Finite Group Databasebeta

← C2×#11737960 #14226711

Subgroups — C2×#11737960 #14226711

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×#90373C211yesmaximal, characteristic, complemented
2C2×#90253C211yesmaximal, characteristic, complemented
3C2×C7×#463C211yesmaximal, characteristic, complemented
4C2×#89943C211yesmaximal, characteristic, complemented
5C2×#89935C211yesmaximal, characteristic, complemented
6C2×#89931C211yesmaximal, characteristic, complemented
7C2×#89922C211yesmaximal, characteristic, complemented
8C2×#89829C211yesmaximal, characteristic, complemented
9C2×#89779C211yesmaximal, characteristic, complemented
10#11737960C2116yesmaximal, direct product factor
11C2×#89614C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89584C211yesmaximal, characteristic, complemented
14C2×#89571C211yesmaximal, characteristic, complemented
15C2×#89547C211yesmaximal, characteristic, complemented
16C2×#89535C211yesmaximal, characteristic, complemented
17C22×C7×SD16C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#124C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×#6503C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C2×#6501C2211yescharacteristic
27C2×D4×Dic7C2211yescharacteristic
28C22×#1141C2211yescharacteristic
29C2×#6493—21no—
30C2×#6492—21no—
31C22×#1131C2211yescharacteristic
32C22×C8×D7C2211yescharacteristic
33#90373—24no—
34#90373C2218yescomplemented
35#90253—24no—
36#90253C2218yescomplemented
37C2×#6458C2211yescharacteristic
38C2×#6453C2211yescharacteristic
39C2×#6449—21no—
40C2×#6448—21no—
41C2×#6447—21no—
42C2×#6446—21no—
43C2×#6442—21no—
44C2×#6441—21no—
45C2×C4×D28C2211yescharacteristic
46C2×#6435C2211yescharacteristic
47C2×#6432C2211yescharacteristic
48C7×#463C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56#89943C2218yescomplemented
57#89935C2218yescomplemented
58#89931C2218yescomplemented
59#89922C2218yescomplemented
60C2×#6395C2211yescharacteristic
61C2×#6395C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66#89829C2218yescomplemented
67#89779C2218yescomplemented
68C2×#6381C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89614C2218yescomplemented
72#89611C2218yescomplemented
73#89584C2218yescomplemented
74#89571C2218yescomplemented
75#89547C2218yescomplemented
76#89535C2218yescomplemented
77C2×#3257—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C22×C7×D4C2311yescharacteristic
81C23×C4×C7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C22×D28—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×C4×D7C2311yescharacteristic
91C22×Dic14—21no—
92C2×C7×SD16—42no—
93C2×C7×SD16C2314yes—
94C2×C7×D8—42no—
95C2×C7×D8C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×#124—22no—
99C7×#124C2314yes—
100C4×C7×D4—22no—
101C4×C7×D4C2314yes—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C7×C22⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C42×C7C2311yescharacteristic
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110#6509—22no—
111#6509C2314yes—
112Q8×Dic7—22no—
113Q8×Dic7C2314yes—
114C2×#1143—42no—
115C2×#1143C2314yes—
116#6503—22no—
117#6503C2314yes—
118#6501—22no—
119#6501—22no—
120#6501C2314yes—
121#6501C2314yes—
122D4×Dic7—22no—
123D4×Dic7C2314yes—
124C2×#1141—42no—
125C2×#1141C2314yes—
126#6493—28no—
127#6492—28no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4D411yescharacteristic
132C2×(C2×D7)⋊C4D411yescharacteristic
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7—21no—
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7C2311yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4D411yescharacteristic
142C2×Dic7⋊C4D411yescharacteristic
143C2×C4×Dic7—21no—
