Finite Group Databasebeta

← C2×#11738916 #14221646

Subgroups — C2×#11738916 #14221646

Order 1792.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90320C211yesmaximal, characteristic
2C2×#90195C211yesmaximal, characteristic, complemented
3C2×C7×#484C211yesmaximal, characteristic, complemented
4C2×#89817C211yesmaximal, characteristic, complemented
5C2×#89739C211yesmaximal, characteristic, complemented
6#11738916C2116yesmaximal, direct product factor
7C2×#89654C211yesmaximal, characteristic, complemented
8C2×#89653C211yesmaximal, characteristic, complemented
9C2×D7×#107C211yesmaximal, characteristic, complemented
10C2×#89657C211yesmaximal, characteristic, complemented
11C2×#89581C211yesmaximal, characteristic, complemented
12C2×#89587C211yesmaximal, characteristic, complemented
13C2×#89575C211yesmaximal, characteristic, complemented
14C2×#89576C211yesmaximal, characteristic, complemented
15C2×#89499C211yesmaximal, characteristic, complemented
16C2×#89509C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×#1157C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C22×C7×C4⋊C4C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×#6493C2211yescharacteristic
23C2×C4×C22⋊D7—21no—
24C2×C4×C22⋊D7—21no—
25C2×#6489C2211yescharacteristic
26C22×#1131C2211yescharacteristic
27C22×C8×D7C2211yescharacteristic
28#90320—24no—
29#90320C2218yes—
30C2×#6459—21no—
31C2×#6458—21no—
32C2×#6458C2211yescharacteristic
33#90195—24no—
34#90195C2218yescomplemented
35C2×#6456—21no—
36C2×#6455C2211yescharacteristic
37C2×#6455C2211yescharacteristic
38C2×D7×C4⋊C4C2211yescharacteristic
39C2×D7×C4⋊C4C2211yescharacteristic
40C2×D7×C4⋊C4C2211yescharacteristic
41C2×#6450—21no—
42C2×#6447—21no—
43C2×#6447—21no—
44C7×#484C2218yescomplemented
45C2×C7×#107C2211yescharacteristic
46C2×C7×#107C2211yescharacteristic
47C2×C7×#103C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×C22⋊C8C2211yescharacteristic
50C2×#6409C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×C22⋊(C7⋊C8)C2211yescharacteristic
53C2×#6395C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×(C2×D7)⋊C8C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×#6392C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59#89817C2218yescomplemented
60#89739C2218yescomplemented
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6382C2211yescharacteristic
64C2×#6381C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×#6381C2211yescharacteristic
67#89657C2218yescomplemented
68#89654C2218yescomplemented
69#89653C2218yescomplemented
70D7×#107C2218yescomplemented
71#89587C2218yescomplemented
72#89581C2218yescomplemented
73#89576C2218yescomplemented
74#89575C2218yescomplemented
75#89509C2218yescomplemented
76#89499C2218yescomplemented
77C2×#3098—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C23×C4×C7—21no—
