Finite Group Databasebeta

← #13355693

Subgroups — #13355693

Order 1792.

1704 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11744328C211yesmaximal, characteristic, complemented
2C2×#90513C211yesmaximal, characteristic
3C7×#2896C211yesmaximal, characteristic, complemented
4C2×#89911C211yesmaximal, characteristic, complemented
5C2×#89778C211yesmaximal, characteristic, complemented
6C2×#89354C211yesmaximal, characteristic, complemented
7C2×#89326C211yesmaximal, characteristic, complemented
8#11728088C214yesmaximal, complemented
9#11728068C214yesmaximal, complemented
10C22×C7×#41C2211yescharacteristic
11C22×#1157C2211yescharacteristic
12C22×C7×M16C2211yescharacteristic
13C2×C7×#117C2211yescharacteristic
14#90518—22no—
15#90518—22no—
16#41×Dic7—22no—
17#41×Dic7—22no—
18C2×#6514C412yescomplemented
19#90513—22no—
20#90513—22no—
21#90513—22no—
22#90513—22no—
23C2×#6513C414yescomplemented
24C2×#6512C412yescomplemented
25#90503C2212yescomplemented
26C2×#6505C2212yes—
27#90489—22no—
28#90489C2212yescomplemented
29C2×#6495C2212yes—
30C2×#6489—22no—
31C2×#6489C2211yescharacteristic
32C2×#6489C2211yescharacteristic
33C22×#1136C2211yescharacteristic
34C7×#419C2212yescomplemented
35C7×#418C2212yescomplemented
36C7×#417—22no—
37C7×#416—22no—
38#89911—22no—
39#89911C2214yes—
40C2×#6399—22no—
41#89778—22no—
42#89778C2214yes—
43C2×#6380—22no—
44#89354C2214yescomplemented
45#89326C2214yescomplemented
46#20998—71nomaximal, Sylow
47C2×C7×#41—21no—
48C2×C7×#41—21no—
49C2×C7×#41—21no—
50C2×C7×#41—21no—
51C2×C7×#41—21no—
52C2×C7×#41—21no—
53C2×C7×#41C2×C412yes—
54C2×C7×#41C2×C412yes—
55C2×C7×#41D412yes—
56C2×C7×#41D412yes—
57C2×C7×#41D412yes—
58C2×C7×#41D412yes—
59C22×C7×Q8C2311yescharacteristic
60C22×C7×D4—21no—
61C22×C7×D4C2311yescharacteristic
62C23×C4×C7—21no—
63C23×C4×C7C2311yescharacteristic
64C22×C22⋊D7—21no—
65C2×#1157—21no—
66C2×#1157—21no—
67C2×#1157—21no—
68C2×#1157—21no—
69C2×#1157—21no—
70C2×#1157—21no—
71C2×#1157—21no—
72C2×#1157—21no—
73C2×#1157—21no—
74C2×#1157—21no—
75C2×#1157C2×C412yescomplemented
76C2×#1157C2312yes—
77C22×D28C2×C411yescharacteristic, complemented
78C22×C4×D7—21no—
79C22×Dic14C2×C411yescharacteristic, complemented
80C2×C7×M16—21no—
81C2×C7×M16—21no—
82C2×C7×M16—21no—
83C2×C7×M16—21no—
84C2×C7×M16—21no—
85C2×C7×M16C2312yes—
86C22×C7×C8—21no—
87C7×#117—21no—
88C7×#117—21no—
89C7×#117—21no—
90C7×#117C2312yes—
91C2×C7×C4⋊C4—21no—
92C2×C7×C22⋊C4—21no—
93C2×C42×C7—21no—
94C2×C22⋊Dic7—21no—
95C2×C22⋊Dic7—24no—
96C2×C22⋊Dic7D412yes—
97#6514—24no—
98#6514—24no—
99#6513—28no—
100#6513—28no—
101#6512—24no—
102#6512—24no—
103Q8×Dic7—24no—
104Q8×Dic7—24no—
105C2×#1144C2×C414yescomplemented
106#6505—24no—
107#6505—24no—
108C2×#1143C2×C414yescomplemented
109D4×Dic7—28no—
110D4×Dic7—28no—
111D4×Dic7—24no—
112D4×Dic7—24no—
113C2×#1142C2×C414yescomplemented
114#6495—24no—
115#6495—24no—
116C2×#1141C2×C414yescomplemented
117#6489—24no—
118#6489—24no—
119#6489—21no—
120#6489—21no—
121#6489—21no—
122#6489—21no—
123#6489—24no—
124#6489D412yes—
125#6489D412yes—
