Finite Group Databasebeta

← C2×#11740882 #14226700

Subgroups — C2×#11740882 #14226700

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×C7×#540C211yesmaximal, characteristic, complemented
2C2×#90225C211yesmaximal, characteristic, complemented
3#11740882C2116yesmaximal, direct product factor
4C2×#89847C211yesmaximal, characteristic, complemented
5C2×#89844C211yesmaximal, characteristic, complemented
6C2×#89835C211yesmaximal, characteristic, complemented
7C2×#89838C211yesmaximal, characteristic, complemented
8C2×#89811C211yesmaximal, characteristic, complemented
9C2×#89814C211yesmaximal, characteristic, complemented
10C2×#89810C211yesmaximal, characteristic, complemented
11C2×#89813C211yesmaximal, characteristic, complemented
12C2×#89788C211yesmaximal, characteristic, complemented
13C2×#89788C211yesmaximal, characteristic, complemented
14C2×#89780C211yesmaximal, characteristic, complemented
15C2×#89779C211yesmaximal, characteristic, complemented
16C2×#89771C211yesmaximal, characteristic, complemented
17C7×#540—24no—
18C7×#540C2218yescomplemented
19C2×C7×#127C2211yescharacteristic
20C2×C7×#125C2211yescharacteristic
21C2×C7×#123—21no—
22C2×C7×#123—21no—
23C2×C7×#121—21no—
24C2×C7×#121—21no—
25C2×C7×#121C2211yescharacteristic
26C2×C7×#121C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×#1142C2211yescharacteristic
31C22×#1142C2211yescharacteristic
32C22×#1141C2211yescharacteristic
33C22×#1141C2211yescharacteristic
34C2×#6493C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90225—24no—
39#90225C2218yescomplemented
40C2×#6461—21no—
41C2×#6459—21no—
42C2×#6448—21no—
43C2×#6446—21no—
44C2×#6438C2211yescharacteristic
45C2×C4×D28C2211yescharacteristic
46C2×#6432C2211yescharacteristic
47C2×C4×Dic14C2211yescharacteristic
48C2×#6406C2211yescharacteristic
49C2×#6406C2211yescharacteristic
50C2×#6406C2211yescharacteristic
51C2×#6406C2211yescharacteristic
52#89847C2218yescomplemented
53#89844C2218yescomplemented
54#89838C2218yescomplemented
55#89835C2218yescomplemented
56#89814C2218yescomplemented
57#89813C2218yescomplemented
58#89811C2218yescomplemented
59#89810C2218yescomplemented
60#89788C2218yescomplemented
61#89788C2218yescomplemented
62#89780C2218yescomplemented
63#89779C2218yescomplemented
64#89771C2218yescomplemented
65C2×#6384C2211yescharacteristic
66C2×#6384C2211yescharacteristic
67C2×#6383C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6382C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×C4⋊(C7⋊C8)C2211yescharacteristic
77C2×#3257—71nomaximal, Sylow
78C22×C7×D4—21no—
79C22×C7×D4—21no—
80C22×C7×D4—21no—
81C22×C7×D4—21no—
82C22×C7×D4C2311yescharacteristic
83C22×C7×D4C2311yescharacteristic
84C23×C4×C7—21no—
85C23×C4×C7—21no—
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—21no—
88C22×D28C2311yescharacteristic
89C22×C4×D7—21no—
90C22×Dic14—21no—
91C22×Dic14C2311yescharacteristic
92C7×#127—22no—
93C7×#127C2314yes—
94C7×#125—22no—
95C7×#125C2314yes—
96C7×#123—28no—
97C7×#123—28no—
98C7×#121—22no—
99C7×#121—22no—
100C7×#121—28no—
101C7×#121—28no—
102C7×#121C2314yes—
103C7×#121C2314yes—
104C4×C7×D4—22no—
