Finite Group Databasebeta

← C2×#11737293 #14221932

Subgroups — C2×#11737293 #14221932

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×#90269C211yesmaximal, characteristic, complemented
2C2×C4×#1161C211yesmaximal, characteristic
3C2×C7×#441C211yesmaximal, characteristic, complemented
4C2×#89959C211yesmaximal, characteristic
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89798C211yesmaximal, characteristic, complemented
7C2×#89802C211yesmaximal, characteristic, complemented
8#11737293C2116yesmaximal, direct product factor
9C2×#89642C211yesmaximal, characteristic, complemented
10C2×#89639C211yesmaximal, characteristic, complemented
11C2×#89590C211yesmaximal, characteristic, complemented
12C2×#89582C211yesmaximal, characteristic
13C2×#89586C211yesmaximal, characteristic, complemented
14C2×#89566C211yesmaximal, characteristic, complemented
15C2×#89482C211yesmaximal, characteristic, complemented
16C2×#89477C211yesmaximal, characteristic, complemented
17C22×#1161C2211yescharacteristic
18C22×C7×Q16C2211yescharacteristic
19C2×C4×C7×Q8C2211yescharacteristic
20C2×C4×C7×Q8C2211yescharacteristic
21C2×#6509C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×#6507C2211yescharacteristic
24C22×#1144C2211yescharacteristic
25C22×#1143C2211yescharacteristic
26C22×#1132C2211yescharacteristic
27#90269—24no—
28#90269C2218yescomplemented
29C4×#1161—24no—
30C4×#1161C2218yes—
31C2×#6460C2211yescharacteristic
32C2×#6459—21no—
33C2×#6456—21no—
34C2×#6456C2211yescharacteristic
35C2×#6455—21no—
36C2×#6455C2211yescharacteristic
37C2×#6452—21no—
38C2×#6451C2211yescharacteristic
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#89959C2218yes—
54#89954C2218yescomplemented
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#89642C2218yescomplemented
70#89639C2218yescomplemented
71#89590C2218yescomplemented
72#89586C2218yescomplemented
73#89582C2218yes—
74#89566C2218yescomplemented
75#89482C2218yescomplemented
76#89477C2218yescomplemented
77C2×#3116—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C2×#1161—24no—
81C2×#1161—24no—
82C2×#1161—22no—
83C2×#1161C2314yes—
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#6509—22no—
110#6509C2314yes—
111Q8×Dic7—22no—
112Q8×Dic7C2314yes—
113#6507—22no—
114#6507C2314yes—
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#6460—22no—
144#6460C2314yes—
145#6459—28no—
146#6456—28no—
147#6456—22no—
148#6456C2314yes—
149#6455—22no—
150#6455—28no—
151#6455C2314yes—
152#6452—28no—
153#6451—22no—
154#6451C2314yes—
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×#533—71no—
184C2×C4×#41—71no—
185#3116—716no—
186C2×#485—71no—
187C2×#485—71no—
188C2×#477—71no—
189C2×#476—71no—
190C2×#462—71no—
191C2×#461—71no—
192C2×#452—71no—
193C2×#452—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
222#1161—216no—
223#1161—28no—
224#1161—28no—
225C2×D28—28no—
226C2×D28—24no—
227C2×D28—21no—
228C2×D28—22no—
229C2×D28#4114yes—
230C2×D28C2412yes—
231C2×C4×D7—28no—
232C2×C4×D7—22no—
233C2×C4×D7—22no—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—24no—
237C2×C4×D7—24no—
238C2×C4×D7—42no—
239C2×C4×D7—44no—