126#6489C2312yes—
127#6489C2312yes—
128C2×C4⋊Dic7—24no—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—21no—
131C2×C4×Dic7—24no—
132C2×C4×Dic7—21no—
133C2×C4×Dic7D412yes—
134C2×#1136—21no—
135C2×#1136—21no—
136C2×#1136—21no—
137C2×#1136—21no—
138C2×#1136C2×C412yescomplemented
139C2×#1136C2312yes—
140C22×C7⋊C8C2×C412yescomplemented
141C7×#103—24no—
142C7×#102—24no—
143#6399—28no—
144#6380—28no—
145C2×#575—71no—
146#3428—71no—
147C2×#421—71no—
148#2896D711yescharacteristic, complemented
149C2×#410—71no—
150#1905—74no—
151#1904—74no—
152C2×#344—71no—
153C2×H(3,ℤ/4)—71no—
154C24×C7—21no—
155C24×C7C2×D411yescharacteristic
156C23×D7—21no—
157C7×#41—22no—
158C7×#41—22no—
159C7×#41—22no—
160C7×#41—22no—
161C7×#41—22no—
162C7×#41—22no—
163C7×#41—22no—
164C7×#41—22no—
165C7×#41—22no—
166C7×#41—22no—
167C7×#41—22no—
168C7×#41—22no—
169C7×#41C22⋊C414yes—
170C7×#41C22⋊C414yes—
171C7×#41C22⋊C414yes—
172C7×#41C22⋊C414yes—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8C22×C412yes—
177C2×C7×Q8C2×D412yes—
178C2×C7×Q8C2×D412yes—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—22no—
182C2×C7×D4—22no—
183C2×C7×D4—22no—
184C2×C7×D4—22no—
185C2×C7×D4—21no—
186C2×C7×D4—21no—
187C2×C7×D4—21no—
188C2×C7×D4C22×C412yes—
189C2×C7×D4C2×D412yes—
190C2×C7×D4C2×D412yes—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—22no—
196C22×C4×C7—22no—
197C22×C4×C7—22no—
198C22×C4×C7—41no—
199C22×C4×C7C22×C411yescharacteristic
200C22×C4×C7C22×C411yescharacteristic
201C22×C4×C7C2×D411yescharacteristic
202C22×C4×C7C2×D411yescharacteristic
203C22×C4×C7C2×D411yescharacteristic
204C22×C4×C7C2×D411yescharacteristic
205C22×C4×C7C2×D411yescharacteristic
206C22×C4×C7C2×D411yescharacteristic
207C22×C4×C7C2×D411yescharacteristic
208C22×C4×C7#4111yescharacteristic
209C22×C4×C7#4111yescharacteristic
210C22×C4×C7#4111yescharacteristic
211C22×C4×C7#4111yescharacteristic
212C22×C4×C7C2411yescharacteristic
213C2×C22⋊D7—22no—
214C2×C22⋊D7—22no—
215C2×C22⋊D7—41no—
216C2×C22⋊D7—41no—
217C2×C22⋊D7—41no—
218C2×C22⋊D7—41no—
219C22×Dic7—21no—
220C22×Dic7—28no—
221C22×Dic7—22no—
222C22×Dic7—22no—
223#1157—22no—
224#1157—22no—
225#1157—22no—
226#1157—22no—
227#1157—22no—
228#1157—22no—
229#1157—22no—
230#1157—22no—
231#1157—41no—
232#1157—41no—
233#1157—41no—
234#1157—41no—
235#1157—41no—
236#1157—41no—
237#1157—41no—
238#1157—41no—
239C2×D28—21no—
240C2×D28—21no—
241C2×D28—21no—
242C2×D28—21no—
243C2×D28—21no—
244C2×D28C22×C412yes—
245C2×C4×D7—22no—
246C2×C4×D7—22no—
247C2×C4×D7—41no—
248C2×C4×D7—41no—
249C2×C4×D7—41no—
250C2×C4×D7—41no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—21no—
254C2×Dic14—21no—
255C2×Dic14—21no—
256C2×Dic14C22×C412yes—
257C7×M16—22no—
258C7×M16—22no—
259C7×M16—41no—
260C7×M16—41no—
261C2×C7×C8—22no—
262C2×C7×C8—41no—
263C2×C7×C8—41no—
264C7×C4⋊C4—22no—
265C7×C4⋊C4—41no—
266C7×C22⋊C4—22no—
267C7×C22⋊C4—41no—
268C42×C7—22no—
269C42×C7—41no—
270C22⋊Dic7—28no—
271C22⋊Dic7—22no—
272C22⋊Dic7—22no—
273C22⋊Dic7—22no—
274C22⋊Dic7C2×D414yes—
275#1144—28no—
276#1143—28no—
