Finite Group Databasebeta

← #13355698

Subgroups — #13355698

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
1C2×#90513C211yesmaximal, characteristic
2#11742799C211yesmaximal, characteristic, complemented
3C2×C7×#410C211yesmaximal, characteristic, complemented
4C2×#90008C211yesmaximal, characteristic, complemented
5#11739658C211yesmaximal, characteristic, complemented
6C2×#89328C211yesmaximal, characteristic, complemented
7C2×#89326C211yesmaximal, characteristic, complemented
8#11727806C214yesmaximal, complemented
9#11727803C214yesmaximal, complemented
10C22×C7×#41C2211yescharacteristic
11C22×#1157C2211yescharacteristic
12C2×C7×#117C2211yescharacteristic
13C2×C7×#117C2211yescharacteristic
14C2×#6514C2212yes—
15#90513—22no—
16#90513—22no—
17#90513—22no—
18#90513—22no—
19C2×#6513C414yescomplemented
20C2×#6512C2212yes—
21C2×#6505C412yescomplemented
22C2×#6495C412yescomplemented
23C2×#6489C2211yescharacteristic
24C22×#1136C2211yescharacteristic
25C22×#1136C2211yescharacteristic
26#90214—22no—
27#90213—22no—
28#90212C2212yescomplemented
29D7×#117—22no—
30#90207C2212yescomplemented
31#90195—22no—
32#90177—22no—
33C4×#1157—22no—
34C7×#410—22no—
35C7×#410C2214yes—
36C2×C7×#99—22no—
37#90008—22no—
38#90008C2214yes—
39C2×#6411—22no—
40#89776C2212yescomplemented
41#89774—22no—
42#89773C2212yescomplemented
43#89738—22no—
44#89328C2214yescomplemented
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×#41—21no—
54C2×C7×#41—21no—
55C2×C7×#41—21no—
56C2×C7×#41—21no—
57C2×C7×#41C2×C412yescomplemented
58C2×C7×#41C2312yes—
59C22×C7×Q8C2×C411yescharacteristic, complemented
60C22×C7×D4—21no—
61C22×C7×D4C2×C411yescharacteristic, complemented
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×#1157C2×C412yes—
72C2×#1157C2×C412yes—
73C2×#1157D412yes—
74C2×#1157D412yes—
75C2×#1157D412yes—
76C2×#1157D412yes—
77C22×D28C2311yescharacteristic
78C22×C4×D7—21no—
79C22×Dic14C2311yescharacteristic
80C7×#117—21no—
81C7×#117—21no—
82C7×#117—21no—
83C7×#117—21no—
84C7×#117—21no—
85C7×#117D412yes—
86C7×#117C2312yes—
87C7×#117C2312yes—
88C2×C7×C4⋊C4—21no—
89C2×C7×C4⋊C4—21no—
90C2×C7×C22⋊C4—21no—
91C2×C7×C22⋊C4D412yes—
92C2×C42×C7—21no—
93C2×C42×C7—21no—
94C2×C22⋊Dic7—21no—
95#6514—24no—
96#6514—24no—
97#6513—28no—
98#6513—28no—
99#6512—24no—
100#6512—24no—
101C2×#1144C2×C414yescomplemented
102#6505—24no—
103#6505—24no—
104C2×#1143C2×C414yescomplemented
105C2×#1142C2×C414yescomplemented
106#6495—24no—
107#6495—24no—
108C2×#1141C2×C414yescomplemented
109C4×C22⋊D7—28no—
110#6489—21no—
111#6489—21no—
112#6489D412yes—
113#6489C2312yes—
114C2×C4⋊Dic7—21no—
115C2×C4×Dic7D412yes—
116C2×#1136—21no—
117C2×#1136—21no—
118C2×#1136—21no—
119C2×#1136—21no—
120C2×#1136—21no—
121C2×#1136—21no—
122C2×#1136—21no—
123C2×#1136—21no—
124C2×#1136—21no—
125C2×#1136C2×C412yescomplemented
126C2×#1136C2312yes—
127C2×#1136C2312yes—
128C22×C7⋊C8—21no—
129C22×C7⋊C8C2×C412yescomplemented
130#6456—24no—
131#6455—24no—
132D7×C4⋊C4—24no—
133#6450—24no—
134(C22⋊D7)⋊C4—28no—
135D7×C22⋊C4—24no—
136#6440—24no—
137C4×D28—24no—
138#6435—24no—
139C42×D7—24no—
140C4×Dic14—24no—
141C7×#99—28no—
142#6411—28no—
143#6384—24no—
144#6383—24no—
145C2×#575—71no—
146#3428—71no—
147C2×#421—71no—
148#2896—71no—
