Finite Group Databasebeta

← #13259192

Subgroups — #13259192

Order 1792.

1192 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11742799C211yesmaximal, characteristic
2C2×#89904C211yesmaximal, characteristic
3#11741207C211yesmaximal, characteristic
4C2×C7×#344C211yesmaximal, characteristic, complemented
5C2×#89354C211yesmaximal, characteristic, complemented
6C2×#89354C211yesmaximal, characteristic, complemented
7C2×#89328C211yesmaximal, characteristic, complemented
8C22×#1157C2211yescharacteristic
9C22×C7×M16C2211yescharacteristic
10C22×C7×M16C2211yescharacteristic
11C2×C7×#117C2211yescharacteristic
12C2×#6489C2211yescharacteristic
13C22×#1136C2211yescharacteristic
14C22×#1136C2211yescharacteristic
15#90214—22no—
16#90213—22no—
17#90212—21no—
18D7×#117—22no—
19#90207—21no—
20#90195—22no—
21#90177C414yes—
22C4×#1157—22no—
23C2×#6398—21no—
24#89904—22no—
25#89904C414yescomplemented
26C2×#6397—21no—
27#89901C414yescomplemented
28#89898—22no—
29#89882—22no—
30C7×#344—22no—
31#89354—22no—
32#89354—22no—
33#89328—22no—
34#10756—71nomaximal, Sylow
35C23×C4×C7C2311yescharacteristic
36C22×C22⋊D7C2×C412yes—
37C2×#1157—21no—
38C2×#1157—21no—
39C2×#1157—21no—
40C2×#1157—21no—
41C2×#1157—21no—
42C2×#1157—21no—
43C2×#1157—21no—
44C2×#1157—21no—
45C2×#1157C2×C412yes—
46C2×#1157C2×C412yes—
47C2×#1157D412yes—
48C2×#1157Q812yes—
49C22×D28D411yescharacteristic
50C22×C4×D7D412yes—
51C22×Dic14D411yescharacteristic
52C2×C7×M16—21no—
53C2×C7×M16—21no—
54C2×C7×M16—21no—
55C2×C7×M16—21no—
56C2×C7×M16—21no—
57C2×C7×M16—21no—
58C2×C7×M16—21no—
59C2×C7×M16—21no—
60C2×C7×M16—21no—
61C2×C7×M16—21no—
62C2×C7×M16C2×C412yescomplemented
63C2×C7×M16C2×C412yescomplemented
64C22×C7×C8—21no—
65C22×C7×C8—21no—
66C7×#117—21no—
67C7×#117—21no—
68C7×#117D412yes—
69C7×#117D412yes—
70C2×C7×C4⋊C4—21no—
71C2×C7×C22⋊C4C2×C412yes—
72C2×C42×C7—21no—
73C2×C22⋊Dic7C2×C412yes—
74C4×C22⋊D7—28no—
75#6489—21no—
76#6489—21no—
77#6489D412yes—
78#6489D412yes—
79C2×C4⋊Dic7—21no—
80C2×C4×Dic7—21no—
81C2×#1136—21no—
82C2×#1136—21no—
83C2×#1136—21no—
84C2×#1136—21no—
85C2×#1136—21no—
86C2×#1136—21no—
87C2×#1136—21no—
88C2×#1136—21no—
89C2×#1136—21no—
90C2×#1136—21no—
91C2×#1136—21no—
92C2×#1136C2×C412yescomplemented
93C22×C7⋊C8—21no—
94C22×C7⋊C8C2×C412yescomplemented
95#6456—24no—
96#6455—24no—
97D7×C4⋊C4—24no—
98#6450—24no—
99(C22⋊D7)⋊C4—28no—
100D7×C22⋊C4—24no—
101#6440—24no—
102C4×D28—24no—
103#6435—24no—
104C42×D7—24no—
105C4×Dic14—24no—
106#6398—24no—
107#6397—24no—
108(C2×D7)⋊C8—28no—
109#3428—71no—
110C2×#413—71no—
111#2879—71no—
112C2×#344—71no—
113C2×#344—71no—
114C2×#344—71no—
115C2×#344D711yescharacteristic, complemented
116C24×C7C22×C411yescharacteristic
117C23×D7C22⋊C412yes—
118C22×C4×C7—22no—
119C22×C4×C7C22×C411yescharacteristic
120C22×C4×C7C22×C411yescharacteristic
121C22×C4×C7C2×D411yescharacteristic