277#1142—28no—
278#1141—28no—
279C4⋊Dic7—28no—
280C4⋊Dic7—22no—
281C4⋊Dic7—22no—
282C4⋊Dic7—22no—
283C4⋊Dic7—22no—
284C4×Dic7—28no—
285C4×Dic7—22no—
286C4×Dic7—22no—
287C4×Dic7—22no—
288C4×Dic7C2×D414yes—
289#1136—22no—
290#1136—22no—
291#1136—22no—
292#1136—22no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8—22no—
295C2×C7⋊C8C22×C414yes—
296C22×#41—71no—
297C22×#41C2×D711yescharacteristic
298#575—142no—
299#575—142no—
300#575—142no—
301#575—142no—
302C2×#137—72no—
303C2×#137—72no—
304C2×AGL(1,ℤ/8)—72no—
305C2×AGL(1,ℤ/8)—72no—
306C2×#135—74no—
307C22×M16—71no—
308C22×M16C2×D711yescharacteristic
309#520—142no—
310#520—142no—
311#519—72no—
312#518—72no—
313#518—142no—
314C4×#41—142no—
315C4×#41—142no—
316C2×#117—71no—
317C2×#117—71no—
318C2×#117—142no—
319C2×#117C2×D711yescharacteristic
320#421—74no—
321#421—142no—
322C2×#104—142no—
323#419C2×D712yescomplemented
324#418C2×D712yescomplemented
325#417—22no—
326#416—22no—
327#410—74no—
328#410—142no—
329C2×#99—142no—
330#344—74no—
331H(3,ℤ/4)—74no—
332C23×C7—22no—
333C23×C7—22no—
334C23×C7—22no—
335C23×C7—81no—
336C23×C7—82no—
337C23×C7C4×D411yescharacteristic
338C23×C7C4×D411yescharacteristic
339C23×C7#12011yescharacteristic
340C23×C7#12011yescharacteristic
341C23×C7#12111yescharacteristic
342C23×C7#12111yescharacteristic
343C23×C7C22×D411yescharacteristic
344C22×D7—22no—
345C22×D7—41no—
346C22×D7—41no—
347C22×D7—82no—
348C7×Q8—22no—
349C7×Q8—22no—
350C7×Q8—22no—
351C7×Q8C2×C22⋊C414yes—
352C7×D4—24no—
353C7×D4—24no—
354C7×D4—24no—
355C7×D4—24no—
356C7×D4—22no—
357C7×D4—22no—
358C7×D4—22no—
359C7×D4C2×C22⋊C414yes—
360C2×C4×C7—22no—
361C2×C4×C7—22no—
362C2×C4×C7—22no—
363C2×C4×C7—24no—
364C2×C4×C7—24no—
365C2×C4×C7—24no—
366C2×C4×C7—24no—
367C2×C4×C7—42no—
368C2×C4×C7—82no—
369C2×C4×C7C2×C22⋊C411yescharacteristic
370C2×C4×C7C2×C22⋊C411yescharacteristic
371C2×C4×C7C2×C22⋊C411yescharacteristic
372C2×C4×C7C2×C22⋊C411yescharacteristic
373C2×C4×C7C4×D411yescharacteristic
374C2×C4×C7C4×D411yescharacteristic
375C2×C4×C7C4×D411yescharacteristic
376C2×C4×C7C4×D411yescharacteristic
377C2×C4×C7C4×D411yescharacteristic
378C2×C4×C7C4×D411yescharacteristic
379C2×C4×C7#12011yescharacteristic
380C2×C4×C7#12011yescharacteristic
381C2×C4×C7#12111yescharacteristic
382C2×C4×C7#12111yescharacteristic
383C2×C4×C7#12111yescharacteristic
384C2×C4×C7#12111yescharacteristic
385C2×C4×C7#12111yescharacteristic
386C2×C4×C7#12111yescharacteristic
387C2×C4×C7#12311yescharacteristic
388C2×C4×C7#12311yescharacteristic
389C2×C4×C7#12311yescharacteristic
390C2×C4×C7#12311yescharacteristic
391C2×C4×C7C23×C411yescharacteristic
392C2×C4×C7C22×D411yescharacteristic
393C2×C4×C7C22×D411yescharacteristic
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C7C2×#4111yescharacteristic
396C2×C4×C7C2×#4111yescharacteristic
397C22⋊D7—42no—
398C22⋊D7—42no—
399C22⋊D7—42no—
400C22⋊D7—42no—
401C2×Dic7—22no—
402C2×Dic7—24no—
403C2×Dic7—24no—
404C2×Dic7—41no—
405C2×Dic7—41no—
406C2×Dic7—82no—
407C2×Dic7—82no—
408C2×Dic7—88no—
409D28—22no—
410D28—22no—
411D28—41no—
