Finite Group Databasebeta

← C2×#11738657 #14226600

Subgroups — C2×#11738657 #14226600

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90382C211yesmaximal, characteristic
2C2×#90269C211yesmaximal, characteristic, complemented
3C2×C7×#479C211yesmaximal, characteristic, complemented
4C2×#89835C211yesmaximal, characteristic, complemented
5C2×#89800C211yesmaximal, characteristic, complemented
6#11738657C2116yesmaximal, direct product factor
7C2×#89662C211yesmaximal, characteristic, complemented
8C2×#89659C211yesmaximal, characteristic, complemented
9C2×#89626C211yesmaximal, characteristic, complemented
10C2×#89636C211yesmaximal, characteristic
11C2×#89617C211yesmaximal, characteristic, complemented
12C2×D7×C4⋊C8C211yesmaximal, characteristic, complemented
13C2×#89565C211yesmaximal, characteristic, complemented
14C2×#89590C211yesmaximal, characteristic, complemented
15C2×#89585C211yesmaximal, characteristic, complemented
16C2×#89579C211yesmaximal, characteristic
17C2×C7×#125C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C2×#6509C2211yescharacteristic
20C2×#6507C2211yescharacteristic
21C22×#1144C2211yescharacteristic
22C22×#1143C2211yescharacteristic
23C22×Dic28C2211yescharacteristic
24C22×#1132C2211yescharacteristic
25C22×C8×D7C2211yescharacteristic
26C22×C8×D7C2211yescharacteristic
27#90382—24no—
28#90382C2218yes—
29#90269—24no—
30#90269C2218yescomplemented
31C2×#6461—21no—
32C2×#6460C2211yescharacteristic
33C2×#6460C2211yescharacteristic
34C2×#6459—21no—
35C2×#6458C2211yescharacteristic
36C2×#6457—21no—
37C2×#6456—21no—
38C2×#6456C2211yescharacteristic
39C2×#6455—21no—
40C2×#6452—21no—
41C2×#6451C2211yescharacteristic
42C2×#6450C2211yescharacteristic
43C2×#6438C2211yescharacteristic
44C2×#6435—21no—
45C2×C42×D7C2211yescharacteristic
46C2×C4×Dic14—21no—
47C2×C4×Dic14C2211yescharacteristic
48C7×#479C2218yescomplemented
49C2×C7×#107C2211yescharacteristic
50C2×C7×#106C2211yescharacteristic
51C2×C7×C4⋊C8C2211yescharacteristic
52C2×C7×#103C2211yescharacteristic
53C2×C7×#103C2211yescharacteristic
54C2×#6395C2211yescharacteristic
55C2×#6390C2211yescharacteristic
56C2×Dic7⋊C8C2211yescharacteristic
57C2×Dic7⋊C8C2211yescharacteristic
58#89835C2218yescomplemented
59#89800C2218yescomplemented
60C2×#6384C2211yescharacteristic
61C2×#6384C2211yescharacteristic
62C2×#6384C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6382C2211yescharacteristic
65C2×#6381C2211yescharacteristic
66C2×C4⋊(C7⋊C8)C2211yescharacteristic
67#89662C2218yescomplemented
68#89659C2218yescomplemented
69#89636C2218yes—
70#89626C2218yescomplemented
71#89617C2218yescomplemented
72D7×C4⋊C8C2218yescomplemented
73#89590C2218yescomplemented
74#89585C2218yescomplemented
75#89579C2218yes—
76#89565C2218yescomplemented
77C2×#3248—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×D28—21no—
80C22×D28C2311yescharacteristic
81C22×C4×D7—21no—
82C22×C4×D7D411yescharacteristic
83C22×C4×D7D411yescharacteristic
84C22×C4×D7C2311yescharacteristic
85C22×Dic14—21no—
86C22×Dic14C2311yescharacteristic
87C22×Dic14C2311yescharacteristic
88C22×C7×C8C2311yescharacteristic
89C22×C7×C8C2311yescharacteristic
90C7×#125—22no—