144C2×C4×Dic7C2311yescharacteristic
145C22×C7⋊C8C2311yescharacteristic
146C22×C7⋊C8C2311yescharacteristic
147C2×#1131—42no—
148C2×#1131C2314yes—
149C2×C8×D7—42no—
150C2×C8×D7C2314yes—
151#6458—22no—
152#6458C2314yes—
153#6453—22no—
154#6453C2314yes—
155#6449—28no—
156#6448—28no—
157#6447—28no—
158#6446—28no—
159#6442—28no—
160#6441—28no—
161C4×D28—22no—
162C4×D28C2314yes—
163#6435D414yes—
164#6435C2314yes—
165#6432—22no—
166#6432C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#103C2314yes—
169C7×#102C2314yes—
170#6409C2314yes—
171#6406C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6395C2314yes—
175#6395C2314yes—
176#6391C2314yes—
177#6391C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
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×#463D711yescharacteristic, complemented
197C2×#459—71no—
198C2×#424—71no—
199C24×C7—21no—
200C24×C7—21no—
201C23×D7—21no—
202C23×D7C2×D411yescharacteristic
203C2×C7×Q8—21no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8C2412yes—
207C2×C7×D4—21no—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4C2412yes—
214C2×C7×D4C2412yes—
215C22×C4×C7—21no—
216C22×C4×C7—21no—
217C22×C4×C7—24no—
218C22×C4×C7—82no—
219C22×C4×C7C2×D411yescharacteristic
220C22×C4×C7C2×D411yescharacteristic
221C22×C4×C7C2411yescharacteristic
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—24no—
226C2×C22⋊D7—82no—
227C2×C22⋊D7—82no—
228C2×C22⋊D7—82no—
229C2×C22⋊D7—82no—
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—82no—
235C22×Dic7C2×D411yescharacteristic
236C22×Dic7C2×D411yescharacteristic
237C22×Dic7C2×D411yescharacteristic
238C2×D28—22no—
239C2×D28—22no—
240C2×D28—21no—
241C2×D28—24no—
242C2×D28—82no—
243C2×D28C2412yes—
244C2×C4×D7—22no—
245C2×C4×D7—22no—
246C2×C4×D7—24no—
247C2×C4×D7—82no—
248C2×C4×D7C2×D412yes—
249C2×C4×D7C2412yes—
250C2×Dic14—24no—
251C2×Dic14—82no—
252C7×SD16—44no—
253C7×D8—44no—
254C2×C7×C8—22no—
255C2×C7×C8—22no—
256C2×C7×C8C2412yes—
257C2×C7×C8C2412yes—
258C7×C4⋊C4—21no—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268#1143—44no—
269#1141—44no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4C2×D414yes—
274(C2×D7)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—24no—
278C4⋊Dic7—21no—
279C4⋊Dic7—24no—
280C4⋊Dic7—24no—
281C4⋊Dic7C2412yes—
282C4⋊Dic7C2412yes—
283C4⋊Dic7C2412yes—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4C2×D414yes—
287Dic7⋊C4C2×D414yes—
288C4×Dic7—24no—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1131—44no—
296C8×D7—44no—
297C22×SD16—71no—
298C22×SD16C2×D711yescharacteristic
299C22×D8—71no—
300C22×D8C2×D711yescharacteristic
301C22×M16—71no—
302C23×C8—71no—
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—141no—
312C2×#124C2×D711yescharacteristic
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×D4C2×D711yescharacteristic
327C2×#117—71no—
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#463C2×D718yescomplemented
338#460—78no—
339#459—78no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#106—71no—
343C2×#106—71no—
344#424—78no—
345C2×C4⋊C8—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×C4⋊C8C2×D711yescharacteristic
349C2×#103—71no—
350C2×#103C2×D711yescharacteristic
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#102C2×D711yescharacteristic
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—42no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—42no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7C22×D412yes—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—42no—
377C7×D4—22no—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—42no—
382C7×D4—42no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—42no—
