Finite Group Databasebeta

← C2×#11737761 #14222040

Subgroups — C2×#11737761 #14222040

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×#90410C211yesmaximal, characteristic, complemented
2C2×#90237C211yesmaximal, characteristic, complemented
3C2×C7×#459C211yesmaximal, characteristic, complemented
4C2×#89930C211yesmaximal, characteristic, complemented
5C2×#89930C211yesmaximal, characteristic, complemented
6C2×#89924C211yesmaximal, characteristic, complemented
7C2×D8×Dic7C211yesmaximal, characteristic, complemented
8C2×#89847C211yesmaximal, characteristic, complemented
9C2×#89781C211yesmaximal, characteristic, complemented
10#11737761C2116yesmaximal, direct product factor
11C2×#89601C211yesmaximal, characteristic, complemented
12C2×#89612C211yesmaximal, characteristic, complemented
13C2×#89549C211yesmaximal, characteristic, complemented
14C2×#89546C211yesmaximal, characteristic, complemented
15C2×#89529C211yesmaximal, characteristic, complemented
16C2×#89530C211yesmaximal, characteristic, complemented
17C22×#1159C2211yescharacteristic
18C22×C7×D8C2211yescharacteristic
19C22×C7×D8C2211yescharacteristic
20C2×C7×#127C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×#6502—21no—
23C2×#6502—21no—
24C2×#6501C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C2×#6498—21no—
27C2×#6498—21no—
28C2×D4×Dic7C2211yescharacteristic
29C2×D4×Dic7C2211yescharacteristic
30C2×D4×Dic7C2211yescharacteristic
31C22×#1142C2211yescharacteristic
32C22×#1142C2211yescharacteristic
33C2×C4×C22⋊D7—21no—
34C22×Dic7⋊C4—21no—
35#90410—24no—
36#90410C2218yescomplemented
37#90237—24no—
38#90237C2218yescomplemented
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×#6450C2211yescharacteristic
41C2×(C22⋊D7)⋊C4—21no—
42C2×#6440—21no—
43C2×#6435C2211yescharacteristic
44C2×#6433C2211yescharacteristic
45C2×C4×Dic14C2211yescharacteristic
46C7×#459C2218yescomplemented
47C2×C7×C4⋊C8C2211yescharacteristic
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89930C2218yescomplemented
55#89930C2218yescomplemented
56#89924C2218yescomplemented
57D8×Dic7C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×(C2×D7)⋊C8C2211yescharacteristic
60C2×#6392C2211yescharacteristic
61C2×#6391C2211yescharacteristic
62C2×#6390C2211yescharacteristic
63C2×#6390C2211yescharacteristic
64C2×#6389C2211yescharacteristic
65C2×C8×Dic7C2211yescharacteristic
66#89847C2218yescomplemented
67#89781C2218yescomplemented
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×C4⋊(C7⋊C8)C2211yescharacteristic
71#89612C2218yescomplemented
72#89601C2218yescomplemented
73#89549C2218yescomplemented
74#89546C2218yescomplemented
75#89530C2218yescomplemented
76#89529C2218yescomplemented
77C2×#3119—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—
89C23×Dic7—21no—
90C23×Dic7—21no—
91C2×#1159—24no—
92C2×#1159—22no—
93C2×#1159—24no—
94C2×#1159C2314yes—
95C22×C4×D7—21no—
96C22×C4×D7C2311yescharacteristic
97C22×Dic14C2311yescharacteristic
98C2×C7×D8—24no—
99C2×C7×D8—24no—
100C2×C7×D8C2314yes—
101C2×C7×D8C2314yes—
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C7×#127—22no—
105C7×#127C2314yes—
106C4×C7×D4—22no—
107C4×C7×D4C2314yes—
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C22⋊C4—21no—
110C2×C42×C7C2311yescharacteristic
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116#6502—28no—
117#6502—28no—
118#6501—22no—
119#6501—22no—
120#6501C2314yes—
121#6501C2314yes—
122#6498—28no—
123#6498—28no—
124D4×Dic7—22no—
125D4×Dic7—22no—
126D4×Dic7—22no—
127D4×Dic7C2314yes—
128D4×Dic7C2314yes—
129D4×Dic7C2314yes—
130C2×#1142—24no—
131C2×#1142—24no—
132C2×#1142C2314yes—
133C2×#1142C2314yes—
134C4×C22⋊D7—28no—
135C2×(C2×D7)⋊C4D411yescharacteristic
136C2×(C2×D7)⋊C4D411yescharacteristic