149C2×#410D711yescharacteristic, complemented
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—41no—
166C7×#41—41no—
167C7×#41—41no—
168C7×#41—41no—
169C7×#41—41no—
170C7×#41—41no—
171C7×#41—41no—
172C7×#41—41no—
173C2×C7×Q8—21no—
174C2×C7×Q8—21no—
175C2×C7×Q8—21no—
176C2×C7×Q8—21no—
177C2×C7×Q8—21no—
178C2×C7×Q8C22×C412yes—
179C2×C7×D4—22no—
180C2×C7×D4—22no—
181C2×C7×D4—21no—
182C2×C7×D4—21no—
183C2×C7×D4—21no—
184C2×C7×D4—21no—
185C2×C7×D4—21no—
186C2×C7×D4—41no—
187C2×C7×D4—41no—
188C2×C7×D4—41no—
189C2×C7×D4—41no—
190C2×C7×D4C22×C412yes—
191C22×C4×C7—21no—
192C22×C4×C7—22no—
193C22×C4×C7—22no—
194C22×C4×C7—22no—
195C22×C4×C7—41no—
196C22×C4×C7—41no—
197C22×C4×C7—41no—
198C22×C4×C7—41no—
199C22×C4×C7—41no—
200C22×C4×C7C22×C411yescharacteristic
201C22×C4×C7C22×C411yescharacteristic
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×C7C2×D411yescharacteristic
209C22×C4×C7#4111yescharacteristic
210C22×C4×C7#4111yescharacteristic
211C22×C4×C7#4111yescharacteristic
212C22×C4×C7#4111yescharacteristic
213C22×C4×C7C2411yescharacteristic
214C2×C22⋊D7—22no—
215C2×C22⋊D7—22no—
216C2×C22⋊D7—22no—
217C2×C22⋊D7—22no—
218C2×C22⋊D7—22no—
219C2×C22⋊D7—22no—
220C22×Dic7—21no—
221C22×Dic7—22no—
222#1157—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—22no—
232#1157—22no—
233#1157—22no—
234#1157C22⋊C414yes—
235#1157C22⋊C414yes—
236#1157C22⋊C414yes—
237#1157C22⋊C414yes—
238C2×D28—21no—
239C2×D28—21no—
240C2×D28—21no—
241C2×D28C22×C412yes—
242C2×D28C2×D412yes—
243C2×D28C2×D412yes—
244C2×C4×D7—22no—
245C2×C4×D7—22no—
246C2×C4×D7—22no—
247C2×C4×D7—22no—
248C2×C4×D7—22no—
249C2×C4×D7—22no—
250C2×C4×D7—28no—
251C2×Dic14—21no—
252C2×Dic14—21no—
253C2×Dic14—21no—
254C2×Dic14C22×C412yes—
255C2×Dic14C2×D412yes—
256C2×Dic14C2×D412yes—
257C7×C4⋊C4—22no—
258C7×C4⋊C4—22no—
259C7×C4⋊C4—22no—
260C7×C4⋊C4—41no—
261C7×C22⋊C4—22no—
262C7×C22⋊C4—22no—
263C7×C22⋊C4—41no—
264C7×C22⋊C4C2×D414yes—
265C42×C7—22no—
266C42×C7—22no—
267C42×C7—22no—
268C42×C7—41no—
269C22⋊Dic7—22no—
270C22⋊Dic7—22no—
271#1144—28no—
272#1143—28no—
273#1142—28no—
274#1141—28no—
275(C2×D7)⋊C4—28no—
276C4⋊Dic7—22no—
277C4⋊Dic7—22no—
278Dic7⋊C4—28no—
279C4×Dic7—28no—
280C4×Dic7—22no—
281C4×Dic7C2×D414yes—
282#1136—22no—
283#1136—22no—
284#1136—22no—
285#1136—22no—
286#1136—22no—
287#1136—22no—
288#1136—41no—
289#1136—41no—
290C2×C7⋊C8—22no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8—41no—
294C2×C7⋊C8—41no—
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×M16—71no—
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—142no—
318C2×#117C2×D711yescharacteristic
319C2×#117C2×D711yescharacteristic
320#421—74no—
321#421—142no—
322C2×#104—142no—
323#419—72no—
324#418—72no—
325#417—142no—
326#416—142no—
327#410—22no—
328#410C2×D714yes—
329C2×#99—22no—
330#344—74no—
331H(3,ℤ/4)—74no—
332C23×C7—22no—
333C23×C7—41no—
334C23×C7—41no—
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—22no—
346C22×D7—22no—
347C22×D7—82no—
348C7×Q8—22no—
349C7×Q8—22no—
350C7×Q8—41no—
351C7×Q8—41no—
352C7×D4—22no—
353C7×D4—22no—
354C7×D4—42no—
355C7×D4—42no—
356C7×D4—42no—
357C7×D4—42no—
358C7×D4—41no—
359C7×D4—41no—
360C2×C4×C7—22no—
361C2×C4×C7—24no—
362C2×C4×C7—41no—
363C2×C4×C7—41no—
364C2×C4×C7—42no—
365C2×C4×C7—42no—
