Finite Group Databasebeta

← C2×#11738757 #14222038

Subgroups — C2×#11738757 #14222038

Order 1792.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90310C211yesmaximal, characteristic, complemented
2C2×#90195C211yesmaximal, characteristic, complemented
3C2×C7×#481C211yesmaximal, characteristic, complemented
4C2×#89809C211yesmaximal, characteristic, complemented
5C2×#89739C211yesmaximal, characteristic, complemented
6#11738757C2116yesmaximal, direct product factor
7C2×#89629C211yesmaximal, characteristic, complemented
8C2×#89643C211yesmaximal, characteristic, complemented
9C2×#89641C211yesmaximal, characteristic, complemented
10C2×#89624C211yesmaximal, characteristic, complemented
11C2×#89534C211yesmaximal, characteristic, complemented
12C2×#89558C211yesmaximal, characteristic, complemented
13C2×#89529C211yesmaximal, characteristic, complemented
14C2×#89528C211yesmaximal, characteristic, complemented
15C2×#89506C211yesmaximal, characteristic, complemented
16C2×#89492C211yesmaximal, characteristic, complemented
17C22×#1157C2211yescharacteristic
18C2×C7×#121C2211yescharacteristic
19C22×C7×C4⋊C4C2211yescharacteristic
20C2×#6503C2211yescharacteristic
21C2×#6502—21no—
22C2×#6501—21no—
23C2×D4×Dic7C2211yescharacteristic
24C22×#1142C2211yescharacteristic
25C22×#1141C2211yescharacteristic
26C2×#6493C2211yescharacteristic
27C2×C4×C22⋊D7—21no—
28C2×C4×C22⋊D7—21no—
29C2×#6489C2211yescharacteristic
30C22×D56C2211yescharacteristic
31C22×#1132C2211yescharacteristic
32#90310—24no—
33#90310C2218yescomplemented
34#90195—24no—
35#90195C2218yescomplemented
36C2×#6456C2211yescharacteristic
37C2×#6456C2211yescharacteristic
38C2×#6456C2211yescharacteristic
39C2×#6455—21no—
40C2×D7×C4⋊C4—21no—
41C2×#6453C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6450C2211yescharacteristic
44C2×#6449—21no—
45C2×#6446—21no—
46C7×#481C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#106C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6390C2211yescharacteristic
55C2×#6389C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58C2×C8×Dic7C2211yescharacteristic
59#89809C2218yescomplemented
60C2×#6384C2211yescharacteristic
61#89739C2218yescomplemented
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89643C2218yescomplemented
68#89641C2218yescomplemented
69#89629C2218yescomplemented
70#89624C2218yescomplemented
71#89558C2218yescomplemented
72#89534C2218yescomplemented
73#89529C2218yescomplemented
74#89528C2218yescomplemented
75#89506C2218yescomplemented
76#89492C2218yescomplemented
77C2×#3119—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⋊D7—21no—
85C22×C22⋊D7—21no—
86C23×Dic7—21no—
87C2×#1157—22no—
88C2×#1157—24no—
89C2×#1157—24no—
90C2×#1157C2314yes—
91C22×D28C2311yescharacteristic
92C22×D28C2311yescharacteristic
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×Dic14C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C22×C7×C8C2311yescharacteristic
100C7×#121—22no—
101C7×#121C2314yes—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—22no—
104C2×C7×C4⋊C4C2314yes—
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C22⋊Dic7—21no—
110C2×C22⋊Dic7D411yescharacteristic
111C2×C22⋊Dic7D411yescharacteristic