122C22×C4×C7C2×D411yescharacteristic
123C22×C4×C7C2×D411yescharacteristic
124C22×C4×C7C2×D411yescharacteristic
125C22×C4×C7C2×D411yescharacteristic
126C22×C4×C7C2×D411yescharacteristic
127C22×C4×C7C2×D411yescharacteristic
128C22×C4×C7C2×Q811yescharacteristic
129C22×C4×C7#4111yescharacteristic
130C22×C4×C7#4111yescharacteristic
131C22×C4×C7#4111yescharacteristic
132C22×C4×C7#4111yescharacteristic
133C2×C22⋊D7—22no—
134C2×C22⋊D7—22no—
135C2×C22⋊D7—22no—
136C2×C22⋊D7—22no—
137C2×C22⋊D7C4214yes—
138C2×C22⋊D7C4⋊C414yes—
139C22×Dic7—22no—
140C22×Dic7C22⋊C412yes—
141#1157—22no—
142#1157—22no—
143#1157—22no—
144#1157—22no—
145#1157—22no—
146#1157—22no—
147#1157—22no—
148#1157—22no—
149#1157—22no—
150#1157—22no—
151#1157—22no—
152#1157—22no—
153#1157—22no—
154#1157—22no—
155#1157—22no—
156#1157—22no—
157C2×D28—21no—
158C2×D28—21no—
159C2×D28—21no—
160C2×D28—21no—
161C2×D28C22⋊C412yes—
162C2×D28C4⋊C412yes—
163C2×C4×D7—22no—
164C2×C4×D7—22no—
165C2×C4×D7—22no—
166C2×C4×D7—22no—
167C2×C4×D7—28no—
168C2×C4×D7C22⋊C414yes—
169C2×C4×D7C4⋊C414yes—
170C2×Dic14—21no—
171C2×Dic14—21no—
172C2×Dic14—21no—
173C2×Dic14—21no—
174C2×Dic14C22⋊C412yes—
175C2×Dic14C4⋊C412yes—
176C7×M16—22no—
177C7×M16—22no—
178C7×M16—22no—
179C7×M16—22no—
180C7×M16—41no—
181C7×M16—41no—
182C7×M16—41no—
183C7×M16—41no—
184C2×C7×C8—22no—
185C2×C7×C8—22no—
186C2×C7×C8—41no—
187C2×C7×C8—41no—
188C2×C7×C8—41no—
189C2×C7×C8—41no—
190C7×C4⋊C4—22no—
191C7×C4⋊C4—22no—
192C7×C22⋊C4—22no—
193C7×C22⋊C4C22⋊C414yes—
194C42×C7—22no—
195C42×C7—22no—
196C22⋊Dic7—22no—
197C22⋊Dic7C22⋊C414yes—
198(C2×D7)⋊C4—28no—
199C4⋊Dic7—22no—
200C4⋊Dic7—22no—
201Dic7⋊C4—28no—
202C4×Dic7—28no—
203C4×Dic7—22no—
204C4×Dic7—22no—
205#1136—22no—
206#1136—22no—
207#1136—41no—
208#1136—41no—
209#1136—41no—
210#1136—41no—
211#1136—41no—
212#1136—41no—
213C2×C7⋊C8—22no—
214C2×C7⋊C8—22no—
215C2×C7⋊C8—22no—
216C2×C7⋊C8—22no—
217C2×C7⋊C8—41no—
218C2×C7⋊C8—41no—
219C22×#41—71no—
220C22×M16—71no—
221C22×M16—71no—
222C22×M16C2×D711yescharacteristic
223C22×M16C2×D711yescharacteristic
224#520—142no—
225#520—142no—
226#519—141no—
227#518—74no—
228#518—141no—
229C4×#41—142no—
230C4×#41—142no—
231C2×#117—71no—
232C2×#117—142no—
233C2×#117C2×D711yescharacteristic
234#413—74no—
235#413—142no—
236C2×#101—141no—
237C2×#100—141no—
238#408—74no—
239#408—142no—
240#407—142no—
241#344—22no—
242#344—142no—
243#344—142no—
244#344—142no—
245C23×C7—81no—
246C23×C7C2×C4211yescharacteristic
247C23×C7C2×C22⋊C411yescharacteristic
248C23×C7C2×C22⋊C411yescharacteristic
249C23×C7C2×C22⋊C411yescharacteristic
250C23×C7C2×C4⋊C411yescharacteristic
251C23×C7#11711yescharacteristic
252C23×C7#11711yescharacteristic
253C22×D7—22no—
254C22×D7—22no—
255C22×D7—82no—
256C22×D7#9514yes—
257C2×C4×C7—24no—
258C2×C4×C7—82no—
259C2×C4×C7C2×C22⋊C411yescharacteristic