105C4×C7×D4—22no—
106C4×C7×D4C2314yes—
107C4×C7×D4C2314yes—
108C7×#117D414yes—
109C7×#117C2314yes—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4D411yescharacteristic
113C2×C7×C4⋊C4D411yescharacteristic
114C2×C7×C4⋊C4C2311yescharacteristic
115C2×C7×C4⋊C4C2311yescharacteristic
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C7×C22⋊C4—21no—
119C2×C7×C22⋊C4—21no—
120C2×C7×C22⋊C4D411yescharacteristic
121C2×C7×C22⋊C4D411yescharacteristic
122C2×C42×C7C2311yescharacteristic
123C2×C42×C7C2311yescharacteristic
124C2×C22⋊Dic7—21no—
125C2×#1142—42no—
126C2×#1142—42no—
127C2×#1142C2314yes—
128C2×#1142C2314yes—
129C2×#1141—42no—
130C2×#1141—42no—
131C2×#1141C2314yes—
132C2×#1141C2314yes—
133#6493—22no—
134#6493C2314yes—
135C2×(C2×D7)⋊C4—21no—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4—21no—
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7C2311yescharacteristic
141C2×C4⋊Dic7C2311yescharacteristic
142#6487—22no—
143#6487C2314yes—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×C4×Dic7—21no—
147C2×#1136—42no—
148C2×#1136C2314yes—
149C22×C7⋊C8—42no—
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C22×C7⋊C8C2311yescharacteristic
154C22×C7⋊C8C2314yes—
155#6461—28no—
156#6459—28no—
157#6448—28no—
158#6446—28no—
159#6438—22no—
160#6438C2314yes—
161C4×D28—22no—
162C4×D28C2314yes—
163#6432—22no—
164#6432C2314yes—
165C4×Dic14—22no—
166C4×Dic14C2314yes—
167#6406C2314yes—
168#6406C2314yes—
169#6406C2314yes—
170#6406C2314yes—
171#6384C2314yes—
172#6384C2314yes—
173#6383C2314yes—
174#6383C2314yes—
175#6382C2314yes—
176#6382C2314yes—
177#6381C2314yes—
178#6381C2314yes—
179C4⋊(C7⋊C8)C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#542—71no—
184C2×#540D711yescharacteristic, complemented
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×#459—71no—
198C2×#424—71no—
199C24×C7—21no—
200C24×C7—21no—
201C24×C7C2×D411yescharacteristic
202C23×D7—21no—
203C2×C7×D4—24no—
204C2×C7×D4—24no—
205C2×C7×D4—21no—
206C2×C7×D4—21no—
207C2×C7×D4—24no—
208C2×C7×D4—24no—
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—82no—
216C2×C7×D4—82no—
217C2×C7×D4C2412yes—
218C2×C7×D4C2412yes—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—21no—
222C22×C4×C7—21no—
223C22×C4×C7—24no—
224C22×C4×C7—24no—
225C22×C4×C7—82no—
226C22×C4×C7—82no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2×D411yescharacteristic
230C22×C4×C7C2×D412yes—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D411yescharacteristic
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C2×C22⋊D7—24no—
236C2×C22⋊D7—82no—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C2×D28—22no—
241C2×D28—22no—
242C2×D28—21no—
243C2×D28C2412yes—
244C2×C4×D7—24no—
245C2×C4×D7—82no—
246C2×Dic14—22no—
247C2×Dic14—22no—
248C2×Dic14—21no—
249C2×Dic14—24no—
250C2×Dic14—82no—
251C2×Dic14C2412yes—
252C7×C4⋊C4—24no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4—21no—
255C7×C4⋊C4—21no—
256C7×C4⋊C4C2×D414yes—
257C7×C4⋊C4C2×D414yes—
258C7×C4⋊C4C2412yes—
259C7×C4⋊C4C2412yes—
260C7×C22⋊C4—24no—
261C7×C22⋊C4—24no—
262C7×C22⋊C4—24no—
263C7×C22⋊C4—24no—
