Finite Group Databasebeta

← C2×#11738963 #14221632

Subgroups — C2×#11738963 #14221632

Order 1792.

2170 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90319C211yesmaximal, characteristic
2C2×#90214C211yesmaximal, characteristic
3C2×C7×#485C211yesmaximal, characteristic, complemented
4C2×#89816C211yesmaximal, characteristic, complemented
5C2×#89768C211yesmaximal, characteristic, complemented
6#11738963C2116yesmaximal, direct product factor
7C2×#89656C211yesmaximal, characteristic, complemented
8C2×#89653C211yesmaximal, characteristic, complemented
9C2×#89632C211yesmaximal, characteristic, complemented
10C2×#89639C211yesmaximal, characteristic, complemented
11C2×#89587C211yesmaximal, characteristic, complemented
12C2×#89577C211yesmaximal, characteristic, complemented
13C2×#89574C211yesmaximal, characteristic, complemented
14C2×D7×#103C211yesmaximal, characteristic, complemented
15C2×#89499C211yesmaximal, characteristic
16C2×#89493C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C22×C4⋊Dic7C2211yescharacteristic
23C2×#6487C2211yescharacteristic
24C22×#1131C2211yescharacteristic
25C22×C8×D7C2211yescharacteristic
26#90319—24no—
27#90319C2218yes—
28#90214—24no—
29#90214C2218yes—
30C2×#6460C2211yescharacteristic
31C2×#6457—21no—
32C2×#6455C2211yescharacteristic
33C2×#6455C2211yescharacteristic
34C2×#6455C2211yescharacteristic
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×D7×C4⋊C4C2211yescharacteristic
37C2×#6451—21no—
38C2×#6448—21no—
39C2×#6446—21no—
40C2×(C22⋊D7)⋊C4—21no—
41C2×(C22⋊D7)⋊C4—21no—
42C2×C4×D28—21no—
43C2×C4×Dic14—21no—
44C7×#485C2218yescomplemented
45C2×C7×#107C2211yescharacteristic
46C2×C7×#106C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×(C2×D7)⋊C8C2211yescharacteristic
54C2×(C2×D7)⋊C8C2211yescharacteristic
55C2×#6391C2211yescharacteristic
56C2×#6391C2211yescharacteristic
57C2×#6390C2211yescharacteristic
58C2×#6390C2211yescharacteristic
59#89816C2218yescomplemented
60#89768C2218yescomplemented
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89656C2218yescomplemented
68#89653C2218yescomplemented
69#89639C2218yescomplemented
70#89632C2218yescomplemented
71#89587C2218yescomplemented
72#89577C2218yescomplemented
73#89574C2218yescomplemented
74D7×#103C2218yescomplemented
75#89499C2218yes—
76#89493C2218yescomplemented
77C2×#3097—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7C2311yescharacteristic
80C22×C22⋊D7D411yescharacteristic
81C22×C22⋊D7D411yescharacteristic
82C23×Dic7—21no—
83C2×Q8×D7—22no—
84C2×Q8×D7—24no—
85C2×Q8×D7—24no—
86C2×Q8×D7C2314yes—
87C2×#1157—24no—
88C2×#1157—24no—
89C2×#1157D414yes—
90C2×#1157C2314yes—
91C22×D28D411yescharacteristic
92C22×C4×D7—21no—
93C22×C4×D7—21no—
94C22×C4×D7—21no—
95C22×C4×D7C2311yescharacteristic
96C22×C4×D7C2311yescharacteristic
97C22×Dic14—21no—
98C22×Dic14D411yescharacteristic
99C22×Dic14C2311yescharacteristic
100C22×C7×C8C2311yescharacteristic
101C22×C7×C8C2311yescharacteristic
102C7×C22⋊Q8—22no—
103C7×C22⋊Q8C2314yes—
104C7×#117—22no—
105C7×#117C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C22⋊C4—21no—
111C2×C7×C22⋊C4—21no—
112C2×C42×C7—21no—
113C2×C22⋊Dic7—21no—
114#6509—22no—
115#6509C2314yes—
116C2×(C2×D7)⋊C4—21no—
117C2×(C2×D7)⋊C4—21no—