260C2×C4×C7C2×C22⋊C411yescharacteristic
261C2×C4×C7C2×C4⋊C411yescharacteristic
262C2×C4×C7C2×C4⋊C411yescharacteristic
263C2×C4×C7C4×D411yescharacteristic
264C2×C4×C7C4×D411yescharacteristic
265C2×C4×C7C4×D411yescharacteristic
266C2×C4×C7C4×D411yescharacteristic
267C2×C4×C7C4×D411yescharacteristic
268C2×C4×C7C4×D411yescharacteristic
269C2×C4×C7C4×D411yescharacteristic
270C2×C4×C7C4×D411yescharacteristic
271C2×C4×C7#12011yescharacteristic
272C2×C4×C7#12011yescharacteristic
273C2×C4×C7#12011yescharacteristic
274C2×C4×C7#12011yescharacteristic
275C2×C4×C7#12111yescharacteristic
276C2×C4×C7#12111yescharacteristic
277C2×C4×C7#12111yescharacteristic
278C2×C4×C7#12111yescharacteristic
279C2×C4×C7C22⋊Q811yescharacteristic
280C2×C4×C7C22⋊Q811yescharacteristic
281C2×C4×C7C22⋊Q811yescharacteristic
282C2×C4×C7C22⋊Q811yescharacteristic
283C2×C4×C7#12311yescharacteristic
284C2×C4×C7#12311yescharacteristic
285C2×C4×C7#12311yescharacteristic
286C2×C4×C7#12311yescharacteristic
287C22⋊D7—24no—
288C22⋊D7—24no—
289C22⋊D7—24no—
290C22⋊D7—24no—
291C2×Dic7—22no—
292C2×Dic7—22no—
293C2×Dic7—24no—
294C2×Dic7—82no—
295C2×Dic7#9514yes—
296D28—22no—
297D28—22no—
298D28—22no—
299D28—22no—
300C4×D7—24no—
301C4×D7—24no—
302C4×D7—24no—
303C4×D7—24no—
304C4×D7—88no—
305Dic14—22no—
306Dic14—22no—
307Dic14—22no—
308Dic14—22no—
309C7×C8—42no—
310C7×C8—42no—
311C7⋊C8—42no—
312C7⋊C8—42no—
313C2×#41—72no—
314C2×#41—72no—
315C2×#41—72no—
316C2×#41—72no—
317C2×#41—141no—
318C2×#41—141no—
319C2×#41—141no—
320C2×#41—141no—
321C2×#41—141no—
322C2×#41—141no—
323C2×#41—141no—
324C2×#41—141no—
325C22×Q8—71no—
326C22×D4—72no—
327C22×D4—71no—
328C23×C4—72no—
329C23×C4C22×D711yescharacteristic
330C2×M16—21no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—72no—
341C2×M16—141no—
342C2×M16—141no—
343C2×M16—141no—
344C2×M16—141no—
345C2×M16—141no—
346C2×M16—141no—
347C2×M16—141no—
348C2×M16—141no—
349C2×M16—141no—
350C2×M16—141no—
351C2×M16—141no—
352C2×M16C4×D712yescomplemented
353C2×M16C4×D712yescomplemented
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—72no—
357C22×C8—141no—
358C4×Q8—144no—
359C4×Q8—144no—
360C4×D4—144no—
361C4×D4—148no—
362C4×D4—144no—
363C4×D4—148no—
364#117—21no—
365#117—21no—
366#117—72no—
367#117—72no—
368#117—144no—
369#117—144no—
370#117—144no—
371#117—141no—
372#117—141no—
373#117D2812yes—
374#117C22⋊D712yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—144no—
377C2×C4⋊C4—141no—
378C2×C22⋊C4—72no—
379C2×C22⋊C4—144no—
380C2×C22⋊C4C4×D712yes—
381C2×C42—21no—
382C2×C42—144no—
383C2×C42—141no—
384#101—144no—
385#100—144no—
386C22⋊C8—148no—
387C22×C7—41no—
388C22×C7—41no—
389C22×C7—41no—
390C22×C7—41no—
391C22×C7—41no—
392C22×C7—41no—
393C22×C7—41no—
394C22×C7C2×#9511yescharacteristic
395C22×C7C4×C22⋊C411yescharacteristic
396C22×C7C4×C22⋊C411yescharacteristic