366C2×C4×C7—42no—
367C2×C4×C7—42no—
368C2×C4×C7—42no—
369C2×C4×C7—82no—
370C2×C4×C7—82no—
371C2×C4×C7C2×C22⋊C411yescharacteristic
372C2×C4×C7C2×C22⋊C411yescharacteristic
373C2×C4×C7C2×C22⋊C411yescharacteristic
374C2×C4×C7C2×C22⋊C411yescharacteristic
375C2×C4×C7C4×D411yescharacteristic
376C2×C4×C7C4×D411yescharacteristic
377C2×C4×C7C4×D411yescharacteristic
378C2×C4×C7C4×D411yescharacteristic
379C2×C4×C7C4×D411yescharacteristic
380C2×C4×C7C4×D411yescharacteristic
381C2×C4×C7#12011yescharacteristic
382C2×C4×C7#12011yescharacteristic
383C2×C4×C7#12111yescharacteristic
384C2×C4×C7#12111yescharacteristic
385C2×C4×C7#12111yescharacteristic
386C2×C4×C7#12111yescharacteristic
387C2×C4×C7#12111yescharacteristic
388C2×C4×C7#12111yescharacteristic
389C2×C4×C7#12311yescharacteristic
390C2×C4×C7#12311yescharacteristic
391C2×C4×C7#12311yescharacteristic
392C2×C4×C7#12311yescharacteristic
393C2×C4×C7C23×C411yescharacteristic
394C2×C4×C7C22×D411yescharacteristic
395C2×C4×C7C22×D411yescharacteristic
396C2×C4×C7C22×D411yescharacteristic
397C2×C4×C7C2×#4111yescharacteristic
398C2×C4×C7C2×#4111yescharacteristic
399C22⋊D7—24no—
400C22⋊D7—24no—
401C22⋊D7—24no—
402C22⋊D7—24no—
403C2×Dic7—22no—
404C2×Dic7—22no—
405C2×Dic7—22no—
406C2×Dic7—24no—
407C2×Dic7—82no—
408D28—22no—
409D28—22no—
410D28—22no—
411D28C2×C22⋊C414yes—
412C4×D7—24no—
413C4×D7—24no—
414C4×D7—24no—
415C4×D7—24no—
416C4×D7—88no—
417Dic14—22no—
418Dic14—22no—
419Dic14—22no—
420Dic14C2×C22⋊C414yes—
421C7⋊C8—24no—
422C7⋊C8—42no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—72no—
434C2×#41—72no—
435C2×#41—72no—
436C2×#41—72no—
437C2×#41—72no—
438C2×#41—72no—
439C2×#41—141no—
440C2×#41—141no—
441C2×#41—141no—
442C2×#41—141no—
443C2×#41—141no—
444C2×#41—141no—
445C2×#41C4×D712yescomplemented
446C2×#41C22×D712yes—
447C22×Q8—71no—
448C22×Q8C4×D711yescharacteristic, complemented
449C22×D4—21no—
450C22×D4—71no—
451C22×D4—141no—
452C22×D4C4×D711yescharacteristic, complemented
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—72no—
471C2×M16—72no—
472C2×M16—72no—
473C2×M16—141no—
474C2×M16—141no—
475C2×M16—141no—
476C2×M16—141no—
477C2×M16—141no—
478C2×M16—141no—
479C2×M16—141no—
480C2×M16—141no—
481C2×M16—141no—
482C22×C8—72no—
483C22×C8—141no—
484C4×Q8—144no—
485C4×Q8—144no—
486C4×D4—144no—
487C4×D4—144no—
488C4×D4—148no—
489C4×D4—148no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—72no—
496#117—72no—
497#117—144no—
498#117—144no—
499#117—141no—
500#117—141no—
501#117—144no—
502#117C22⋊D712yes—
503#117C22×D712yes—
504#117C22×D712yes—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—144no—
508C2×C4⋊C4—141no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—141no—
511C2×C22⋊C4—144no—
512C2×C22⋊C4C22⋊D712yes—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—72no—
516C2×C42—144no—
517#104—148no—
518#103—144no—
519#102—144no—
520#99—28no—
521C22×C7—41no—
522C22×C7—41no—
523C22×C7—41no—
524C22×C7—41no—
525C22×C7—41no—
526C22×C7—41no—
527C22×C7—41no—
528C22×C7—42no—
529C22×C7—82no—
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—24no—
540C2×D7—44no—
541C2×D7—82no—
542C2×D7—82no—
543C4×C7—44no—
544C4×C7—42no—
545C4×C7—82no—
546C4×C7#38611yescharacteristic
547C4×C7#38611yescharacteristic