118C2×(C2×D7)⋊C4—21no—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×C4⋊Dic7—21no—
122C2×C4⋊Dic7—22no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7C2311yescharacteristic
125C2×C4⋊Dic7C2311yescharacteristic
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2314yes—
128#6487—22no—
129#6487C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7—21no—
137C22×C7⋊C8C2311yescharacteristic
138C22×C7⋊C8C2311yescharacteristic
139C2×#1131—24no—
140C2×#1131C2314yes—
141C2×C8×D7—24no—
142C2×C8×D7C2314yes—
143#6460—22no—
144#6460C2314yes—
145#6457—28no—
146#6455—22no—
147#6455—22no—
148#6455—22no—
149#6455C2314yes—
150#6455C2314yes—
151#6455C2314yes—
152D7×C4⋊C4—22no—
153D7×C4⋊C4—22no—
154D7×C4⋊C4C2314yes—
155D7×C4⋊C4C2314yes—
156#6451—28no—
157#6448—28no—
158#6446—28no—
159(C22⋊D7)⋊C4—28no—
160(C22⋊D7)⋊C4—28no—
161C4×D28—28no—
162C4×Dic14—28no—
163C7×#107C2314yes—
164C7×#106C2314yes—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171(C2×D7)⋊C8C2314yes—
172(C2×D7)⋊C8C2314yes—
173#6391C2314yes—
174#6391C2314yes—
175#6390C2314yes—
176#6390C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6382C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182#6381C2314yes—
183C2×#536—71no—
184C2×#520—71no—
185#3097—716no—
186C2×#484—71no—
187C2×#484—71no—
188C2×#485—71no—
189C2×#485—71no—
190C2×#485—71no—
191C2×#485D711yescharacteristic, complemented
192C2×#483—71no—
193C2×#483—71no—
194C2×#428—71no—
195C2×#427—71no—
196C2×#419—71no—
197C22×#103—71no—
198C2×#408—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7C2×D411yescharacteristic
201C23×D7C2×D411yescharacteristic
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8C2412yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—21no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7C2×D414yes—
219C2×C22⋊D7C2×D414yes—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C22×Dic7—21no—
223C22×Dic7—21no—
224C22×Dic7—24no—
225C22×Dic7—82no—
226C22×Dic7C2×D411yescharacteristic
227C22×Dic7C2×D411yescharacteristic
228Q8×D7—28no—
229Q8×D7—28no—
230Q8×D7—48no—
231#1157—216no—
232#1157—28no—
233#1157—28no—
234C2×D28—24no—
235C2×D28C2×D414yes—
236C2×C4×D7—22no—
237C2×C4×D7—22no—
238C2×C4×D7—24no—
239C2×C4×D7—24no—
240C2×C4×D7—24no—
241C2×C4×D7—44no—
242C2×C4×D7—82no—
243C2×C4×D7—82no—
244C2×C4×D7C2×D412yes—
245C2×C4×D7C2×D412yes—
246C2×C4×D7#4114yes—
247C2×C4×D7#4114yes—
248C2×C4×D7C2412yes—
249C2×C4×D7C2412yes—
250C2×Dic14—24no—
251C2×Dic14—22no—
252C2×Dic14—22no—
253C2×Dic14—21no—
254C2×Dic14—24no—
255C2×Dic14—44no—
256C2×Dic14C2×D414yes—
257C2×Dic14C2412yes—
258C2×C7×C8—22no—
259C2×C7×C8—22no—
260C2×C7×C8C2412yes—
261C2×C7×C8C2412yes—
262C7×C4⋊C4—24no—
263C7×C4⋊C4—21no—
264C7×C4⋊C4—21no—
265C7×C4⋊C4—21no—
266C7×C4⋊C4C2412yes—
267C7×C4⋊C4C2412yes—
268C7×C4⋊C4C2412yes—
269C7×C22⋊C4—24no—
270C7×C22⋊C4—24no—
271C42×C7—24no—
272C22⋊Dic7—24no—
273(C2×D7)⋊C4—24no—
274(C2×D7)⋊C4—24no—
275(C2×D7)⋊C4—24no—
276(C2×D7)⋊C4—24no—
277(C2×D7)⋊C4—24no—
278C4⋊Dic7—24no—
279C4⋊Dic7—21no—
280C4⋊Dic7—21no—
281C4⋊Dic7—21no—
282C4⋊Dic7—24no—
283C4⋊Dic7C2412yes—
284C4⋊Dic7C2412yes—
285C4⋊Dic7C2412yes—
286Dic7⋊C4—24no—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289Dic7⋊C4—24no—
290C4×Dic7—24no—