397C22×C7#37911yescharacteristic
398C22×C7#38011yescharacteristic
399C22×C7#38011yescharacteristic
400C22×C7#38111yescharacteristic
401C2×D7—24no—
402C2×D7—44no—
403C2×D7—44no—
404C2×D7—82no—
405C4×C7—44no—
406C4×C7#38511yescharacteristic
407C4×C7#38511yescharacteristic
408C4×C7#38511yescharacteristic
409C4×C7#38511yescharacteristic
410C4×C7#38611yescharacteristic
411C4×C7#38611yescharacteristic
412C4×C7#38611yescharacteristic
413C4×C7#38611yescharacteristic
414Dic7—24no—
415Dic7—44no—
416C24—72no—
417C24C2×C4×D711yescharacteristic
418#41—142no—
419#41—142no—
420#41—142no—
421#41—142no—
422#41—142no—
423#41—142no—
424#41—142no—
425#41—142no—
426#41—142no—
427#41—142no—
428#41—142no—
429#41—142no—
430#41—142no—
431#41—142no—
432#41—142no—
433#41—142no—
434C2×Q8—72no—
435C2×Q8—72no—
436C2×Q8—141no—
437C2×Q8—141no—
438C2×Q8—141no—
439C2×Q8—141no—
440C2×D4—74no—
441C2×D4—74no—
442C2×D4—72no—
443C2×D4—72no—
444C2×D4—142no—
445C2×D4—142no—
446C2×D4—142no—
447C2×D4—142no—
448C2×D4—141no—
449C2×D4—141no—
450C2×D4—141no—
451C2×D4—141no—
452C22×C4—22no—
453C22×C4—72no—
454C22×C4—74no—
455C22×C4—74no—
456C22×C4—148no—
457C22×C4—142no—
458C22×C4—142no—
459C22×C4—142no—
460C22×C4—142no—
461C22×C4—142no—
462C22×C4C2×C4×D711yescharacteristic
463C22×C4C2×C4×D711yescharacteristic
464C22×C4C2×D2811yescharacteristic
465C22×C4#115711yescharacteristic
466C22×C4#115711yescharacteristic
467C22×C4D4×D711yescharacteristic
468C22×C4D4×D711yescharacteristic
469C22×C4D4×D711yescharacteristic
470C22×C4D4×D711yescharacteristic
471C22×C4D4×D711yescharacteristic
472C22×C4#115911yescharacteristic
473C22×C4Q8×D711yescharacteristic
474C22×C4#116111yescharacteristic
475C22×C4C2×C22⋊D711yescharacteristic
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—142no—
485M16—142no—
486M16—281no—
487M16—281no—
488M16—281no—
489M16—281no—
490M16—281no—
491M16—281no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—142no—
499C2×C8—142no—
500C2×C8—142no—
501C2×C8—142no—
502C2×C8—281no—
503C2×C8—281no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—148no—
507C4⋊C4—142no—
508C4⋊C4—142no—
509C22⋊C4—22no—
510C22⋊C4—74no—
511C22⋊C4—148no—
512C22⋊C4—142no—
513C22⋊C4(C2×D7)⋊C414yes—
514C42—22no—
515C42—22no—
516C42—148no—
517C42—142no—
518C42—142no—
519C2×C7—21no—
520C2×C7—21no—
521C2×C7—21no—
522C2×C7—21no—
523C2×C7—21no—
524C2×C7—21no—
525C2×C7—21no—
526C2×C7C22⋊#9511yescharacteristic
527D7—44no—
528C23—74no—
529C23—81no—
530C23—142no—
531C23—142no—
532C23—562no—
533C23C42×D711yescharacteristic
534C23#643511yescharacteristic
535C23D7×C22⋊C411yescharacteristic
536C23D7×C22⋊C411yescharacteristic
537C23D7×C4⋊C411yescharacteristic
538C23#645511yescharacteristic
539C23C2×(C2×D7)⋊C411yescharacteristic
540Q8—142no—
541Q8—142no—
542Q8—142no—
543Q8—142no—
544D4—144no—
545D4—144no—