264C7×C22⋊C4C2×D414yes—
265C7×C22⋊C4C2×D414yes—
266C42×C7C2×D412yes—
267C42×C7C2×D412yes—
268C42×C7C2412yes—
269C42×C7C2412yes—
270C22⋊Dic7—24no—
271#1142—44no—
272#1142—44no—
273#1141—44no—
274#1141—44no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278(C2×D7)⋊C4—24no—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7—24no—
282C4⋊Dic7C2412yes—
283C4⋊Dic7C2412yes—
284Dic7⋊C4—24no—
285Dic7⋊C4—24no—
286C4×Dic7—24no—
287#1136—44no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—22no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—44no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C22×SD16—71no—
298C22×SD16—71no—
299C22×D8—71no—
300C22×D8—71no—
301C22×M16—71no—
302C23×C8—71no—
303#542—78no—
304#542—144no—
305#540—24no—
306#540C2×D718yescomplemented
307C2×C4⋊Q8—71no—
308C2×#127C2×D711yescharacteristic
309C2×#126—141no—
310C2×#125C2×D711yescharacteristic
311C2×#124—71no—
312C2×#124—141no—
313C2×#123—21no—
314C2×#123—21no—
315C2×#123—141no—
316C2×C22⋊Q8—71no—
317C2×C22⋊Q8—141no—
318C2×#121—21no—
319C2×#121—21no—
320C2×#121—71no—
321C2×#121C2×D711yescharacteristic
322C2×#121C2×D711yescharacteristic
323C2×C4×Q8—71no—
324C2×C4×D4—71no—
325C2×C4×D4C2×D711yescharacteristic
326C2×C4×D4C2×D711yescharacteristic
327C2×#117C2×D711yescharacteristic
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#459—78no—
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⋊C8—71no—
349C2×#103—71no—
350C2×#103—71no—
351C2×#102—71no—
352C2×#102—71no—
353C2×#102—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#102—71no—
357C23×C7—22no—
358C23×C7—22no—
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—42no—
363C23×C7—42no—
364C23×C7—42no—
365C23×C7—42no—
366C23×C7—42no—
367C23×C7—42no—
368C23×C7C22×D412yes—
369C23×C7C22×D411yescharacteristic
370C22×D7—22no—
371C22×D7—42no—
372C22×D7—42no—
373C22×D7—42no—
374C7×D4—22no—
375C7×D4—22no—
376C7×D4—22no—
377C7×D4—22no—
378C7×D4—42no—
379C7×D4—42no—
380C7×D4—84no—
381C7×D4—84no—
382C7×D4—84no—
383C7×D4—84no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—24no—
390C2×C4×C7—22no—
391C2×C4×C7—22no—
392C2×C4×C7—22no—
393C2×C4×C7—22no—
394C2×C4×C7—42no—
395C2×C4×C7—42no—
396C2×C4×C7—84no—
397C2×C4×C7—84no—
398C2×C4×C7C22×D412yes—
399C2×C4×C7C22×D412yes—
400C2×C4×C7C22×D412yes—
401C2×C4×C7C22×D412yes—
402C2×C4×C7C22×D412yes—
403C2×C4×C7C22×D411yescharacteristic
404C2×C4×C7H(5,𝔽2)12yes—
405C2×C4×C72−1+412yes—
406C2×C4×C7C2511yescharacteristic
407C22⋊D7—84no—
408C2×Dic7—22no—
409C2×Dic7—22no—
410C2×Dic7—22no—
411C2×Dic7—42no—
412C2×Dic7—42no—
413C2×Dic7—42no—
414D28—22no—
415D28—22no—
416D28—42no—
417C4×D7—84no—
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—21no—
431C22×D4—21no—
432C22×D4—71no—
433C22×D4—141no—
434C22×D4C22×D711yescharacteristic
435C22×D4C22×D711yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—141no—
439C23×C4C22×D711yescharacteristic
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—282no—
443C2×SD16—282no—
444C2×D8—74no—
445C2×D8—74no—
446C2×D8—282no—
447C2×D8—282no—
448C2×M16—74no—
449C2×M16—282no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—71no—
