Finite Group Databasebeta

← C2×#11737256 #14221920

Subgroups — C2×#11737256 #14221920

Order 1792.

2430 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1161C211yesmaximal, characteristic, complemented
2C2×#90239C211yesmaximal, characteristic, complemented
3C2×C7×#440C211yesmaximal, characteristic, complemented
4C2×#89944C211yesmaximal, characteristic, complemented
5C2×#89935C211yesmaximal, characteristic, complemented
6C2×#89798C211yesmaximal, characteristic, complemented
7C2×#89786C211yesmaximal, characteristic, complemented
8#11737256C2116yesmaximal, direct product factor
9C2×#89662C211yesmaximal, characteristic, complemented
10C2×#89657C211yesmaximal, characteristic, complemented
11C2×#89583C211yesmaximal, characteristic, complemented
12C2×#89563C211yesmaximal, characteristic, complemented
13C2×#89558C211yesmaximal, characteristic, complemented
14C2×#89551C211yesmaximal, characteristic, complemented
15C2×#89483C211yesmaximal, characteristic, complemented
16C2×#89477C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×#1157—21no—
19C22×C7×SD16C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×C4×C7×D4C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C22×#1143C2211yescharacteristic
24C2×#6503C2211yescharacteristic
25C2×#6501C2211yescharacteristic
26C22×#1141C2211yescharacteristic
27C2×C4×C22⋊D7—21no—
28C22×D56C2211yescharacteristic
29C4×#1161—24no—
30C4×#1161C2218yescomplemented
31#90239—24no—
32#90239C2218yescomplemented
33C2×#6458C2211yescharacteristic
34C2×#6456—21no—
35C2×#6456C2211yescharacteristic
36C2×#6455—21no—
37C2×#6455C2211yescharacteristic
38C2×#6451C2211yescharacteristic
39C2×#6448—21no—
40C2×#6447—21no—
41C2×C4×D28—21no—
42C2×C4×D28C2211yescharacteristic
43C2×C4×D28C2211yescharacteristic
44C2×C42×D7—21no—
45C2×C42×D7C2211yescharacteristic
46C7×#440C2218yescomplemented
47C2×C7×#107C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6406C2211yescharacteristic
53#89944C2218yescomplemented
54#89935C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×#6395C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×(C2×D7)⋊C8C2211yescharacteristic
59C2×#6391C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62#89798C2218yescomplemented
63#89786C2218yescomplemented
64C2×#6383C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89662C2218yescomplemented
70#89657C2218yescomplemented
71#89583C2218yescomplemented
72#89563C2218yescomplemented
73#89558C2218yescomplemented
74#89551C2218yescomplemented
75#89483C2218yescomplemented
76#89477C2218yescomplemented
77C2×#3115—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×D4C2311yescharacteristic
80C23×C4×C7—21no—
81C22×C22⋊D7—21no—
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C2×#1161—24no—
85C2×#1161—24no—
86C2×#1161—22no—
87C2×#1161C2314yes—
88C2×#1157—28no—
89C2×#1157—48no—
90C22×D28—21no—
91C22×D28—21no—