112#6503—22no—
113#6503C2314yes—
114#6502—28no—
115#6501—28no—
116D4×Dic7—22no—
117D4×Dic7C2314yes—
118C2×#1142—24no—
119C2×#1142C2314yes—
120C2×#1141—24no—
121C2×#1141C2314yes—
122#6493—22no—
123#6493C2314yes—
124C4×C22⋊D7—28no—
125C4×C22⋊D7—28no—
126C2×(C2×D7)⋊C4—21no—
127C2×(C2×D7)⋊C4—21no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130#6489D414yes—
131#6489C2314yes—
132C2×C4⋊Dic7—21no—
133C2×C4⋊Dic7D411yescharacteristic
134C2×C4⋊Dic7D411yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×Dic7⋊C4—21no—
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C2×C4×Dic7—21no—
140C2×C4×Dic7—21no—
141C2×C4×Dic7C2311yescharacteristic
142C2×C4×Dic7C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C22×C7⋊C8C2311yescharacteristic
145C2×D56—24no—
146C2×D56C2314yes—
147C2×#1132—24no—
148C2×#1132C2314yes—
149#6456—22no—
150#6456—22no—
151#6456—22no—
152#6456C2314yes—
153#6456C2314yes—
154#6456C2314yes—
155#6455—28no—
156D7×C4⋊C4—28no—
157#6453—22no—
158#6453C2314yes—
159#6450—22no—
160#6450—22no—
161#6450C2314yes—
162#6450C2314yes—
163#6449—28no—
164#6446—28no—
165C7×#106C2314yes—
166C7×#106C2314yes—
167C7×#102C2314yes—
168C7×#102C2314yes—
169C7×C22⋊C8C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6395C2314yes—
172#6390C2314yes—
173#6389C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176C8×Dic7C2314yes—
177#6384C2314yes—
178#6383C2314yes—
179#6383C2314yes—
180#6383C2314yes—
181#6381C2314yes—
182#6381C2314yes—
183C2×#540—71no—
184C2×#520—71no—
185#3119—716no—
186C2×#481D711yescharacteristic, complemented
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#460—71no—
191C2×#459—71no—
192C2×#449—71no—
193C2×#449—71no—
194C2×#442—71no—
195C2×#440—71no—
196C2×C4×SD16—71no—
197C2×C4×D8—71no—
198C2×#433—71no—
199C24×C7—21no—
200C24×C7C2×D411yescharacteristic
201C23×D7—21no—
202C23×D7—21no—
203C2×C7×D4—24no—
204C2×C7×D4—21no—
205C2×C7×D4—22no—
206C2×C7×D4—22no—
207C2×C7×D4—82no—
208C2×C7×D4C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—24no—
215C22×C4×C7—82no—
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D412yes—
218C22×C4×C7C2412yes—
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—28no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—24no—
224C2×C22⋊D7—24no—
225C2×C22⋊D7—82no—
226C2×C22⋊D7—82no—
227C2×C22⋊D7—82no—
228C22×Dic7—21no—
229C22×Dic7—21no—
230C22×Dic7—24no—
231C22×Dic7—82no—
232C22×Dic7C2×D411yescharacteristic
233C22×Dic7C2×D411yescharacteristic
234C22×Dic7C2×D411yescharacteristic
235C22×Dic7C2×D411yescharacteristic
236#1157—216no—
237#1157—28no—
238#1157—28no—
239C2×D28—21no—
240C2×D28—22no—
241C2×D28—22no—
242C2×D28—22no—
243C2×D28—21no—
244C2×D28#4114yes—
245C2×D28C2412yes—
246C2×D28C2412yes—
247C2×C4×D7—28no—
248C2×C4×D7—24no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—24no—
252C2×C4×D7—82no—
253C2×C4×D7—82no—
254C2×C4×D7—82no—
255C2×Dic14—21no—
256C2×Dic14—22no—
257C2×Dic14#4114yes—
258C2×Dic14C2412yes—
259C2×C7×C8—22no—
260C2×C7×C8—22no—
261C2×C7×C8C2412yes—
262C2×C7×C8C2412yes—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4—24no—
267C7×C4⋊C4C2412yes—
268C7×C4⋊C4C2412yes—
269C7×C4⋊C4C2412yes—
270C7×C22⋊C4—24no—
271C22⋊Dic7—24no—