291C4×Dic7—24no—
292C4×Dic7—24no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8—22no—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297#1131—28no—
298C8×D7—28no—
299C22×#41—71no—
300C23×Q8—71no—
301C22×M16—71no—
302C23×C8—71no—
303#536—78no—
304#536—144no—
305C2×C4⋊Q8—141no—
306C2×#124—141no—
307C2×#123—141no—
308C2×#123—141no—
309C2×C22⋊Q8—71no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8—71no—
312C2×C22⋊Q8C2×D711yescharacteristic
313#520—78no—
314#520—144no—
315C2×C4×Q8—141no—
316C2×C4×D4—141no—
317C2×C4×D4—141no—
318C2×C4×D4—141no—
319C2×#117—71no—
320C2×#117—71no—
321C2×#117—71no—
322C2×#117C2×D711yescharacteristic
323C22×C4⋊C4—71no—
324C22×C4⋊C4—71no—
325C22×C4⋊C4—71no—
326#485—78no—
327#485—78no—
328#485—78no—
329#485C2×D718yescomplemented
330#484—78no—
331#484—78no—
332#483—78no—
333#483—78no—
334#428—78no—
335#427—78no—
336C2×#107—71no—
337C2×#107—71no—
338C2×#107—71no—
339C2×#107C2×D711yescharacteristic
340C2×#106—71no—
341C2×#106—71no—
342C2×#106—71no—
343C2×#106C2×D711yescharacteristic
344#419—78no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103—71no—
350C2×#103—71no—
351C2×#103—78no—
352C2×#103C2×D711yescharacteristic
353C2×#103C2×D711yescharacteristic
354#408—78no—
355C2×C22⋊C8—71no—
356C2×C22⋊C8—71no—
357C2×C22⋊C8—71no—
358C2×C22⋊C8C2×D711yescharacteristic
359C23×C7—22no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7C22×D412yes—
363C23×C7C22×D411yescharacteristic
364C22×D7—22no—
365C22×D7—22no—
366C22×D7—22no—
367C22×D7—22no—
368C22×D7—22no—
369C22×D7#12314yes—
370C22×D7C22×D412yes—
371C22×D7C22×D412yes—
372C7×Q8—22no—
373C7×Q8—22no—
374C7×Q8—42no—
375C2×C4×C7—22no—
376C2×C4×C7—24no—
377C2×C4×C7—22no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—42no—
384C2×C4×C7—42no—
385C2×C4×C7—42no—
386C2×C4×C7—42no—
387C2×C4×C7C22×D412yes—
388C2×C4×C7C22×D411yescharacteristic
389C2×C4×C7C2×#4112yes—
390C2×C4×C7C2×#4112yes—
391C2×C4×C7C2511yescharacteristic
392C22⋊D7—28no—
393C22⋊D7—28no—
394C2×Dic7—22no—
395C2×Dic7—22no—
396C2×Dic7—22no—
397C2×Dic7—22no—
398C2×Dic7—22no—
399C2×Dic7—42no—
400C2×Dic7—42no—
401C2×Dic7—42no—
402C2×Dic7—42no—
403C2×Dic7—84no—
404C2×Dic7#12314yes—
405C2×Dic7C22×D412yes—
406C2×Dic7C22×D412yes—
407D28—28no—
408C4×D7—24no—
409C4×D7—22no—
410C4×D7—22no—
411C4×D7—48no—
412C4×D7—84no—
413C4×D7—84no—
414C4×D7#12318yes—
415C4×D7C2×#4114yes—
416C4×D7C2×#4114yes—
417Dic14—28no—
418Dic14—22no—
419Dic14—22no—
420Dic14—42no—
421Dic14—48no—
422C7×C8—22no—
423C7×C8—22no—
424C7⋊C8—22no—
425C7⋊C8—22no—
426C2×#41—74no—
427C2×#41—74no—
428C2×#41—144no—
429C2×#41—144no—
430C22×Q8—71no—
431C22×Q8—74no—
432C22×Q8—71no—
433C22×Q8—141no—
434C22×Q8—142no—
435C22×Q8—144no—
436C22×Q8—144no—
437C22×Q8C22×D711yescharacteristic
438C22×D4—71no—
439C22×D4—71no—
440C22×D4—71no—
441C23×C4—71no—
442C23×C4—71no—
443C23×C4—141no—
444C23×C4—141no—
445C23×C4—141no—
446C23×C4—141no—
447C23×C4C22×D711yescharacteristic
448C2×M16—74no—
449C2×M16—144no—
450C22×C8—71no—
451C22×C8—71no—
452C22×C8—74no—
453C22×C8—144no—
454C22×C8C22×D711yescharacteristic
455C22×C8C22×D711yescharacteristic
456C4⋊Q8—148no—
457#124—148no—
458#123—148no—
459#123—148no—
460C22⋊Q8—22no—
461C22⋊Q8—74no—
462C22⋊Q8—74no—
463C22⋊Q8—74no—