92C22×D28C2311yescharacteristic
93C22×D28C2311yescharacteristic
94C22×C4×D7—21no—
95C22×C4×D7—21no—
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×C4×D7D411yescharacteristic
99C22×C4×D7D411yescharacteristic
100C22×C4×D7C2311yescharacteristic
101C22×Dic14—21no—
102C2×C7×SD16—24no—
103C2×C7×SD16C2314yes—
104C22×C7×C8C2311yescharacteristic
105C22×C7×C8C2311yescharacteristic
106C4×C7×Q8—22no—
107C4×C7×Q8C2314yes—
108C4×C7×D4—22no—
109C4×C7×D4C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4—21no—
114C2×C42×C7—21no—
115C2×C42×C7C2311yescharacteristic
116C2×C22⋊Dic7—21no—
117Q8×Dic7—22no—
118Q8×Dic7C2314yes—
119C2×#1143—24no—
120C2×#1143C2314yes—
121#6503—22no—
122#6503C2314yes—
123#6501—22no—
124#6501C2314yes—
125C2×#1141—24no—
126C2×#1141C2314yes—
127C4×C22⋊D7—28no—
128C2×(C2×D7)⋊C4—21no—
129C2×(C2×D7)⋊C4—21no—
130C2×(C2×D7)⋊C4—21no—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×C4⋊Dic7—21no—
134C2×C4⋊Dic7C2311yescharacteristic
135C2×C4⋊Dic7C2311yescharacteristic
136C2×Dic7⋊C4—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C2×C4×Dic7D411yescharacteristic
140C2×C4×Dic7D411yescharacteristic
141C2×C4×Dic7C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143C22×C7⋊C8C2311yescharacteristic
144C2×D56—24no—
145C2×D56C2314yes—
146#6458—22no—
147#6458C2314yes—
148#6456—28no—
149#6456—22no—
150#6456C2314yes—
151#6455—22no—
152#6455—28no—
153#6455C2314yes—
154#6451—22no—
155#6451C2314yes—
156#6448—28no—
157#6447—28no—
158C4×D28—28no—
159C4×D28—22no—
160C4×D28—22no—
161C4×D28C2314yes—
162C4×D28C2314yes—
163C42×D7—28no—
164C42×D7D414yes—
165C42×D7C2314yes—
166C7×#107C2314yes—
167C7×#103C2314yes—
168C7×#102C2314yes—
169C7×#97C2314yes—
170#6409C2314yes—
171#6406C2314yes—
172#6395C2314yes—
173#6395C2314yes—
174(C2×D7)⋊C8C2314yes—
175(C2×D7)⋊C8C2314yes—
176#6391C2314yes—
177Dic7⋊C8C2314yes—
178Dic7⋊C8C2314yes—
179#6383C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183#6377C2314yes—
184C2×#532—71no—
185C2×C4×#41—71no—
186#3115—716no—
187C2×#482—71no—
188C2×#482—71no—
189C2×#475—71no—
190C2×#474—71no—
191C2×#460—71no—
192C2×#459—71no—
193C2×#449—71no—
194C2×#449—71no—
195C2×#442—71no—
196C2×#442—71no—
197C2×#440—71no—
198C2×#440D711yescharacteristic, complemented
199C2×#432—71no—
200C24×C7—21no—
201C23×D7—21no—
202C23×D7—21no—
203C23×D7C2×D411yescharacteristic
204C2×C7×Q8—21no—
205C2×C7×Q8—22no—
206C2×C7×Q8#4114yescomplemented
207C2×C7×Q8C2412yes—
208C2×C7×D4—21no—
209C2×C7×D4—22no—
210C2×C7×D4—22no—
211C2×C7×D4C2412yes—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7—24no—
216C22×C4×C7—44no—
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D411yescharacteristic
219C22×C4×C7C2411yescharacteristic
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—24no—
223C2×C22⋊D7—44no—
224C2×C22⋊D7—44no—
225C2×C22⋊D7—44no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231#1161—216no—