240C2×C4×D7—44no—
241C2×C4×D7C2×D412yes—
242C2×C4×D7C2×D414yes—
243C2×C4×D7C2×D414yes—
244C2×C4×D7C2412yes—
245C2×Dic14—22no—
246C2×Dic14—22no—
247C2×Dic14—21no—
248C2×Dic14—24no—
249C2×Dic14—44no—
250C2×Dic14C2412yes—
251C7×Q16—28no—
252C2×C7×C8—22no—
253C2×C7×C8—22no—
254C2×C7×C8C2412yes—
255C2×C7×C8C2412yes—
256C7×C4⋊C4—21no—
257C7×C4⋊C4—24no—
258C7×C4⋊C4—24no—
259C7×C4⋊C4—21no—
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×D414yes—
289C4×Dic7C2×D412yes—
290C4×Dic7C2412yes—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8C2412yes—
294C2×C7⋊C8C2412yes—
295#1132—28no—
296C22×#41—71no—
297C22×Q16—71no—
298C22×Q16C2×D711yescharacteristic
299C22×SD16—71no—
300C22×SD16—71no—
301#533—78no—
302#533—144no—
303C2×C4⋊Q8—71no—
304C2×C4⋊Q8—71no—
305C2×#125—141no—
306C2×C22⋊Q8—71no—
307C2×C22⋊Q8—71no—
308C2×C22⋊Q8—141no—
309C4×#41—78no—
310C4×#41—144no—
311C2×C4×Q8—71no—
312C2×C4×Q8—71no—
313C2×C4×Q8—141no—
314C2×C4×Q8C2×D711yescharacteristic
315C2×C4×Q8C2×D711yescharacteristic
316C2×C4×D4—71no—
317C2×C4×D4—71no—
318C2×C4×D4—141no—
319C2×C4×D4—141no—
320C2×#117—71no—
321C2×#117—141no—
322C2×#117—141no—
323C22×C42—71no—
324C22×C42—141no—
325#485—78no—
326#485—78no—
327#477—78no—
328#476—78no—
329#462—78no—
330#461—78no—
331#452—78no—
332#452—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—24no—
359C22×D7—22no—
360C22×D7—22no—
361C22×D7—22no—
362C22×D7—42no—
363C22×D7—42no—
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—22no—
389C2×Dic7—22no—
390C2×Dic7—22no—
391C2×Dic7—22no—
392C2×Dic7—42no—
393C2×Dic7—42no—
394C2×Dic7—42no—
395C2×Dic7#13714yes—
396C2×Dic7C22×D412yes—
397C2×Dic7C22×D412yes—
398C2×Dic7C22×D412yes—
399D28—216no—
400D28—24no—
401D28—22no—
402D28C2×#4114yes—
403C4×D7—216no—
404C4×D7—24no—
405C4×D7—22no—
406C4×D7—22no—
407C4×D7—28no—
408C4×D7—44no—
409C4×D7—48no—
410C4×D7—48no—
411Dic14—22no—
412Dic14—22no—
413Dic14—48no—
414Dic14—42no—
415C7×C8—22no—
416C7×C8—22no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C2×#41—74no—
420C2×#41—142no—
421C2×#41—144no—
422C2×#41—144no—
423C22×Q8—71no—
424C22×Q8—141no—
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
447C4⋊Q8—74no—
448C4⋊Q8—74no—
449C4⋊Q8—142no—
450C4⋊Q8—142no—
451#125—148no—
452C22⋊Q8—74no—
453C22⋊Q8—74no—
454C22⋊Q8—142no—
455C22⋊Q8—148no—
456C22⋊Q8—142no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—74no—
460C4×Q8—74no—
461C4×Q8—148no—
462C4×Q8—142no—
463C4×Q8—142no—
464C4×Q8C22×D714yes—
465C4×Q8C22×D714yes—
466C4×D4—74no—
467C4×D4—74no—
468C4×D4—148no—
469C4×D4—142no—
470C4×D4—148no—
471C4×D4—142no—
472#117—74no—
473#117—148no—
474#117—148no—
475#117—142no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—71no—
479C2×C4⋊C4—71no—
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—22no—
529C2×D7—24no—
530C2×D7—22no—
531C2×D7—22no—
532C2×D7—44no—
533C2×D7—48no—
534C2×D7—42no—
535C2×D7—42no—
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—22no—
547Dic7—42no—
548Dic7—42no—
549Dic7—42no—
550Dic7C2×#13714yes—
551C24—71no—
552C24—141no—
553#41—148no—
554#41—1416no—
555#41—148no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—72no—
562C2×Q8—144no—
