Finite Group Databasebeta

← C2×#11738191 #14226596

Subgroups — C2×#11738191 #14226596

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×#90313C211yesmaximal, characteristic, complemented
2C2×#90315C211yesmaximal, characteristic
3C2×C7×#467C211yesmaximal, characteristic, complemented
4C2×#89957C211yesmaximal, characteristic, complemented
5C2×#89954C211yesmaximal, characteristic, complemented
6C2×#89886C211yesmaximal, characteristic
7C22×Dic7⋊C8C211yesmaximal, characteristic, complemented
8C2×#89823C211yesmaximal, characteristic, complemented
9C2×#89820C211yesmaximal, characteristic
10#11738191C2116yesmaximal, direct product factor
11C2×#89649C211yesmaximal, characteristic, complemented
12C2×#89662C211yesmaximal, characteristic, complemented
13C2×#89570C211yesmaximal, characteristic, complemented
14C2×#89590C211yesmaximal, characteristic, complemented
15C2×#89571C211yesmaximal, characteristic, complemented
16C2×#89563C211yesmaximal, characteristic, complemented
17C22×C7×Q16C2211yescharacteristic
18C23×C7×C8C2211yescharacteristic
19C2×C7×C22⋊Q8C2211yescharacteristic
20C2×C7×C22⋊Q8C2211yescharacteristic
21C2×#6510C2211yescharacteristic
22C2×Q8×Dic7C2211yescharacteristic
23C2×Q8×Dic7C2211yescharacteristic
24C2×#6507C2211yescharacteristic
25C22×#1144C2211yescharacteristic
26C22×#1143C2211yescharacteristic
27C2×#6493C2211yescharacteristic
28C2×#6487C2211yescharacteristic
29C22×C4×Dic7C2211yescharacteristic
30C23×C7⋊C8C2211yescharacteristic
31C22×#1132C2211yescharacteristic
32#90315—24no—
33#90315C2218yes—
34#90313—24no—
35#90313C2218yescomplemented
36C2×#6461—21no—
37C2×#6456C2211yescharacteristic
38C2×#6455—21no—
39C2×#6453C2211yescharacteristic
40C2×#6452—21no—
41C2×#6451C2211yescharacteristic
42C2×#6450—21no—
43C2×#6450C2211yescharacteristic
44C2×#6449—21no—
45C2×(C22⋊D7)⋊C4—21no—
46C2×#6441—21no—
47C2×#6440—21no—
48C7×#467C2218yescomplemented
49C2×C7×#107C2211yescharacteristic
50C2×C7×#103C2211yescharacteristic
51C2×C7×#103C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54#89957C2218yescomplemented
55#89954C2218yescomplemented
56#89886C2218yes—
57C2×#6395C2211yescharacteristic
58C2×#6391C2211yescharacteristic
59C2×#6390C2211yescharacteristic
60C2×Dic7⋊C8C2211yescharacteristic
61C2×Dic7⋊C8C2211yescharacteristic
62C2×Dic7⋊C8C2211yescharacteristic
63C2×Dic7⋊C8C2211yescharacteristic
64C2×Dic7⋊C8C2218yescomplemented
65#89823C2218yescomplemented
66#89820C2218yes—
67C2×#6384C2211yescharacteristic
68C2×#6383C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89662C2218yescomplemented
72#89649C2218yescomplemented
73#89590C2218yescomplemented
74#89571C2218yescomplemented
75#89570C2218yescomplemented
76#89563C2218yescomplemented
77C2×#3248—71nomaximal, Sylow
78C22×C7×Q8C2311yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C22×C22⋊D7—21no—
82C23×Dic7D411yescharacteristic
83C23×Dic7D411yescharacteristic
84C22×D28C2311yescharacteristic
85C22×C4×D7—21no—
86C22×Dic14—21no—
87C22×Dic14C2311yescharacteristic
88C2×C7×Q16—42no—
89C2×C7×Q16C2314yes—
90C22×C7×C8—42no—
91C22×C7×C8C2311yescharacteristic