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139C2×C4⋊Dic7C2311yescharacteristic
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—28no—
146C2×Dic7⋊C4D411yescharacteristic
147C2×Dic7⋊C4D411yescharacteristic
148C2×C4×Dic7—21no—
149C2×C4×Dic7—21no—
150C2×C4×Dic7C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153D7×C4⋊C4—22no—
154D7×C4⋊C4C2314yes—
155#6450—22no—
156#6450C2314yes—
157(C22⋊D7)⋊C4—28no—
158#6440—28no—
159#6435D414yes—
160#6435C2314yes—
161#6433—22no—
162#6433C2314yes—
163C4×Dic14—22no—
164C4×Dic14C2314yes—
165C7×C4⋊C8C2314yes—
166C7×#102C2314yes—
167C7×#102C2314yes—
168#6406C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6406C2314yes—
172(C2×D7)⋊C8C2314yes—
173(C2×D7)⋊C8C2314yes—
174#6392C2314yes—
175#6391C2314yes—
176#6390C2314yes—
177#6390C2314yes—
178#6389C2314yes—
179C8×Dic7C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#540—71no—
184C2×#520—71no—
185#3119—716no—
186C2×#481—71no—
187C2×#480—71no—
188C2×#479—71no—
189C2×#478—71no—
190C2×#460—71no—
191C2×#459D711yescharacteristic, complemented
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×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—82no—
214C2×C7×D4—82no—
215C2×C7×D4#4114yes—
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—28no—
226C2×C22⋊D7—24no—
227C2×C22⋊D7—24no—
228C2×C22⋊D7—24no—
229C2×C22⋊D7—82no—
230C2×C22⋊D7—82no—
231C22×Dic7—28no—
232C22×Dic7—21no—
233C22×Dic7—24no—
234C22×Dic7—21no—
235C22×Dic7—21no—
236C22×Dic7—21no—
237C22×Dic7—24no—
238C22×Dic7—24no—
239C22×Dic7—24no—
240C22×Dic7—82no—
241C22×Dic7—82no—
242C22×Dic7—82no—
243C22×Dic7C2×D411yescharacteristic
244C22×Dic7C2×D411yescharacteristic
245C22×Dic7C2×D411yescharacteristic
246#1159—216no—
247#1159—28no—
248#1159—28no—
249C2×C4×D7—22no—
250C2×C4×D7—22no—
251C2×C4×D7—24no—
252C2×C4×D7—82no—
253C2×C4×D7C2×D412yes—
254C2×C4×D7C2412yes—
255C2×Dic14—21no—
256C2×Dic14—22no—
257C2×Dic14#4114yes—
258C2×Dic14C2412yes—
259C7×D8—28no—
260C7×D8—28no—
261C2×C7×C8—22no—
262C2×C7×C8—22no—
263C2×C7×C8C2412yes—
264C2×C7×C8C2412yes—
265C7×C4⋊C4—21no—
266C7×C4⋊C4C2412yes—
267C7×C22⋊C4—24no—
268C42×C7C2×D412yes—
269C42×C7C2412yes—
270C22⋊Dic7—24no—
271C22⋊Dic7—24no—
272C22⋊Dic7—24no—
273C22⋊Dic7—24no—
274C22⋊Dic7—24no—
275#1142—28no—
276#1142—28no—
277(C2×D7)⋊C4C2×D414yes—
278(C2×D7)⋊C4C2×D414yes—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7C2412yes—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285Dic7⋊C4—24no—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290Dic7⋊C4C2×D414yes—
291Dic7⋊C4C2×D414yes—
292C4×Dic7—24no—
293C4×Dic7—24no—
294C4×Dic7C2×D412yes—
295C4×Dic7C2412yes—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8C2412yes—
299C2×C7⋊C8C2412yes—
300C22×#41—71no—
301C22×SD16—71no—
302C22×SD16—71no—
303C22×D8C2×D711yescharacteristic
304C22×D8C2×D711yescharacteristic
305#540—78no—
306#540—144no—
307C2×#127C2×D711yescharacteristic
308C2×#125—71no—
309C2×#123—141no—
310C2×#123—141no—
311C2×#121—71no—
312C2×#121—71no—
313C2×#121—141no—
314C2×#121—141no—
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—141no—
323C2×C4×D4—141no—
324C2×C4×D4C2×D711yescharacteristic
325C2×#117—71no—
326C2×#117—141no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4—141no—
329#481—78no—
330#480—78no—
331#479—78no—
332#478—78no—
333#460—78no—
334#459C2×D718yescomplemented
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×#106—71no—
345C2×#106—71no—
346C2×C4⋊C8—71no—
347C2×C4⋊C8C2×D711yescharacteristic
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⋊C8—71no—
358C2×#97—71no—
359C2×C4×C8—71no—
360C23×C7—24no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7—42no—
369C23×C7—42no—
370C23×C7—42no—
371C23×C7—42no—