548C4×C7#38611yescharacteristic
549C4×C7#38611yescharacteristic
550C4×C7C22×C22⋊C411yescharacteristic
551C4×C7C2×C4×D411yescharacteristic
552C4×C7C2×#12111yescharacteristic
553C4×C7C2×#12311yescharacteristic
554Dic7—24no—
555Dic7—44no—
556C24—21no—
557C24—141no—
558C24C2×C22⋊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—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—74no—
576#41—74no—
577#41—74no—
578#41—74no—
579#41—142no—
580#41—142no—
581#41—142no—
582#41—142no—
583#41—142no—
584#41—142no—
585#41—142no—
586#41—142no—
587#41—142no—
588#41—142no—
589#41—142no—
590#41—142no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—72no—
597C2×Q8—72no—
598C2×Q8—72no—
599C2×Q8—141no—
600C2×Q8—141no—
601C2×Q8—141no—
602C2×Q8C2×C4×D712yes—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—72no—
615C2×D4—72no—
616C2×D4—72no—
617C2×D4—142no—
618C2×D4—142no—
619C2×D4—142no—
620C2×D4—142no—
621C2×D4—142no—
622C2×D4—142no—
623C2×D4—141no—
624C2×D4—141no—
625C2×D4—141no—
626C2×D4C2×C4×D712yes—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—148no—
637C22×C4—141no—
638C22×C4—142no—
639C22×C4—142no—
640C22×C4—142no—
641C22×C4—142no—
642C22×C4—142no—
643C22×C4—142no—
644C22×C4—142no—
645C22×C4C2×C4×D711yescharacteristic
646C22×C4C2×C4×D711yescharacteristic
647C22×C4#115711yescharacteristic
648C22×C4#115711yescharacteristic
649C22×C4D4×D711yescharacteristic
650C22×C4D4×D711yescharacteristic
651C22×C4D4×D711yescharacteristic
652C22×C4D4×D711yescharacteristic
653C22×C4D4×D711yescharacteristic
654C22×C4D4×D711yescharacteristic
655C22×C4#115911yescharacteristic
656C22×C4#115911yescharacteristic
657C22×C4C2×C22⋊D711yescharacteristic
658C22×C4C23×D711yescharacteristic
659Q16—148no—
660SD16—148no—
661SD16—148no—
662D8—148no—
663M16—142no—
664M16—142no—
665M16—142no—
666M16—142no—
667M16—142no—
668M16—142no—
669M16—281no—
670M16—281no—
671C2×C8—74no—
672C2×C8—142no—
673C2×C8—142no—
674C2×C8—142no—
675C2×C8—281no—
676C2×C8—281no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—41no—
681C4⋊C4—148no—
682C4⋊C4—142no—
683C4⋊C4—142no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—41no—
687C22⋊C4—148no—
688C22⋊C4—142no—
689C22⋊C4—142no—
690C22⋊C4C2×C22⋊D714yes—
691C42—22no—
692C42—22no—
693C42—22no—
694C42—41no—
695C42—74no—
696C42—148no—
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—82no—
706C2×C7C2×#38611yescharacteristic
707D7—44no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—81no—
712C23—82no—
713C23—142no—
714C23—142no—
715C23—142no—
716C23—562no—
717C23C4×C22⋊D711yescharacteristic
718C23C4×C22⋊D711yescharacteristic
719C23#650011yescharacteristic
720C23#650011yescharacteristic
721C23#650111yescharacteristic
722C23#650111yescharacteristic
723C23C22×C22⋊D711yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—41no—
727Q8—41no—
728Q8—74no—
729Q8—142no—
730Q8—142no—
731Q8—142no—
732D4—22no—
733D4—22no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—41no—
739D4—41no—
740D4—74no—
741D4—144no—
742D4—144no—
743D4—144no—
744D4—144no—
745D4—142no—
746D4—142no—
747D4—142no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—142no—
760C2×C4—142no—
761C2×C4—142no—
762C2×C4—144no—
763C2×C4—144no—
764C2×C4—144no—
765C2×C4—144no—