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C22×C22⋊D7D411yescharacteristic
83C22×C22⋊D7D411yescharacteristic
84C2×#1161—22no—
85C2×#1161—24no—
86C2×#1161—24no—
87C2×#1161C2314yes—
88C2×#1157—24no—
89C2×#1157—24no—
90C2×#1157D414yes—
91C2×#1157C2314yes—
92C22×D28—21no—
93C22×D28—21no—
94C22×D28D411yescharacteristic
95C22×D28C2311yescharacteristic
96C22×C4×D7—21no—
97C22×C4×D7—21no—
98C22×C4×D7—21no—
99C22×C4×D7—21no—
100C22×C4×D7C2311yescharacteristic
101C22×C4×D7C2311yescharacteristic
102C22×Dic14D411yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C22×C7×C8C2311yescharacteristic
105C7×C22⋊Q8—22no—
106C7×C22⋊Q8C2314yes—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—22no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4C2314yes—
111C2×C7×C4⋊C4C2311yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C4⋊C4C2311yescharacteristic
114C2×C7×C22⋊C4—21no—
115C2×C22⋊Dic7—21no—
116#6509—22no—
117#6509C2314yes—
118#6493—22no—
119#6493C2314yes—
120C4×C22⋊D7—28no—
121C4×C22⋊D7—28no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×(C2×D7)⋊C4—21no—
125C2×(C2×D7)⋊C4—21no—
126C2×(C2×D7)⋊C4—21no—
127#6489—22no—
128#6489C2314yes—
129C2×C4⋊Dic7C2311yescharacteristic
130C2×C4⋊Dic7C2311yescharacteristic
131C2×C4⋊Dic7C2311yescharacteristic
132C2×Dic7⋊C4—21no—
133C2×Dic7⋊C4—21no—
134C2×Dic7⋊C4—21no—
135C2×Dic7⋊C4—21no—
136C2×C4×Dic7—21no—
137C2×C4×Dic7—21no—
138C2×C4×Dic7—21no—
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×#1131—24no—
142C2×#1131C2314yes—
143C2×C8×D7—24no—
144C2×C8×D7C2314yes—
145#6459—28no—
146#6458—28no—
147#6458—22no—
148#6458C2314yes—
149#6456—28no—
150#6455—22no—
151#6455—22no—
152#6455C2314yes—
153#6455C2314yes—
154D7×C4⋊C4—22no—
155D7×C4⋊C4—22no—
156D7×C4⋊C4—22no—
157D7×C4⋊C4C2314yes—
158D7×C4⋊C4C2314yes—
159D7×C4⋊C4C2314yes—
160#6450—28no—
161#6447—28no—
162#6447—28no—
163C7×#107C2314yes—
164C7×#107C2314yes—
165C7×#103C2314yes—
166C7×#103C2314yes—
167C7×C22⋊C8C2314yes—
168#6409C2314yes—
169#6409C2314yes—
170C22⋊(C7⋊C8)C2314yes—
171#6395C2314yes—
172#6395C2314yes—
173(C2×D7)⋊C8C2314yes—
174(C2×D7)⋊C8C2314yes—
175#6392C2314yes—
176#6391C2314yes—
177#6383C2314yes—
178#6383C2314yes—
179#6382C2314yes—
180#6381C2314yes—
181#6381C2314yes—
182#6381C2314yes—
183C2×#537—71no—
184C2×#520—71no—
185#3098—716no—
186C2×#484—71no—
187C2×#484D711yescharacteristic, complemented
188C2×#485—71no—
189C2×#485—71no—
190C2×#482—71no—
191C2×#482—71no—
192C2×#480—71no—
193C2×#480—71no—
194C2×#428—71no—
195C22×#107—71no—
196C2×#417—71no—
197C2×#416—71no—
198C2×#408—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C23×D7C2×D411yescharacteristic
202C23×D7C2×D411yescharacteristic
203C2×C7×Q8—21no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8C2412yes—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—24no—
