Finite Group Databasebeta

← C2×#11737279 #14221948

Subgroups — C2×#11737279 #14221948

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90271C211yesmaximal, characteristic
2C2×C4×Q8×D7C211yesmaximal, characteristic, complemented
3C2×C7×#441C211yesmaximal, characteristic, complemented
4C2×#89958C211yesmaximal, characteristic, complemented
5C2×#89957C211yesmaximal, characteristic, complemented
6C2×#89798C211yesmaximal, characteristic, complemented
7C2×#89802C211yesmaximal, characteristic, complemented
8#11737279C2116yesmaximal, direct product factor
9C2×#89629C211yesmaximal, characteristic, complemented
10C2×#89635C211yesmaximal, characteristic
11C2×#89570C211yesmaximal, characteristic, complemented
12C2×#89581C211yesmaximal, characteristic, complemented
13C2×#89578C211yesmaximal, characteristic
14C2×#89568C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89477C211yesmaximal, characteristic, complemented
17C22×Q8×D7C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×#6509C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C22×#1144C2211yescharacteristic
25C22×#1143C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27#90271—24no—
28#90271C2218yes—
29C4×Q8×D7—24no—
30C4×Q8×D7C2218yescomplemented
31C2×#6461—21no—
32C2×#6458C2211yescharacteristic
33C2×#6457—21no—
34C2×D7×C4⋊C4—21no—
35C2×D7×C4⋊C4C2211yescharacteristic
36C2×#6453C2211yescharacteristic
37C2×#6450—21no—
38C2×#6450C2211yescharacteristic
39C2×C4×D28—21no—
40C2×C4×D28C2211yescharacteristic
41C2×#6435—21no—
42C2×C42×D7—21no—
43C2×C42×D7C2211yescharacteristic
44C2×C4×Dic14—21no—
45C2×C4×Dic14C2211yescharacteristic
46C7×#441C2218yescomplemented
47C2×C7×#106C2211yescharacteristic
48C2×C7×#103C2211yescharacteristic
49C2×C7×#103C2211yescharacteristic
50C2×C7×#97C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53#89958C2218yescomplemented
54#89957C2218yescomplemented
55C2×#6395C2211yescharacteristic
56C2×(C2×D7)⋊C8C2211yescharacteristic
57C2×(C2×D7)⋊C8C2211yescharacteristic
58C2×#6392C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62#89802C2218yescomplemented
63#89798C2218yescomplemented
64C2×#6384C2211yescharacteristic
65C2×#6383C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6381C2211yescharacteristic
68C2×#6377C2211yescharacteristic
69#89635C2218yes—
70#89629C2218yescomplemented
71#89581C2218yescomplemented
72#89578C2218yes—
73#89570C2218yescomplemented
74#89568C2218yescomplemented
75#89482C2218yescomplemented
76#89477C2218yescomplemented
77C2×#3117—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×Q8×D7—24no—
81C2×Q8×D7—22no—
82C2×Q8×D7—24no—
83C2×Q8×D7C2314yes—
84C22×D28—21no—
85C22×D28C2311yescharacteristic
86C22×C4×D7—21no—
87C22×C4×D7—21no—
88C22×C4×D7—21no—
89C22×C4×D7D411yescharacteristic
90C22×C4×D7D411yescharacteristic
91C22×C4×D7C2311yescharacteristic
92C22×Dic14—21no—
93C22×Dic14C2311yescharacteristic
94C2×C7×Q16—24no—
95C2×C7×Q16C2314yes—
96C22×C7×C8C2311yescharacteristic
97C22×C7×C8C2311yescharacteristic
98C4×C7×Q8—22no—
99C4×C7×Q8—22no—
100C4×C7×Q8C2314yes—
101C4×C7×Q8C2314yes—