453C22×C8—71no—
454C22×C8—74no—
455C22×C8—282no—
456C4⋊Q8—74no—
457C4⋊Q8—142no—
458#127—22no—
459#127C22×D714yes—
460#126—148no—
461#125—22no—
462#125C22×D714yes—
463#124—74no—
464#124—148no—
465#124—142no—
466#123—28no—
467#123—28no—
468#123—148no—
469C22⋊Q8—74no—
470C22⋊Q8—142no—
471C22⋊Q8—148no—
472#121—22no—
473#121—22no—
474#121—28no—
475#121—28no—
476#121—74no—
477#121—142no—
478#121C22×D714yes—
479#121C22×D714yes—
480C4×Q8—74no—
481C4×Q8—142no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—74no—
485C4×D4—142no—
486C4×D4C22×D714yes—
487C4×D4C22×D714yes—
488#117C22⋊D714yes—
489#117C22×D714yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4—141no—
497C2×C4⋊C4C22⋊D711yescharacteristic
498C2×C4⋊C4C22⋊D711yescharacteristic
499C2×C4⋊C4C22×D711yescharacteristic
500C2×C4⋊C4C22×D711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C22⋊C4—141no—
510C2×C22⋊C4C22⋊D711yescharacteristic
511C2×C22⋊C4C22⋊D711yescharacteristic
512C2×C42—141no—
513C2×C42C22×D711yescharacteristic
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⋊C8—74no—
523#103—74no—
524#103—74no—
525#102—74no—
526#102—74no—
527#102—74no—
528#102—74no—
529#102—74no—
530#102—74no—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7—42no—
536C22×C7—42no—
537C22×C7—42no—
538C22×C7—42no—
539C22×C7—42no—
540C22×C7—42no—
541C22×C7—84no—
542C22×C7—84no—
543C22×C7#53712yes—
544C22×C7#57612yes—
545C22×C7#57712yes—
546C22×C7C23×D411yescharacteristic
547C2×D7—42no—
548C2×D7—42no—
549C2×D7—42no—
550C2×D7—84no—
551C4×C7—22no—
552C4×C7—22no—
553C4×C7—22no—
554C4×C7—22no—
555C4×C7—22no—
556C4×C7—42no—
557C4×C7—42no—
558C4×C7#53712yes—
559C4×C7C2×H(5,𝔽2)11yescharacteristic
560C4×C7C2×2−1+411yescharacteristic
561Dic7—42no—
562Dic7—42no—
563Dic7—42no—
564C24—21no—
565C24—21no—
566C24—141no—
567C24C2×C22⋊D711yescharacteristic
568C2×Q8—72no—
569C2×Q8—141no—
570C2×Q8—144no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8—562no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—72no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4—144no—
590C2×D4—142no—
591C2×D4—142no—
592C2×D4—141no—
593C2×D4—562no—
594C2×D4C23×D712yes—
595C2×D4C23×D712yes—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—141no—
605C22×C4—141no—
606C22×C4—141no—
607C22×C4—144no—
608C22×C4—562no—
609C22×C4C2×C22⋊D712yes—
610C22×C4C2×C22⋊D711yescharacteristic
611C22×C4C2×C22⋊D711yescharacteristic
612C22×C4C2×C22⋊D711yescharacteristic
613C22×C4C2×C22⋊D711yescharacteristic
614C22×C4C2×C22⋊D711yescharacteristic
615C22×C4C23×D712yes—
616C22×C4C23×D711yescharacteristic
617SD16—284no—
618SD16—284no—
619D8—284no—
620D8—284no—
621M16—284no—
622C2×C8—72no—
623C2×C8—72no—
624C2×C8—72no—
625C2×C8—72no—
626C2×C8—142no—
627C2×C8—142no—
628C2×C8—142no—
629C2×C8—142no—
630C2×C8—284no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—72no—
636C4⋊C4—72no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—141no—
640C4⋊C4—141no—
641C4⋊C4—144no—
642C4⋊C4C2×C22⋊D714yes—
643C4⋊C4C2×C22⋊D714yes—
644C4⋊C4C23×D712yes—
645C4⋊C4C23×D712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—144no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4C2×C22⋊D714yes—