464C22⋊Q8—142no—
465C22⋊Q8—142no—
466C22⋊Q8—142no—
467C22⋊Q8C22×D714yes—
468C4×Q8—148no—
469C4×D4—148no—
470C4×D4—148no—
471C4×D4—148no—
472#117—22no—
473#117—74no—
474#117—74no—
475#117—74no—
476#117—142no—
477#117—142no—
478#117—142no—
479#117C22×D714yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—71no—
482C2×C4⋊C4—71no—
483C2×C4⋊C4—74no—
484C2×C4⋊C4—71no—
485C2×C4⋊C4—74no—
486C2×C4⋊C4—74no—
487C2×C4⋊C4—142no—
488C2×C4⋊C4—142no—
489C2×C4⋊C4—141no—
490C2×C4⋊C4—141no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—142no—
495C2×C4⋊C4—141no—
496C2×C4⋊C4C22×D711yescharacteristic
497C2×C4⋊C4C22×D711yescharacteristic
498C2×C4⋊C4C22×D711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—141no—
502C2×C22⋊C4—141no—
503C2×C22⋊C4—141no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C42—21no—
508C2×C42—141no—
509C2×C42—141no—
510C2×C42—141no—
511#107—74no—
512#107—74no—
513#107—74no—
514#107C22×D714yes—
515#106—74no—
516#106—74no—
517#106—74no—
518#106C22×D714yes—
519#103—74no—
520#103—74no—
521#103—74no—
522#103—74no—
523#103—74no—
524#103—74no—
525#103C22×D714yes—
526#103C22×D714yes—
527C22⋊C8—74no—
528C22⋊C8—74no—
529C22⋊C8—74no—
530C22⋊C8C22×D714yes—
531C22×C7—22no—
532C22×C7—22no—
533C22×C7—22no—
534C22×C7—44no—
535C22×C7C2×#12312yes—
536C22×C7#57712yes—
537C22×C7#57812yes—
538C22×C7C23×D411yescharacteristic
539C2×D7—28no—
540C2×D7—22no—
541C2×D7—22no—
542C2×D7—22no—
543C2×D7—22no—
544C2×D7—22no—
545C2×D7—44no—
546C2×D7C2×#12314yes—
547C4×C7—22no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7—42no—
551C4×C7—42no—
552C4×C7C2×#12312yes—
553C4×C7C22×#4111yescharacteristic
554C4×C7C22×#4111yescharacteristic
555Dic7—22no—
556Dic7—42no—
557Dic7—42no—
558Dic7—42no—
559Dic7—42no—
560Dic7C2×#12314yes—
561C24—71no—
562C24—71no—
563C24D4×D711yescharacteristic
564#41—1416no—
565#41—148no—
566#41—148no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—74no—
571C2×Q8—72no—
572C2×Q8—144no—
573C2×Q8—144no—
574C2×Q8—148no—
575C2×Q8—148no—
576C2×Q8—141no—
577C2×Q8—142no—
578C2×Q8—142no—
579C2×Q8—284no—
580C2×Q8—288no—
581C2×Q8C23×D712yes—
582C2×D4—74no—
583C2×D4—74no—
584C2×D4—74no—
585C2×D4—144no—
586C2×D4—144no—
587C2×D4—144no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—71no—
595C22×C4—72no—
596C22×C4—74no—
597C22×C4—74no—
598C22×C4—72no—
599C22×C4—71no—
600C22×C4—72no—
601C22×C4—72no—
602C22×C4—144no—
603C22×C4—144no—
604C22×C4—144no—
605C22×C4—142no—
606C22×C4—142no—
607C22×C4—141no—
608C22×C4—141no—
609C22×C4—141no—
610C22×C4—141no—
611C22×C4—144no—
612C22×C4—284no—
613C22×C4—562no—
614C22×C4—562no—
615C22×C4—562no—
616C22×C4D4×D712yes—
617C22×C4D4×D711yescharacteristic
618C22×C4C23×D712yes—
619C22×C4C23×D711yescharacteristic
620M16—148no—
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—72no—
624C2×C8—72no—
625C2×C8—148no—
626C2×C8—142no—
627C2×C8—142no—
628C2×C8C23×D712yes—
629C2×C8C23×D712yes—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—72no—
635C4⋊C4—72no—
636C4⋊C4—72no—
637C4⋊C4—144no—
638C4⋊C4—144no—
639C4⋊C4—144no—
640C4⋊C4—144no—
641C4⋊C4—144no—
642C4⋊C4—141no—
643C4⋊C4—141no—
644C4⋊C4—144no—
645C4⋊C4—141no—
646C4⋊C4C23×D712yes—
647C4⋊C4C23×D712yes—
648C4⋊C4C23×D712yes—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—144no—