372C23×C7C22×D411yescharacteristic
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—22no—
376C22×D7C22×D412yes—
377C7×D4—24no—
378C7×D4—22no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—22no—
382C7×D4—22no—
383C7×D4—42no—
384C7×D4—42no—
385C7×D4—84no—
386C7×D4—84no—
387C7×D4C2×#4114yes—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—42no—
392C2×C4×C7—84no—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D411yescharacteristic
396C2×C4×C7C2×#4112yes—
397C2×C4×C7C2×#4112yes—
398C2×C4×C7C2511yescharacteristic
399C22⋊D7—216no—
400C22⋊D7—84no—
401C22⋊D7—84no—
402C2×Dic7—216no—
403C2×Dic7—24no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414C2×Dic7—84no—
415C2×Dic7—84no—
416C2×Dic7—84no—
417C2×Dic7C22×D412yes—
418C2×Dic7C22×D412yes—
419C2×Dic7C22×D412yes—
420C4×D7—24no—
421C4×D7—22no—
422C4×D7—22no—
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—142no—
433C2×#41—144no—
434C2×#41—144no—
435C22×Q8—71no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—141no—
439C22×D4—141no—
440C22×D4—141no—
441C22×D4C22×D711yescharacteristic
442C22×D4C22×D711yescharacteristic
443C22×D4C22×D711yescharacteristic
444C23×C4—21no—
445C23×C4—71no—
446C23×C4—141no—
447C23×C4—141no—
448C23×C4—141no—
449C23×C4—141no—
450C23×C4—141no—
451C2×SD16—74no—
452C2×SD16—74no—
453C2×SD16—144no—
454C2×SD16—144no—
455C2×D8—24no—
456C2×D8—24no—
457C2×D8C22×D714yes—
458C2×D8C22×D714yes—
459C22×C8—71no—
460C22×C8—71no—
461C22×C8C22×D711yescharacteristic
462C22×C8C22×D711yescharacteristic
463#127—22no—
464#127C22×D714yes—
465#125—74no—
466#125—142no—
467#123—148no—
468#123—148no—
469#121—74no—
470#121—74no—
471#121—148no—
472#121—148no—
473#121—142no—
474#121—142no—
475C4×Q8—74no—
476C4×Q8—74no—
477C4×Q8—142no—
478C4×Q8—142no—
479C4×D4—22no—
480C4×D4—74no—
481C4×D4—74no—
482C4×D4—74no—
483C4×D4—142no—
484C4×D4—142no—
485C4×D4—142no—
486C4×D4—148no—
487C4×D4—148no—
488C4×D4C22×D714yes—
489#117—74no—
490#117—74no—
491#117—148no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—148no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
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—141no—
516C2×C42—141no—
517C2×C42C22×D711yescharacteristic
518#107—74no—
519#107—74no—
520#106—74no—
521#106—74no—
522C4⋊C8—74no—
523C4⋊C8C22×D714yes—
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⋊C8—74no—
534#97—74no—
535C4×C8—74no—
536C22×C7—24no—
537C22×C7—48no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—42no—
542C22×C7—42no—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—84no—
547C22×C7—84no—
548C22×C7#52512yes—
549C22×C7#57612yes—
550C22×C7#57712yes—
551C22×C7C23×D411yescharacteristic
552C2×D7—22no—
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—44no—
556C4×C7—22no—
557C4×C7—22no—
558C4×C7—42no—
559C4×C7#52512yes—
560C4×C7C22×#4111yescharacteristic
561C4×C7C22×#4111yescharacteristic
562Dic7—24no—
563Dic7—22no—
564Dic7—22no—
565Dic7—22no—
566Dic7—42no—
567Dic7—42no—
568Dic7—42no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24—71no—
573#41—148no—
574#41—1416no—
575#41—148no—
576C2×Q8—74no—
577C2×Q8—72no—
578C2×Q8—141no—
579C2×Q8—142no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—82no—
591C2×D4—82no—
592C2×D4—144no—
593C2×D4—148no—
594C2×D4—144no—
595C2×D4—144no—
596C2×D4—562no—
597C2×D4—562no—
598C2×D4#115914yes—
599C2×D4C23×D712yes—
600C2×D4C23×D712yes—
601C2×D4C23×D712yes—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—71no—
605C22×C4—71no—
606C22×C4—71no—
607C22×C4—72no—
608C22×C4—72no—
609C22×C4—82no—
610C22×C4—144no—
611C22×C4—144no—
612C22×C4—144no—
613C22×C4—144no—
614C22×C4—144no—
615C22×C4—148no—
616C22×C4—141no—
617C22×C4—142no—
618C22×C4—142no—
619C22×C4—141no—
620C22×C4—141no—
