Finite Group Databasebeta

← #13360195

Subgroups — #13360195

Order 1792.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2275C211yesmaximal, characteristic
2C2×#89791C211yesmaximal, characteristic
3C2×C4×#1142C211yesmaximal, characteristic
4C2×#89790C211yesmaximal, characteristic
5#11730833C211yesmaximal, characteristic, complemented
6#11729366C211yesmaximal, characteristic
7#11729366C211yesmaximal, characteristic
8#11729359C211yesmaximal, characteristic
9#11727240C211yesmaximal, characteristic, complemented
10#11727229C211yesmaximal, characteristic, complemented
11C4×#6384C211yesmaximal, characteristic, complemented
12#11727222C211yesmaximal, characteristic, complemented
13#11727219C211yesmaximal, characteristic, complemented
14#11727218C211yesmaximal, characteristic, complemented
15#11727190C211yesmaximal, characteristic, complemented
16C2×C4×C7×D4C2211yescharacteristic
17C2×C4×C7×D4C2211yescharacteristic
18C2×C4×C7×D4C2211yescharacteristic
19C22×#1142C2211yescharacteristic
20C22×#1142C2211yescharacteristic
21C2×#6432C2211yescharacteristic
22C2×C4×Dic14C2211yescharacteristic
23C2×C4×Dic14C2211yescharacteristic
24C4×C7×C4⋊C4C2211yescharacteristic
25C4×C7×C4⋊C4C2211yescharacteristic
26C4×C7×C4⋊C4C2211yescharacteristic
27C4×C7×C22⋊C4—21no—
28C4×C7×C22⋊C4—21no—
29C4×C7×C22⋊C4—21no—
30C7×#376C2211yescharacteristic
31C2×C7×#95—21no—
32C2×#6406C2211yescharacteristic
33C2×#6406C2211yescharacteristic
34#89791C418yescomplemented
35#89790—24no—
36C4×#1142—24no—
37C2×#6384C2211yescharacteristic
38C2×#6384C2211yescharacteristic
39C2×#6384C2211yescharacteristic
40C2×#6384C2211yescharacteristic
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45#89708C2211yescharacteristic
46#89701C2211yescharacteristic
47#89701C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51C2×C4×C7⋊C8C2211yescharacteristic
52#89425—21no—
53#89425—21no—
54#89425—21no—
55#89425—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#21514—71nomaximal, Sylow
63C22×C7×D4C2311yescharacteristic
64C23×C4×C7—21no—
65C23×C4×C7—21no—
66C23×C4×C7—21no—
67C22×Dic14C2311yescharacteristic
68C22×Dic14C2311yescharacteristic
69C4×C7×D4—22no—
70C4×C7×D4—22no—
71C4×C7×D4—22no—
72C4×C7×D4—22no—
73C4×C7×D4C2×C414yes—
74C4×C7×D4D414yes—
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C22⋊C4—21no—
79C2×C7×C22⋊C4—21no—
80C2×C7×C22⋊C4—21no—
81C2×C42×C7—21no—
82C2×C42×C7—21no—
83C2×C42×C7—21no—
84C2×C42×C7C2311yescharacteristic
85C2×C42×C7C2311yescharacteristic
86C2×C42×C7C2311yescharacteristic
87C2×#1142—22no—
88C2×#1142—22no—
89C2×#1142—22no—
90C2×#1142—22no—
91C2×#1142C2×C414yes—
92C2×#1142C2×C414yes—
93C2×C4⋊Dic7—21no—
94C2×C4⋊Dic7—21no—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×Dic7⋊C4—21no—
98C2×Dic7⋊C4—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105#6432—22no—
106#6432C2×C414yescomplemented
107C4×Dic14—22no—
108C4×Dic14—22no—
109C4×Dic14—22no—
110C4×Dic14—22no—
111C7×#95—21no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95D411yescharacteristic
115C7×#95D411yescharacteristic
116C7×#95D411yescharacteristic
117C7×#95D411yescharacteristic
118#6406—22no—
119#6406—22no—
120C7⋊#95—21no—
121C7⋊#95—21no—
122C7⋊#95—21no—
123C7⋊#95—21no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126#6384—22no—
127#6384—22no—
128#6384—22no—
129#6384—22no—
130#6384C2×C414yescomplemented
131#6384C2×C414yescomplemented
132#6382—22no—
133#6381—22no—
134C4⋊(C7⋊C8)—22no—
135C4⋊(C7⋊C8)C2×C414yescomplemented
136#6377—22no—
137C4×C7⋊C8—22no—
138C2×#461—71no—
139C2×#440—71no—
140C2×C4×SD16—71no—
141#2327—71no—
142#2275D711yescharacteristic
143#1981—71no—
144#1949—71no—
145#1928—71no—
146#1927—71no—
147#1877—71no—