272C22⋊Dic7C2×D414yes—
273C22⋊Dic7C2×D414yes—
274#1142—28no—
275#1141—28no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280C4⋊Dic7—21no—
281C4⋊Dic7—24no—
282C4⋊Dic7C2×D414yes—
283C4⋊Dic7C2×D414yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7C2×D412yes—
291C4×Dic7C2×D412yes—
292C4×Dic7C2412yes—
293C4×Dic7C2412yes—
294C2×C7⋊C8—22no—
295C2×C7⋊C8—22no—
296C2×C7⋊C8C2412yes—
297C2×C7⋊C8C2412yes—
298D56—28no—
299#1132—28no—
300C22×#41—71no—
301C22×SD16—71no—
302C22×SD16—71no—
303C22×D8—71no—
304C22×D8—71no—
305#540—78no—
306#540—144no—
307C2×#127—71no—
308C2×#125—71no—
309C2×#123—141no—
310C2×#123—141no—
311C2×#121—71no—
312C2×#121—141no—
313C2×#121—141no—
314C2×#121C2×D711yescharacteristic
315#520—78no—
316#520—144no—
317C2×C4×Q8—71no—
318C2×C4×Q8—71no—
319C2×C4×D4—71no—
320C2×C4×D4—71no—
321C2×C4×D4—71no—
322C2×C4×D4—71no—
323C2×C4×D4—141no—
324C2×C4×D4—141no—
325C2×#117—71no—
326C2×#117—141no—
327C22×C4⋊C4—141no—
328C22×C4⋊C4C2×D711yescharacteristic
329#481C2×D718yescomplemented
330#480—78no—
331#479—78no—
332#478—78no—
333#460—78no—
334#459—78no—
335#449—78no—
336#449—78no—
337#442—78no—
338#440—78no—
339C4×SD16—78no—
340C4×D8—78no—
341#433—78no—
342C2×#107—71no—
343C2×#107—71no—
344C2×#106C2×D711yescharacteristic
345C2×#106C2×D711yescharacteristic
346C2×C4⋊C8—71no—
347C2×C4⋊C8—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#102—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102C2×D711yescharacteristic
355C2×#102C2×D711yescharacteristic
356C2×C22⋊C8—71no—
357C2×C22⋊C8C2×D711yescharacteristic
358C2×#97—71no—
359C2×C4×C8—71no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7C22×D412yes—
368C23×C7C22×D411yescharacteristic
369C22×D7—24no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—42no—
373C22×D7—42no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7—42no—
377C7×D4—22no—
378C7×D4—22no—
379C7×D4—42no—
380C7×D4—84no—
381C2×C4×C7—22no—
382C2×C4×C7—24no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7—84no—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C2×#4112yes—
395C2×C4×C7C2×#4112yes—
396C2×C4×C7C2511yescharacteristic
397C22⋊D7—216no—
398C22⋊D7—84no—
399C22⋊D7—84no—
400C22⋊D7—84no—
401C2×Dic7—24no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—42no—
409C2×Dic7—84no—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414D28—24no—
415D28—22no—
416D28—22no—
417D28—22no—
418D28—42no—
419D28C2×#4114yes—
420C4×D7—216no—
421C4×D7—84no—
422C4×D7—84no—
423C4×D7—84no—
424Dic14—24no—
425Dic14—22no—
426Dic14C2×#4114yes—
427C7×C8—22no—
428C7×C8—22no—
429C7⋊C8—22no—
430C7⋊C8—22no—
431C2×#41—74no—
432C2×#41—144no—
433C2×#41—144no—
434C2×#41—142no—
435C22×Q8—71no—
436C22×D4—21no—
437C22×D4—71no—
438C22×D4—71no—
439C22×D4—141no—
440C22×D4—141no—
441C22×D4—141no—
442C22×D4—141no—
443C22×D4C22×D711yescharacteristic
444C23×C4—21no—
445C23×C4—141no—
446C23×C4—141no—
447C23×C4—141no—
448C23×C4—141no—
449C23×C4—141no—
450C23×C4C22×D711yescharacteristic
451C2×SD16—74no—
452C2×SD16—74no—
453C2×SD16—144no—
454C2×SD16—144no—
455C2×D8—74no—
456C2×D8—74no—
457C2×D8—144no—
458C2×D8—144no—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8C22×D711yescharacteristic