232#1161—28no—
233#1161—28no—
234#1157—432no—
235C2×D28—28no—
236C2×D28—24no—
237C2×D28—21no—
238C2×D28—22no—
239C2×D28—22no—
240C2×D28—22no—
241C2×D28—24no—
242C2×D28—21no—
243C2×D28—44no—
244C2×D28#4114yescomplemented
245C2×D28C2412yes—
246C2×D28C2412yes—
247C2×C4×D7—28no—
248C2×C4×D7—22no—
249C2×C4×D7—22no—
250C2×C4×D7—24no—
251C2×C4×D7—24no—
252C2×C4×D7—24no—
253C2×C4×D7—24no—
254C2×C4×D7—24no—
255C2×C4×D7—42no—
256C2×C4×D7—44no—
257C2×C4×D7—44no—
258C2×C4×D7—44no—
259C2×C4×D7C2×D412yes—
260C2×C4×D7C2×D414yes—
261C2×C4×D7C2×D414yes—
262C2×C4×D7C2412yes—
263C2×Dic14—24no—
264C2×Dic14—44no—
265C7×SD16—28no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8C2412yes—
269C2×C7×C8C2412yes—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—24no—
272C7×C4⋊C4—21no—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
275C7×C22⋊C4—24no—
276C42×C7—24no—
277C42×C7C2×D412yes—
278C42×C7C2412yes—
279C22⋊Dic7—24no—
280#1143—28no—
281#1141—28no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4—24no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4—24no—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—24no—
290C4⋊Dic7C2412yes—
291C4⋊Dic7C2412yes—
292Dic7⋊C4—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7C2×D414yes—
296C4×Dic7C2×D412yes—
297C4×Dic7C2×D414yes—
298C4×Dic7C2412yes—
299C2×C7⋊C8—22no—
300C2×C7⋊C8—22no—
301C2×C7⋊C8C2412yes—
302C2×C7⋊C8C2412yes—
303D56—28no—
304C22×#41—71no—
305C22×#41—141no—
306C22×SD16—71no—
307C22×SD16C2×D711yescharacteristic
308C22×D8—71no—
309C22×D8—71no—
310#532—78no—
311#532—144no—
312C2×C4⋊Q8—71no—
313C2×#127—71no—
314C2×#124—141no—
315C2×#121—71no—
316C2×#121—71no—
317C2×#121—141no—
318C4×#41—78no—
319C4×#41—144no—
320C2×C4×Q8—71no—
321C2×C4×Q8C2×D711yescharacteristic
322C2×C4×D4—71no—
323C2×C4×D4—71no—
324C2×C4×D4—71no—
325C2×C4×D4—141no—
326C2×C4×D4—141no—
327C2×C4×D4—141no—
328C2×C4×D4C2×D711yescharacteristic
329C2×#117—71no—
330C2×#117—141no—
331C22×C42—71no—
332C22×C42—141no—
333#482—78no—
334#482—78no—
335#475—78no—
336#474—78no—
337#460—78no—
338#459—78no—
339#449—78no—
340#449—78no—
341#442—78no—
342#442—78no—
343#440—78no—
344#440C2×D718yescomplemented
345#432—78no—
346C2×#107—71no—
347C2×#107C2×D711yescharacteristic
348C2×#106—71no—
349C2×#106—71no—
350C2×C4⋊C8—71no—
351C2×C4⋊C8—71no—
352C2×#103—71no—
353C2×#103C2×D711yescharacteristic
354C2×#102—71no—
355C2×#102—71no—
356C2×#102—71no—
357C2×#102—71no—
358C2×#102—71no—
359C2×#102C2×D711yescharacteristic
360C2×C22⋊C8—71no—
361C2×C22⋊C8—71no—
362C2×#97—71no—
363C2×#97C2×D711yescharacteristic
364C23×C7—22no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7C22×D411yescharacteristic
369C22×D7—22no—
370C22×D7—24no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—22no—
374C22×D7—22no—
375C22×D7—42no—
376C22×D7—42no—
377C22×D7—42no—
378C22×D7—42no—
379C22×D7—42no—