656C22⋊C4C2×C22⋊D714yes—
657C42—144no—
658C42C2×C22⋊D712yes—
659C42C2×C22⋊D712yes—
660C42C23×D712yes—
661C42C23×D712yes—
662C2×C7—42no—
663C2×C7—82no—
664C2×C7—82no—
665C2×C7#325714yescomplemented
666C2×C7C2×#53711yescharacteristic
667C2×C7C2×#57611yescharacteristic
668C2×C7C2×#57711yescharacteristic
669D7—82no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—142no—
682C23—282no—
683C23—282no—
684C23—282no—
685C23C22×C22⋊D712yes—
686C23C22×C22⋊D711yescharacteristic
687Q8—142no—
688Q8—142no—
689Q8—282no—
690Q8—564no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—42no—
696D4—42no—
697D4—84no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—142no—
702D4—142no—
703D4—282no—
704D4—564no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4—142no—
720C2×C4—142no—
721C2×C4—142no—
722C2×C4—282no—
723C2×C4—282no—
724C2×C4—282no—
725C2×C4—564no—
726C2×C4#655312yes—
727C2×C4#655412yes—
728C2×C4C22×C22⋊D712yes—
729C2×C4C22×C22⋊D712yes—
730C2×C4C22×C22⋊D712yes—
731C2×C4C22×C22⋊D712yes—
732C2×C4C22×C22⋊D712yes—
733C2×C4C22×C22⋊D711yescharacteristic
734C2×C4C24×D711yescharacteristic
735C8—142no—
736C8—142no—
737C8—142no—
738C8—142no—
739C7C2×#325711yescharacteristic, complemented, Sylow
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—282no—
753C22—282no—
754C22—282no—
755C22—564no—
756C22#9052412yes—
757C22#9052612yes—
758C22#9052712yes—
759C22C23×C22⋊D711yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—282no—
768C4—282no—
769C4—282no—
770C4#9052412yes—
771C4C2×#655311yescharacteristic
772C4C2×#655411yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—562no—
777C2#1174088214yesdirect product factor
778C2C2×#9052411yescharacteristic
779C2C2×#9052611yescharacteristic
780C2C2×#9052711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#540C2
socleC23×C7C22×D4
hypercenterC2×#540D7
hypocenterC7C2×#3257
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C7×#540C2semidirect
2. C2×#90225C2semidirect
3. #11740882C2direct (N × H)
4. C2×#89847C2semidirect
5. C2×#89844C2semidirect
6. C2×#89835C2semidirect
7. C2×#89838C2semidirect
8. C2×#89811C2semidirect
9. C2×#89814C2semidirect
10. C2×#89810C2semidirect
11. C2×#89813C2semidirect
12. C2×#89788C2semidirect
13. C2×#89788C2semidirect
14. C2×#89780C2semidirect
15. C2×#89779C2semidirect
16. C2×#89771C2semidirect
18. C7×#540C22semidirect
39. #90225C22semidirect
52. #89847C22semidirect
53. #89844C22semidirect
54. #89838C22semidirect
55. #89835C22semidirect
56. #89814C22semidirect
57. #89813C22semidirect
58. #89811C22semidirect
59. #89810C22semidirect
60. #89788C22semidirect
61. #89788C22semidirect
62. #89780C22semidirect
63. #89779C22semidirect
64. #89771C22semidirect
184. C2×#540D7semidirect
306. #540C2×D7semidirect
665. C2×C7#3257semidirect
739. C7C2×#3257semidirect
777. C2#11740882direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5402
C2×#902252
#117408822
C2×#898472
C2×#898442
C2×#898352
C2×#898382
C2×#898112
C2×#898142
C2×#898102
C2×#898132
C2×#897882
C2×#897802
C2×#897792
C2×#897712
C2×#32577