Finite Group Databasebeta

← C2×#11736916 #14232361

Subgroups — C2×#11736916 #14232361

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90256C211yesmaximal, characteristic, complemented
2C2×#90246C211yesmaximal, characteristic, complemented
3C2×C7×#435C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89893C211yesmaximal, characteristic, complemented
6C2×#89887C211yesmaximal, characteristic, complemented
7C22×#6391C211yesmaximal, characteristic, complemented
8#11736916C2116yesmaximal, direct product factor
9C2×#89619C211yesmaximal, characteristic, complemented
10C2×#89614C211yesmaximal, characteristic, complemented
11C2×#89507C211yesmaximal, characteristic, complemented
12C2×#89507C211yesmaximal, characteristic, complemented
13C2×#89509C211yesmaximal, characteristic, complemented
14C2×#89508C211yesmaximal, characteristic, complemented
15C2×#89483C211yesmaximal, characteristic, complemented
16C2×#89474C211yesmaximal, characteristic, complemented
17C22×#1159—21no—
18C22×C7×M16C2211yescharacteristic
19C23×C7×C8C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6502—21no—
22C2×#6493C2211yescharacteristic
23C2×#6493C2211yescharacteristic
24C2×#6493C2211yescharacteristic
25C2×#6493C2211yescharacteristic
26C2×#6489C2211yescharacteristic
27C22×C4⋊Dic7C2211yescharacteristic
28C22×C4⋊Dic7C2211yescharacteristic
29C22×C4⋊Dic7C2211yescharacteristic
30C22×D56C2211yescharacteristic
31#90256—24no—
32#90256C2218yescomplemented
33#90246—24no—
34#90246C2218yescomplemented
35C2×#6461—21no—
36C2×#6460—21no—
37C2×#6449—21no—
38C2×#6449—21no—
39C2×#6446—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×C4×D28C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×#6433C2211yescharacteristic
44C2×#6432C2211yescharacteristic
45C7×#435C2218yescomplemented
46C2×C7×C4⋊C8C2211yescharacteristic
47C2×C7×C22⋊C8C2211yescharacteristic
48C2×C7×C22⋊C8C2211yescharacteristic
49C2×C7×#97C2211yescharacteristic
50#89907C2218yescomplemented
51#89893C2218yescomplemented
52#89887C2218yescomplemented
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6392C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6392C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6391C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×#6391C2211yescharacteristic
67C2×#6391C2211yescharacteristic
68C2×#6391C2218yescomplemented
69#89619C2218yescomplemented
70#89614C2218yescomplemented
71#89509C2218yescomplemented
72#89508C2218yescomplemented
73#89507C2218yescomplemented
74#89507C2218yescomplemented
75#89483C2218yescomplemented
76#89474C2218yescomplemented
77C2×#3345—71nomaximal, Sylow
78C22×C7×D4D411yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C23×Dic7—21no—
86C23×Dic7—21no—
87C23×Dic7—21no—
88C2×#1159—28no—
89C2×#1159—48no—
90C22×D28C2311yescharacteristic
91C22×D28C2311yescharacteristic
92C22×C4×D7—21no—
93C22×C4×D7—21no—
94C22×Dic14—21no—
95C2×C7×M16—24no—
96C2×C7×M16C2314yes—
97C22×C7×C8—24no—
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2314yes—
102C22×C7×C8C2311yescharacteristic
103C4×C7×D4D414yes—
104C4×C7×D4C2314yes—
105C2×C7×C4⋊C4D411yescharacteristic
106C2×C7×C22⋊C4D411yescharacteristic