214C22×C4×C7—82no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—24no—
221C2×C22⋊D7—24no—
222C2×C22⋊D7—82no—
223C2×C22⋊D7C2×D414yes—
224C2×C22⋊D7C2×D414yes—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230#1161—28no—
231#1161—28no—
232#1161—48no—
233#1157—216no—
234#1157—28no—
235#1157—28no—
236C2×D28—24no—
237C2×D28—22no—
238C2×D28—22no—
239C2×D28—24no—
240C2×D28—21no—
241C2×D28—24no—
242C2×D28—44no—
243C2×D28—82no—
244C2×D28C2×D414yes—
245C2×D28C2412yes—
246C2×C4×D7—22no—
247C2×C4×D7—22no—
248C2×C4×D7—24no—
249C2×C4×D7—24no—
250C2×C4×D7—24no—
251C2×C4×D7—24no—
252C2×C4×D7—44no—
253C2×C4×D7—82no—
254C2×C4×D7—82no—
255C2×C4×D7—82no—
256C2×C4×D7C2×D412yes—
257C2×C4×D7C2×D412yes—
258C2×C4×D7#4114yes—
259C2×C4×D7#4114yes—
260C2×C4×D7C2412yes—
261C2×C4×D7C2412yes—
262C2×Dic14—24no—
263C2×Dic14C2×D414yes—
264C2×C7×C8—22no—
265C2×C7×C8—22no—
266C2×C7×C8C2412yes—
267C2×C7×C8C2412yes—
268C7×C4⋊C4—24no—
269C7×C4⋊C4—21no—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4—24no—
273C7×C4⋊C4C2412yes—
274C7×C4⋊C4C2412yes—
275C7×C4⋊C4C2412yes—
276C7×C22⋊C4—24no—
277C22⋊Dic7—24no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283C4⋊Dic7—21no—
284C4⋊Dic7—21no—
285C4⋊Dic7—21no—
286C4⋊Dic7C2412yes—
287C4⋊Dic7C2412yes—
288C4⋊Dic7C2412yes—
289Dic7⋊C4—24no—
290Dic7⋊C4—24no—
291Dic7⋊C4—24no—
292Dic7⋊C4—24no—
293C4×Dic7—24no—
294C4×Dic7—24no—
295C4×Dic7—24no—
296C2×C7⋊C8—22no—
297C2×C7⋊C8—22no—
298C2×C7⋊C8C2412yes—
299C2×C7⋊C8C2412yes—
300#1131—28no—
301C8×D7—28no—
302C22×#41—71no—
303C22×#41—71no—
304C22×M16—71no—
305C23×C8—71no—
306#537—78no—
307#537—144no—
308C2×C22⋊Q8—71no—
309C2×C22⋊Q8—141no—
310C2×C22⋊Q8C2×D711yescharacteristic
311C2×#121—71no—
312C2×#121—71no—
313C2×#121—141no—
314C2×#121—141no—
315C2×#121—141no—
316#520—78no—
317#520—144no—
318C2×C4×Q8—141no—
319C2×C4×D4—141no—
320C2×C4×D4—141no—
321C2×C4×D4—141no—
322C2×#117—71no—
323C2×#117—71no—
324C2×#117—71no—
325C22×C4⋊C4—71no—
326C22×C4⋊C4—71no—
327C22×C4⋊C4—71no—
328C22×C4⋊C4C2×D711yescharacteristic
329#485—78no—
330#485—78no—
331#484—78no—
332#484C2×D718yescomplemented
333#482—78no—
334#482—78no—
335#480—78no—
336#480—78no—
337#428—78no—
338C2×#107—71no—
339C2×#107—71no—
340C2×#107—71no—
341C2×#107—71no—
342C2×#107—78no—
343C2×#107C2×D711yescharacteristic
344C2×#107C2×D711yescharacteristic
345C2×#106—71no—
346C2×#106—71no—
347#417—78no—
348#416—78no—
349C2×#103—71no—
350C2×#103—71no—
351C2×#103C2×D711yescharacteristic
352C2×#103C2×D711yescharacteristic
353C2×#102—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#102—71no—
357#408—78no—
358C2×C22⋊C8—71no—
359C2×C22⋊C8—71no—
360C2×C22⋊C8—71no—
361C2×C22⋊C8C2×D711yescharacteristic
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7C22×D412yes—
366C23×C7C22×D411yescharacteristic
367C22×D7—22no—
368C22×D7—22no—
369C22×D7—22no—