102C2×C7×C4⋊C4—21no—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4C2311yescharacteristic
105C2×C7×C4⋊C4C2311yescharacteristic
106C2×C42×C7—21no—
107C2×C42×C7—21no—
108C2×C42×C7C2311yescharacteristic
109#6510—22no—
110#6510C2314yes—
111#6509—22no—
112#6509C2314yes—
113Q8×Dic7—22no—
114Q8×Dic7C2314yes—
115C2×#1144—24no—
116C2×#1144C2314yes—
117C2×#1143—24no—
118C2×#1143C2314yes—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×(C2×D7)⋊C4—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128C2×Dic7⋊C4—21no—
129C2×Dic7⋊C4—21no—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
132C2×Dic7⋊C4—21no—
133C2×C4×Dic7—21no—
134C2×C4×Dic7—21no—
135C2×C4×Dic7—21no—
136C2×C4×Dic7D411yescharacteristic
137C2×C4×Dic7D411yescharacteristic
138C2×C4×Dic7C2311yescharacteristic
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C2×#1132—24no—
142C2×#1132C2314yes—
143#6461—28no—
144#6458—22no—
145#6458C2314yes—
146#6457—28no—
147D7×C4⋊C4—28no—
148D7×C4⋊C4—22no—
149D7×C4⋊C4C2314yes—
150#6453—22no—
151#6453C2314yes—
152#6450—28no—
153#6450—22no—
154#6450C2314yes—
155C4×D28—28no—
156C4×D28—22no—
157C4×D28C2314yes—
158#6435—28no—
159C42×D7—28no—
160C42×D7D414yes—
161C42×D7C2314yes—
162C4×Dic14—22no—
163C4×Dic14—28no—
164C4×Dic14C2314yes—
165C7×#106C2314yes—
166C7×#103C2314yes—
167C7×#103C2314yes—
168C7×#97C2314yes—
169#6409C2314yes—
170#6409C2314yes—
171#6395C2314yes—
172(C2×D7)⋊C8C2314yes—
173(C2×D7)⋊C8C2314yes—
174#6392C2314yes—
175#6390C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182#6377C2314yes—
183C2×#529—71no—
184C22×C4×Q8—71no—
185#3117—716no—
186C2×#484—71no—
187C2×#481—71no—
188C2×#479—71no—
189C2×#479—71no—
190C2×#464—71no—
191C2×#464—71no—
192C2×#451—71no—
193C2×#448—71no—
194C2×#441—71no—
195C2×#441D711yescharacteristic, complemented
196C2×#440—71no—
197C2×#440—71no—
198C2×#432—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8#4114yes—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C22×C4×C7—21no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7C2×D411yescharacteristic
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2411yescharacteristic
216C22×Dic7—21no—
217C22×Dic7—21no—
218C22×Dic7—21no—
219C22×Dic7C2×D411yescharacteristic
220C22×Dic7C2×D411yescharacteristic
221C22×Dic7C2×D411yescharacteristic
222Q8×D7—216no—
223Q8×D7—28no—
224Q8×D7—28no—
225C2×D28—22no—
226C2×D28—22no—
227C2×D28—24no—
228C2×D28—21no—
229C2×D28—44no—
230C2×D28C2412yes—
231C2×C4×D7—28no—
232C2×C4×D7—24no—
233C2×C4×D7—24no—
234C2×C4×D7—22no—
235C2×C4×D7—22no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—42no—
239C2×C4×D7—44no—
240C2×C4×D7—44no—
241C2×C4×D7C2×D414yes—
242C2×C4×D7C2×D412yes—
243C2×C4×D7C2×D414yes—
244C2×C4×D7C2412yes—
245C2×Dic14—28no—
246C2×Dic14—21no—
247C2×Dic14—22no—
248C2×Dic14—24no—
249C2×Dic14#4114yes—
250C2×Dic14C2412yes—
251C7×Q16—28no—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—24no—
257C7×C4⋊C4—21no—
258C7×C4⋊C4—21no—
259C7×C4⋊C4—24no—
260C7×C4⋊C4C2412yes—
261C7×C4⋊C4C2412yes—
262C42×C7—24no—
263C42×C7—24no—
264C42×C7C2×D412yes—
265C42×C7C2412yes—
266#1144—28no—
