Finite Group Databasebeta

← C2×#11736538 #14226708

Subgroups — C2×#11736538 #14226708

Order 1792.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90225C211yesmaximal, characteristic, complemented
2C2×#90226C211yesmaximal, characteristic, complemented
3C2×C7×#424C211yesmaximal, characteristic, complemented
4C2×#89907C211yesmaximal, characteristic, complemented
5C2×#89906C211yesmaximal, characteristic, complemented
6C2×#89887C211yesmaximal, characteristic, complemented
7C2×#89886C211yesmaximal, characteristic, complemented
8#11736538C2116yesmaximal, direct product factor
9C2×#89601C211yesmaximal, characteristic, complemented
10C2×#89620C211yesmaximal, characteristic, complemented
11C2×#89619C211yesmaximal, characteristic, complemented
12C2×#89614C211yesmaximal, characteristic, complemented
13C2×#89618C211yesmaximal, characteristic, complemented
14C2×#89616C211yesmaximal, characteristic, complemented
15C2×#89616C211yesmaximal, characteristic, complemented
16C2×#89615C211yesmaximal, characteristic, complemented
17C22×C7×M16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×#117C2211yescharacteristic
20C2×#6493C2211yescharacteristic
21C2×#6493C2211yescharacteristic
22C2×#6493C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×D56C2211yescharacteristic
25C22×D56C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27C22×#1132C2211yescharacteristic
28#90226—24no—
29#90226C2218yescomplemented
30#90225—24no—
31#90225C2218yescomplemented
32C2×#6461—21no—
33C2×#6459—21no—
34C2×#6457—21no—
35C2×#6457—21no—
36C2×#6448—21no—
37C2×#6447—21no—
38C2×#6447—21no—
39C2×#6446—21no—
40C2×#6438C2211yescharacteristic
41C2×#6437C2211yescharacteristic
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C4×D28C2211yescharacteristic
45C2×#6433C2211yescharacteristic
46C2×#6432C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#424C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×C4⋊C8C2211yescharacteristic
51C2×C7×C4⋊C8C2211yescharacteristic
52C2×C7×C4⋊C8C2211yescharacteristic
53#89907C2218yescomplemented
54#89906C2218yescomplemented
55#89887C2218yescomplemented
56#89886C2218yescomplemented
57C2×#6395C2211yescharacteristic
58C2×#6395C2211yescharacteristic
59C2×#6395C2211yescharacteristic
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6395C2211yescharacteristic
63C2×#6392C2211yescharacteristic
64C2×#6392C2211yescharacteristic
65C2×#6391C2211yescharacteristic
66C2×#6391C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6390C2211yescharacteristic
69#89620C2218yescomplemented
70#89619C2218yescomplemented
71#89618C2218yescomplemented
72#89616C2218yescomplemented
73#89616C2218yescomplemented
74#89615C2218yescomplemented
75#89614C2218yescomplemented
76#89601C2218yescomplemented
77C2×#3257—71nomaximal, Sylow
78C23×C4×C7C2311yescharacteristic
79C22×C22⋊D7—21no—
80C22×C22⋊D7—21no—
81C22×C22⋊D7—21no—
82C22×D28—21no—
83C22×D28—21no—
84C22×D28C2311yescharacteristic
85C22×D28C2311yescharacteristic
86C22×D28C2311yescharacteristic
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×M16—42no—
93C2×C7×M16C2314yes—
94C22×C7×C8—42no—
95C22×C7×C8C2311yescharacteristic