92C22×C7×C8C2311yescharacteristic
93C22×C7×C8C2314yes—
94C7×C22⋊Q8—22no—
95C7×C22⋊Q8—22no—
96C7×C22⋊Q8C2314yes—
97C7×C22⋊Q8C2314yes—
98C2×C7×C4⋊C4—21no—
99C2×C7×C4⋊C4—21no—
100C2×C7×C4⋊C4C2311yescharacteristic
101C2×C7×C4⋊C4C2311yescharacteristic
102C2×C7×C22⋊C4—21no—
103C2×C7×C22⋊C4—21no—
104C2×C22⋊Dic7—21no—
105#6510—22no—
106#6510C2314yes—
107Q8×Dic7—22no—
108Q8×Dic7—22no—
109Q8×Dic7C2314yes—
110Q8×Dic7C2314yes—
111#6507—22no—
112#6507C2314yes—
113C2×#1144—42no—
114C2×#1144C2314yes—
115C2×#1143—42no—
116C2×#1143C2314yes—
117#6493—22no—
118#6493C2314yes—
119C2×(C2×D7)⋊C4—21no—
120C2×(C2×D7)⋊C4—21no—
121C2×(C2×D7)⋊C4—21no—
122C2×(C2×D7)⋊C4—21no—
123C2×C4⋊Dic7—21no—
124C2×C4⋊Dic7—21no—
125C2×C4⋊Dic7—21no—
126C2×C4⋊Dic7C2311yescharacteristic
127C2×C4⋊Dic7C2311yescharacteristic
128#6487—22no—
129#6487C2314yes—
130C2×Dic7⋊C4—21no—
131C2×Dic7⋊C4—21no—
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—
139C2×C4×Dic7D411yescharacteristic
140C2×C4×Dic7D411yescharacteristic
141C2×C4×Dic7D414yes—
142C2×C4×Dic7C2311yescharacteristic
143C2×C4×Dic7C2311yescharacteristic
144C2×C4×Dic7C2314yes—
145C22×C7⋊C8—42no—
146C22×C7⋊C8C2311yescharacteristic
147C22×C7⋊C8C2311yescharacteristic
148C22×C7⋊C8C2314yes—
149C2×#1132—42no—
150C2×#1132C2314yes—
151#6461—28no—
152#6456—22no—
153#6456C2314yes—
154#6455—28no—
155#6453—22no—
156#6453C2314yes—
157#6452—28no—
158#6451—22no—
159#6451C2314yes—
160#6450—28no—
161#6450—22no—
162#6450C2314yes—
163#6449—28no—
164(C22⋊D7)⋊C4—28no—
165#6441—28no—
166#6440—28no—
167C7×#107C2314yes—
168C7×#103C2314yes—
169C7×#103C2314yes—
170#6409C2314yes—
171#6409C2314yes—
172#6395C2314yes—
173#6391C2314yes—
174#6390C2314yes—
175Dic7⋊C8C2314yes—
176Dic7⋊C8C2314yes—
177Dic7⋊C8C2314yes—
178Dic7⋊C8C2314yes—
179#6384C2314yes—
180#6383C2314yes—
181#6382C2314yes—
182#6381C2314yes—
183C2×#533—71no—
184C2×#529—71no—
185#3248—716no—
186C2×#479—71no—
187C2×#479—71no—
188C2×#475—71no—
189C2×#474—71no—
190C2×#467—71no—
191C2×#467D711yescharacteristic, complemented
192C2×#465—71no—
193C2×#465—71no—
194C2×#464—71no—
195C2×#464—71no—
196C2×#462—71no—
197C2×#461—71no—
198C22×C4⋊C8—71no—
199C24×C7C2×D411yescharacteristic
200C23×D7—21no—
201C2×C7×Q8—21no—
202C2×C7×Q8—21no—
203C2×C7×Q8—22no—
204C2×C7×Q8—22no—
205C2×C7×Q8—22no—
206C2×C7×Q8—22no—
207C2×C7×Q8C2412yes—
208C2×C7×Q8C2412yes—
209C22×C4×C7—22no—
210C22×C4×C7—22no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7—21no—
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D412yes—
217C22×C4×C7C2412yes—
218C22×C4×C7C2411yescharacteristic
219C2×C22⋊D7—24no—
220C2×C22⋊D7—44no—
221C22×Dic7—24no—
222C22×Dic7—24no—
223C22×Dic7—21no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7C2×D414yes—
227C22×Dic7C2×D414yes—
228C22×Dic7C2×D411yescharacteristic
229C22×Dic7C2×D411yescharacteristic
230C22×Dic7C2×D411yescharacteristic
231C22×Dic7C2×D411yescharacteristic
232C2×D28—22no—
233C2×D28—22no—
234C2×D28—21no—
235C2×D28C2412yes—
236C2×C4×D7—24no—
237C2×C4×D7—44no—
238C2×Dic14—22no—
239C2×Dic14—22no—
240C2×Dic14—21no—
241C2×Dic14—24no—
242C2×Dic14—44no—
243C2×Dic14C2412yes—