91C7×#125C2314yes—
92C4×C7×Q8—22no—
93C4×C7×Q8C2314yes—
94C2×C7×C4⋊C4—21no—
95C2×C7×C4⋊C4—21no—
96C2×C7×C4⋊C4—21no—
97C2×C7×C4⋊C4C2311yescharacteristic
98C2×C7×C4⋊C4C2311yescharacteristic
99C2×C7×C4⋊C4C2311yescharacteristic
100C2×C42×C7—21no—
101C2×C42×C7C2311yescharacteristic
102#6509—22no—
103#6509C2314yes—
104#6507—22no—
105#6507C2314yes—
106C2×#1144—42no—
107C2×#1144C2314yes—
108C2×#1143—42no—
109C2×#1143C2314yes—
110C2×(C2×D7)⋊C4—21no—
111C2×(C2×D7)⋊C4—21no—
112C2×(C2×D7)⋊C4—21no—
113C2×(C2×D7)⋊C4—21no—
114C2×(C2×D7)⋊C4—21no—
115C2×(C2×D7)⋊C4—21no—
116C2×(C2×D7)⋊C4—21no—
117C2×C4⋊Dic7—21no—
118C2×C4⋊Dic7—21no—
119C2×C4⋊Dic7C2311yescharacteristic
120C2×Dic7⋊C4—21no—
121C2×Dic7⋊C4—21no—
122C2×Dic7⋊C4—21no—
123C2×Dic7⋊C4—21no—
124C2×Dic7⋊C4—21no—
125C2×Dic7⋊C4—21no—
126C2×C4×Dic7—21no—
127C2×C4×Dic7—21no—
128C2×C4×Dic7D411yescharacteristic
129C2×C4×Dic7D411yescharacteristic
130C2×C4×Dic7C2311yescharacteristic
131C22×C7⋊C8C2311yescharacteristic
132C22×C7⋊C8C2311yescharacteristic
133C2×Dic28—42no—
134C2×Dic28C2314yes—
135C2×#1132—42no—
136C2×#1132C2314yes—
137C2×C8×D7—42no—
138C2×C8×D7—42no—
139C2×C8×D7C2314yes—
140C2×C8×D7C2314yes—
141#6461—28no—
142#6460—22no—
143#6460—22no—
144#6460C2314yes—
145#6460C2314yes—
146#6459—28no—
147#6458—22no—
148#6458C2314yes—
149#6457—28no—
150#6456—28no—
151#6456—22no—
152#6456C2314yes—
153#6455—28no—
154#6452—28no—
155#6451—22no—
156#6451C2314yes—
157#6450—22no—
158#6450C2314yes—
159#6438—22no—
160#6438C2314yes—
161#6435—28no—
162C42×D7D414yes—
163C42×D7C2314yes—
164C4×Dic14—22no—
165C4×Dic14—28no—
166C4×Dic14C2314yes—
167C7×#107C2314yes—
168C7×#106C2314yes—
169C7×C4⋊C8C2314yes—
170C7×#103C2314yes—
171C7×#103C2314yes—
172#6395C2314yes—
173#6390C2314yes—
174Dic7⋊C8C2314yes—
175Dic7⋊C8C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6384C2314yes—
179#6383C2314yes—
180#6382C2314yes—
181#6381C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183C2×#533—71no—
184C2×#529—71no—
185#3248—716no—
186C2×#479—71no—
187C2×#479D711yescharacteristic, complemented
188C2×#475—71no—
189C2×#474—71no—
190C2×#467—71no—
191C2×#467—71no—
192C2×#465—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#462—71no—
197C2×#461—71no—
198C22×C4⋊C8—71no—
199C23×D7—21no—
200C23×D7C2×D411yescharacteristic
201C2×C7×Q8—21no—
202C2×C7×Q8—22no—
203C2×C7×Q8—22no—
204C2×C7×Q8C2412yes—
205C22×C4×C7—21no—
206C22×C4×C7—21no—
207C22×C4×C7—21no—
208C22×C4×C7—21no—
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2411yescharacteristic
212C22×Dic7—21no—
213C22×Dic7—21no—
214C22×Dic7—21no—
215C22×Dic7C2×D411yescharacteristic
216C22×Dic7C2×D411yescharacteristic
217C22×Dic7C2×D411yescharacteristic
218C2×D28—22no—
219C2×D28—22no—
220C2×D28—24no—
221C2×D28—21no—
222C2×D28—44no—
223C2×D28C2412yes—
224C2×C4×D7—24no—
225C2×C4×D7—22no—
226C2×C4×D7—22no—
227C2×C4×D7—24no—
228C2×C4×D7—24no—
229C2×C4×D7—44no—
230C2×C4×D7C2×D412yes—
231C2×C4×D7C2×D414yes—
232C2×C4×D7C2×D414yes—
233C2×C4×D7C2412yes—
234C2×Dic14—22no—
235C2×Dic14—22no—
236C2×Dic14—22no—
237C2×Dic14—22no—
238C2×Dic14—21no—
239C2×Dic14—21no—
240C2×Dic14—24no—
241C2×Dic14—44no—
242C2×Dic14C2412yes—
243C2×Dic14C2412yes—