370C22×D7—22no—
371C22×D7—22no—
372C22×D7—22no—
373C22×D7—42no—
374C22×D7—42no—
375C22×D7—42no—
376C22×D7#12314yes—
377C22×D7C22×D412yes—
378C22×D7C22×D412yes—
379C7×Q8—22no—
380C7×Q8—22no—
381C7×Q8—42no—
382C2×C4×C7—22no—
383C2×C4×C7—24no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—22no—
388C2×C4×C7—22no—
389C2×C4×C7—22no—
390C2×C4×C7—42no—
391C2×C4×C7—42no—
392C2×C4×C7—42no—
393C2×C4×C7—42no—
394C2×C4×C7—84no—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C2×#4112yes—
398C2×C4×C7C2×#4112yes—
399C2×C4×C7C2511yescharacteristic
400C22⋊D7—28no—
401C22⋊D7—28no—
402C22⋊D7—84no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—22no—
407C2×Dic7—42no—
408C2×Dic7—42no—
409C2×Dic7—42no—
410C2×Dic7#12314yes—
411C2×Dic7C22×D412yes—
412C2×Dic7C22×D412yes—
413D28—28no—
414D28—22no—
415D28—22no—
416D28—48no—
417D28—42no—
418D28—84no—
419C4×D7—24no—
420C4×D7—22no—
421C4×D7—22no—
422C4×D7—48no—
423C4×D7—84no—
424C4×D7—84no—
425C4×D7—84no—
426C4×D7#12318yes—
427C4×D7C2×#4114yes—
428C4×D7C2×#4114yes—
429Dic14—28no—
430C7×C8—22no—
431C7×C8—22no—
432C7⋊C8—22no—
433C7⋊C8—22no—
434C2×#41—74no—
435C2×#41—74no—
436C2×#41—74no—
437C2×#41—144no—
438C2×#41—144no—
439C2×#41—142no—
440C2×#41—144no—
441C2×#41—144no—
442C22×Q8—71no—
443C22×Q8C22×D711yescharacteristic
444C22×D4—71no—
445C22×D4—71no—
446C22×D4—71no—
447C22×D4—71no—
448C22×D4—141no—
449C22×D4—141no—
450C22×D4—141no—
451C23×C4—21no—
452C23×C4—71no—
453C23×C4—71no—
454C23×C4—141no—
455C23×C4—141no—
456C23×C4—141no—
457C23×C4—141no—
458C23×C4C22×D711yescharacteristic
459C2×M16—74no—
460C2×M16—144no—
461C22×C8—71no—
462C22×C8—71no—
463C22×C8—74no—
464C22×C8—144no—
465C22×C8C22×D711yescharacteristic
466C22×C8C22×D711yescharacteristic
467C22⋊Q8—22no—
468C22⋊Q8—74no—
469C22⋊Q8—148no—
470C22⋊Q8—142no—
471C22⋊Q8C22×D714yes—
472#121—74no—
473#121—74no—
474#121—148no—
475#121—148no—
476#121—142no—
477#121—148no—
478#121—142no—
479C4×Q8—148no—
480C4×D4—148no—
481C4×D4—148no—
482C4×D4—148no—
483#117—74no—
484#117—74no—
485#117—74no—
486#117—142no—
487#117—142no—
488#117—142no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—71no—
493C2×C4⋊C4—71no—
494C2×C4⋊C4—71no—
495C2×C4⋊C4—74no—
496C2×C4⋊C4—74no—
497C2×C4⋊C4—74no—
498C2×C4⋊C4—142no—
499C2×C4⋊C4—142no—
500C2×C4⋊C4—142no—
501C2×C4⋊C4—141no—
502C2×C4⋊C4—141no—
503C2×C4⋊C4—141no—
504C2×C4⋊C4—141no—
505C2×C4⋊C4C22×D711yescharacteristic
506C2×C4⋊C4C22×D711yescharacteristic
507C2×C4⋊C4C22×D711yescharacteristic
508C2×C4⋊C4C22×D714yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—141no—
512C2×C22⋊C4—141no—
513C2×C22⋊C4—141no—
514C2×C22⋊C4—141no—
515C2×C22⋊C4—141no—
516C2×C42—141no—
517C2×C42—141no—
518C2×C42—141no—
519#107—74no—
520#107—74no—
521#107—74no—
522#107—74no—
523#107C22×D714yes—
524#107C22×D714yes—
525#106—74no—
526#106—74no—
527#103—74no—