267#1143—28no—
268(C2×D7)⋊C4—24no—
269(C2×D7)⋊C4—24no—
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⋊Dic7C2412yes—
278C4⋊Dic7C2412yes—
279Dic7⋊C4—24no—
280Dic7⋊C4—24no—
281Dic7⋊C4—24no—
282Dic7⋊C4—24no—
283Dic7⋊C4—24no—
284C4×Dic7—24no—
285C4×Dic7—24no—
286C4×Dic7—24no—
287C4×Dic7C2×D414yes—
288C4×Dic7C2×D412yes—
289C4×Dic7C2×D414yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1132—28no—
296C23×Q8—71no—
297C22×Q16—71no—
298C22×Q16C2×D711yescharacteristic
299C22×SD16—71no—
300C22×SD16—71no—
301#529—78no—
302#529—144no—
303C2×#126—141no—
304C2×#125—71no—
305C2×#124—71no—
306C2×#123—141no—
307C2×C22⋊Q8—71no—
308C2×#121—71no—
309C2×C4×Q8—71no—
310C2×C4×Q8—78no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—141no—
314C2×C4×Q8—141no—
315C2×C4×Q8—144no—
316C2×C4×Q8C2×D711yescharacteristic
317C2×C4×Q8C2×D711yescharacteristic
318C2×C4×D4—71no—
319C2×C4×D4—141no—
320C2×#117—141no—
321C22×C4⋊C4—71no—
322C22×C4⋊C4—141no—
323C22×C42—71no—
324C22×C42—141no—
325#484—78no—
326#481—78no—
327#479—78no—
328#479—78no—
329#464—78no—
330#464—78no—
331#451—78no—
332#448—78no—
333#441—78no—
334#441C2×D718yescomplemented
335#440—78no—
336#440—78no—
337#432—78no—
338C2×#107—71no—
339C2×#107—71no—
340C2×#106—71no—
341C2×#106C2×D711yescharacteristic
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×#103—71no—
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103C2×D711yescharacteristic
349C2×#103C2×D711yescharacteristic
350C2×#102—71no—
351C2×#102—71no—
352C2×C22⋊C8—71no—
353C2×C22⋊C8—71no—
354C2×#97—71no—
355C2×#97C2×D711yescharacteristic
356C23×C7C22×D411yescharacteristic
357C22×D7—22no—
358C22×D7—22no—
359C22×D7—22no—
360C22×D7—42no—
361C22×D7—42no—
362C22×D7—42no—
363C22×D7#13714yes—
364C22×D7C22×D412yes—
365C7×Q8—24no—
366C7×Q8—22no—
367C7×Q8—22no—
368C7×Q8—22no—
369C7×Q8—42no—
370C7×Q8C2×#4114yes—
371C2×C4×C7—24no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—22no—
377C2×C4×C7—22no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7—42no—
381C2×C4×C7C22×D412yes—
382C2×C4×C7C22×D412yes—
383C2×C4×C7C22×D411yescharacteristic
384C2×C4×C7C2×#4112yes—
385C2×C4×C7C2×#4112yes—
386C2×C4×C7C2511yescharacteristic
387C2×Dic7—22no—
388C2×Dic7—24no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399D28—22no—
400D28—22no—
401D28—48no—
402D28—42no—
403C4×D7—216no—
404C4×D7—28no—
405C4×D7—24no—
406C4×D7—22no—
407C4×D7—22no—
408C4×D7—44no—
409C4×D7—48no—
410C4×D7—48no—
411Dic14—216no—
412Dic14—24no—
413Dic14—22no—
414Dic14C2×#4114yes—
415C7×C8—22no—
416C7×C8—22no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C22×Q8—74no—
420C22×Q8—71no—
421C22×Q8—141no—
422C22×Q8—142no—
423C22×Q8—144no—
424C22×Q8—144no—
425C22×Q8C22×D711yescharacteristic
426C22×Q8C22×D711yescharacteristic
427C22×D4—71no—
428C22×D4—141no—
429C23×C4—71no—
430C23×C4—71no—
431C23×C4—71no—
432C23×C4—141no—
433C23×C4—141no—
434C23×C4—141no—
435C2×Q16—24no—
436C2×Q16—74no—
437C2×Q16—144no—
438C2×Q16C22×D714yes—
439C2×SD16—74no—
440C2×SD16—74no—
441C2×SD16—144no—
442C2×SD16—144no—
443C22×C8—71no—
444C22×C8—71no—