244C2×C7×C8—22no—
245C2×C7×C8—22no—
246C2×C7×C8C2412yes—
247C2×C7×C8C2412yes—
248C7×C4⋊C4—21no—
249C7×C4⋊C4—21no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C4⋊C4C2412yes—
257C42×C7—24no—
258C42×C7C2×D412yes—
259C42×C7C2412yes—
260#1144—44no—
261#1143—44no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267(C2×D7)⋊C4—24no—
268(C2×D7)⋊C4—24no—
269C4⋊Dic7—21no—
270C4⋊Dic7—24no—
271C4⋊Dic7—24no—
272C4⋊Dic7C2412yes—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278Dic7⋊C4—24no—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D414yes—
282C4×Dic7C2×D412yes—
283C4×Dic7C2×D414yes—
284C4×Dic7C2412yes—
285C2×C7⋊C8—22no—
286C2×C7⋊C8—22no—
287C2×C7⋊C8C2412yes—
288C2×C7⋊C8C2412yes—
289Dic28—44no—
290#1132—44no—
291C8×D7—44no—
292C8×D7—44no—
293C22×Q16—71no—
294C22×Q16—71no—
295C22×SD16—71no—
296C22×SD16—71no—
297C23×C8—71no—
298C23×C8—71no—
299#533—78no—
300#533—144no—
301C2×C4⋊Q8—71no—
302C2×C4⋊Q8—71no—
303#529—78no—
304#529—144no—
305C2×#126—141no—
306C2×#125—141no—
307C2×#125C2×D711yescharacteristic
308C2×#124—71no—
309C2×#123—141no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8—71no—
312C2×C22⋊Q8—71no—
313C2×C22⋊Q8—141no—
314C2×#121—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×Q8—141no—
318C2×C4×Q8C2×D711yescharacteristic
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×#117—141no—
322C2×#117—141no—
323C22×C42—71no—
324#479—78no—
325#479C2×D718yescomplemented
326#475—78no—
327#474—78no—
328#467—78no—
329#467—78no—
330#465—78no—
331#465—78no—
332#464—78no—
333#464—78no—
334#462—78no—
335#461—78no—
336C2×#107—71no—
337C2×#107C2×D711yescharacteristic
338C2×#106—71no—
339C2×#106C2×D711yescharacteristic
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—78no—
344C2×C4⋊C8C2×D711yescharacteristic
345C2×#103—71no—
346C2×#103—71no—
347C2×#103—71no—
348C2×#103—71no—
349C2×#103C2×D711yescharacteristic
350C2×#103C2×D711yescharacteristic
351C2×#102—71no—
352C2×#102—71no—
353C23×C7C22×D411yescharacteristic
354C22×D7—22no—
355C22×D7—22no—
356C22×D7—22no—
357C22×D7—42no—
358C22×D7—42no—
359C22×D7—42no—
360C22×D7#13714yes—
361C22×D7C22×D412yes—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—42no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D411yescharacteristic
378C2×C4×C7H(5,𝔽2)12yes—
379C2×C4×C72−1+412yes—
380C2×C4×C7C2511yescharacteristic
381C2×Dic7—22no—
382C2×Dic7—22no—
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388C2×Dic7—42no—
389C2×Dic7#13514yes—
390C2×Dic7C22×D412yes—
391C2×Dic7C22×D412yes—
392C2×Dic7C22×D412yes—
393D28—22no—
394D28—22no—
395D28—48no—
396D28—42no—
397C4×D7—28no—
398C4×D7—24no—
399C4×D7—22no—
400C4×D7—22no—
401C4×D7—28no—
402C4×D7—48no—
403Dic14—22no—
404Dic14—22no—
405Dic14—22no—
406Dic14—22no—
407Dic14—42no—
408Dic14—42no—
409Dic14—48no—
410C7×C8—22no—
411C7×C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C22×Q8—71no—
415C22×Q8—71no—
416C22×Q8—141no—
417C22×Q8C22×D711yescharacteristic
418C22×D4—71no—
419C22×D4—141no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—71no—
423C23×C4—141no—
424C2×Q16—74no—
425C2×Q16—74no—
426C2×Q16—282no—
427C2×Q16—282no—
428C2×SD16—74no—
429C2×SD16—74no—
430C2×SD16—282no—