380C22×D7C22×D412yes—
381C7×Q8—24no—
382C7×Q8—22no—
383C7×Q8C2×#4114yescomplemented
384C7×D4—22no—
385C7×D4—22no—
386C7×D4—42no—
387C2×C4×C7—24no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—48no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D412yes—
398C2×C4×C7C22×D411yescharacteristic
399C2×C4×C7C2×#4112yes—
400C2×C4×C7C2×#4112yes—
401C2×C4×C7C2511yescharacteristic
402C22⋊D7—48no—
403C22⋊D7—48no—
404C22⋊D7—48no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—22no—
408C2×Dic7—22no—
409C2×Dic7—42no—
410C2×Dic7—42no—
411C2×Dic7AGL(1,ℤ/8)14yes—
412C2×Dic7C22×D412yes—
413C2×Dic7C22×D412yes—
414C2×Dic7C22×D412yes—
415D28—216no—
416D28—24no—
417D28—22no—
418D28—22no—
419D28—22no—
420D28—48no—
421D28—42no—
422D28C2×#4114yescomplemented
423C4×D7—216no—
424C4×D7—24no—
425C4×D7—22no—
426C4×D7—22no—
427C4×D7—28no—
428C4×D7—44no—
429C4×D7—48no—
430C4×D7—48no—
431C4×D7—48no—
432Dic14—48no—
433C7×C8—22no—
434C7×C8—22no—
435C7⋊C8—22no—
436C7⋊C8—22no—
437C2×#41—74no—
438C2×#41—148no—
439C2×#41—142no—
440C2×#41—144no—
441C2×#41—144no—
442C2×#41—288no—
443C22×Q8—141no—
444C22×Q8C22×D711yescharacteristic
445C22×D4—71no—
446C22×D4—71no—
447C22×D4—141no—
448C22×D4—141no—
449C22×D4—141no—
450C22×D4—141no—
451C22×D4—141no—
452C22×D4C22×D711yescharacteristic
453C23×C4—21no—
454C23×C4—71no—
455C23×C4—71no—
456C23×C4—71no—
457C23×C4—141no—
458C23×C4—141no—
459C23×C4—141no—
460C23×C4—141no—
461C2×SD16—24no—
462C2×SD16—74no—
463C2×SD16—144no—
464C2×SD16C22×D714yes—
465C2×D8—74no—
466C2×D8—74no—
467C2×D8—144no—
468C2×D8—144no—
469C22×C8—71no—
470C22×C8—71no—
471C22×C8C22×D711yescharacteristic
472C22×C8C22×D711yescharacteristic
473C4⋊Q8—74no—
474C4⋊Q8—142no—
475#127—74no—
476#127—142no—
477#124—148no—
478#121—74no—
479#121—74no—
480#121—148no—
481#121—142no—
482#121—142no—
483C4×Q8—22no—
484C4×Q8—74no—
485C4×Q8—142no—
486C4×Q8C22×D714yes—
487C4×D4—22no—
488C4×D4—74no—
489C4×D4—74no—
490C4×D4—74no—
491C4×D4—148no—
492C4×D4—142no—
493C4×D4—148no—
494C4×D4—148no—
495C4×D4—142no—
496C4×D4—142no—
497C4×D4C22×D714yes—
498#117—74no—
499#117—148no—
500#117—142no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—71no—
503C2×C4⋊C4—71no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4—141no—
506C2×C4⋊C4C22×D711yescharacteristic
507C2×C4⋊C4C22×D711yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C42—21no—
516C2×C42—71no—
517C2×C42—71no—
518C2×C42—71no—
519C2×C42—74no—
520C2×C42—74no—
521C2×C42—148no—
522C2×C42—141no—
523C2×C42—141no—
524C2×C42C22×D711yescharacteristic
525#107—74no—
526#107C22×D714yes—
527#106—74no—
528#106—74no—
529C4⋊C8—74no—
530C4⋊C8—74no—
531#103—74no—
532#103C22×D714yes—
533#102—74no—
534#102—74no—
535#102—74no—
536#102—74no—
537#102—74no—
538#102C22×D714yes—
539C22⋊C8—74no—
540C22⋊C8—74no—
541#97—74no—
542#97C22×D714yes—
543C22×C7—42no—
544C22×C7—42no—
545C22×C7—42no—