528#103—74no—
529#103C22×D714yes—
530#103C22×D714yes—
531#102—74no—
532#102—74no—
533#102—74no—
534#102—74no—
535C22⋊C8—74no—
536C22⋊C8—74no—
537C22⋊C8—74no—
538C22⋊C8C22×D714yes—
539C22×C7—22no—
540C22×C7—22no—
541C22×C7—22no—
542C22×C7—44no—
543C22×C7C2×#12312yes—
544C22×C7#57612yes—
545C22×C7#57812yes—
546C22×C7C23×D411yescharacteristic
547C2×D7—28no—
548C2×D7—22no—
549C2×D7—22no—
550C2×D7—22no—
551C2×D7—22no—
552C2×D7—22no—
553C2×D7—44no—
554C2×D7—42no—
555C2×D7—42no—
556C2×D7—42no—
557C2×D7—84no—
558C2×D7C2×#12314yes—
559C4×C7—22no—
560C4×C7—42no—
561C4×C7—42no—
562C4×C7—42no—
563C4×C7—42no—
564C4×C7C2×#12312yes—
565C4×C7C22×#4111yescharacteristic
566C4×C7C22×#4111yescharacteristic
567Dic7—22no—
568Dic7—42no—
569Dic7—42no—
570Dic7—42no—
571Dic7C2×#12314yes—
572C24—71no—
573C24—71no—
574C24—141no—
575C24D4×D711yescharacteristic
576#41—1416no—
577#41—148no—
578#41—148no—
579#41—148no—
580#41—148no—
581#41—288no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—74no—
586C2×Q8—144no—
587C2×Q8C23×D712yes—
588C2×D4—74no—
589C2×D4—74no—
590C2×D4—74no—
591C2×D4—72no—
592C2×D4—144no—
593C2×D4—144no—
594C2×D4—144no—
595C2×D4—144no—
596C2×D4—144no—
597C2×D4—144no—
598C2×D4—141no—
599C2×D4—142no—
600C2×D4—142no—
601C2×D4—284no—
602C2×D4—562no—
603C2×D4—562no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—71no—
612C22×C4—72no—
613C22×C4—74no—
614C22×C4—74no—
615C22×C4—72no—
616C22×C4—71no—
617C22×C4—72no—
618C22×C4—72no—
619C22×C4—82no—
620C22×C4—144no—
621C22×C4—144no—
622C22×C4—144no—
623C22×C4—144no—
624C22×C4—142no—
625C22×C4—142no—
626C22×C4—141no—
627C22×C4—141no—
628C22×C4—141no—
629C22×C4—284no—
630C22×C4—562no—
631C22×C4—562no—
632C22×C4—562no—
633C22×C4D4×D712yes—
634C22×C4D4×D711yescharacteristic
635C22×C4C23×D712yes—
636C22×C4C23×D711yescharacteristic
637M16—148no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—72no—
641C2×C8—72no—
642C2×C8—148no—
643C2×C8—142no—
644C2×C8—142no—
645C2×C8C23×D712yes—
646C2×C8C23×D712yes—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—21no—
652C4⋊C4—72no—
653C4⋊C4—72no—
654C4⋊C4—72no—
655C4⋊C4—144no—
656C4⋊C4—144no—
657C4⋊C4—144no—
658C4⋊C4—144no—
659C4⋊C4—141no—
660C4⋊C4—141no—
661C4⋊C4—141no—
662C4⋊C4C23×D712yes—
663C4⋊C4C23×D712yes—
664C4⋊C4C23×D712yes—
665C22⋊C4—24no—
666C22⋊C4—144no—
667C22⋊C4—144no—
668C22⋊C4—144no—
669C22⋊C4—144no—
670C22⋊C4—144no—
671C22⋊C4—144no—
672C42—144no—
673C42—144no—
674C42—144no—
675C2×C7—42no—
676C2×C7#309814yescomplemented
677C2×C7C22×#12311yescharacteristic
678C2×C7C2×#57611yescharacteristic
679C2×C7C2×#57811yescharacteristic
680D7—24no—
681D7—42no—
682D7—82no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—74no—
687C23—72no—
688C23—72no—
689C23—142no—
690C23—142no—
691C23—142no—
692C23—142no—
693C23—142no—
694C23—142no—
695C23—282no—
696C23—282no—