563C2×Q8—141no—
564C2×Q8—142no—
565C2×Q8—142no—
566C2×Q8—284no—
567C2×Q8#115714yes—
568C2×Q8C23×D712yes—
569C2×Q8C23×D712yes—
570C2×D4—74no—
571C2×D4—72no—
572C2×D4—144no—
573C2×D4—148no—
574C2×D4—142no—
575C2×D4—141no—
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—144no—
590C22×C4—148no—
591C22×C4—142no—
592C22×C4—142no—
593C22×C4—141no—
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—74no—
641C42—72no—
642C42—72no—
643C42—144no—
644C42—144no—
645C42—144no—
646C42D4×D712yes—
647C42C23×D712yes—
648C2×C7#311614yescomplemented
649C2×C7C2×#52511yescharacteristic
650C2×C7C22×#13711yescharacteristic
651C2×C7C2×#57511yescharacteristic
652D7—42no—
653D7—44no—
654C23—72no—
655C23—142no—
656C23—142no—
657C23—144no—
658C23—142no—
659C23—142no—
660C23—282no—
661C23—282no—
662C23C2×D4×D711yescharacteristic
663Q8—24no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—142no—
669Q8—142no—
670Q8—288no—
671Q8—282no—
672Q8C2×#115714yes—
673D4—74no—
674D4—1416no—
675D4—144no—
676D4—142no—
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—74no—
688C2×C4—72no—
689C2×C4—72no—
690C2×C4—72no—
691C2×C4—148no—
692C2×C4—1416no—
693C2×C4—142no—
694C2×C4—142no—
695C2×C4—144no—
696C2×C4—142no—
697C2×C4—142no—
698C2×C4—142no—
699C2×C4—142no—
700C2×C4—142no—
701C2×C4—284no—
702C2×C4—288no—
703C2×C4—288no—
704C2×C4—282no—
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×#311611yescharacteristic, complemented, Sylow
718C22—142no—
719C22—142no—
720C22—144no—
721C22—142no—
722C22—282no—
723C22—282no—
724C22—284no—
725C22—288no—
726C22#9023812yes—
727C22D7×#13712yes—
728C22#9046812yes—
729C22C22×D4×D711yescharacteristic
730C4—22no—
731C4—22no—
732C4—24no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—74no—
737C4—142no—
738C4—142no—
739C4—282no—
740C4—282no—
741C4—282no—
742C4#9023812yes—
743C4C22×#115711yescharacteristic
744C4C2×D7×#4111yescharacteristic
745C2—282no—
746C2—284no—
747C2#1173729314yesdirect 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 radicalC22×#1161C22
hypercenterC2×#441D7
hypocenterC7C2×#3116
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
1. C2×#90269C2semidirect
3. C2×C7×#441C2semidirect
5. C2×#89954C2semidirect
6. C2×#89798C2semidirect
7. C2×#89802C2semidirect
8. #11737293C2direct (N × H)
9. C2×#89642C2semidirect
10. C2×#89639C2semidirect
11. C2×#89590C2semidirect
13. C2×#89586C2semidirect
14. C2×#89566C2semidirect
15. C2×#89482C2semidirect
16. C2×#89477C2semidirect
28. #90269C22semidirect
46. C7×#441C22semidirect
54. #89954C22semidirect
62. #89802C22semidirect
63. #89798C22semidirect
69. #89642C22semidirect
70. #89639C22semidirect
71. #89590C22semidirect
72. #89586C22semidirect
74. #89566C22semidirect
75. #89482C22semidirect
76. #89477C22semidirect
195. C2×#441D7semidirect
334. #441C2×D7semidirect
648. C2×C7#3116semidirect
717. C7C2×#3116semidirect
747. C2#11737293direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#902692
C2×C4×#11612
C2×C7×#4412
C2×#899592
C2×#899542
C2×#897982
C2×#898022
#117372932
C2×#896422
C2×#896392
C2×#895902
C2×#895822
C2×#895862
C2×#895662
C2×#894822
C2×#894772
C2×#31167