107C2×C7×C22⋊C4D411yescharacteristic
108C2×C42×C7C2311yescharacteristic
109C2×C22⋊Dic7—21no—
110#6502—28no—
111#6493—22no—
112#6493—22no—
113#6493—22no—
114#6493—22no—
115#6493C2314yes—
116#6493C2314yes—
117#6493C2314yes—
118#6493C2314yes—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125#6489—22no—
126#6489C2314yes—
127C2×C4⋊Dic7—21no—
128C2×C4⋊Dic7—21no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4⋊Dic7—22no—
132C2×C4⋊Dic7—22no—
133C2×C4⋊Dic7—22no—
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2314yes—
140C2×C4⋊Dic7C2314yes—
141C2×C4⋊Dic7C2311yescharacteristic
142C2×C4⋊Dic7C2314yes—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×C4×Dic7—21no—
146C2×D56—24no—
147C2×D56C2314yes—
148#6461—28no—
149#6460—28no—
150#6449—28no—
151#6449—28no—
152#6446—28no—
153(C22⋊D7)⋊C4—28no—
154C4×D28—22no—
155C4×D28—22no—
156C4×D28C2314yes—
157C4×D28C2314yes—
158#6433—22no—
159#6433C2314yes—
160#6432—22no—
161#6432C2314yes—
162C7×C4⋊C8C2314yes—
163C7×C22⋊C8C2314yes—
164C7×C22⋊C8C2314yes—
165C7×#97C2314yes—
166#6395C2314yes—
167#6395C2314yes—
168#6395C2314yes—
169#6395C2314yes—
170#6395C2314yes—
171#6395C2314yes—
172#6392C2314yes—
173#6392C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6391C2314yes—
177#6391C2314yes—
178#6391C2314yes—
179#6391C2314yes—
180#6391C2314yes—
181C2×#553—71no—
182C2×#547—71no—
183#3345—716no—
184C2×#501—71no—
185C2×#481—71no—
186C2×#481—71no—
187C2×#482—71no—
188C2×#480—71no—
189C2×#478—71no—
190C2×#476—71no—
191C2×#469—71no—
192C2×#466—71no—
193C2×#442—71no—
194C2×#435D711yescharacteristic, complemented
195C2×#428—71no—
196C22×#106—71no—
197C24×C7C2×D411yescharacteristic
198C24×C7C2×D411yescharacteristic
199C23×D7—21no—
200C23×D7—21no—
201C2×C7×D4—24no—
202C2×C7×D4C2×D414yes—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7—22no—
206C22×C4×C7—22no—
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D412yes—
212C22×C4×C7C2×D412yes—
213C22×C4×C7C2412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—24no—
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C2×C22⋊D7—44no—
222C2×C22⋊D7—44no—
223C2×C22⋊D7—82no—
224C22×Dic7—24no—
225C22×Dic7—24no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—24no—
233C22×Dic7—44no—
234C22×Dic7—44no—
235C22×Dic7—82no—
236#1159—432no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—22no—
240C2×D28—22no—
241C2×D28—21no—
242C2×D28—21no—
243C2×D28C2412yes—
244C2×D28C2412yes—
245C2×C4×D7—24no—
246C2×C4×D7—24no—
247C2×C4×D7—44no—
248C2×C4×D7—82no—
249C2×Dic14—24no—
250C2×Dic14—44no—
251C7×M16—28no—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8—28no—
256C2×C7×C8#4114yescomplemented
257C2×C7×C8C2412yes—
258C2×C7×C8C2412yes—
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C7×C4⋊C4C2×D414yes—
262C7×C22⋊C4C2×D414yes—
263C7×C22⋊C4C2×D414yes—
264C42×C7C2×D412yes—
265C42×C7C2412yes—
266C22⋊Dic7—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—24no—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—21no—
279C4⋊Dic7—21no—
280C4⋊Dic7—24no—
281C4⋊Dic7—24no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291C4×Dic7—24no—
292D56—28no—
293C22×#41—141no—
294C22×D8—71no—