431C2×SD16—282no—
432C22×C8—71no—
433C22×C8—71no—
434C22×C8—74no—
435C22×C8—74no—
436C22×C8—282no—
437C22×C8—282no—
438C22×C8C22×D711yescharacteristic
439C22×C8C22×D711yescharacteristic
440C4⋊Q8—74no—
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443C4⋊Q8—142no—
444#126—148no—
445#125—22no—
446#125—148no—
447#125C22×D714yes—
448#124—74no—
449#124—142no—
450#123—148no—
451C22⋊Q8—74no—
452C22⋊Q8—74no—
453C22⋊Q8—74no—
454C22⋊Q8—142no—
455C22⋊Q8—142no—
456C22⋊Q8—148no—
457C22⋊Q8—142no—
458#121—74no—
459#121—142no—
460C4×Q8—22no—
461C4×Q8—74no—
462C4×Q8—74no—
463C4×Q8—148no—
464C4×Q8—142no—
465C4×Q8—142no—
466C4×Q8C22×D714yes—
467C4×D4—74no—
468C4×D4—142no—
469C4×D4—148no—
470#117—148no—
471#117—148no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—71no—
476C2×C4⋊C4—141no—
477C2×C4⋊C4—141no—
478C2×C4⋊C4—141no—
479C2×C4⋊C4—141no—
480C2×C4⋊C4—141no—
481C2×C4⋊C4—141no—
482C2×C4⋊C4—141no—
483C2×C4⋊C4—141no—
484C2×C4⋊C4C22×D711yescharacteristic
485C2×C4⋊C4C22×D711yescharacteristic
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C22⋊C4—141no—
488C2×C22⋊C4—141no—
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—71no—
496C2×C42—71no—
497C2×C42—71no—
498C2×C42—74no—
499C2×C42—74no—
500C2×C42—141no—
501C2×C42—141no—
502C2×C42C22×D711yescharacteristic
503#107—74no—
504#107C22×D714yes—
505#106—74no—
506#106C22×D714yes—
507C4⋊C8—74no—
508C4⋊C8—74no—
509C4⋊C8—74no—
510C4⋊C8C22×D714yes—
511#103—74no—
512#103—74no—
513#103—74no—
514#103—74no—
515#103C22×D714yes—
516#103C22×D714yes—
517#102—74no—
518#102—74no—
519C22×C7#53712yes—
520C22×C7C2×#13512yes—
521C22×C7C2×#13712yes—
522C22×C7C23×D411yescharacteristic
523C2×D7—22no—
524C2×D7—28no—
525C2×D7—22no—
526C2×D7—42no—
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—84no—
530C2×D7C2×#13714yes—
531C4×C7—22no—
532C4×C7—22no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7—42no—
537C4×C7#53712yes—
538C4×C7C2×H(5,𝔽2)11yescharacteristic
539C4×C7C2×2−1+411yescharacteristic
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7C2×#13514yes—
546C24—71no—
547C24—141no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—72no—
552C2×Q8—72no—
553C2×Q8—144no—
554C2×Q8—141no—
555C2×Q8—141no—
556C2×Q8—142no—
557C2×Q8—142no—
558C2×Q8—142no—
559C2×Q8—142no—
560C2×Q8—284no—
561C2×Q8C23×D712yes—
562C2×D4—72no—
563C2×D4—144no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—284no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—71no—
573C22×C4—71no—
574C22×C4—71no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—72no—
578C22×C4—72no—
579C22×C4—144no—
580C22×C4—144no—
581C22×C4—144no—
582C22×C4—142no—
583C22×C4—142no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—141no—
587C22×C4—284no—
588C22×C4D4×D711yescharacteristic
589C22×C4D4×D711yescharacteristic
590C22×C4C23×D711yescharacteristic
591Q16—284no—
592Q16—284no—
593SD16—284no—
594SD16—284no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—72no—
598C2×C8—72no—
599C2×C8—142no—
600C2×C8—142no—
601C2×C8—284no—
602C2×C8—284no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—72no—
612C4⋊C4—144no—
613C4⋊C4—144no—
614C4⋊C4—144no—
615C4⋊C4—144no—
