Finite Group Databasebeta

← C2×#11739310 #14234785

Subgroups — C2×#11739310 #14234785

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90412C211yesmaximal, characteristic, complemented
2C2×#90372C211yesmaximal, characteristic
3C2×C7×#497C211yesmaximal, characteristic, complemented
4C2×#89962C211yesmaximal, characteristic, complemented
5C2×#89957C211yesmaximal, characteristic, complemented
6C2×#89954C211yesmaximal, characteristic, complemented
7C2×Q16×Dic7C211yesmaximal, characteristic, complemented
8C2×#89947C211yesmaximal, characteristic
9C2×#89935C211yesmaximal, characteristic
10C2×#89934C211yesmaximal, characteristic, complemented
11C2×#89936C211yesmaximal, characteristic, complemented
12C2×#89855C211yesmaximal, characteristic, complemented
13C2×#89826C211yesmaximal, characteristic, complemented
14#11739310C2116yesmaximal, direct product factor
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89473C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×SD16C2211yescharacteristic
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×#124C2211yescharacteristic
23C2×#6510C2211yescharacteristic
24C2×Q8×Dic7C2211yescharacteristic
25C2×Q8×Dic7C2211yescharacteristic
26C2×Q8×Dic7C2211yescharacteristic
27C2×#6507C2211yescharacteristic
28C2×#6507C2211yescharacteristic
29C22×#1144C2211yescharacteristic
30C22×#1143C2211yescharacteristic
31C22×#1143C2211yescharacteristic
32C2×#6503C2211yescharacteristic
33C2×D4×Dic7C2211yescharacteristic
34C22×#1142C2211yescharacteristic
35C22×#1132C2211yescharacteristic
36#90412—24no—
37#90412C2218yescomplemented
38#90372—24no—
39#90372C2218yes—
40C2×#6453—21no—
41C2×#6452—21no—
42C2×#6452—21no—
43C2×#6450—21no—
44C2×#6449—21no—
45C2×#6448—21no—
46C2×#6446—21no—
47C2×(C22⋊D7)⋊C4—21no—
48C2×C4×D28C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C7×#497C2218yescomplemented
52C2×C7×#97C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6409C2211yescharacteristic
55C2×#6409C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57#89962C2218yescomplemented
58#89957C2218yescomplemented
59Q16×Dic7C2218yescomplemented
60#89954C2218yescomplemented
61#89947C2218yes—
62#89936C2218yescomplemented
63#89935C2218yes—
64#89934C2218yescomplemented
65C2×#6395C2211yescharacteristic
66C2×#6392C2211yescharacteristic
67C2×#6390C2211yescharacteristic
68C2×#6389C2211yescharacteristic
69C2×Dic7⋊C8C2211yescharacteristic
70C2×Dic7⋊C8C2211yescharacteristic
71C2×C8×Dic7C2211yescharacteristic
72#89855C2218yescomplemented
73#89826C2218yescomplemented
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75#89482C2218yescomplemented
76#89473C2218yescomplemented
77C2×#3400—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C23×Dic7—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×Dic14D411yescharacteristic
88C22×Dic14C2311yescharacteristic
89C2×C7×Q16—24no—
90C2×C7×Q16—42no—
91C2×C7×Q16C2314yes—
92C2×C7×Q16C2314yes—
93C2×C7×SD16—24no—
94C2×C7×SD16—42no—
95C2×C7×SD16C2314yes—
96C2×C7×SD16C2314yes—
97C22×C7×C8C2311yescharacteristic
98C22×C7×C8C2311yescharacteristic
99C7×C4⋊Q8—22no—
100C7×C4⋊Q8C2314yes—
101C7×#124—22no—