295C22×M16C2×D711yescharacteristic
296C23×C8C2×D711yescharacteristic
297#553—78no—
298#553—144no—
299#547—78no—
300#547—144no—
301C2×C4⋊Q8—71no—
302C2×#126—141no—
303C2×#125—71no—
304C2×#123—141no—
305C2×#123—141no—
306C2×#123—141no—
307C2×C22⋊Q8—141no—
308C2×#121—71no—
309C2×#121—71no—
310C2×#121—71no—
311C2×#121—71no—
312C2×#121—141no—
313C2×C4×D4—71no—
314C2×C4×D4—71no—
315C2×C4×D4—141no—
316C2×C4×D4C2×D711yescharacteristic
317C2×#117—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321#501—78no—
322#482—78no—
323#481—78no—
324#481—78no—
325#480—78no—
326#478—78no—
327#476—78no—
328#469—78no—
329#466—78no—
330#442—78no—
331#435C2×D718yescomplemented
332#428—78no—
333C2×#107—71no—
334C2×#107—71no—
335C2×#107—71no—
336C2×#106—71no—
337C2×#106—71no—
338C2×#106—71no—
339C2×#106—71no—
340C2×#106—78no—
341C2×#106—71no—
342C2×#106—71no—
343C2×C4⋊C8C2×D711yescharacteristic
344C2×#102—71no—
345C2×#102—71no—
346C2×#102—71no—
347C2×#102—71no—
348C2×#102—71no—
349C2×#102—71no—
350C2×C22⋊C8C2×D711yescharacteristic
351C2×C22⋊C8C2×D711yescharacteristic
352C2×#97C2×D711yescharacteristic
353C23×C7—22no—
354C23×C7—22no—
355C23×C7—22no—
356C23×C7—22no—
357C23×C7—22no—
358C23×C7AGL(1,ℤ/8)14yes—
359C23×C7C22×D412yes—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—42no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×D4—28no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—24no—
376C2×C4×C7—24no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D411yescharacteristic
386C2×C4×C7C2×#4112yes—
387C2×C4×C72−1+412yes—
388C2×C4×C7C2511yescharacteristic
389C22⋊D7—48no—
390C22⋊D7—48no—
391C22⋊D7—48no—
392C22⋊D7—84no—
393C2×Dic7—22no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—48no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—48no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—84no—
408D28—22no—
409D28—22no—
410D28—22no—
411D28—22no—
412D28—42no—
413D28—42no—
414C4×D7—48no—
415C4×D7—84no—
416Dic14—48no—
417C7×C8—22no—
418C7×C8—22no—
419C7×C8—22no—
420C7×C8C2×#4114yescomplemented
421C2×#41—148no—
422C2×#41—288no—
423C22×Q8—141no—
424C22×D4—71no—
425C22×D4—71no—
426C22×D4—141no—
427C22×D4—141no—
428C22×D4—141no—
429C22×D4—141no—
430C22×D4D2811yescharacteristic
431C23×C4—141no—
432C23×C4—141no—
433C23×C4—141no—
434C23×C4—141no—
435C23×C4—141no—
436C23×C4C22×D711yescharacteristic
437C23×C4C22×D711yescharacteristic
438C2×D8—74no—
439C2×D8—144no—
440C2×M16—24no—
441C2×M16C22×D714yes—
442C22×C8—24no—
443C22×C8C22×D711yescharacteristic
444C22×C8C22×D714yes—
445C22×C8C22×D711yescharacteristic
446C22×C8C22×D711yescharacteristic
447C22×C8C22×D711yescharacteristic
448C4⋊Q8—74no—
449C4⋊Q8—142no—
450#126—148no—
451#125—74no—
452#125—142no—
453#123—148no—
454#123—148no—
455#123—148no—
456C22⋊Q8—148no—
457#121—74no—
458#121—74no—
459#121—74no—
460#121—74no—
461#121—148no—
462#121—142no—
463#121—142no—
464#121—142no—
465#121—142no—
466C4×D4—74no—
467C4×D4—74no—
468C4×D4—148no—
469C4×D4—142no—
470C4×D4—142no—
471C4×D4D2814yes—
472C4×D4C22×D714yes—
473#117—74no—
474#117—142no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—71no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
