Finite Group Databasebeta

← C2×#11737791 #14226702

Subgroups — C2×#11737791 #14226702

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×#90410C211yesmaximal, characteristic, complemented
2C2×#90252C211yesmaximal, characteristic, complemented
3C2×C7×#459C211yesmaximal, characteristic, complemented
4C2×#89931C211yesmaximal, characteristic, complemented
5C2×#89929C211yesmaximal, characteristic, complemented
6C2×#89925C211yesmaximal, characteristic, complemented
7C2×#89925C211yesmaximal, characteristic, complemented
8C2×#89847C211yesmaximal, characteristic, complemented
9C2×#89781C211yesmaximal, characteristic, complemented
10#11737791C2116yesmaximal, direct product factor
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89611C211yesmaximal, characteristic, complemented
13C2×#89552C211yesmaximal, characteristic, complemented
14C2×#89550C211yesmaximal, characteristic, complemented
15C2×#89533C211yesmaximal, characteristic, complemented
16C2×#89531C211yesmaximal, characteristic, complemented
17C22×C7×D8C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C2×C7×#127C2211yescharacteristic
20C2×C4×C7×D4C2211yescharacteristic
21C2×#6502—21no—
22C2×#6502—21no—
23C2×#6501C2211yescharacteristic
24C2×#6501C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C2×#6499C2211yescharacteristic
27C2×#6498—21no—
28C2×#6498—21no—
29C2×D4×Dic7C2211yescharacteristic
30C2×D4×Dic7C2211yescharacteristic
31C22×#1142C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C2×#6492—21no—
34C2×#6487—21no—
35C22×#1131C2211yescharacteristic
36C22×C8×D7C2211yescharacteristic
37#90410—24no—
38#90410C2218yescomplemented
39#90252—24no—
40#90252C2218yescomplemented
41C2×#6460C2211yescharacteristic
42C2×#6451C2211yescharacteristic
43C2×#6448—21no—
44C2×#6442—21no—
45C2×#6435C2211yescharacteristic
46C2×#6433C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C7×#459C2218yescomplemented
49C2×C7×C4⋊C8C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56#89931C2218yescomplemented
57#89929C2218yescomplemented
58#89925C2218yescomplemented
59#89925C2218yescomplemented
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×Dic7⋊C8C2211yescharacteristic
65C2×Dic7⋊C8C2211yescharacteristic
66#89847C2218yescomplemented
67#89781C2218yescomplemented
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89611C2218yescomplemented
72#89601C2218yescomplemented
73#89552C2218yescomplemented
74#89550C2218yescomplemented
75#89533C2218yescomplemented
76#89531C2218yescomplemented
77C2×#3257—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C22×C7×D4C2311yescharacteristic
83C23×C4×C7—21no—
84C22×C22⋊D7—21no—
85C22×C22⋊D7—21no—
86C22×C22⋊D7—21no—
87C23×Dic7—21no—
88C23×Dic7—21no—
89C22×C4×D7C2311yescharacteristic
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C2×C7×D8—42no—
93C2×C7×D8—42no—
94C2×C7×D8C2314yes—
95C2×C7×D8C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C7×#127—22no—
99C7×#127C2314yes—
100C4×C7×D4—22no—
101C4×C7×D4C2314yes—
102C2×C7×C4⋊C4C2311yescharacteristic
103C2×C7×C22⋊C4—21no—
104C2×C42×C7C2311yescharacteristic
105C2×C22⋊Dic7—21no—
106C2×C22⋊Dic7—21no—
107C2×C22⋊Dic7—21no—
108C2×C22⋊Dic7—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7—21no—
111C2×C22⋊Dic7—21no—
112#6502—28no—
113#6502—28no—
114#6501—22no—
115#6501—22no—
116#6501—22no—
117#6501C2314yes—
118#6501C2314yes—
119#6501C2314yes—
120#6499—22no—
121#6499C2314yes—
122#6498—28no—
123#6498—28no—
124D4×Dic7—22no—
125D4×Dic7—22no—
126D4×Dic7C2314yes—
127D4×Dic7C2314yes—
128C2×#1142—42no—
129C2×#1142—42no—
130C2×#1142C2314yes—
131C2×#1142C2314yes—
132#6492—28no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4D411yescharacteristic
135C2×(C2×D7)⋊C4D411yescharacteristic
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140#6487—28no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4D411yescharacteristic
146C2×Dic7⋊C4D411yescharacteristic
147C2×C4×Dic7—21no—
148C2×C4×Dic7C2311yescharacteristic
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C2×#1131—42no—
152C2×#1131C2314yes—
153C2×C8×D7—42no—
154C2×C8×D7C2314yes—
155#6460—22no—
156#6460C2314yes—
157#6451—22no—
158#6451C2314yes—
159#6448—28no—
160#6442—28no—
161#6435D414yes—
162#6435C2314yes—