412D28—41no—
413C4×D7—42no—
414C4×D7—42no—
415C4×D7—42no—
416C4×D7—42no—
417Dic14—22no—
418Dic14—22no—
419Dic14—41no—
420Dic14—41no—
421C7×C8—42no—
422C7⋊C8—24no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—72no—
430C2×#41—72no—
431C2×#41—141no—
432C2×#41—141no—
433C2×#41—141no—
434C2×#41—141no—
435C2×#41—141no—
436C2×#41—141no—
437C2×#41—141no—
438C2×#41—141no—
439C2×#41—141no—
440C2×#41—141no—
441C2×#41C4×D712yes—
442C2×#41C4×D712yes—
443C2×#41D2812yes—
444C2×#41D2812yes—
445C2×#41C22⋊D712yes—
446C2×#41C22⋊D712yes—
447C22×Q8—71no—
448C22×Q8C22×D711yescharacteristic
449C22×D4—21no—
450C22×D4—71no—
451C22×D4—141no—
452C22×D4C22×D711yescharacteristic
453C23×C4—21no—
454C23×C4—141no—
455C23×C4C22×D711yescharacteristic
456#137—144no—
457#137—144no—
458#137—144no—
459#137—144no—
460AGL(1,ℤ/8)—144no—
461AGL(1,ℤ/8)—144no—
462AGL(1,ℤ/8)—144no—
463AGL(1,ℤ/8)—144no—
464#135—148no—
465#135—148no—
466C2×Q16—74no—
467C2×SD16—74no—
468C2×SD16—74no—
469C2×D8—74no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—72no—
476C2×M16—72no—
477C2×M16—141no—
478C2×M16—141no—
479C2×M16—141no—
480C2×M16—141no—
481C2×M16C22×D712yes—
482C22×C8—21no—
483C22×C8—72no—
484C4×Q8—144no—
485C4×Q8—144no—
486C4×D4—144no—
487C4×D4—148no—
488C4×D4—148no—
489C4×D4—144no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—72no—
494#117—72no—
495#117—72no—
496#117—72no—
497#117—144no—
498#117—144no—
499#117—144no—
500#117—141no—
501#117—141no—
502#117—141no—
503#117—141no—
504#117C22×D712yes—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—144no—
507C2×C4⋊C4—141no—
508C2×C4⋊C4—141no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—72no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4—141no—
513C2×C42—21no—
514C2×C42—72no—
515C2×C42—144no—
516C2×C42—141no—
517#104—148no—
518#103—24no—
519#102—24no—
520#99—148no—
521C22×C7—24no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—41no—
529C22×C7—44no—
530C22×C7—82no—
531C22×C7—82no—
532C22×C7#38611yescharacteristic
533C22×C7#38611yescharacteristic
534C22×C7#38611yescharacteristic
535C22×C7#38611yescharacteristic
536C22×C7C2×C4×D411yescharacteristic
537C22×C7C2×#12011yescharacteristic
538C22×C7C2×#12111yescharacteristic
539C2×D7—42no—
540C2×D7—82no—
541C2×D7—82no—
542C2×D7—82no—
543C4×C7—24no—
544C4×C7—82no—
545C4×C7#38611yescharacteristic
546C4×C7#38611yescharacteristic
547C4×C7#38611yescharacteristic
548C4×C7#38611yescharacteristic
549C4×C7C22×C22⋊C411yescharacteristic
550C4×C7C2×C4×D411yescharacteristic
551C4×C7C2×#12111yescharacteristic
552C4×C7C2×#12311yescharacteristic
553Dic7—44no—
554Dic7—44no—
555Dic7—42no—
556C24—21no—
557C24—141no—
558C24D4×D711yescharacteristic
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—142no—
572#41—142no—
573#41—142no—
574#41—142no—
575#41—142no—
576#41—142no—
577#41—142no—
578#41—142no—
579#41—281no—
580#41—281no—
581#41—281no—
582#41—281no—
583#41—281no—
584#41—281no—
585#41—281no—
586#41—281no—
587#41(C2×D7)⋊C414yes—
588#41(C2×D7)⋊C414yes—
589#41(C2×D7)⋊C414yes—