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2314yes—
100C7×#117D414yes—
101C7×#117C2314yes—
102C2×C7×C4⋊C4D411yescharacteristic
103C2×C7×C4⋊C4D411yescharacteristic
104C2×C7×C22⋊C4D411yescharacteristic
105C2×C7×C22⋊C4D411yescharacteristic
106C2×C42×C7C2311yescharacteristic
107C2×C42×C7C2311yescharacteristic
108C2×C22⋊Dic7—21no—
109#6493—22no—
110#6493—22no—
111#6493—22no—
112#6493C2314yes—
113#6493C2314yes—
114#6493C2314yes—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128#6487—22no—
129#6487C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×C4×Dic7—21no—
135C2×D56—42no—
136C2×D56—42no—
137C2×D56C2314yes—
138C2×D56C2314yes—
139C2×#1132—42no—
140C2×#1132—42no—
141C2×#1132C2314yes—
142C2×#1132C2314yes—
143#6461—28no—
144#6459—28no—
145#6457—28no—
146#6457—28no—
147#6448—28no—
148#6447—28no—
149#6447—28no—
150#6446—28no—
151#6438—22no—
152#6438C2314yes—
153#6437—22no—
154#6437C2314yes—
155C4×D28—22no—
156C4×D28—22no—
157C4×D28—22no—
158C4×D28C2314yes—
159C4×D28C2314yes—
160C4×D28C2314yes—
161#6433—22no—
162#6433C2314yes—
163#6432—22no—
164#6432C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×C4⋊C8C2314yes—
168C7×C4⋊C8C2314yes—
169C7×C4⋊C8C2314yes—
170C7×C4⋊C8C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6395C2314yes—
177#6392C2314yes—
178#6392C2314yes—
179#6391C2314yes—
180#6391C2314yes—
181#6390C2314yes—
182#6390C2314yes—
183C2×#542—71no—
184C2×#540—71no—
185#3257—716no—
186C2×#479—71no—
187C2×#478—71no—
188C2×#476—71no—
189C2×#474—71no—
190C2×#469—71no—
191C2×#468—71no—
192C2×#466—71no—
193C2×#465—71no—
194C2×#460—71no—
195C2×#463—71no—
196C2×#463—71no—
197C2×#459—71no—
198C2×#424D711yescharacteristic, complemented
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C23×D7—21no—
202C23×D7—21no—
203C22×C4×C7—22no—
204C22×C4×C7—22no—
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7C2×D412yes—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2412yes—
212C22×C4×C7C2411yescharacteristic
213C2×C22⋊D7—24no—
214C2×C22⋊D7—24no—
215C2×C22⋊D7—24no—
216C2×C22⋊D7—82no—
217C2×C22⋊D7—82no—
218C2×C22⋊D7—82no—
219C22×Dic7—21no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C2×D28—22no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—22no—
228C2×D28—22no—
229C2×D28—22no—
230C2×D28—21no—
231C2×D28—21no—
232C2×D28—21no—
233C2×D28—24no—
234C2×D28—24no—
235C2×D28—82no—
236C2×D28—82no—
237C2×D28C2412yes—
238C2×D28C2412yes—
239C2×D28C2412yes—
240C2×C4×D7—24no—
241C2×C4×D7—24no—
242C2×C4×D7—24no—
243C2×C4×D7—82no—
244C2×C4×D7—82no—
245C2×C4×D7—82no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—21no—
249C2×Dic14—24no—
250C2×Dic14—82no—
251C2×Dic14C2412yes—
252C7×M16—44no—
253C2×C7×C8—22no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8—22no—
257C2×C7×C8—44no—
258C2×C7×C8C2412yes—
259C2×C7×C8C2412yes—
260C2×C7×C8C2412yes—
261C2×C7×C8C2412yes—
262C7×C4⋊C4C2×D414yes—
263C7×C4⋊C4C2×D414yes—
264C7×C22⋊C4C2×D414yes—
265C7×C22⋊C4C2×D414yes—
266C42×C7C2×D412yes—
267C42×C7C2×D412yes—
268C42×C7C2412yes—
269C42×C7C2412yes—
270C22⋊Dic7—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7—24no—
282C4⋊Dic7—21no—