480C2×C4⋊C4—74no—
481C2×C4⋊C4—74no—
482C2×C4⋊C4—74no—
483C2×C4⋊C4—71no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—142no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4D2811yescharacteristic
494C2×C22⋊C4—141no—
495C2×C22⋊C4—141no—
496C2×C22⋊C4—141no—
497C2×C22⋊C4—141no—
498C2×C22⋊C4—141no—
499C2×C22⋊C4—141no—
500C2×C22⋊C4—141no—
501C2×C22⋊C4D2811yescharacteristic
502C2×C22⋊C4D2811yescharacteristic
503C2×C42—141no—
504C2×C42C22×D711yescharacteristic
505#107—74no—
506#107—74no—
507#107—74no—
508#106—74no—
509#106—74no—
510#106—74no—
511#106—74no—
512#106—74no—
513#106—74no—
514C4⋊C8C22×D714yes—
515#102—74no—
516#102—74no—
517#102—74no—
518#102—74no—
519#102—74no—
520#102—74no—
521C22⋊C8C22×D714yes—
522C22⋊C8C22×D714yes—
523#97C22×D714yes—
524C22×C7—28no—
525C22×C7—22no—
526C22×C7—22no—
527C22×C7—22no—
528C22×C7—22no—
529C22×C7—22no—
530C22×C7—44no—
531C22×C7#54712yes—
532C22×C7C2×AGL(1,ℤ/8)14yes—
533C22×C7C2×AGL(1,ℤ/8)12yes—
534C22×C7#57712yes—
535C22×C7C23×D411yescharacteristic
536C2×D7—42no—
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—84no—
543C2×D7—84no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—22no—
548C4×C7#54712yes—
549C4×C7C22×#4111yescharacteristic
550C4×C7C2×2−1+411yescharacteristic
551Dic7—42no—
552Dic7—42no—
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556Dic7—42no—
557C24—141no—
558C24—141no—
559C24C2×D2811yescharacteristic
560C24C2×D2811yescharacteristic
561#41—2832no—
562C2×Q8—144no—
563C2×Q8—284no—
564C2×D4—24no—
565C2×D4—72no—
566C2×D4—72no—
567C2×D4—144no—
568C2×D4—144no—
569C2×D4—144no—
570C2×D4—144no—
571C2×D4—141no—
572C2×D4—141no—
573C2×D4—142no—
574C2×D4—142no—
575C2×D4—142no—
576C2×D4—142no—
577C2×D4—284no—
578C2×D4—284no—
579C2×D4—284no—
580C2×D4—562no—
581C2×D4C2×D2814yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—144no—
587C22×C4—144no—
588C22×C4—141no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—141no—
593C22×C4—141no—
594C22×C4—144no—
595C22×C4—144no—
596C22×C4—144no—
597C22×C4—284no—
598C22×C4—284no—
599C22×C4—284no—
600C22×C4—562no—
601C22×C4—562no—
602C22×C4C2×D2812yes—
603C22×C4C2×D2812yes—
604C22×C4C2×D2811yescharacteristic
605C22×C4C2×D2811yescharacteristic
606C22×C4C2×D2811yescharacteristic
607C22×C4C2×D2811yescharacteristic
608C22×C4C23×D712yes—
609C22×C4C23×D712yes—
610C22×C4C23×D711yescharacteristic
611D8—148no—
612M16—28no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—28no—
617C2×C8#115914yescomplemented
618C2×C8C23×D712yes—
619C2×C8C23×D712yes—
620C2×C8C23×D712yes—
621C2×C8C23×D712yes—
622C4⋊C4—72no—
623C4⋊C4—72no—
624C4⋊C4—72no—
625C4⋊C4—72no—
626C4⋊C4—72no—
627C4⋊C4—72no—
628C4⋊C4—144no—
629C4⋊C4—144no—
630C4⋊C4—141no—
631C4⋊C4—141no—
632C4⋊C4—141no—
633C4⋊C4—141no—
634C4⋊C4—141no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—141no—
639C4⋊C4—144no—
640C4⋊C4C2×D2814yes—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C22⋊C4—144no—
644C22⋊C4—144no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4C2×D2814yes—
649C22⋊C4C2×D2814yes—
650C42—144no—
651C42C2×D2812yes—
652C42C23×D712yes—
653C2×C7—24no—
654C2×C7—42no—
655C2×C7#334514yescomplemented
656C2×C7C2×#54711yescharacteristic