590#41(C2×D7)⋊C414yes—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—72no—
595C2×Q8—141no—
596C2×Q8—141no—
597C2×Q8—141no—
598C2×Q8—141no—
599C2×Q8—141no—
600C2×Q8C2×C4×D712yes—
601C2×Q8C2×D2812yes—
602C2×Q8C2×C22⋊D712yes—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—72no—
613C2×D4—142no—
614C2×D4—142no—
615C2×D4—141no—
616C2×D4—141no—
617C2×D4—141no—
618C2×D4—141no—
619C2×D4—141no—
620C2×D4—281no—
621C2×D4—281no—
622C2×D4—281no—
623C2×D4—281no—
624C2×D4C2×C4×D712yes—
625C2×D4C2×D2812yes—
626C2×D4C2×C22⋊D712yes—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—41no—
635C22×C4—141no—
636C22×C4—148no—
637C22×C4—142no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—281no—
642C22×C4—281no—
643C22×C4—281no—
644C22×C4—281no—
645C22×C4C2×C4×D711yescharacteristic
646C22×C4C2×C4×D711yescharacteristic
647C22×C4C2×D2811yescharacteristic
648C22×C4C2×D2811yescharacteristic
649C22×C4D4×D711yescharacteristic
650C22×C4D4×D711yescharacteristic
651C22×C4D4×D711yescharacteristic
652C22×C4#115911yescharacteristic
653C22×C4#115911yescharacteristic
654C22×C4#115911yescharacteristic
655C22×C4#115911yescharacteristic
656C22×C4C2×C22⋊D711yescharacteristic
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659Q16—148no—
660SD16—148no—
661SD16—148no—
662D8—148no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—142no—
668M16—142no—
669M16—142no—
670M16—142no—
671C2×C8—22no—
672C2×C8—41no—
673C2×C8—41no—
674C2×C8—74no—
675C2×C8—142no—
676C2×C8—142no—
677C4⋊C4—22no—
678C4⋊C4—41no—
679C4⋊C4—148no—
680C4⋊C4—142no—
681C4⋊C4—142no—
682C4⋊C4—142no—
683C4⋊C4—142no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C22⋊C4—74no—
687C22⋊C4—148no—
688C22⋊C4—142no—
689C22⋊C4—142no—
690C22⋊C4—142no—
691C42—22no—
692C42—41no—
693C42—74no—
694C42—148no—
695C42—142no—
696C42—142no—
697C42—142no—
698C2×C7—21no—
699C2×C7—21no—
700C2×C7—21no—
701C2×C7—21no—
702C2×C7—21no—
703C2×C7—21no—
704C2×C7—21no—
705C2×C7—44no—
706C2×C7C2×#38611yescharacteristic
707D7—82no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—81no—
712C23—82no—
713C23—142no—
714C23—281no—
715C23—281no—
716C23—562no—
717C23(C22⋊D7)⋊C411yescharacteristic
718C23(C22⋊D7)⋊C411yescharacteristic
719C23#644511yescharacteristic
720C23#644511yescharacteristic
721C23#650211yescharacteristic
722C23#650211yescharacteristic
723C23C2×D4×D711yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—142no—
728Q8—142no—
729Q8—281no—
730Q8—281no—
731Q8C2×(C2×D7)⋊C414yes—
732D4—24no—
733D4—24no—
734D4—24no—
735D4—24no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—142no—
740D4—142no—
741D4—282no—
742D4—282no—
743D4—282no—
744D4—282no—
745D4—281no—
746D4—281no—
747D4C2×(C2×D7)⋊C414yes—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—42no—
756C2×C4—82no—
757C2×C4—142no—
758C2×C4—144no—
759C2×C4—144no—
760C2×C4—281no—
761C2×C4—281no—
762C2×C4—282no—
763C2×C4—282no—
764C2×C4—282no—
765C2×C4—282no—
766C2×C4—562no—
767C2×C4—562no—
768C2×C4—568no—
769C2×C4(C22⋊D7)⋊C411yescharacteristic
770C2×C4(C22⋊D7)⋊C411yescharacteristic