445C22×C8C22×D711yescharacteristic
446C22×C8C22×D711yescharacteristic
447#126—148no—
448#125—74no—
449#125—142no—
450#124—74no—
451#124—142no—
452#123—148no—
453C22⋊Q8—74no—
454C22⋊Q8—142no—
455#121—74no—
456#121—142no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—74no—
462C4×Q8—148no—
463C4×Q8—148no—
464C4×Q8—142no—
465C4×Q8—142no—
466C4×Q8—142no—
467C4×Q8C22×D714yes—
468C4×Q8C22×D714yes—
469C4×D4—74no—
470C4×D4—148no—
471C4×D4—142no—
472#117—148no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—71no—
477C2×C4⋊C4—74no—
478C2×C4⋊C4—142no—
479C2×C4⋊C4—148no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4—141no—
485C2×C4⋊C4—141no—
486C2×C4⋊C4—141no—
487C2×C4⋊C4C22×D711yescharacteristic
488C2×C4⋊C4C22×D711yescharacteristic
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—71no—
497C2×C42—71no—
498C2×C42—71no—
499C2×C42—74no—
500C2×C42—74no—
501C2×C42—148no—
502C2×C42—141no—
503C2×C42—141no—
504C2×C42—141no—
505C2×C42C22×D711yescharacteristic
506#107—74no—
507#107—74no—
508#106—74no—
509#106C22×D714yes—
510C4⋊C8—74no—
511C4⋊C8—74no—
512#103—74no—
513#103—74no—
514#103—74no—
515#103—74no—
516#103C22×D714yes—
517#103C22×D714yes—
518#102—74no—
519#102—74no—
520C22⋊C8—74no—
521C22⋊C8—74no—
522#97—74no—
523#97C22×D714yes—
524C22×C7#52512yes—
525C22×C7C2×#13712yes—
526C22×C7#57512yes—
527C22×C7C23×D411yescharacteristic
528C2×D7—28no—
529C2×D7—22no—
530C2×D7—22no—
531C2×D7—42no—
532C2×D7—42no—
533C2×D7—42no—
534C2×D7—84no—
535C2×D7C2×#13714yes—
536C4×C7—24no—
537C4×C7—22no—
538C4×C7—22no—
539C4×C7—42no—
540C4×C7—42no—
541C4×C7—42no—
542C4×C7#52512yes—
543C4×C7C22×#4111yescharacteristic
544C4×C7C22×#4111yescharacteristic
545Dic7—22no—
546Dic7—24no—
547Dic7—22no—
548Dic7—22no—
549Dic7—42no—
550Dic7—42no—
551C24—71no—
552C24—141no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—74no—
559C2×Q8—72no—
560C2×Q8—144no—
561C2×Q8—148no—
562C2×Q8—148no—
563C2×Q8—1416no—
564C2×Q8—148no—
565C2×Q8—142no—
566C2×Q8—141no—
567C2×Q8#115714yes—
568C2×Q8C23×D712yes—
569C2×Q8C23×D712yes—
570C2×D4—72no—
571C2×D4—144no—
572C2×D4—142no—
573C2×D4—141no—
574C2×D4—142no—
575C2×D4—284no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—71no—
581C22×C4—71no—
582C22×C4—71no—
583C22×C4—74no—
584C22×C4—72no—
585C22×C4—72no—
586C22×C4—74no—
587C22×C4—144no—
588C22×C4—144no—
589C22×C4—148no—
590C22×C4—144no—
591C22×C4—141no—
592C22×C4—142no—
593C22×C4—142no—
594C22×C4—141no—
595C22×C4—141no—
596C22×C4—144no—
597C22×C4—282no—
598C22×C4—284no—
599C22×C4—284no—
600C22×C4D4×D711yescharacteristic
601C22×C4D4×D711yescharacteristic
602C22×C4C23×D711yescharacteristic
603Q16—28no—
604Q16—148no—
605SD16—148no—
606SD16—148no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—72no—
610C2×C8—72no—
611C2×C8—142no—
612C2×C8—142no—
613C2×C8C23×D712yes—
614C2×C8C23×D712yes—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—72no—
620C4⋊C4—72no—
621C4⋊C4—144no—
622C4⋊C4—144no—
623C4⋊C4—144no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—144no—
627C4⋊C4—144no—
628C4⋊C4—141no—
629C4⋊C4—141no—
630C4⋊C4C23×D712yes—
631C4⋊C4C23×D712yes—