621C22×C4—141no—
622C22×C4—562no—
623C22×C4—562no—
624C22×C4—562no—
625C22×C4—562no—
626C22×C4D4×D711yescharacteristic
627C22×C4D4×D711yescharacteristic
628C22×C4C23×D711yescharacteristic
629SD16—148no—
630SD16—148no—
631D8—28no—
632D8—28no—
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—21no—
642C4⋊C4—74no—
643C4⋊C4—74no—
644C4⋊C4—72no—
645C4⋊C4—72no—
646C4⋊C4—72no—
647C4⋊C4—144no—
648C4⋊C4—144no—
649C4⋊C4—144no—
650C4⋊C4—144no—
651C4⋊C4—144no—
652C4⋊C4—141no—
653C4⋊C4—141no—
654C4⋊C4—141no—
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—144no—
667C42—144no—
668C42D4×D712yes—
669C42C23×D712yes—
670C2×C7—44no—
671C2×C7—82no—
672C2×C7—82no—
673C2×C7#311914yescomplemented
674C2×C7C2×#52511yescharacteristic
675C2×C7C2×#57611yescharacteristic
676C2×C7C2×#57711yescharacteristic
677D7—42no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—72no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23C2×D4×D711yescharacteristic
695Q8—74no—
696Q8—144no—
697Q8—142no—
698D4—24no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—84no—
707D4—84no—
708D4—1416no—
709D4—564no—
710D4—564no—
711D4C2×#115914yes—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—72no—
717C2×C4—72no—
718C2×C4—72no—
719C2×C4—84no—
720C2×C4—1416no—
721C2×C4—142no—
722C2×C4—142no—
723C2×C4—142no—
724C2×C4—144no—
725C2×C4—142no—
726C2×C4—144no—
727C2×C4—142no—
728C2×C4—142no—
729C2×C4—142no—
730C2×C4—142no—
731C2×C4—142no—
732C2×C4—282no—
733C2×C4—282no—
734C2×C4—282no—
735C2×C4—564no—
736C2×C4—564no—
737C2×C4—564no—
738C2×C4—564no—
739C2×C4C2×D4×D712yes—
740C2×C4C2×D4×D712yes—
741C2×C4C2×D4×D711yescharacteristic
742C2×C4C2×#115912yes—
743C2×C4D7×#4112yes—
744C2×C4C24×D711yescharacteristic
745C8—22no—
746C8—22no—
747C8—142no—
748C8—142no—
749C7C2×#311911yescharacteristic, complemented, Sylow
750C22—24no—
751C22—42no—
752C22—48no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—142no—
763C22—142no—
764C22—142no—
765C22—284no—
766C22#9029712yes—
767C22#9044812yes—
768C22#9046612yes—
769C22C22×D4×D711yescharacteristic
770C4—22no—
771C4—22no—
772C4—42no—
773C4—142no—
774C4—142no—
775C4—144no—
776C4—142no—
777C4—282no—
778C4—282no—
779C4—282no—
780C4#9029712yes—
781C4C22×#115911yescharacteristic
782C4C2×D7×#4111yescharacteristic
783C2—44no—
784C2—82no—
785C2—82no—
786C2—282no—
787C2#1173776114yesdirect product factor
788C2C2×#9029711yescharacteristic
789C2C2×#9044811yescharacteristic
790C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#459C2
socleC23×C7C22×D4
hypercenterC2×#459D7
hypocenterC7C2×#3119
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×#90237C2semidirect
3. C2×C7×#459C2semidirect
4. C2×#89930C2semidirect
5. C2×#89930C2semidirect
6. C2×#89924C2semidirect
7. C2×D8×Dic7C2semidirect
8. C2×#89847C2semidirect
9. C2×#89781C2semidirect
10. #11737761C2direct (N × H)
11. C2×#89601C2semidirect
12. C2×#89612C2semidirect
13. C2×#89549C2semidirect
14. C2×#89546C2semidirect
15. C2×#89529C2semidirect
16. C2×#89530C2semidirect
36. #90410C22semidirect
38. #90237C22semidirect
46. C7×#459C22semidirect
54. #89930C22semidirect
55. #89930C22semidirect
56. #89924C22semidirect
57. D8×Dic7C22semidirect
66. #89847C22semidirect
67. #89781C22semidirect
71. #89612C22semidirect
72. #89601C22semidirect
73. #89549C22semidirect
74. #89546C22semidirect
75. #89530C22semidirect
76. #89529C22semidirect
191. C2×#459D7semidirect
334. #459C2×D7semidirect
673. C2×C7#3119semidirect
749. C7C2×#3119semidirect
787. C2#11737761direct (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×#902372
C2×C7×#4592
C2×#899302
C2×#899242
C2×D8×Dic72
C2×#898472
C2×#897812
#117377612
C2×#896012
C2×#896122
C2×#895492
C2×#895462
C2×#895292
C2×#895302
C2×#31197