546C22×C7—84no—
547C22×C7#52512yes—
548C22×C7C2×AGL(1,ℤ/8)12yes—
549C22×C7#57512yes—
550C22×C7C23×D411yescharacteristic
551C2×D7—22no—
552C2×D7—24no—
553C2×D7—22no—
554C2×D7—22no—
555C2×D7—44no—
556C2×D7—48no—
557C2×D7—42no—
558C2×D7—42no—
559C2×D7—42no—
560C2×D7—42no—
561C2×D7—42no—
562C2×D7—84no—
563C4×C7—24no—
564C4×C7—22no—
565C4×C7—22no—
566C4×C7—42no—
567C4×C7—42no—
568C4×C7#52512yes—
569C4×C7C22×#4111yescharacteristic
570C4×C7C22×#4111yescharacteristic
571Dic7—22no—
572Dic7—22no—
573Dic7—42no—
574Dic7—42no—
575Dic7C2×AGL(1,ℤ/8)14yes—
576C24—21no—
577C24—71no—
578C24—141no—
579C24—141no—
580#41—148no—
581#41—1416no—
582#41—148no—
583#41—2832no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—144no—
587C2×Q8—284no—
588C2×Q8#115714yescomplemented
589C2×Q8C23×D712yes—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—74no—
594C2×D4—72no—
595C2×D4—72no—
596C2×D4—144no—
597C2×D4—148no—
598C2×D4—144no—
599C2×D4—144no—
600C2×D4—144no—
601C2×D4—144no—
602C2×D4—142no—
603C2×D4—142no—
604C2×D4—141no—
605C2×D4—141no—
606C2×D4—142no—
607C2×D4—284no—
608C2×D4—284no—
609C2×D4—284no—
610C2×D4—284no—
611C2×D4C23×D712yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—44no—
617C22×C4—71no—
618C22×C4—71no—
619C22×C4—71no—
620C22×C4—72no—
621C22×C4—74no—
622C22×C4—72no—
623C22×C4—74no—
624C22×C4—144no—
625C22×C4—144no—
626C22×C4—144no—
627C22×C4—148no—
628C22×C4—142no—
629C22×C4—142no—
630C22×C4—141no—
631C22×C4—141no—
632C22×C4—144no—
633C22×C4—144no—
634C22×C4—282no—
635C22×C4—284no—
636C22×C4—284no—
637C22×C4—284no—
638C22×C4D4×D711yescharacteristic
639C22×C4D4×D711yescharacteristic
640C22×C4C23×D711yescharacteristic
641SD16—28no—
642SD16—148no—
643D8—148no—
644D8—148no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—72no—
648C2×C8—72no—
649C2×C8—142no—
650C2×C8—142no—
651C2×C8C23×D712yes—
652C2×C8C23×D712yes—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—72no—
657C4⋊C4—72no—
658C4⋊C4—144no—
659C4⋊C4—144no—
660C4⋊C4—141no—
661C4⋊C4—141no—
662C4⋊C4C23×D712yes—
663C4⋊C4C23×D712yes—
664C22⋊C4—24no—
665C22⋊C4—144no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C42—24no—
672C42—74no—
673C42—74no—
674C42—72no—
675C42—72no—
676C42—144no—
677C42—144no—
678C42D4×D712yes—
679C42C23×D712yes—
680C2×C7—82no—
681C2×C7#311514yescomplemented
682C2×C7C2×#52511yescharacteristic
683C2×C7C22×AGL(1,ℤ/8)11yescharacteristic
684C2×C7C2×#57511yescharacteristic
685D7—42no—
686D7—44no—
687D7—82no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—72no—
693C23—142no—
694C23—142no—
695C23—144no—
696C23—142no—
697C23—142no—
698C23—142no—
699C23—282no—
700C23—282no—
701C23—282no—
702C23—282no—
703C23—282no—
704C23C2×D4×D711yescharacteristic
705Q8—24no—
706Q8—22no—
707Q8—288no—
708Q8C2×#115714yescomplemented
709D4—22no—
710D4—22no—
711D4—42no—
712D4—74no—
713D4—1416no—
714D4—144no—
715D4—142no—
716D4—142no—