462C22×C8C22×D711yescharacteristic
463#127—74no—
464#127—142no—
465#125—74no—
466#125—142no—
467#123—148no—
468#123—148no—
469#121—22no—
470#121—74no—
471#121—148no—
472#121—148no—
473#121—142no—
474#121C22×D714yes—
475C4×Q8—74no—
476C4×Q8—74no—
477C4×Q8—142no—
478C4×Q8—142no—
479C4×D4—74no—
480C4×D4—74no—
481C4×D4—74no—
482C4×D4—74no—
483C4×D4—142no—
484C4×D4—142no—
485C4×D4—142no—
486C4×D4—142no—
487C4×D4—148no—
488C4×D4—148no—
489#117—74no—
490#117—74no—
491#117—148no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—148no—
498C2×C4⋊C4—141no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4C22×D711yescharacteristic
503C2×C4⋊C4C22×D711yescharacteristic
504C2×C4⋊C4C22×D714yes—
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—71no—
508C2×C22⋊C4—71no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C42—71no—
515C2×C42—71no—
516C2×C42—141no—
517C2×C42—141no—
518#107—74no—
519#107—74no—
520#106C22×D714yes—
521#106C22×D714yes—
522C4⋊C8—74no—
523C4⋊C8—74no—
524#103—74no—
525#103—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102C22×D714yes—
531#102C22×D714yes—
532C22⋊C8—74no—
533C22⋊C8C22×D714yes—
534#97—74no—
535C4×C8—74no—
536C22×C7—22no—
537C22×C7—22no—
538C22×C7—22no—
539C22×C7—44no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—84no—
544C22×C7#52512yes—
545C22×C7#57612yes—
546C22×C7#57712yes—
547C22×C7C23×D411yescharacteristic
548C2×D7—24no—
549C2×D7—48no—
550C2×D7—42no—
551C2×D7—42no—
552C2×D7—42no—
553C2×D7—42no—
554C2×D7—42no—
555C2×D7—84no—
556C4×C7—22no—
557C4×C7—42no—
558C4×C7—42no—
559C4×C7—42no—
560C4×C7#52512yes—
561C4×C7C22×#4111yescharacteristic
562C4×C7C22×#4111yescharacteristic
563Dic7—24no—
564Dic7—22no—
565Dic7—22no—
566Dic7—22no—
567Dic7—22no—
568Dic7—42no—
569C24—21no—
570C24—141no—
571C24—141no—
572C24D4×D711yescharacteristic
573#41—148no—
574#41—148no—
575#41—1416no—
576C2×Q8—74no—
577C2×Q8—72no—
578C2×Q8—141no—
579C2×Q8—142no—
580C2×D4—24no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—74no—
585C2×D4—72no—
586C2×D4—72no—
587C2×D4—82no—
588C2×D4—144no—
589C2×D4—144no—
590C2×D4—148no—
591C2×D4—144no—
592C2×D4—144no—
593C2×D4—141no—
594C2×D4—141no—
595C2×D4—142no—
596C2×D4—142no—
597C2×D4—142no—
598C2×D4—562no—
599C2×D4—562no—
600C2×D4—562no—
601C2×D4C23×D712yes—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—71no—
609C22×C4—71no—
610C22×C4—71no—
611C22×C4—71no—
612C22×C4—82no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—144no—
616C22×C4—148no—
617C22×C4—144no—
618C22×C4—141no—
619C22×C4—144no—
620C22×C4—141no—
621C22×C4—562no—
622C22×C4—562no—
623C22×C4—562no—
624C22×C4—562no—
625C22×C4D4×D712yes—
626C22×C4D4×D711yescharacteristic
627C22×C4C23×D712yes—
628C22×C4C23×D711yescharacteristic
629SD16—148no—
630SD16—148no—
631D8—148no—
632D8—148no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—72no—
636C2×C8—72no—
637C2×C8—142no—
638C2×C8—142no—
639C2×C8C23×D712yes—
640C2×C8C23×D712yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—74no—
646C4⋊C4—74no—
647C4⋊C4—72no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—141no—
653C4⋊C4C23×D712yes—
654C4⋊C4C23×D712yes—
655C4⋊C4C23×D712yes—
656C22⋊C4—24no—
657C22⋊C4—74no—
658C22⋊C4—74no—