652C22⋊C4—144no—
653C22⋊C4—144no—
654C22⋊C4—144no—
655C22⋊C4—144no—
656C22⋊C4—144no—
657C42—24no—
658C42—144no—
659C42—144no—
660C42—144no—
661C2×C7—42no—
662C2×C7#309714yescomplemented
663C2×C7C22×#12311yescharacteristic
664C2×C7C2×#57711yescharacteristic
665C2×C7C2×#57811yescharacteristic
666D7—24no—
667D7—42no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—74no—
672C23—72no—
673C23—72no—
674C23—142no—
675C23—142no—
676C23—142no—
677C23—142no—
678C23—142no—
679C23C2×D4×D712yes—
680C23C2×D4×D711yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—42no—
684Q8—148no—
685Q8—142no—
686Q8—142no—
687Q8—288no—
688Q8—282no—
689D4—148no—
690D4—148no—
691D4—148no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
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—42no—
704C2×C4—74no—
705C2×C4—72no—
706C2×C4—78no—
707C2×C4—74no—
708C2×C4—74no—
709C2×C4—72no—
710C2×C4—142no—
711C2×C4—144no—
712C2×C4—142no—
713C2×C4—142no—
714C2×C4—142no—
715C2×C4—142no—
716C2×C4—142no—
717C2×C4—142no—
718C2×C4—288no—
719C2×C4—282no—
720C2×C4—282no—
721C2×C4—282no—
722C2×C4—282no—
723C2×C4—564no—
724C2×C4—564no—
725C2×C4—564no—
726C2×C4C2×D4×D712yes—
727C2×C4C2×D4×D711yescharacteristic
728C2×C4D7×#4112yes—
729C2×C4D7×#4112yes—
730C2×C4C24×D711yescharacteristic
731C8—22no—
732C8—22no—
733C8—142no—
734C8—142no—
735C7C2×#309711yescharacteristic, complemented, Sylow
736C22—22no—
737C22—22no—
738C22—22no—
739C22—44no—
740C22—74no—
741C22—142no—
742C22—148no—
743C22—142no—
744C22—142no—
745C22—142no—
746C22—142no—
747C22—284no—
748C22D7×#12312yes—
749C22#9046112yes—
750C22#9047012yes—
751C22C22×D4×D711yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—74no—
758C4—142no—
759C4—282no—
760C4—282no—
761C4—282no—
762C4—282no—
763C4D7×#12312yes—
764C4C2×D7×#4111yescharacteristic
765C4C2×D7×#4111yescharacteristic
766C2—42no—
767C2—144no—
768C2—282no—
769C2#1173896314yesdirect product factor
770C2C2×D7×#12311yescharacteristic
771C2C2×#9046111yescharacteristic
772C2C2×#9047011yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#485C2
socleC23×C7C22×D4
prime radicalC22×#1157C22
hypercenterC2×#485D7
hypocenterC7C2×#3097
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. C2×C7×#485C2semidirect
4. C2×#89816C2semidirect
5. C2×#89768C2semidirect
6. #11738963C2direct (N × H)
7. C2×#89656C2semidirect
8. C2×#89653C2semidirect
9. C2×#89632C2semidirect
10. C2×#89639C2semidirect
11. C2×#89587C2semidirect
12. C2×#89577C2semidirect
13. C2×#89574C2semidirect
14. C2×D7×#103C2semidirect
16. C2×#89493C2semidirect
44. C7×#485C22semidirect
59. #89816C22semidirect
60. #89768C22semidirect
67. #89656C22semidirect
68. #89653C22semidirect
69. #89639C22semidirect
70. #89632C22semidirect
71. #89587C22semidirect
72. #89577C22semidirect
73. #89574C22semidirect
74. D7×#103C22semidirect
76. #89493C22semidirect
191. C2×#485D7semidirect
329. #485C2×D7semidirect
662. C2×C7#3097semidirect
735. C7C2×#3097semidirect
769. C2#11738963direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903192
C2×#902142
C2×C7×#4852
C2×#898162
C2×#897682
#117389632
C2×#896562
C2×#896532
C2×#896322
C2×#896392
C2×#895872
C2×#895772
C2×#895742
C2×D7×#1032
C2×#894992
C2×#894932
C2×#30977