244C7×Q16—44no—
245C2×C7×C8—22no—
246C2×C7×C8—22no—
247C2×C7×C8—44no—
248C2×C7×C8C2412yes—
249C2×C7×C8C2412yes—
250C7×C4⋊C4—21no—
251C7×C4⋊C4—24no—
252C7×C4⋊C4—21no—
253C7×C4⋊C4—24no—
254C7×C4⋊C4C2412yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C22⋊Dic7—24no—
259#1144—44no—
260#1143—44no—
261(C2×D7)⋊C4—24no—
262(C2×D7)⋊C4—24no—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265C4⋊Dic7—21no—
266C4⋊Dic7—21no—
267C4⋊Dic7—24no—
268C4⋊Dic7—24no—
269C4⋊Dic7—24no—
270C4⋊Dic7C2412yes—
271C4⋊Dic7C2412yes—
272Dic7⋊C4—24no—
273Dic7⋊C4—24no—
274Dic7⋊C4—24no—
275Dic7⋊C4—24no—
276Dic7⋊C4—24no—
277Dic7⋊C4—24no—
278C4×Dic7—24no—
279C4×Dic7—24no—
280C4×Dic7—24no—
281C4×Dic7C2×D414yes—
282C4×Dic7C2×D412yes—
283C4×Dic7C2×D412yes—
284C4×Dic7C2×D414yes—
285C4×Dic7C2412yes—
286C4×Dic7C2412yes—
287C2×C7⋊C8—22no—
288C2×C7⋊C8—22no—
289C2×C7⋊C8—44no—
290C2×C7⋊C8C2412yes—
291C2×C7⋊C8C2412yes—
292#1132—44no—
293C22×Q16—71no—
294C22×Q16C2×D711yescharacteristic
295C22×SD16—71no—
296C22×SD16—71no—
297C23×C8—71no—
298C23×C8C2×D711yescharacteristic
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—71no—
307C2×#125—141no—
308C2×#124—71no—
309C2×#123—141no—
310C2×C22⋊Q8—71no—
311C2×C22⋊Q8—141no—
312C2×C22⋊Q8C2×D711yescharacteristic
313C2×C22⋊Q8C2×D711yescharacteristic
314C2×#121—71no—
315C2×C4×Q8—71no—
316C2×C4×Q8—71no—
317C2×C4×Q8—71no—
318C2×C4×Q8—141no—
319C2×C4×D4—71no—
320C2×C4×D4—141no—
321C2×#117—141no—
322C2×#117—141no—
323C22×C42—71no—
324#479—78no—
325#479—78no—
326#475—78no—
327#474—78no—
328#467—78no—
329#467C2×D718yescomplemented
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×#106—71no—
340C2×C4⋊C8—71no—
341C2×C4⋊C8—71no—
342C2×C4⋊C8—71no—
343C2×C4⋊C8—71no—
344C2×C4⋊C8—78no—
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×C7—22no—
354C23×C7—22no—
355C23×C7#13714yes—
356C23×C7C22×D412yes—
357C23×C7C22×D411yescharacteristic
358C22×D7—22no—
359C22×D7—42no—
360C22×D7—42no—
361C22×D7—42no—
362C7×Q8—22no—
363C7×Q8—22no—
364C7×Q8—22no—
365C7×Q8—22no—
366C7×Q8—42no—
367C7×Q8—42no—
368C2×C4×C7—22no—
369C2×C4×C7—24no—
370C2×C4×C7—22no—
371C2×C4×C7—22no—
372C2×C4×C7—22no—
373C2×C4×C7—22no—
374C2×C4×C7—22no—
375C2×C4×C7—22no—
376C2×C4×C7—42no—
377C2×C4×C7—42no—
378C2×C4×C7—42no—
379C2×C4×C7—42no—
380C2×C4×C7C22×D412yes—
381C2×C4×C7C22×D411yescharacteristic
382C2×C4×C7H(5,𝔽2)12yes—
383C2×C4×C72−1+412yes—
384C2×C4×C7C2511yescharacteristic
385C22⋊D7—48no—
386C2×Dic7—22no—
387C2×Dic7—28no—
388C2×Dic7—22no—
389C2×Dic7—22no—
390C2×Dic7—28no—
391C2×Dic7—22no—
392C2×Dic7—22no—
393C2×Dic7—22no—
394C2×Dic7—42no—
395C2×Dic7—42no—
396C2×Dic7—42no—
397C2×Dic7#13514yes—
398C2×Dic7C22×D412yes—
399C2×Dic7C22×D412yes—
400C2×Dic7C22×D412yes—
401C2×Dic7C22×D412yes—
402D28—22no—
403D28—22no—
404D28—42no—
405C4×D7—48no—
406Dic14—22no—
407Dic14—22no—
408Dic14—42no—
409Dic14—48no—
410C7×C8—22no—
411C7×C8—22no—
412C7⋊C8—22no—
413C7⋊C8—22no—
414C22×Q8—71no—
415C22×Q8—141no—
416C22×Q8C22×D711yescharacteristic
417C22×Q8C22×D711yescharacteristic
418C22×D4—71no—
419C22×D4—141no—
420C23×C4—71no—
421C23×C4—71no—
422C23×C4—141no—