163#6433—22no—
164#6433C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167C7×C4⋊C8C2314yes—
168C7×#102C2314yes—
169C7×#102C2314yes—
170#6406C2314yes—
171#6406C2314yes—
172#6406C2314yes—
173#6406C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178Dic7⋊C8C2314yes—
179Dic7⋊C8C2314yes—
180#6382C2314yes—
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×#463—71no—
197C2×#459D711yescharacteristic, complemented
198C2×#424—71no—
199C24×C7—21no—
200C24×C7—21no—
201C24×C7—21no—
202C23×D7C2×D411yescharacteristic
203C2×C7×D4—21no—
204C2×C7×D4—21no—
205C2×C7×D4—21no—
206C2×C7×D4—24no—
207C2×C7×D4—24no—
208C2×C7×D4—22no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4—22no—
212C2×C7×D4—22no—
213C2×C7×D4—22no—
214C2×C7×D4—82no—
215C2×C7×D4—82no—
216C2×C7×D4C2412yes—
217C2×C7×D4C2412yes—
218C2×C7×D4C2412yes—
219C22×C4×C7—21no—
220C22×C4×C7—24no—
221C22×C4×C7—82no—
222C22×C4×C7C2×D411yescharacteristic
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2411yescharacteristic
225C2×C22⋊D7—24no—
226C2×C22⋊D7—24no—
227C2×C22⋊D7—24no—
228C2×C22⋊D7—82no—
229C2×C22⋊D7—82no—
230C2×C22⋊D7—82no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C22×Dic7—21no—
234C22×Dic7—21no—
235C22×Dic7—24no—
236C22×Dic7—24no—
237C22×Dic7—82no—
238C22×Dic7—82no—
239C22×Dic7C2×D411yescharacteristic
240C22×Dic7C2×D411yescharacteristic
241C22×Dic7C2×D411yescharacteristic
242C2×C4×D7—22no—
243C2×C4×D7—22no—
244C2×C4×D7C2×D412yes—
245C2×C4×D7C2412yes—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—21no—
249C2×Dic14—24no—
250C2×Dic14—82no—
251C2×Dic14C2412yes—
252C7×D8—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—
261C42×C7C2×D412yes—
262C42×C7C2412yes—
263C22⋊Dic7—24no—
264C22⋊Dic7—24no—
265C22⋊Dic7—24no—
266C22⋊Dic7—24no—
267C22⋊Dic7—24no—
268C22⋊Dic7—24no—
269C22⋊Dic7—24no—
270#1142—44no—
271#1142—44no—
272(C2×D7)⋊C4—24no—
273(C2×D7)⋊C4C2×D414yes—
274(C2×D7)⋊C4C2×D414yes—
275C4⋊Dic7—21no—
276C4⋊Dic7—21no—
277C4⋊Dic7—21no—
278C4⋊Dic7—24no—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281C4⋊Dic7C2412yes—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
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×SD16—71no—
299C22×D8C2×D711yescharacteristic
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×#127C2×D711yescharacteristic
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×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#463—78no—
338#460—78no—
339#459C2×D718yescomplemented
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×#103—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102—71no—
355C2×#102C2×D711yescharacteristic
356C2×#102C2×D711yescharacteristic
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7C22×D412yes—
374C7×D4—22no—
375C7×D4—22no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—42no—
381C7×D4—42no—
382C7×D4—42no—
383C7×D4—84no—
384C7×D4—84no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
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—
399C2×Dic7—22no—
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—42no—
410C2×Dic7—84no—
411C2×Dic7—84no—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415C4×D7—24no—
416C4×D7—22no—
417C4×D7—22no—
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—21no—
429C22×D4—21no—
430C22×D4—141no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4C22×D711yescharacteristic
434C22×D4C22×D711yescharacteristic
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—71no—
438C23×C4—141no—
439C23×C4—141no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—282no—
443C2×SD16—282no—
444C2×D8—42no—
445C2×D8—42no—
446C2×D8C22×D714yes—
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—22no—
459#127C22×D714yes—
460#126—148no—
461#125—74no—
462#125—142no—
463#124—74no—
464#124—142no—
465#124—148no—
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—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—71no—
503C2×C22⋊C4—71no—
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⋊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#103—74no—
525#102—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102C22×D714yes—
530#102C22×D714yes—
531C22×C7—42no—
532C22×C7—42no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—84no—