657C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
658C2×C7C2×#57711yescharacteristic
659D7—82no—
660D7—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—142no—
667C23—142no—
668C23—282no—
669C23—282no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23—282no—
674C23#647114yes—
675C23C22×D2812yes—
676C23C22×D2812yes—
677C23C22×D2811yescharacteristic
678Q8—288no—
679D4—28no—
680D4—142no—
681D4—142no—
682D4—142no—
683D4—142no—
684D4—288no—
685D4—288no—
686D4—288no—
687D4—282no—
688D4—282no—
689D4—564no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—142no—
704C2×C4—142no—
705C2×C4—142no—
706C2×C4—288no—
707C2×C4—288no—
708C2×C4—282no—
709C2×C4—282no—
710C2×C4—282no—
711C2×C4—288no—
712C2×C4—282no—
713C2×C4—282no—
714C2×C4—282no—
715C2×C4—564no—
716C2×C4—564no—
717C2×C4C22×D2812yes—
718C2×C4C22×D2812yes—
719C2×C4C22×D2812yes—
720C2×C4C22×D2812yes—
721C2×C4C22×D2811yescharacteristic
722C2×C4C2×#115912yes—
723C2×C4#655412yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8C2×#115914yescomplemented
729C7C2×#334511yescharacteristic, complemented, Sylow
730C22—28no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—282no—
738C22—282no—
739C22—282no—
740C22—282no—
741C22—282no—
742C22—282no—
743C22—564no—
744C22—564no—
745C22#9024612yes—
746C22C2×#647114yes—
747C22C2×#647112yes—
748C22#9044212yes—
749C22C23×D2811yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—282no—
755C4—282no—
756C4—282no—
757C4—282no—
758C4—282no—
759C4—282no—
760C4#9024612yes—
761C4C22×#115911yescharacteristic
762C4C2×#655411yescharacteristic
763C2—24no—
764C2—42no—
765C2—562no—
766C2—562no—
767C2#1173691614yesdirect product factor
768C2C2×#9024611yescharacteristic
769C2C22×#647111yescharacteristic
770C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#435C2
socleC23×C7C22×D4
hypercenterC2×#435D7
hypocenterC7C2×#3345
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#90256C2semidirect
2. C2×#90246C2semidirect
3. C2×C7×#435C2semidirect
4. C2×#89907C2semidirect
5. C2×#89893C2semidirect
6. C2×#89887C2semidirect
7. C22×#6391C2semidirect
8. #11736916C2direct (N × H)
9. C2×#89619C2semidirect
10. C2×#89614C2semidirect
11. C2×#89507C2semidirect
12. C2×#89507C2semidirect
13. C2×#89509C2semidirect
14. C2×#89508C2semidirect
15. C2×#89483C2semidirect
16. C2×#89474C2semidirect
32. #90256C22semidirect
34. #90246C22semidirect
45. C7×#435C22semidirect
50. #89907C22semidirect
51. #89893C22semidirect
52. #89887C22semidirect
68. C2×#6391C22semidirect
69. #89619C22semidirect
70. #89614C22semidirect
71. #89509C22semidirect
72. #89508C22semidirect
73. #89507C22semidirect
74. #89507C22semidirect
75. #89483C22semidirect
76. #89474C22semidirect
194. C2×#435D7semidirect
256. C2×C7×C8#41semidirect
331. #435C2×D7semidirect
420. C7×C8C2×#41semidirect
617. C2×C8#1159semidirect
655. C2×C7#3345semidirect
728. C8C2×#1159semidirect
729. C7C2×#3345semidirect
767. C2#11736916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902562
C2×#902462
C2×C7×#4352
C2×#899072
C2×#898932
C2×#898872
C22×#63912
#117369162
C2×#896192
C2×#896142
C2×#895072
C2×#895092
C2×#895082
C2×#894832
C2×#894742
C2×#33457