546D4—144no—
547D4—144no—
548D4—142no—
549D4—142no—
550D4—142no—
551D4—142no—
552C2×C4—24no—
553C2×C4—74no—
554C2×C4—82no—
555C2×C4—142no—
556C2×C4—142no—
557C2×C4—144no—
558C2×C4—144no—
559C2×C4—144no—
560C2×C4—144no—
561C2×C4—144no—
562C2×C4—568no—
563C2×C4—562no—
564C2×C4C4×D2811yescharacteristic
565C2×C4C4×D2811yescharacteristic
566C2×C4D7×C22⋊C411yescharacteristic
567C2×C4D7×C22⋊C411yescharacteristic
568C2×C4(C22⋊D7)⋊C411yescharacteristic
569C2×C4(C22⋊D7)⋊C411yescharacteristic
570C2×C4#644511yescharacteristic
571C2×C4#644511yescharacteristic
572C2×C4#644611yescharacteristic
573C2×C4#644611yescharacteristic
574C2×C4#644711yescharacteristic
575C2×C4#644711yescharacteristic
576C2×C4D7×C4⋊C411yescharacteristic
577C2×C4D7×C4⋊C411yescharacteristic
578C2×C4#645611yescharacteristic
579C2×C4#645611yescharacteristic
580C2×C4#645711yescharacteristic
581C2×C4#645711yescharacteristic
582C2×C4#645811yescharacteristic
583C2×C4#645911yescharacteristic
584C2×C4#645911yescharacteristic
585C2×C4#646011yescharacteristic
586C2×C4C4×C22⋊D711yescharacteristic
587C2×C4C4×C22⋊D711yescharacteristic
588C2×C4#650011yescharacteristic
589C2×C4#650011yescharacteristic
590C2×C4#650111yescharacteristic
591C2×C4#650911yescharacteristic
592C8—42no—
593C8—42no—
594C8—282no—
595C8—282no—
596C7#1075611yescharacteristic, complemented, Sylow
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—144no—
605C22—284no—
606C22—284no—
607C22—562no—
608C22D7×#9511yescharacteristic
609C22#8943611yescharacteristic
610C22#8943811yescharacteristic
611C22#8943911yescharacteristic
612C22C4×(C2×D7)⋊C411yescharacteristic
613C22#8972711yescharacteristic
614C22#8975911yescharacteristic
615C4—44no—
616C4—144no—
617C4—284no—
618C4#8943711yescharacteristic
619C4#8943711yescharacteristic
620C4#8944011yescharacteristic
621C4#8944011yescharacteristic
622C4#8972811yescharacteristic
623C4#8972811yescharacteristic
624C4#8976111yescharacteristic
625C4#8976111yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—284no—
634C2(C2×D7)⋊#9511yescharacteristic
subgroupG/H
centerC4#89437
commutatorC23×C7C2×C42
FrattiniC23×C4C22×D7
FittingC2×C7×#344C2
socleC2×C7C22⋊#95
prime radicalC22×#1157C22
cosocleC23×C4×C7C23
hypercenterC2×#344D7
hypocenterC7#10756
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×C7×#344C2semidirect
5. C2×#89354C2semidirect
6. C2×#89354C2semidirect
7. C2×#89328C2semidirect
25. #89904C4semidirect
27. #89901C4semidirect
62. C2×C7×M16C2×C4semidirect
63. C2×C7×M16C2×C4semidirect
92. C2×#1136C2×C4semidirect
94. C22×C7⋊C8C2×C4semidirect
115. C2×#344D7semidirect
352. C2×M16C4×D7semidirect
353. C2×M16C4×D7semidirect
596. C7#10756semidirect

Maximal subgroups

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

subgroupindex
#117427992
C2×#899042
#117412072
C2×C7×#3442
C2×#893542
C2×#893282
#107567