102C7×#124C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C22⋊C4—21no—
106C2×C7×C22⋊C4—21no—
107C2×C42×C7C2311yescharacteristic
108C2×C22⋊Dic7—21no—
109#6510—22no—
110#6510C2314yes—
111Q8×Dic7—22no—
112Q8×Dic7—22no—
113Q8×Dic7—22no—
114Q8×Dic7C2314yes—
115Q8×Dic7C2314yes—
116Q8×Dic7C2314yes—
117#6507—22no—
118#6507—22no—
119#6507C2314yes—
120#6507C2314yes—
121C2×#1144—42no—
122C2×#1144C2314yes—
123C2×#1143—42no—
124C2×#1143—42no—
125C2×#1143C2314yes—
126C2×#1143C2314yes—
127#6503—22no—
128#6503C2314yes—
129D4×Dic7—22no—
130D4×Dic7C2314yes—
131C2×#1142—42no—
132C2×#1142C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×(C2×D7)⋊C4—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7—21no—
138C2×C4⋊Dic7—21no—
139C2×C4⋊Dic7D411yescharacteristic
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4D411yescharacteristic
148C2×Dic7⋊C4D411yescharacteristic
149C2×C4×Dic7—21no—
150C2×C4×Dic7—21no—
151C2×C4×Dic7—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7C2311yescharacteristic
154C2×C4×Dic7C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157C2×#1132—24no—
158C2×#1132C2314yes—
159#6453—28no—
160#6452—28no—
161#6452—28no—
162#6450—28no—
163#6449—28no—
164#6448—28no—
165#6446—28no—
166(C22⋊D7)⋊C4—28no—
167C4×D28—22no—
168C4×D28C2314yes—
169C4×Dic14—22no—
170C4×Dic14D414yes—
171C4×Dic14C2314yes—
172C4×Dic14C2314yes—
173C7×#97C2314yes—
174#6409C2314yes—
175#6409C2314yes—
176#6409C2314yes—
177#6406C2314yes—
178#6395C2314yes—
179#6392C2314yes—
180#6390C2314yes—
181#6389C2314yes—
182Dic7⋊C8C2314yes—
183Dic7⋊C8C2314yes—
184C8×Dic7C2314yes—
185C4⋊(C7⋊C8)C2314yes—
186C2×#559—71no—
187C2×#557—71no—
188#3400—716no—
189C2×#497—71no—
190C2×#497D711yescharacteristic, complemented
191C2×#492—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#462—71no—
195C2×#460—71no—
196C2×#461—71no—
197C2×#461—71no—
198C2×#446—71no—
199C2×#440—71no—
200C2×#440—71no—
201C2×C4×Q16—71no—
202C24×C7—21no—
203C23×D7—21no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—21no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8—22no—
213C2×C7×Q8C2412yes—
214C2×C7×Q8C2412yes—
215C2×C7×Q8C2412yes—
216C2×C7×D4—21no—
217C2×C7×D4—22no—
218C2×C7×D4—22no—
219C2×C7×D4C2412yes—
220C22×C4×C7—21no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2411yescharacteristic
226C2×C22⋊D7—24no—
227C2×C22⋊D7—24no—
228C2×C22⋊D7—44no—
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
238C22×Dic7C2×D411yescharacteristic
239C2×D28—22no—
240C2×D28—22no—
241C2×D28—21no—
242C2×D28C2412yes—
243C2×C4×D7—24no—
244C2×C4×D7—82no—
245C2×Dic14—24no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—21no—
249C2×Dic14C2×D414yes—
250C2×Dic14C2412yes—
251C7×Q16—28no—
252C7×Q16—44no—
253C7×SD16—28no—
254C7×SD16—44no—
255C2×C7×C8—22no—
256C2×C7×C8#4114yes—
257C2×C7×C8C2412yes—
258C2×C7×C8C2412yes—
259C7×C4⋊C4—24no—
260C7×C4⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C42×C7C2×D412yes—
264C42×C7C2412yes—
265C22⋊Dic7—24no—
266#1144—44no—
267#1143—44no—
268#1143—44no—
269#1142—44no—
270(C2×D7)⋊C4—24no—
271(C2×D7)⋊C4—24no—
272(C2×D7)⋊C4—24no—
273C4⋊Dic7—21no—