283C4⋊Dic7—21no—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286C4⋊Dic7C2412yes—
287C4⋊Dic7C2412yes—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292C4×Dic7—24no—
293D56—44no—
294D56—44no—
295#1132—44no—
296#1132—44no—
297C22×SD16—71no—
298C22×SD16—71no—
299C22×D8—71no—
300C22×D8—71no—
301C22×M16C2×D711yescharacteristic
302C23×C8C2×D711yescharacteristic
303#542—78no—
304#542—144no—
305#540—78no—
306#540—144no—
307C2×C4⋊Q8—71no—
308C2×#127—71no—
309C2×#126—141no—
310C2×#125—71no—
311C2×#124—71no—
312C2×#124—141no—
313C2×#123—141no—
314C2×#123—141no—
315C2×#123—141no—
316C2×C22⋊Q8—71no—
317C2×C22⋊Q8—141no—
318C2×#121—71no—
319C2×#121—71no—
320C2×#121—71no—
321C2×#121—141no—
322C2×#121—141no—
323C2×C4×Q8—71no—
324C2×C4×D4—71no—
325C2×C4×D4—71no—
326C2×C4×D4—71no—
327C2×#117C2×D711yescharacteristic
328#479—78no—
329#478—78no—
330#476—78no—
331#474—78no—
332#469—78no—
333#468—78no—
334#466—78no—
335#465—78no—
336#463—78no—
337#463—78no—
338#460—78no—
339#459—78no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#106—71no—
343C2×#106—71no—
344#424C2×D718yescomplemented
345C2×C4⋊C8C2×D711yescharacteristic
346C2×C4⋊C8C2×D711yescharacteristic
347C2×C4⋊C8C2×D711yescharacteristic
348C2×C4⋊C8C2×D711yescharacteristic
349C2×#103—71no—
350C2×#103—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#102—71no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7C22×D412yes—
361C23×C7C22×D411yescharacteristic
362C22×D7—22no—
363C22×D7—22no—
364C22×D7—22no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7—42no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—24no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D412yes—
384C2×C4×C7C22×D412yes—
385C2×C4×C7C22×D412yes—
386C2×C4×C7C22×D412yes—
387C2×C4×C7C22×D411yescharacteristic
388C2×C4×C7H(5,𝔽2)12yes—
389C2×C4×C72−1+412yes—
390C2×C4×C7C2511yescharacteristic
391C22⋊D7—84no—
392C22⋊D7—84no—
393C22⋊D7—84no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—42no—
404D28—22no—
405D28—22no—
406D28—22no—
407D28—22no—
408D28—22no—
409D28—22no—
410D28—42no—
411D28—42no—
412D28—42no—
413D28—84no—
414D28—84no—
415C4×D7—84no—
416C4×D7—84no—
417C4×D7—84no—
418Dic14—22no—
419Dic14—22no—
420Dic14—42no—
421Dic14—84no—
422C7×C8—22no—
423C7×C8—22no—
424C7×C8—22no—
425C7×C8—22no—
426C22×Q8—71no—
427C22×Q8—141no—
428C22×D4—71no—
429C22×D4—71no—
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4—141no—
435C22×D4—141no—
436C23×C4—141no—
437C23×C4—141no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—282no—
443C2×SD16—282no—
444C2×D8—74no—
445C2×D8—74no—
446C2×D8—282no—
447C2×D8—282no—
448C2×M16—42no—
449C2×M16C22×D714yes—
450C22×C8—42no—
451C22×C8C22×D711yescharacteristic
452C22×C8C22×D711yescharacteristic
453C22×C8C22×D711yescharacteristic
454C22×C8C22×D711yescharacteristic
455C22×C8C22×D714yes—
456C4⋊Q8—74no—
457C4⋊Q8—142no—
458#127—74no—
459#127—142no—
460#126—148no—
461#125—74no—
462#125—142no—
463#124—74no—
464#124—148no—
465#124—142no—
466#123—148no—
467#123—148no—
468#123—148no—
469C22⋊Q8—74no—
470C22⋊Q8—142no—
471C22⋊Q8—148no—
472#121—74no—
473#121—74no—
474#121—74no—
475#121—142no—