423C23×C4C22×D711yescharacteristic
424C2×Q16—42no—
425C2×Q16—74no—
426C2×Q16—282no—
427C2×Q16C22×D714yes—
428C2×SD16—74no—
429C2×SD16—74no—
430C2×SD16—282no—
431C2×SD16—282no—
432C22×C8—42no—
433C22×C8—71no—
434C22×C8—71no—
435C22×C8—74no—
436C22×C8—282no—
437C22×C8C22×D711yescharacteristic
438C22×C8C22×D711yescharacteristic
439C22×C8C22×D714yes—
440C4⋊Q8—74no—
441C4⋊Q8—74no—
442C4⋊Q8—142no—
443C4⋊Q8—142no—
444#126—148no—
445#125—74no—
446#125—142no—
447#125—148no—
448#124—74no—
449#124—142no—
450#123—148no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—74no—
454C22⋊Q8—148no—
455C22⋊Q8—142no—
456C22⋊Q8C22×D714yes—
457C22⋊Q8C22×D714yes—
458#121—74no—
459#121—142no—
460C4×Q8—74no—
461C4×Q8—74no—
462C4×Q8—74no—
463C4×Q8—142no—
464C4×Q8—148no—
465C4×Q8—142no—
466C4×Q8—142no—
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—71no—
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⋊C4—141no—
485C2×C4⋊C4C22×D711yescharacteristic
486C2×C4⋊C4C22×D711yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—141no—
490C2×C22⋊C4—141no—
491C2×C22⋊C4—141no—
492C2×C22⋊C4—141no—
493C2×C22⋊C4—141no—
494C2×C42—71no—
495C2×C42—71no—
496C2×C42—74no—
497C2×C42—71no—
498C2×C42—71no—
499C2×C42—74no—
500C2×C42—141no—
501C2×C42—141no—
502C2×C42—141no—
503#107—74no—
504#107C22×D714yes—
505#106—74no—
506#106—74no—
507C4⋊C8—74no—
508C4⋊C8—74no—
509C4⋊C8—74no—
510C4⋊C8—74no—
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—22no—
520C22×C7—28no—
521C22×C7—22no—
522C22×C7#53712yes—
523C22×C7C2×#13512yes—
524C22×C7C2×#13714yes—
525C22×C7C2×#13712yes—
526C22×C7C23×D411yescharacteristic
527C2×D7—42no—
528C2×D7—42no—
529C2×D7—42no—
530C2×D7—84no—
531C4×C7—22no—
532C4×C7—42no—
533C4×C7—42no—
534C4×C7—42no—
535C4×C7—42no—
536C4×C7#53712yes—
537C4×C7C2×H(5,𝔽2)11yescharacteristic
538C4×C7C2×2−1+411yescharacteristic
539Dic7—22no—
540Dic7—22no—
541Dic7—22no—
542Dic7—42no—
543Dic7—42no—
544Dic7—42no—
545Dic7C2×#13514yes—
546C24—141no—
547C24D4×D711yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—72no—
555C2×Q8—144no—
556C2×Q8—141no—
557C2×Q8—142no—
558C2×Q8—142no—
559C2×Q8—284no—
560C2×Q8C23×D712yes—
561C2×Q8C23×D712yes—
562C2×D4—72no—
563C2×D4—144no—
564C2×D4—141no—
565C2×D4—142no—
566C2×D4—142no—
567C2×D4—284no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—71no—
575C22×C4—74no—
576C22×C4—74no—
577C22×C4—71no—
578C22×C4—71no—
579C22×C4—71no—
580C22×C4—144no—
581C22×C4—144no—
582C22×C4—144no—
583C22×C4—141no—
584C22×C4—141no—
585C22×C4—141no—
586C22×C4—284no—
587C22×C4D4×D712yes—
588C22×C4D4×D711yescharacteristic
589C22×C4C23×D712yes—
590C22×C4C23×D711yescharacteristic
591Q16—44no—
592Q16—284no—
593SD16—284no—
594SD16—284no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—44no—
598C2×C8—72no—
599C2×C8—72no—
600C2×C8—142no—
601C2×C8—142no—
602C2×C8—284no—
603C2×C8C23×D712yes—
604C2×C8C23×D712yes—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—72no—
610C4⋊C4—72no—
611C4⋊C4—144no—
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⋊C4—141no—
622C4⋊C4C23×D712yes—
623C4⋊C4C23×D712yes—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—144no—