274C4⋊Dic7—21no—
275C4⋊Dic7—24no—
276C4⋊Dic7—24no—
277C4⋊Dic7—24no—
278C4⋊Dic7C2×D414yes—
279C4⋊Dic7C2412yes—
280C4⋊Dic7C2412yes—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286Dic7⋊C4C2×D414yes—
287Dic7⋊C4C2×D414yes—
288C4×Dic7—24no—
289C4×Dic7—24no—
290C4×Dic7—24no—
291C4×Dic7—24no—
292C4×Dic7C2×D412yes—
293C4×Dic7C2×D412yes—
294C4×Dic7C2412yes—
295C4×Dic7C2412yes—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8C2412yes—
299C2×C7⋊C8C2412yes—
300#1132—28no—
301C22×Q16—71no—
302C22×Q16C2×D711yescharacteristic
303C22×Q16C2×D711yescharacteristic
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307C22×SD16—71no—
308C22×SD16C2×D711yescharacteristic
309C22×SD16C2×D711yescharacteristic
310#559—78no—
311#559—144no—
312#557—78no—
313#557—144no—
314C2×C4⋊Q8—71no—
315C2×C4⋊Q8—71no—
316C2×C4⋊Q8C2×D711yescharacteristic
317C2×#127—71no—
318C2×#125—141no—
319C2×#125—141no—
320C2×#125—141no—
321C2×#124—71no—
322C2×#124—141no—
323C2×#124C2×D711yescharacteristic
324C2×#123—141no—
325C2×#123—141no—
326C2×C4×Q8—71no—
327C2×C4×Q8—71no—
328C2×C4×Q8—71no—
329C2×C4×Q8—71no—
330C2×C4×Q8—71no—
331C2×C4×Q8—141no—
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×C4×D4—141no—
335#497—78no—
336#497C2×D718yescomplemented
337#492—78no—
338#464—78no—
339#464—78no—
340#462—78no—
341#461—78no—
342#461—78no—
343#460—78no—
344#446—78no—
345#440—78no—
346#440—78no—
347C4×Q16—78no—
348C2×#107—71no—
349C2×C4⋊C8—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8—71no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#103—71no—
355C2×#103—71no—
356C2×#102—71no—
357C2×#102—71no—
358C2×#97—71no—
359C2×#97C2×D711yescharacteristic
360C2×C4×C8—71no—
361C23×C7—22no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7C22×D411yescharacteristic
366C22×D7—22no—
367C22×D7—42no—
368C22×D7—42no—
369C22×D7—42no—
370C7×Q8—22no—
371C7×Q8—22no—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—22no—
375C7×Q8—22no—
376C7×Q8—42no—
377C7×Q8—42no—
378C7×Q8—42no—
379C7×D4—22no—
380C7×D4—22no—
381C7×D4—42no—
382C2×C4×C7—22no—
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—42no—
390C2×C4×C7C22×D412yes—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C2×#4112yes—
394C2×C4×C7H(5,𝔽2)12yes—
395C2×C4×C7C2511yescharacteristic
396C22⋊D7—48no—
397C22⋊D7—84no—
398C2×Dic7—22no—
399C2×Dic7—22no—
400C2×Dic7—22no—
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407C2×Dic7—84no—
408C2×Dic7#13714yes—
409C2×Dic7C22×D412yes—
410C2×Dic7C22×D412yes—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413D28—22no—
414D28—22no—
415D28—42no—
416C4×D7—84no—
417Dic14—28no—
418Dic14—22no—
419Dic14—22no—
420Dic14—42no—
421C7×C8—22no—
422C7×C8C2×#4114yes—
423C7⋊C8—22no—
424C7⋊C8—22no—
425C22×Q8—71no—
426C22×Q8—71no—
427C22×Q8C22×D711yescharacteristic
428C22×Q8C22×D711yescharacteristic
429C22×Q8C22×D711yescharacteristic
430C22×D4—71no—
431C22×D4—141no—
432C22×D4—141no—
433C22×D4C22×D711yescharacteristic
434C23×C4—141no—
435C23×C4—141no—
436C2×Q16—24no—
437C2×Q16—42no—
438C2×Q16—74no—
439C2×Q16—282no—
440C2×Q16C22×D714yes—
441C2×Q16C22×D714yes—
442C2×SD16—24no—
443C2×SD16—42no—