697C23—282no—
698C23C2×D4×D712yes—
699C23C2×D4×D711yescharacteristic
700Q8—22no—
701Q8—22no—
702Q8—42no—
703Q8—148no—
704D4—148no—
705D4—148no—
706D4—148no—
707D4—142no—
708D4—142no—
709D4—288no—
710D4—282no—
711D4—564no—
712D4—564no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—74no—
726C2×C4—72no—
727C2×C4—78no—
728C2×C4—74no—
729C2×C4—74no—
730C2×C4—72no—
731C2×C4—84no—
732C2×C4—142no—
733C2×C4—144no—
734C2×C4—142no—
735C2×C4—142no—
736C2×C4—142no—
737C2×C4—142no—
738C2×C4—142no—
739C2×C4—288no—
740C2×C4—282no—
741C2×C4—282no—
742C2×C4—282no—
743C2×C4—564no—
744C2×C4—564no—
745C2×C4—564no—
746C2×C4C2×D4×D712yes—
747C2×C4C2×D4×D711yescharacteristic
748C2×C4D7×#4112yes—
749C2×C4D7×#4112yes—
750C2×C4C24×D711yescharacteristic
751C8—22no—
752C8—22no—
753C8—142no—
754C8—142no—
755C7C2×#309811yescharacteristic, complemented, Sylow
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—74no—
761C22—142no—
762C22—148no—
763C22—142no—
764C22—142no—
765C22—142no—
766C22—142no—
767C22—284no—
768C22—282no—
769C22—282no—
770C22—282no—
771C22—564no—
772C22D7×#12312yes—
773C22#9045712yes—
774C22#9046512yes—
775C22C22×D4×D711yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—74no—
782C4—142no—
783C4—282no—
784C4—282no—
785C4—282no—
786C4D7×#12312yes—
787C4C2×D7×#4111yescharacteristic
788C4C2×D7×#4111yescharacteristic
789C2—42no—
790C2—144no—
791C2—282no—
792C2—562no—
793C2#1173891614yesdirect product factor
794C2C2×D7×#12311yescharacteristic
795C2C2×#9045711yescharacteristic
796C2C2×#9046511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#484C2
socleC23×C7C22×D4
prime radicalC2×#90320C2
hypercenterC2×#484D7
hypocenterC7C2×#3098
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C2×#90195C2semidirect
3. C2×C7×#484C2semidirect
4. C2×#89817C2semidirect
5. C2×#89739C2semidirect
6. #11738916C2direct (N × H)
7. C2×#89654C2semidirect
8. C2×#89653C2semidirect
9. C2×D7×#107C2semidirect
10. C2×#89657C2semidirect
11. C2×#89581C2semidirect
12. C2×#89587C2semidirect
13. C2×#89575C2semidirect
14. C2×#89576C2semidirect
15. C2×#89499C2semidirect
16. C2×#89509C2semidirect
34. #90195C22semidirect
44. C7×#484C22semidirect
59. #89817C22semidirect
60. #89739C22semidirect
67. #89657C22semidirect
68. #89654C22semidirect
69. #89653C22semidirect
70. D7×#107C22semidirect
71. #89587C22semidirect
72. #89581C22semidirect
73. #89576C22semidirect
74. #89575C22semidirect
75. #89509C22semidirect
76. #89499C22semidirect
187. C2×#484D7semidirect
332. #484C2×D7semidirect
676. C2×C7#3098semidirect
755. C7C2×#3098semidirect
793. C2#11738916direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903202
C2×#901952
C2×C7×#4842
C2×#898172
C2×#897392
#117389162
C2×#896542
C2×#896532
C2×D7×#1072
C2×#896572
C2×#895812
C2×#895872
C2×#895752
C2×#895762
C2×#894992
C2×#895092
C2×#30987