—144no—
644C4⋊C4—144no—
645C4⋊C4—144no—
646C4⋊C4—141no—
647C4⋊C4—141no—
648C4⋊C4—141no—
649C4⋊C4—144no—
650C4⋊C4C23×D712yes—
651C4⋊C4C23×D712yes—
652C4⋊C4C23×D712yes—
653C22⋊C4—24no—
654C22⋊C4—74no—
655C22⋊C4—74no—
656C22⋊C4—144no—
657C22⋊C4—144no—
658C22⋊C4—144no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C42—72no—
662C42—72no—
663C2×C7—24no—
664C2×C7—82no—
665C2×C7#333414yescomplemented
666C2×C7C2×#54711yescharacteristic
667C2×C7C23×D811yescharacteristic
668C2×C7C2×#57811yescharacteristic
669D7—24no—
670D7—82no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—74no—
678C23—72no—
679C23—142no—
680C23—142no—
681C23—142no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23D7×D814yes—
686C23C2×D4×D712yes—
687C23C2×D4×D711yescharacteristic
688Q8—288no—
689Q8—288no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—42no—
694D4—716no—
695D4—142no—
696D4—142no—
697D4—288no—
698D4—288no—
699D4—288no—
700D4—282no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—74no—
713C2×C4—72no—
714C2×C4—72no—
715C2×C4—72no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—144no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—288no—
725C2×C4—288no—
726C2×C4—288no—
727C2×C4—288no—
728C2×C4—282no—
729C2×C4—282no—
730C2×C4—282no—
731C2×C4—288no—
732C2×C4C2×D4×D712yes—
733C2×C4C2×D4×D711yescharacteristic
734C2×C4D7×#4112yes—
735C2×C4#655412yes—
736C2×C4C24×D711yescharacteristic
737C8—22no—
738C8—22no—
739C8—74no—
740C8—142no—
741C7C2×#333411yescharacteristic, complemented, Sylow
742C22—22no—
743C22—22no—
744C22—28no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—74no—
749C22—84no—
750C22—142no—
751C22—142no—
752C22—148no—
753C22—282no—
754C22—282no—
755C22—282no—
756C22—564no—
757C22#9034612yes—
758C22C2×D7×D814yes—
759C22C2×D7×D812yes—
760C22#9047012yes—
761C22C22×D4×D711yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—74no—
767C4—142no—
768C4—142no—
769C4—282no—
770C4—282no—
771C4—282no—
772C4#9034612yes—
773C4C2×D7×#4111yescharacteristic
774C4C2×#655411yescharacteristic
775C2—24no—
776C2—82no—
777C2—144no—
778C2—562no—
779C2#1173873614yesdirect product factor
780C2C2×#9034611yescharacteristic
781C2C22×D7×D811yescharacteristic
782C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#480C2
socleC23×C7C22×D4
hypercenterC2×#480D7
hypocenterC7C2×#3334
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#90302C2semidirect
2. C2×#90198C2semidirect
3. C2×C7×#480C2semidirect
4. C2×#89810C2semidirect
5. C22×#6381C2semidirect
6. #11738736C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89654C2semidirect
9. C2×D7×#107C2semidirect
10. C2×#89646C2semidirect
11. C2×#89546C2semidirect
12. C2×#89547C2semidirect
13. C2×#89531C2semidirect
14. C2×#89528C2semidirect
15. C2×(C22⋊D7)⋊C8C2semidirect
16. C2×#89508C2semidirect
32. #90302C22semidirect
35. #90198C22semidirect
45. C7×#480C22semidirect
59. #89810C22semidirect
66. C2×#6381C22semidirect
67. #89662C22semidirect
68. #89654C22semidirect
69. D7×#107C22semidirect
70. #89646C22semidirect
71. #89547C22semidirect
72. #89546C22semidirect
73. #89531C22semidirect
74. #89528C22semidirect
75. #89508C22semidirect
76. (C22⋊D7)⋊C8C22semidirect
189. C2×#480D7semidirect
223. C2×C22⋊D7D8semidirect
293. C2×C7⋊C8#41semidirect
329. #480C2×D7semidirect
396. C22⋊D7C2×D8semidirect
426. C7⋊C8C2×#41semidirect
665. C2×C7#3334semidirect
741. C7C2×#3334semidirect
779. C2#11738736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903022
C2×#901982
C2×C7×#4802
C2×#898102
C22×#63812
#117387362
C2×#896622
C2×#896542
C2×D7×#1072
C2×#896462
C2×#895462
C2×#895472
C2×#895312
C2×#895282
C2×(C22⋊D7)⋊C82
C2×#895082
C2×#33347