627C22⋊C4—144no—
628C22⋊C4—144no—
629C22⋊C4—144no—
630C22⋊C4—144no—
631C42—74no—
632C42—72no—
633C42—72no—
634C42—74no—
635C42—72no—
636C42—72no—
637C42—144no—
638C42—144no—
639C42—144no—
640C2×C7—24no—
641C2×C7#324814yescomplemented
642C2×C7C2×#53711yescharacteristic
643C2×C7C22×#13511yescharacteristic
644C2×C7C22×#13711yescharacteristic
645D7—82no—
646C23—22no—
647C23—22no—
648C23—142no—
649C23—282no—
650C23—282no—
651C23—282no—
652C23#648114yes—
653C23C2×D4×D712yes—
654C23C2×D4×D711yescharacteristic
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—42no—
660Q8—42no—
661Q8—142no—
662Q8—142no—
663Q8—288no—
664Q8—282no—
665D4—142no—
666D4—142no—
667D4—288no—
668D4—282no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—74no—
682C2×C4—72no—
683C2×C4—72no—
684C2×C4—72no—
685C2×C4—72no—
686C2×C4—148no—
687C2×C4—148no—
688C2×C4—142no—
689C2×C4—142no—
690C2×C4—142no—
691C2×C4—142no—
692C2×C4—142no—
693C2×C4—142no—
694C2×C4—288no—
695C2×C4—282no—
696C2×C4—282no—
697C2×C4—282no—
698C2×C4C2×D4×D712yes—
699C2×C4C2×D4×D711yescharacteristic
700C2×C4#654812yes—
701C2×C4#655412yes—
702C2×C4C24×D711yescharacteristic
703C8—22no—
704C8—22no—
705C8—142no—
706C8—142no—
707C7C2×#324811yescharacteristic, complemented, Sylow
708C22—22no—
709C22—28no—
710C22—22no—
711C22—282no—
712C22—282no—
713C22—282no—
714C22—564no—
715C22#9028812yes—
716C22C2×#648114yes—
717C22C2×#648112yes—
718C22D7×#13512yes—
719C22C22×D4×D711yescharacteristic
720C4—22no—
721C4—42no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—74no—
726C4—142no—
727C4—142no—
728C4—142no—
729C4—282no—
730C4—282no—
731C4—282no—
732C4#9028812yes—
733C4C2×#654811yescharacteristic
734C4C2×#655411yescharacteristic
735C2—24no—
736C2—562no—
737C2#1173819114yesdirect product factor
738C2C2×#9028811yescharacteristic
739C2C22×#648111yescharacteristic
740C2C2×D7×#13511yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#467C2
socleC23×C7C22×D4
prime radicalC2×#6493C22
hypercenterC2×#467D7
hypocenterC7C2×#3248
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#90313C2semidirect
3. C2×C7×#467C2semidirect
4. C2×#89957C2semidirect
5. C2×#89954C2semidirect
7. C22×Dic7⋊C8C2semidirect
8. C2×#89823C2semidirect
10. #11738191C2direct (N × H)
11. C2×#89649C2semidirect
12. C2×#89662C2semidirect
13. C2×#89570C2semidirect
14. C2×#89590C2semidirect
15. C2×#89571C2semidirect
16. C2×#89563C2semidirect
35. #90313C22semidirect
48. C7×#467C22semidirect
54. #89957C22semidirect
55. #89954C22semidirect
64. C2×Dic7⋊C8C22semidirect
65. #89823C22semidirect
71. #89662C22semidirect
72. #89649C22semidirect
73. #89590C22semidirect
74. #89571C22semidirect
75. #89570C22semidirect
76. #89563C22semidirect
191. C2×#467D7semidirect
329. #467C2×D7semidirect
641. C2×C7#3248semidirect
707. C7C2×#3248semidirect
737. C2#11738191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#903132
C2×#903152
C2×C7×#4672
C2×#899572
C2×#899542
C2×#898862
C22×Dic7⋊C82
C2×#898232
C2×#898202
#117381912
C2×#896492
C2×#896622
C2×#895702
C2×#895902
C2×#895712
C2×#895632
C2×#32487