541C22×C7—84no—
542C22×C7—84no—
543C22×C7#53712yes—
544C22×C7#57612yes—
545C22×C7#57712yes—
546C22×C7C23×D411yescharacteristic
547C2×D7—22no—
548C2×D7—22no—
549C2×D7—22no—
550C2×D7—44no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—42no—
554C4×C7#53712yes—
555C4×C7C2×H(5,𝔽2)11yescharacteristic
556C4×C7C2×2−1+411yescharacteristic
557Dic7—22no—
558Dic7—22no—
559Dic7—22no—
560Dic7—42no—
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—21no—
565C24—21no—
566C24—21no—
567C24—71no—
568C2×Q8—72no—
569C2×Q8—144no—
570C2×Q8—141no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—562no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—144no—
588C2×D4—144no—
589C2×D4—144no—
590C2×D4—562no—
591C2×D4—562no—
592C2×D4—562no—
593C2×D4C23×D712yes—
594C2×D4C23×D712yes—
595C2×D4C23×D712yes—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—71no—
599C22×C4—71no—
600C22×C4—71no—
601C22×C4—72no—
602C22×C4—72no—
603C22×C4—82no—
604C22×C4—144no—
605C22×C4—144no—
606C22×C4—142no—
607C22×C4—142no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—141no—
612C22×C4—562no—
613C22×C4—562no—
614C22×C4D4×D711yescharacteristic
615C22×C4D4×D711yescharacteristic
616C22×C4C23×D711yescharacteristic
617SD16—284no—
618SD16—284no—
619D8—44no—
620D8—44no—
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—144no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C4⋊C4—141no—
645C4⋊C4C23×D712yes—
646C22⋊C4—24no—
647C22⋊C4—74no—
648C22⋊C4—74no—
649C22⋊C4—144no—
650C22⋊C4—144no—
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—82no—
665C2×C7#325714yescomplemented
666C2×C7C2×#53711yescharacteristic
667C2×C7C2×#57611yescharacteristic
668C2×C7C2×#57711yescharacteristic
669D7—42no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—72no—
683C23—142no—
684C23—142no—
685C23—142no—
686C23C2×D4×D711yescharacteristic
687Q8—142no—
688Q8—142no—
689Q8—282no—
690Q8—564no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—84no—
701D4—84no—
702D4—564no—
703D4—564no—
704D4—564no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—72no—
710C2×C4—72no—
711C2×C4—72no—
712C2×C4—84no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—144no—
717C2×C4—142no—
718C2×C4—142no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—282no—
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—42no—
747C22—42no—
748C22—42no—
749C22—84no—
750C22—84no—
751C22—84no—
752C22—142no—
753C22—142no—
754C22—142no—
755C22—284no—
756C22#9029912yes—
757C22#9044812yes—
758C22#9046612yes—
759C22C22×D4×D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—142no—
764C4—142no—
765C4—142no—
766C4—282no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9029912yes—
771C4C2×#654811yescharacteristic
772C4C2×#655411yescharacteristic
773C2—82no—
774C2—82no—
775C2—82no—
776C2—282no—
777C2#1173779114yesdirect product factor
778C2C2×#9029911yescharacteristic
779C2C2×#9044811yescharacteristic
780C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#459C2
socleC23×C7C22×D4
hypercenterC2×#459D7
hypocenterC7C2×#3257
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#90410C2semidirect
2. C2×#90252C2semidirect
3. C2×C7×#459C2semidirect
4. C2×#89931C2semidirect
5. C2×#89929C2semidirect
6. C2×#89925C2semidirect
7. C2×#89925C2semidirect
8. C2×#89847C2semidirect
9. C2×#89781C2semidirect
10. #11737791C2direct (N × H)
11. C2×#89601C2semidirect
12. C2×#89611C2semidirect
13. C2×#89552C2semidirect
14. C2×#89550C2semidirect
15. C2×#89533C2semidirect
16. C2×#89531C2semidirect
38. #90410C22semidirect
40. #90252C22semidirect
48. C7×#459C22semidirect
56. #89931C22semidirect
57. #89929C22semidirect
58. #89925C22semidirect
59. #89925C22semidirect
66. #89847C22semidirect
67. #89781C22semidirect
71. #89611C22semidirect
72. #89601C22semidirect
73. #89552C22semidirect
74. #89550C22semidirect
75. #89533C22semidirect
76. #89531C22semidirect
197. C2×#459D7semidirect
339. #459C2×D7semidirect
665. C2×C7#3257semidirect
739. C7C2×#3257semidirect
777. C2#11737791direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904102
C2×#902522
C2×C7×#4592
C2×#899312
C2×#899292
C2×#899252
C2×#898472
C2×#897812
#117377912
C2×#896012
C2×#896112
C2×#895522
C2×#895502
C2×#895332
C2×#895312
C2×#32577