444C2×SD16—74no—
445C2×SD16—74no—
446C2×SD16—74no—
447C2×SD16—74no—
448C2×SD16—144no—
449C2×SD16—282no—
450C2×SD16—282no—
451C2×SD16—282no—
452C2×SD16C22×D714yes—
453C2×SD16C22×D714yes—
454C22×C8—71no—
455C22×C8—71no—
456C22×C8C22×D711yescharacteristic
457C22×C8C22×D711yescharacteristic
458C4⋊Q8—22no—
459C4⋊Q8—74no—
460C4⋊Q8—74no—
461C4⋊Q8—142no—
462C4⋊Q8—142no—
463C4⋊Q8C22×D714yes—
464#127—74no—
465#127—142no—
466#125—148no—
467#125—148no—
468#125—148no—
469#124—22no—
470#124—74no—
471#124—142no—
472#124—148no—
473#124C22×D714yes—
474#123—148no—
475#123—148no—
476C4×Q8—74no—
477C4×Q8—74no—
478C4×Q8—74no—
479C4×Q8—74no—
480C4×Q8—74no—
481C4×Q8—74no—
482C4×Q8—142no—
483C4×Q8—142no—
484C4×Q8—142no—
485C4×Q8—148no—
486C4×Q8—142no—
487C4×D4—74no—
488C4×D4—74no—
489C4×D4—142no—
490C4×D4—148no—
491C4×D4—142no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—71no—
496C2×C4⋊C4—71no—
497C2×C4⋊C4—71no—
498C2×C4⋊C4—71no—
499C2×C4⋊C4—141no—
500C2×C4⋊C4—141no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4—141no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C42—71no—
514C2×C42—71no—
515C2×C42—141no—
516C2×C42—141no—
517C2×C42—141no—
518C2×C42—141no—
519C2×C42C22×D711yescharacteristic
520#107—74no—
521C4⋊C8—74no—
522C4⋊C8—74no—
523C4⋊C8—74no—
524#103—74no—
525#103—74no—
526#103—74no—
527#103—74no—
528#102—74no—
529#102—74no—
530#97—74no—
531#97C22×D714yes—
532C4×C8—74no—
533C22×C7—42no—
534C22×C7—42no—
535C22×C7—42no—
536C22×C7—84no—
537C22×C7#55012yes—
538C22×C7C2×#13712yes—
539C22×C7#57712yes—
540C22×C7C23×D411yescharacteristic
541C2×D7—42no—
542C2×D7—42no—
543C2×D7—42no—
544C2×D7—84no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7#55012yes—
551C4×C7C22×#4111yescharacteristic
552C4×C7C2×H(5,𝔽2)11yescharacteristic
553Dic7—22no—
554Dic7—22no—
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7C2×#13714yes—
560C24—21no—
561C24—141no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—74no—
572C2×Q8—72no—
573C2×Q8—144no—
574C2×Q8—141no—
575C2×Q8—142no—
576C2×Q8—142no—
577C2×Q8C23×D712yes—
578C2×Q8C23×D712yes—
579C2×Q8C23×D712yes—
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—72no—
584C2×D4—144no—
585C2×D4—144no—
586C2×D4—141no—
587C2×D4—142no—
588C2×D4—142no—
589C2×D4—284no—
590C2×D4—562no—
591C2×D4C23×D712yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—71no—
596C22×C4—71no—
597C22×C4—71no—
598C22×C4—71no—
599C22×C4—144no—
600C22×C4—141no—
601C22×C4—141no—
602C22×C4—141no—
603C22×C4—144no—
604C22×C4—562no—
605C22×C4—562no—
606C22×C4D4×D711yescharacteristic
607C22×C4D4×D711yescharacteristic
608C22×C4C23×D711yescharacteristic
609Q16—28no—
610Q16—44no—
611Q16—284no—
612SD16—28no—
613SD16—44no—
614SD16—148no—
615SD16—284no—
616SD16—284no—
617SD16—284no—
618C2×C8—22no—
619C2×C8—72no—
620C2×C8—72no—
621C2×C8—142no—
622C2×C8—142no—
623C2×C8#115914yes—
624C2×C8C23×D712yes—
625C2×C8C23×D712yes—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—74no—
629C4⋊C4—74no—
630C4⋊C4—74no—
631C4⋊C4—72no—
632C4⋊C4—72no—
633C4⋊C4—144no—
634C4⋊C4—144no—
635C4⋊C4—144no—
636C4⋊C4—144no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—141no—