476#121—142no—
477#121—142no—
478#121—148no—
479#121—148no—
480C4×Q8—74no—
481C4×Q8—142no—
482C4×D4—74no—
483C4×D4—74no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4—142no—
487C4×D4—142no—
488#117D2814yes—
489#117C22×D714yes—
490C2×C4⋊C4—71no—
491C2×C4⋊C4—71no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4D2811yescharacteristic
500C2×C4⋊C4D2811yescharacteristic
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4D2811yescharacteristic
511C2×C22⋊C4D2811yescharacteristic
512C2×C42—141no—
513C2×C42C22×D711yescharacteristic
514C2×C42C22×D711yescharacteristic
515#107—74no—
516#107—74no—
517#106—74no—
518#106—74no—
519C4⋊C8C22×D714yes—
520C4⋊C8C22×D714yes—
521C4⋊C8C22×D714yes—
522C4⋊C8C22×D714yes—
523#103—74no—
524#103—74no—
525#102—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102—74no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7#53712yes—
536C22×C7#57612yes—
537C22×C7#57712yes—
538C22×C7C23×D411yescharacteristic
539C2×D7—42no—
540C2×D7—42no—
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—42no—
545C2×D7—42no—
546C2×D7—42no—
547C2×D7—42no—
548C2×D7—84no—
549C2×D7—84no—
550C2×D7—84no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—22no—
554C4×C7—22no—
555C4×C7—22no—
556C4×C7#53712yes—
557C4×C7C2×H(5,𝔽2)11yescharacteristic
558C4×C7C2×2−1+411yescharacteristic
559Dic7—42no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—141no—
565C24—141no—
566C24—141no—
567C24C2×D2811yescharacteristic
568C2×Q8—72no—
569C2×Q8—141no—
570C2×Q8—144no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—562no—
574C2×D4—72no—
575C2×D4—72no—
576C2×D4—72no—
577C2×D4—144no—
578C2×D4—144no—
579C2×D4—144no—
580C2×D4—141no—
581C2×D4—141no—
582C2×D4—141no—
583C2×D4—144no—
584C2×D4—144no—
585C2×D4—142no—
586C2×D4—142no—
587C2×D4—142no—
588C2×D4—142no—
589C2×D4—142no—
590C2×D4—142no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4—562no—
594C2×D4—562no—
595C2×D4—562no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—141no—
599C22×C4—141no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—144no—
604C22×C4—144no—
605C22×C4—144no—
606C22×C4—562no—
607C22×C4—562no—
608C22×C4—562no—
609C22×C4C2×D2812yes—
610C22×C4C2×D2811yescharacteristic
611C22×C4C2×D2811yescharacteristic
612C22×C4C2×D2811yescharacteristic
613C22×C4C2×D2811yescharacteristic
614C22×C4C2×D2811yescharacteristic
615C22×C4C23×D712yes—
616C22×C4C23×D711yescharacteristic
617SD16—284no—
618SD16—284no—
619D8—284no—
620D8—284no—
621M16—44no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—44no—
627C2×C8C23×D712yes—
628C2×C8C23×D712yes—
629C2×C8C23×D712yes—
630C2×C8C23×D712yes—
631C4⋊C4—72no—
632C4⋊C4—72no—
633C4⋊C4—72no—
634C4⋊C4—72no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—141no—
640C4⋊C4—141no—
641C4⋊C4—141no—
642C4⋊C4—141no—
643C4⋊C4—144no—
644C4⋊C4C2×D2814yes—
645C4⋊C4C2×D2814yes—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C22⋊C4—144no—
650C22⋊C4—144no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4C2×D2814yes—
656C22⋊C4C2×D2814yes—
657C42—144no—
658C42C2×D2812yes—
659C42C2×D2812yes—
660C42C23×D712yes—
661C42C23×D712yes—
662C2×C7—42no—