616C4⋊C4—144no—
617C4⋊C4—144no—
618C4⋊C4—144no—
619C4⋊C4—144no—
620C4⋊C4—141no—
621C4⋊C4C23×D712yes—
622C4⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C22⋊C4—144no—
625C22⋊C4—144no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—24no—
632C42—74no—
633C42—72no—
634C42—74no—
635C42—72no—
636C42—144no—
637C42—144no—
638C42D4×D712yes—
639C42C23×D712yes—
640C2×C7#324814yescomplemented
641C2×C7C2×#53711yescharacteristic
642C2×C7C22×#13511yescharacteristic
643C2×C7C22×#13711yescharacteristic
644D7—24no—
645D7—82no—
646C23—74no—
647C23—72no—
648C23—142no—
649C23—142no—
650C23—142no—
651C23—282no—
652C23—282no—
653C23—282no—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—142no—
659Q8—142no—
660Q8—142no—
661Q8—142no—
662Q8—288no—
663Q8—282no—
664Q8—282no—
665D4—142no—
666D4—142no—
667D4—288no—
668D4—282no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—74no—
680C2×C4—72no—
681C2×C4—72no—
682C2×C4—72no—
683C2×C4—148no—
684C2×C4—148no—
685C2×C4—142no—
686C2×C4—142no—
687C2×C4—144no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—288no—
694C2×C4—282no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4C2×D4×D712yes—
698C2×C4C2×D4×D712yes—
699C2×C4C2×D4×D711yescharacteristic
700C2×C4#655112yes—
701C2×C4#655312yes—
702C2×C4C24×D711yescharacteristic
703C8—22no—
704C8—22no—
705C8—142no—
706C8—142no—
707C7C2×#324811yescharacteristic, complemented, Sylow
708C22—74no—
709C22—148no—
710C22—142no—
711C22—142no—
712C22—282no—
713C22—282no—
714C22—282no—
715C22—564no—
716C22#9032012yes—
717C22D7×#13512yes—
718C22D7×#13712yes—
719C22C22×D4×D711yescharacteristic
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—74no—
727C4—142no—
728C4—142no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4#9032012yes—
733C4C2×#655111yescharacteristic
734C4C2×#655311yescharacteristic
735C2—144no—
736C2—562no—
737C2#1173865714yesdirect product factor
738C2C2×#9032011yescharacteristic
739C2C2×D7×#13511yescharacteristic
740C2C2×D7×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#479C2
socleC23×C7C22×D4
prime radicalC2×#6458C22
hypercenterC2×#479D7
hypocenterC7C2×#3248
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×#90269C2semidirect
3. C2×C7×#479C2semidirect
4. C2×#89835C2semidirect
5. C2×#89800C2semidirect
6. #11738657C2direct (N × H)
7. C2×#89662C2semidirect
8. C2×#89659C2semidirect
9. C2×#89626C2semidirect
11. C2×#89617C2semidirect
12. C2×D7×C4⋊C8C2semidirect
13. C2×#89565C2semidirect
14. C2×#89590C2semidirect
15. C2×#89585C2semidirect
30. #90269C22semidirect
48. C7×#479C22semidirect
58. #89835C22semidirect
59. #89800C22semidirect
67. #89662C22semidirect
68. #89659C22semidirect
70. #89626C22semidirect
71. #89617C22semidirect
72. D7×C4⋊C8C22semidirect
73. #89590C22semidirect
74. #89585C22semidirect
76. #89565C22semidirect
187. C2×#479D7semidirect
325. #479C2×D7semidirect
640. C2×C7#3248semidirect
707. C7C2×#3248semidirect
737. C2#11738657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903822
C2×#902692
C2×C7×#4792
C2×#898352
C2×#898002
#117386572
C2×#896622
C2×#896592
C2×#896262
C2×#896362
C2×#896172
C2×D7×C4⋊C82
C2×#895652
C2×#895902
C2×#895852
C2×#895792
C2×#32487