642C4⋊C4—141no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—144no—
646C22⋊C4—144no—
647C22⋊C4—144no—
648C22⋊C4—144no—
649C42—72no—
650C42—72no—
651C42—72no—
652C42—72no—
653C42—144no—
654C42—144no—
655C42—144no—
656C42—144no—
657C42D4×D712yes—
658C42C23×D712yes—
659C2×C7—82no—
660C2×C7#340014yescomplemented
661C2×C7C2×#55011yescharacteristic
662C2×C7C22×#13711yescharacteristic
663C2×C7C2×#57711yescharacteristic
664D7—82no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—142no—
670C23—282no—
671C23—282no—
672C23—282no—
673C23C2×D4×D711yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—148no—
684Q8—142no—
685Q8—142no—
686Q8—282no—
687D4—22no—
688D4—22no—
689D4—42no—
690D4—142no—
691D4—142no—
692D4—288no—
693D4—282no—
694D4—564no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—74no—
704C2×C4—72no—
705C2×C4—72no—
706C2×C4—72no—
707C2×C4—72no—
708C2×C4—142no—
709C2×C4—142no—
710C2×C4—142no—
711C2×C4—142no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—282no—
715C2×C4—282no—
716C2×C4—282no—
717C2×C4—564no—
718C2×C4—564no—
719C2×C4C2×D4×D712yes—
720C2×C4C2×D4×D712yes—
721C2×C4C2×D4×D711yescharacteristic
722C2×C4C2×#115912yes—
723C2×C4#654812yes—
724C2×C4C24×D711yescharacteristic
725C8—22no—
726C8—142no—
727C8—142no—
728C8C2×#115914yes—
729C7C2×#340011yescharacteristic, complemented, Sylow
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—282no—
735C22—282no—
736C22—282no—
737C22—564no—
738C22#9040912yes—
739C22D7×#13712yes—
740C22#9046912yes—
741C22C22×D4×D711yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—74no—
748C4—142no—
749C4—142no—
750C4—142no—
751C4—282no—
752C4—282no—
753C4—282no—
754C4#9040912yes—
755C4C22×#115911yescharacteristic
756C4C2×#654811yescharacteristic
757C2—82no—
758C2—562no—
759C2#1173931014yesdirect product factor
760C2C2×#9040911yescharacteristic
761C2C2×D7×#13711yescharacteristic
762C2C2×#9046911yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#497C2
socleC23×C7C22×D4
prime radicalC2×#6503C22
hypercenterC2×#497D7
hypocenterC7C2×#3400
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#90412C2semidirect
3. C2×C7×#497C2semidirect
4. C2×#89962C2semidirect
5. C2×#89957C2semidirect
6. C2×#89954C2semidirect
7. C2×Q16×Dic7C2semidirect
10. C2×#89934C2semidirect
11. C2×#89936C2semidirect
12. C2×#89855C2semidirect
13. C2×#89826C2semidirect
14. #11739310C2direct (N × H)
15. C2×#89482C2semidirect
16. C2×#89473C2semidirect
37. #90412C22semidirect
51. C7×#497C22semidirect
57. #89962C22semidirect
58. #89957C22semidirect
59. Q16×Dic7C22semidirect
60. #89954C22semidirect
62. #89936C22semidirect
64. #89934C22semidirect
72. #89855C22semidirect
73. #89826C22semidirect
75. #89482C22semidirect
76. #89473C22semidirect
190. C2×#497D7semidirect
336. #497C2×D7semidirect
660. C2×C7#3400semidirect
729. C7C2×#3400semidirect
759. C2#11739310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904122
C2×#903722
C2×C7×#4972
C2×#899622
C2×#899572
C2×#899542
C2×Q16×Dic72
C2×#899472
C2×#899352
C2×#899342
C2×#899362
C2×#898552
C2×#898262
#117393102
C2×#894822
C2×#894732
C2×#34007