388C2×C4×C7—42no—
389C2×C4×C7—84no—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7H(5,𝔽2)12yes—
394C2×C4×C72−1+412yes—
395C2×C4×C7C2511yescharacteristic
396C22⋊D7—84no—
397C22⋊D7—84no—
398C22⋊D7—84no—
399C22⋊D7—84no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—42no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—84no—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413D28—22no—
414D28—22no—
415D28—42no—
416D28—84no—
417C4×D7—24no—
418C4×D7—22no—
419C4×D7—22no—
420C4×D7—84no—
421Dic14—84no—
422C7×C8—22no—
423C7×C8—22no—
424C7⋊C8—22no—
425C7⋊C8—22no—
426C22×Q8—141no—
427C22×Q8C22×D711yescharacteristic
428C22×D4—71no—
429C22×D4—141no—
430C22×D4—141no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4—141no—
434C22×D4C22×D711yescharacteristic
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—71no—
438C23×C4—141no—
439C23×C4—141no—
440C2×SD16—42no—
441C2×SD16—74no—
442C2×SD16—282no—
443C2×SD16C22×D714yes—
444C2×D8—42no—
445C2×D8—74no—
446C2×D8—282no—
447C2×D8C22×D714yes—
448C2×M16—74no—
449C2×M16—282no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—74no—
453C22×C8—282no—
454C22×C8C22×D711yescharacteristic
455C22×C8C22×D711yescharacteristic
456C4⋊Q8—74no—
457C4⋊Q8—142no—
458#127—74no—
459#127—142no—
460#126—148no—
461#125—74no—
462#125—142no—
463#124—22no—
464#124—148no—
465#124C22×D714yes—
466#123—148no—
467#123—148no—
468#123—148no—
469C22⋊Q8—74no—
470C22⋊Q8—148no—
471C22⋊Q8—142no—
472#121—74no—
473#121—74no—
474#121—74no—
475#121—148no—
476#121—148no—
477#121—142no—
478#121—142no—
479#121—142no—
480C4×Q8—74no—
481C4×Q8—142no—
482C4×D4—22no—
483C4×D4—74no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4—142no—
487C4×D4C22×D714yes—
488#117—74no—
489#117—74no—
490C2×C4⋊C4—71no—
491C2×C4⋊C4—71no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4—141no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
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×C22⋊C4—141no—
512C2×C42—71no—
513C2×C42—141no—
514C2×C42C22×D711yescharacteristic
515#107—74no—
516#107—74no—
517#106—74no—
518#106—74no—
519C4⋊C8—74no—
520C4⋊C8—74no—
521C4⋊C8—74no—
522C4⋊C8C22×D714yes—
523#103—74no—
524#103C22×D714yes—
525#102—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102C22×D714yes—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—84no—
538C22×C7—84no—
539C22×C7#53712yes—
540C22×C7#57612yes—
541C22×C7#57712yes—
542C22×C7C23×D411yescharacteristic
543C2×D7—22no—
544C2×D7—22no—
545C2×D7—22no—
546C2×D7—44no—
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—84no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—42no—
554C4×C7—42no—
555C4×C7#53712yes—
556C4×C7C2×H(5,𝔽2)11yescharacteristic
557C4×C7C2×2−1+411yescharacteristic
558Dic7—22no—
559Dic7—22no—
560Dic7—22no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—21no—
565C24—21no—
566C24—71no—
567C24—141no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—144no—
572C2×Q8—562no—
573C2×Q8C23×D712yes—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—72no—
581C2×D4—144no—
582C2×D4—144no—
583C2×D4—144no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4—141no—
587C2×D4—142no—
588C2×D4—142no—
589C2×D4—562no—
590C2×D4—562no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4—562no—
594C2×D4C23×D712yes—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—71no—
600C22×C4—71no—
601C22×C4—71no—
602C22×C4—72no—
603C22×C4—72no—
604C22×C4—82no—
605C22×C4—144no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—144no—
612C22×C4—562no—
613C22×C4—562no—
614C22×C4D4×D711yescharacteristic
615C22×C4D4×D711yescharacteristic
616C22×C4C23×D711yescharacteristic
617SD16—44no—
618SD16—284no—