663C2×C7#325714yescomplemented
664C2×C7C2×#53711yescharacteristic
665C2×C7C2×#57611yescharacteristic
666C2×C7C2×#57711yescharacteristic
667D7—82no—
668D7—82no—
669D7—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—142no—
674C23—142no—
675C23—142no—
676C23—282no—
677C23—282no—
678C23—282no—
679C23—282no—
680C23—282no—
681C23—282no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23C22×D2812yes—
686C23C22×D2811yescharacteristic
687Q8—142no—
688Q8—142no—
689Q8—282no—
690Q8—564no—
691D4—142no—
692D4—142no—
693D4—142no—
694D4—142no—
695D4—142no—
696D4—142no—
697D4—282no—
698D4—282no—
699D4—282no—
700D4—564no—
701D4—564no—
702D4—564no—
703D4—564no—
704D4—564no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—282no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—564no—
724C2×C4—564no—
725C2×C4—564no—
726C2×C4C22×D2812yes—
727C2×C4C22×D2812yes—
728C2×C4C22×D2812yes—
729C2×C4C22×D2812yes—
730C2×C4C22×D2812yes—
731C2×C4C22×D2811yescharacteristic
732C2×C4#654812yes—
733C2×C4#655112yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—22no—
737C8—22no—
738C8—22no—
739C7C2×#325711yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—282no—
745C22—282no—
746C22—282no—
747C22—282no—
748C22—282no—
749C22—282no—
750C22—282no—
751C22—282no—
752C22—282no—
753C22—564no—
754C22—564no—
755C22—564no—
756C22#9020112yes—
757C22#9044212yes—
758C22#9044312yes—
759C22C23×D2811yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—282no—
766C4—282no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9020112yes—
771C4C2×#654811yescharacteristic
772C4C2×#655111yescharacteristic
773C2—42no—
774C2—562no—
775C2—562no—
776C2—562no—
777C2#1173653814yesdirect product factor
778C2C2×#9020111yescharacteristic
779C2C2×#9044311yescharacteristic
780C2C2×#9044211yescharacteristic
subgroupG/H
centerC23C22×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#424C2
socleC23×C7C22×D4
hypercenterC2×#424D7
hypocenterC7C2×#3257
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
1. C2×#90225C2semidirect
2. C2×#90226C2semidirect
3. C2×C7×#424C2semidirect
4. C2×#89907C2semidirect
5. C2×#89906C2semidirect
6. C2×#89887C2semidirect
7. C2×#89886C2semidirect
8. #11736538C2direct (N × H)
9. C2×#89601C2semidirect
10. C2×#89620C2semidirect
11. C2×#89619C2semidirect
12. C2×#89614C2semidirect
13. C2×#89618C2semidirect
14. C2×#89616C2semidirect
15. C2×#89616C2semidirect
16. C2×#89615C2semidirect
29. #90226C22semidirect
31. #90225C22semidirect
48. C7×#424C22semidirect
53. #89907C22semidirect
54. #89906C22semidirect
55. #89887C22semidirect
56. #89886C22semidirect
69. #89620C22semidirect
70. #89619C22semidirect
71. #89618C22semidirect
72. #89616C22semidirect
73. #89616C22semidirect
74. #89615C22semidirect
75. #89614C22semidirect
76. #89601C22semidirect
198. C2×#424D7semidirect
344. #424C2×D7semidirect
663. C2×C7#3257semidirect
739. C7C2×#3257semidirect
777. C2#11736538direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902252
C2×#902262
C2×C7×#4242
C2×#899072
C2×#899062
C2×#898872
C2×#898862
#117365382
C2×#896012
C2×#896202
C2×#896192
C2×#896142
C2×#896182
C2×#896162
C2×#896152
C2×#32577