771C2×C4(C22⋊D7)⋊C411yescharacteristic
772C2×C4(C22⋊D7)⋊C411yescharacteristic
773C2×C4(C22⋊D7)⋊C411yescharacteristic
774C2×C4(C22⋊D7)⋊C411yescharacteristic
775C2×C4#644511yescharacteristic
776C2×C4#644511yescharacteristic
777C2×C4#644911yescharacteristic
778C2×C4#644911yescharacteristic
779C2×C4#644911yescharacteristic
780C2×C4#644911yescharacteristic
781C2×C4C2×(C2×D7)⋊C411yescharacteristic
782C2×C4C2×(C2×D7)⋊C411yescharacteristic
783C2×C4C2×(C2×D7)⋊C411yescharacteristic
784C2×C4C2×(C2×D7)⋊C411yescharacteristic
785C2×C4#650211yescharacteristic
786C2×C4#650211yescharacteristic
787C2×C4#650211yescharacteristic
788C2×C4#650211yescharacteristic
789C2×C4#650211yescharacteristic
790C2×C4#650211yescharacteristic
791C2×C4C22×C4×D711yescharacteristic
792C2×C4C22×D2811yescharacteristic
793C2×C4C2×D4×D711yescharacteristic
794C2×C4C2×#115911yescharacteristic
795C2×C4C2×#115911yescharacteristic
796C2×C4C22×C22⋊D711yescharacteristic
797C8—42no—
798C8—144no—
799C7#2099811yescharacteristic, complemented, Sylow
800C22—24no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—44no—
809C22—82no—
810C22—82no—
811C22—282no—
812C22—562no—
813C22—562no—
814C22—562no—
815C22#8973011yescharacteristic
816C22#8973011yescharacteristic
817C22#8973011yescharacteristic
818C22#8973011yescharacteristic
819C22C2×(C22⋊D7)⋊C411yescharacteristic
820C22C2×#644511yescharacteristic
821C22C2×#650211yescharacteristic
822C4—24no—
823C4—82no—
824C4—284no—
825C4—284no—
826C4—282no—
827C4#8973011yescharacteristic
828C4#8973011yescharacteristic
829C4#8973011yescharacteristic
830C4#8973011yescharacteristic
831C4C2×(C22⋊D7)⋊C411yescharacteristic
832C4C2×#644911yescharacteristic
833C4C22×(C2×D7)⋊C411yescharacteristic
834C4C2×#650211yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—44no—
843C2—562no—
844C2C2×#8973011yescharacteristic
subgroupG/H
centerC4#89730
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2896C2
socleC2×C7C2×#386
prime radicalC2×#90513C2
cosocleC22×C4×C7C24
hypercenter#2896D7
hypocenterC7#20998
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #11744328C2semidirect
3. C7×#2896C2semidirect
4. C2×#89911C2semidirect
5. C2×#89778C2semidirect
6. C2×#89354C2semidirect
7. C2×#89326C2semidirect
8. #11728088C2semidirect
9. #11728068C2semidirect
18. C2×#6514C4semidirect
23. C2×#6513C4semidirect
24. C2×#6512C4semidirect
25. #90503C22semidirect
28. #90489C22semidirect
34. C7×#419C22semidirect
35. C7×#418C22semidirect
44. #89354C22semidirect
45. #89326C22semidirect
75. C2×#1157C2×C4semidirect
77. C22×D28C2×C4semidirect
79. C22×Dic14C2×C4semidirect
105. C2×#1144C2×C4semidirect
108. C2×#1143C2×C4semidirect
113. C2×#1142C2×C4semidirect
116. C2×#1141C2×C4semidirect
138. C2×#1136C2×C4semidirect
140. C22×C7⋊C8C2×C4semidirect
148. #2896D7semidirect
323. #419C2×D7semidirect
324. #418C2×D7semidirect
799. C7#20998semidirect

Maximal subgroups

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

subgroupindex
#117443282
C2×#905132
C7×#28962
C2×#899112
C2×#897782
C2×#893542
C2×#893262
#117280882
#117280682
#209987