619D8—44no—
620D8—284no—
621M16—284no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—72no—
625C2×C8—72no—
626C2×C8—142no—
627C2×C8—142no—
628C2×C8—284no—
629C2×C8C23×D712yes—
630C2×C8C23×D712yes—
631C4⋊C4—21no—
632C4⋊C4—74no—
633C4⋊C4—74no—
634C4⋊C4—72no—
635C4⋊C4—72no—
636C4⋊C4—72no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—141no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C4⋊C4—144no—
645C4⋊C4C23×D712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—74no—
650C22⋊C4—74no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C22⋊C4—144no—
657C42—72no—
658C42—72no—
659C42—144no—
660C42D4×D712yes—
661C42C23×D712yes—
662C2×C7—82no—
663C2×C7—82no—
664C2×C7#325714yescomplemented
665C2×C7C2×#53711yescharacteristic
666C2×C7C2×#57611yescharacteristic
667C2×C7C2×#57711yescharacteristic
668D7—42no—
669D7—82no—
670C23—22no—
671C23—22no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—72no—
679C23—142no—
680C23—142no—
681C23—142no—
682C23—142no—
683C23—282no—
684C23—282no—
685C23—282no—
686C23C2×D4×D711yescharacteristic
687Q8—22no—
688Q8—22no—
689Q8—42no—
690Q8—564no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—142no—
698D4—142no—
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—42no—
710C2×C4—42no—
711C2×C4—72no—
712C2×C4—72no—
713C2×C4—72no—
714C2×C4—84no—
715C2×C4—142no—
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—282no—
725C2×C4—282no—
726C2×C4—282no—
727C2×C4—564no—
728C2×C4—564no—
729C2×C4C2×D4×D712yes—
730C2×C4C2×D4×D712yes—
731C2×C4C2×D4×D711yescharacteristic
732C2×C4#654812yes—
733C2×C4#655412yes—
734C2×C4C24×D711yescharacteristic
735C8—22no—
736C8—22no—
737C8—142no—
738C8—142no—
739C7C2×#325711yescharacteristic, complemented, Sylow
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—142no—
749C22—142no—
750C22—142no—
751C22—284no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—564no—
756C22#9029912yes—
757C22#9046112yes—
758C22#9046512yes—
759C22C22×D4×D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—142no—
765C4—142no—
766C4—142no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9029912yes—
771C4C2×#654811yescharacteristic
772C4C2×#655411yescharacteristic
773C2—82no—
774C2—82no—
775C2—282no—
776C2—562no—
777C2#1173796014yesdirect product factor
778C2C2×#9029911yescharacteristic
779C2C2×#9046111yescharacteristic
780C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#463C2
socleC23×C7C22×D4
hypercenterC2×#463D7
hypocenterC7C2×#3257
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#90373C2semidirect
2. C2×#90253C2semidirect
3. C2×C7×#463C2semidirect
4. C2×#89943C2semidirect
5. C2×#89935C2semidirect
6. C2×#89931C2semidirect
7. C2×#89922C2semidirect
8. C2×#89829C2semidirect
9. C2×#89779C2semidirect
10. #11737960C2direct (N × H)
11. C2×#89614C2semidirect
12. C2×#89611C2semidirect
13. C2×#89584C2semidirect
14. C2×#89571C2semidirect
15. C2×#89547C2semidirect
16. C2×#89535C2semidirect
34. #90373C22semidirect
36. #90253C22semidirect
48. C7×#463C22semidirect
56. #89943C22semidirect
57. #89935C22semidirect
58. #89931C22semidirect
59. #89922C22semidirect
66. #89829C22semidirect
67. #89779C22semidirect
71. #89614C22semidirect
72. #89611C22semidirect
73. #89584C22semidirect
74. #89571C22semidirect
75. #89547C22semidirect
76. #89535C22semidirect
196. C2×#463D7semidirect
337. #463C2×D7semidirect
664. C2×C7#3257semidirect
739. C7C2×#3257semidirect
777. C2#11737960direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903732
C2×#902532
C2×C7×#4632
C2×#899432
C2×#899352
C2×#899312
C2×#899222
C2×#898292
C2×#897792
#117379602
C2×#896142
C2×#896112
C2×#895842
C2×#895712
C2×#895472
C2×#895352
C2×#32577