632C22⋊C4—144no—
633C22⋊C4—144no—
634C22⋊C4—144no—
635C22⋊C4—144no—
636C22⋊C4—144no—
637C42—24no—
638C42—24no—
639C42—74no—
640C42—72no—
641C42—74no—
642C42—72no—
643C42—144no—
644C42—144no—
645C42—144no—
646C42D4×D712yes—
647C42C23×D712yes—
648C2×C7#311714yescomplemented
649C2×C7C2×#52511yescharacteristic
650C2×C7C22×#13711yescharacteristic
651C2×C7C2×#57511yescharacteristic
652D7—24no—
653D7—82no—
654C23—74no—
655C23—72no—
656C23—142no—
657C23—142no—
658C23—142no—
659C23—282no—
660C23—282no—
661C23—282no—
662C23C2×D4×D711yescharacteristic
663Q8—24no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—74no—
669Q8—1416no—
670Q8—144no—
671Q8—142no—
672Q8C2×#115714yes—
673D4—142no—
674D4—142no—
675D4—288no—
676D4—282no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—72no—
688C2×C4—72no—
689C2×C4—72no—
690C2×C4—148no—
691C2×C4—1416no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—144no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—284no—
703C2×C4—288no—
704C2×C4—288no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4C2×#115712yes—
708C2×C4C2×D4×D712yes—
709C2×C4C2×D4×D712yes—
710C2×C4C2×D4×D711yescharacteristic
711C2×C4D7×#4112yes—
712C2×C4C24×D711yescharacteristic
713C8—22no—
714C8—22no—
715C8—142no—
716C8—142no—
717C7C2×#311711yescharacteristic, complemented, Sylow
718C22—74no—
719C22—142no—
720C22—142no—
721C22—148no—
722C22—282no—
723C22—282no—
724C22—282no—
725C22—564no—
726C22#9023812yes—
727C22D7×#13712yes—
728C22#9046812yes—
729C22C22×D4×D711yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—142no—
737C4—142no—
738C4—142no—
739C4—144no—
740C4—282no—
741C4—282no—
742C4#9023812yes—
743C4C22×#115711yescharacteristic
744C4C2×D7×#4111yescharacteristic
745C2—144no—
746C2—562no—
747C2#1173727914yesdirect product factor
748C2C2×#9023811yescharacteristic
749C2C2×D7×#13711yescharacteristic
750C2C2×#9046811yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#441C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
hypercenterC2×#441D7
hypocenterC7C2×#3117
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D7C2semidirect
3. C2×C7×#441C2semidirect
4. C2×#89958C2semidirect
5. C2×#89957C2semidirect
6. C2×#89798C2semidirect
7. C2×#89802C2semidirect
8. #11737279C2direct (N × H)
9. C2×#89629C2semidirect
11. C2×#89570C2semidirect
12. C2×#89581C2semidirect
14. C2×#89568C2semidirect
15. C2×#89482C2semidirect
16. C2×#89477C2semidirect
30. C4×Q8×D7C22semidirect
46. C7×#441C22semidirect
53. #89958C22semidirect
54. #89957C22semidirect
62. #89802C22semidirect
63. #89798C22semidirect
70. #89629C22semidirect
71. #89581C22semidirect
73. #89570C22semidirect
74. #89568C22semidirect
75. #89482C22semidirect
76. #89477C22semidirect
195. C2×#441D7semidirect
334. #441C2×D7semidirect
648. C2×C7#3117semidirect
717. C7C2×#3117semidirect
747. C2#11737279direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902712
C2×C4×Q8×D72
C2×C7×#4412
C2×#899582
C2×#899572
C2×#897982
C2×#898022
#117372792
C2×#896292
C2×#896352
C2×#895702
C2×#895812
C2×#895782
C2×#895682
C2×#894822
C2×#894772
C2×#31177