717D4—142no—
718D4—288no—
719D4—288no—
720D4—288no—
721D4—288no—
722D4—282no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—74no—
733C2×C4—72no—
734C2×C4—72no—
735C2×C4—72no—
736C2×C4—148no—
737C2×C4—1416no—
738C2×C4—142no—
739C2×C4—142no—
740C2×C4—144no—
741C2×C4—142no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—284no—
746C2×C4—288no—
747C2×C4—288no—
748C2×C4—288no—
749C2×C4—282no—
750C2×C4—282no—
751C2×C4C2×#115712yes—
752C2×C4C2×D4×D712yes—
753C2×C4C2×D4×D712yes—
754C2×C4C2×D4×D711yescharacteristic
755C2×C4D7×#4112yes—
756C2×C4C24×D711yescharacteristic
757C8—22no—
758C8—22no—
759C8—142no—
760C8—142no—
761C7C2×#311511yescharacteristic, complemented, Sylow
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—142no—
767C22—142no—
768C22—144no—
769C22—142no—
770C22—282no—
771C22—282no—
772C22—284no—
773C22—288no—
774C22—282no—
775C22—282no—
776C22—282no—
777C22—564no—
778C22#9023812yes—
779C22D7×AGL(1,ℤ/8)12yes—
780C22#9046812yes—
781C22C22×D4×D711yescharacteristic
782C4—22no—
783C4—22no—
784C4—24no—
785C4—42no—
786C4—42no—
787C4—74no—
788C4—142no—
789C4—142no—
790C4—282no—
791C4—282no—
792C4#9023812yes—
793C4C22×#115711yescharacteristic
794C4C2×D7×#4111yescharacteristic
795C2—82no—
796C2—282no—
797C2—284no—
798C2—562no—
799C2#1173725614yesdirect product factor
800C2C2×#9023811yescharacteristic
801C2C2×D7×AGL(1,ℤ/8)11yescharacteristic
802C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#440C2
socleC23×C7C22×D4
hypercenterC2×#440D7
hypocenterC7C2×#3115
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×C4×#1161C2semidirect
2. C2×#90239C2semidirect
3. C2×C7×#440C2semidirect
4. C2×#89944C2semidirect
5. C2×#89935C2semidirect
6. C2×#89798C2semidirect
7. C2×#89786C2semidirect
8. #11737256C2direct (N × H)
9. C2×#89662C2semidirect
10. C2×#89657C2semidirect
11. C2×#89583C2semidirect
12. C2×#89563C2semidirect
13. C2×#89558C2semidirect
14. C2×#89551C2semidirect
15. C2×#89483C2semidirect
16. C2×#89477C2semidirect
30. C4×#1161C22semidirect
32. #90239C22semidirect
46. C7×#440C22semidirect
53. #89944C22semidirect
54. #89935C22semidirect
62. #89798C22semidirect
63. #89786C22semidirect
69. #89662C22semidirect
70. #89657C22semidirect
71. #89583C22semidirect
72. #89563C22semidirect
73. #89558C22semidirect
74. #89551C22semidirect
75. #89483C22semidirect
76. #89477C22semidirect
198. C2×#440D7semidirect
206. C2×C7×Q8#41semidirect
244. C2×D28#41semidirect
344. #440C2×D7semidirect
383. C7×Q8C2×#41semidirect
422. D28C2×#41semidirect
588. C2×Q8#1157semidirect
681. C2×C7#3115semidirect
708. Q8C2×#1157semidirect
761. C7C2×#3115semidirect
799. C2#11737256direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#11612
C2×#902392
C2×C7×#4402
C2×#899442
C2×#899352
C2×#897982
C2×#897862
#117372562
C2×#896622
C2×#896572
C2×#895832
C2×#895632
C2×#895582
C2×#895512
C2×#894832
C2×#894772
C2×#31157