766C2×C4—144no—
767C2×C4—568no—
768C2×C4—562no—
769C2×C4D7×C22⋊C411yescharacteristic
770C2×C4D7×C22⋊C411yescharacteristic
771C2×C4D7×C22⋊C411yescharacteristic
772C2×C4D7×C22⋊C411yescharacteristic
773C2×C4(C22⋊D7)⋊C411yescharacteristic
774C2×C4(C22⋊D7)⋊C411yescharacteristic
775C2×C4(C22⋊D7)⋊C411yescharacteristic
776C2×C4(C22⋊D7)⋊C411yescharacteristic
777C2×C4#644611yescharacteristic
778C2×C4#644611yescharacteristic
779C2×C4#644611yescharacteristic
780C2×C4#644611yescharacteristic
781C2×C4#644711yescharacteristic
782C2×C4#644711yescharacteristic
783C2×C4#644711yescharacteristic
784C2×C4#644711yescharacteristic
785C2×C4C4×C22⋊D711yescharacteristic
786C2×C4C4×C22⋊D711yescharacteristic
787C2×C4#650011yescharacteristic
788C2×C4#650011yescharacteristic
789C2×C4#650111yescharacteristic
790C2×C4#650111yescharacteristic
791C2×C4C22×C4×D711yescharacteristic
792C2×C4C2×#115711yescharacteristic
793C2×C4C2×D4×D711yescharacteristic
794C2×C4C2×D4×D711yescharacteristic
795C2×C4C2×D4×D711yescharacteristic
796C2×C4C2×#115911yescharacteristic
797C8—144no—
798C8—282no—
799C7#2099811yescharacteristic, complemented, Sylow
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—42no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—144no—
812C22—284no—
813C22—562no—
814C22—562no—
815C22#8972811yescharacteristic
816C22#8972811yescharacteristic
817C22#8972811yescharacteristic
818C22#8972811yescharacteristic
819C22C2×C4×C22⋊D711yescharacteristic
820C22C2×#650011yescharacteristic
821C22C2×#650111yescharacteristic
822C4—44no—
823C4—42no—
824C4—82no—
825C4—144no—
826C4—284no—
827C4#8972811yescharacteristic
828C4#8972811yescharacteristic
829C4#8972811yescharacteristic
830C4#8972811yescharacteristic
831C4C2×D7×C22⋊C411yescharacteristic
832C4C2×(C22⋊D7)⋊C411yescharacteristic
833C4C2×#644611yescharacteristic
834C4C2×#644711yescharacteristic
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—82no—
843C2—284no—
844C2C2×#8972811yescharacteristic
subgroupG/H
centerC4#89728
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC2×C7×#410C2
socleC2×C7C2×#386
prime radicalC2×#90513C2
cosocleC22×C4×C7C24
hypercenterC2×#410D7
hypocenterC7#20998
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. #11742799C2semidirect
3. C2×C7×#410C2semidirect
4. C2×#90008C2semidirect
5. #11739658C2semidirect
6. C2×#89328C2semidirect
7. C2×#89326C2semidirect
8. #11727806C2semidirect
9. #11727803C2semidirect
19. C2×#6513C4semidirect
21. C2×#6505C4semidirect
22. C2×#6495C4semidirect
28. #90212C22semidirect
30. #90207C22semidirect
40. #89776C22semidirect
42. #89773C22semidirect
44. #89328C22semidirect
45. #89326C22semidirect
57. C2×C7×#41C2×C4semidirect
59. C22×C7×Q8C2×C4semidirect
61. C22×C7×D4C2×C4semidirect
101. C2×#1144C2×C4semidirect
104. C2×#1143C2×C4semidirect
105. C2×#1142C2×C4semidirect
108. C2×#1141C2×C4semidirect
125. C2×#1136C2×C4semidirect
129. C22×C7⋊C8C2×C4semidirect
149. C2×#410D7semidirect
445. C2×#41C4×D7semidirect
448. C22×Q8C4×D7semidirect
452. C22×D4C4×D7semidirect
799. C7#20998semidirect

Maximal subgroups

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

subgroupindex
C2×#905132
#117427992
C2×C7×#4102
C2×#900082
#117396582
C2×#893282
C2×#893262
#117278062
#117278032
#209987