659C22⋊C4—144no—
660C22⋊C4—144no—
661C22⋊C4—144no—
662C22⋊C4—144no—
663C22⋊C4—144no—
664C42—72no—
665C42—72no—
666C42—72no—
667C42—72no—
668C42—144no—
669C42—144no—
670C2×C7—42no—
671C2×C7—82no—
672C2×C7#311914yescomplemented
673C2×C7C2×#52511yescharacteristic
674C2×C7C2×#57611yescharacteristic
675C2×C7C2×#57711yescharacteristic
676D7—44no—
677D7—82no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—144no—
686C23—142no—
687C23—142no—
688C23—282no—
689C23—282no—
690C23—282no—
691C23—282no—
692C23—282no—
693C23C2×D4×D712yes—
694C23C2×D4×D711yescharacteristic
695Q8—74no—
696Q8—144no—
697Q8—142no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—74no—
702D4—84no—
703D4—1416no—
704D4—144no—
705D4—142no—
706D4—142no—
707D4—142no—
708D4—282no—
709D4—564no—
710D4—564no—
711D4—564no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—72no—
723C2×C4—72no—
724C2×C4—72no—
725C2×C4—72no—
726C2×C4—84no—
727C2×C4—1416no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—144no—
733C2×C4—142no—
734C2×C4—142no—
735C2×C4—282no—
736C2×C4—564no—
737C2×C4—564no—
738C2×C4—564no—
739C2×C4—564no—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4D7×#4112yes—
743C2×C4D7×#4112yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#311911yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—144no—
759C22—282no—
760C22—288no—
761C22—282no—
762C22—282no—
763C22—282no—
764C22—282no—
765C22—564no—
766C22#9034712yes—
767C22#9045312yes—
768C22#9046512yes—
769C22C22×D4×D711yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—142no—
775C4—142no—
776C4—144no—
777C4—142no—
778C4—142no—
779C4—282no—
780C4#9034712yes—
781C4C2×D7×#4111yescharacteristic
782C4C2×D7×#4111yescharacteristic
783C2—42no—
784C2—82no—
785C2—284no—
786C2—562no—
787C2#1173875714yesdirect product factor
788C2C2×#9034711yescharacteristic
789C2C2×#9045311yescharacteristic
790C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#481C2
socleC23×C7C22×D4
hypercenterC2×#481D7
hypocenterC7C2×#3119
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#90310C2semidirect
2. C2×#90195C2semidirect
3. C2×C7×#481C2semidirect
4. C2×#89809C2semidirect
5. C2×#89739C2semidirect
6. #11738757C2direct (N × H)
7. C2×#89629C2semidirect
8. C2×#89643C2semidirect
9. C2×#89641C2semidirect
10. C2×#89624C2semidirect
11. C2×#89534C2semidirect
12. C2×#89558C2semidirect
13. C2×#89529C2semidirect
14. C2×#89528C2semidirect
15. C2×#89506C2semidirect
16. C2×#89492C2semidirect
33. #90310C22semidirect
35. #90195C22semidirect
46. C7×#481C22semidirect
59. #89809C22semidirect
61. #89739C22semidirect
67. #89643C22semidirect
68. #89641C22semidirect
69. #89629C22semidirect
70. #89624C22semidirect
71. #89558C22semidirect
72. #89534C22semidirect
73. #89529C22semidirect
74. #89528C22semidirect
75. #89506C22semidirect
76. #89492C22semidirect
186. C2×#481D7semidirect
329. #481C2×D7semidirect
672. C2×C7#3119semidirect
749. C7C2×#3119semidirect
787. C2#11738757direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903102
C2×#901952
C2×C7×#4812
C2×#898092
C2×#897392
#117387572
C2×#896292
C2×#896432
C2×#896412
C2×#896242
C2×#895342
C2×#895582
C2×#895292
C2×#895282
C2×#895062
C2×#894922
C2×#31197