148#1877—71no—
149#1804—71no—
150#1768—71no—
151#1763—71no—
152C4×#103—71no—
153C24×C7—21no—
154C2×C7×D4—21no—
155C2×C7×D4—21no—
156C2×C7×D4—21no—
157C2×C7×D4C22×C412yes—
158C2×C7×D4C2×D412yes—
159C2×C7×D4#4112yes—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—24no—
164C22×C4×C7—24no—
165C22×C4×C7—24no—
166C22×C4×C7—81no—
167C22×C4×C7—81no—
168C22×C4×C7—81no—
169C22×C4×C7—81no—
170C22×C4×C7—81no—
171C22×C4×C7—81no—
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2411yescharacteristic
179C22×Dic7—21no—
180C22×Dic7—21no—
181C22×Dic7—21no—
182C22×Dic7—21no—
183C2×Dic14—21no—
184C2×Dic14—21no—
185C2×Dic14—21no—
186C2×Dic14—21no—
187C2×Dic14—21no—
188C2×Dic14—21no—
189C2×Dic14—21no—
190C2×Dic14—21no—
191C2×Dic14—21no—
192C2×Dic14—21no—
193C2×Dic14C22×C412yes—
194C2×Dic14C22×C412yes—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4C22×C412yes—
199C7×C4⋊C4C2×D412yes—
200C7×C4⋊C4#4112yes—
201C7×C22⋊C4—24no—
202C7×C22⋊C4—24no—
203C7×C22⋊C4—24no—
204C42×C7—21no—
205C42×C7—21no—
206C42×C7—81no—
207C42×C7—81no—
208C42×C7—81no—
209C42×C7C22×C412yes—
210C42×C7C2×D412yes—
211C42×C7#4112yes—
212C42×C7#4112yes—
213#1142—28no—
214#1142—28no—
215C4⋊Dic7—24no—
216C4⋊Dic7—24no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7—21no—
220C4⋊Dic7—21no—
221Dic7⋊C4—42no—
222Dic7⋊C4—42no—
223C4×Dic7—42no—
224C4×Dic7—42no—
225C2×C7⋊C8—21no—
226C2×C7⋊C8—21no—
227C2×C7⋊C8—21no—
228C2×C7⋊C8—21no—
229C2×C7⋊C8—21no—
230C2×C7⋊C8—21no—
231C2×C7⋊C8—21no—
232C2×C7⋊C8—21no—
233C2×C7⋊C8—21no—
234C2×C7⋊C8—21no—
235C2×C7⋊C8C22×C412yes—
236C2×C7⋊C8C22×C412yes—
237C22×SD16—71no—
238C22×SD16—71no—
239C2×C4⋊Q8—71no—
240C2×C4×Q8—71no—
241C2×C4×Q8—71no—
242C2×C4×D4C2×D711yescharacteristic
243C2×C4×D4C2×D711yescharacteristic
244C2×C4×D4C2×D711yescharacteristic
245#461—78no—
246#440—144no—
247C4×SD16—144no—
248C2×#107—71no—
249C2×#106—71no—
250C2×C4⋊C8—71no—
251C2×C4⋊C8—71no—
252C2×#103—71no—
253C2×#103—71no—
254C2×#103—71no—
255C2×#103—71no—
256C2×#103—71no—
257C2×#103—71no—
258C2×#102—71no—
259C2×#102—71no—
260C2×#97—71no—
261C2×C4×C8—71no—
262#391—71no—
263#391—71no—
264#387—141no—
265#387—141no—
266#387—141no—
267#387—141no—
268#382—71no—
269C4×C4⋊C4C2×D711yescharacteristic
270C4×C4⋊C4C2×D711yescharacteristic
271C4×C4⋊C4C2×D711yescharacteristic
272C4×C22⋊C4—21no—
273C4×C22⋊C4—21no—
274C4×C22⋊C4—21no—
275#376C2×D711yescharacteristic
276C2×#95—21no—
277#340—71no—
278#340—71no—
279#340—71no—
280#340—71no—
281#336—71no—
282#336—71no—
283C23×C7—22no—
284C23×C7—22no—
285C23×C7—22no—
286C23×C7—41no—
287C23×C7—41no—
288C23×C7—41no—
289C23×C7—41no—
290C23×C7C22×D411yescharacteristic
291C7×D4—22no—
292C7×D4—22no—
293C7×D4—22no—
294C7×D4C4×D414yes—
295C2×C4×C7—21no—
296C2×C4×C7—21no—
297C2×C4×C7—21no—
298C2×C4×C7—21no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—22no—
304C2×C4×C7—22no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—22no—
308C2×C4×C7—21no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—41no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—84no—
319C2×C4×C7—84no—
320C2×C4×C7—84no—
321C2×C4×C7C4×D412yes—
322C2×C4×C7C4×D412yes—
323C2×C4×C7#12112yes—
324C2×C4×C7#12112yes—
325C2×C4×C7C23×C411yescharacteristic
326C2×C4×C7C22×D411yescharacteristic
327C2×C4×C7C2×#4111yescharacteristic
328C2×C4×C7C2×#4111yescharacteristic
329C2×C4×C7C2×#4111yescharacteristic
330C2×C4×C7C2×#4111yescharacteristic
331C2×Dic7—22no—
332C2×Dic7—22no—
333C2×Dic7—41no—
334C2×Dic7—41no—
335C2×Dic7—41no—
336C2×Dic7—41no—
337C2×Dic7—41no—
338C2×Dic7—41no—
339C2×Dic7—41no—
340C2×Dic7—41no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343Dic14—22no—
344Dic14—22no—
345Dic14—22no—
346Dic14—22no—
347Dic14—41no—
348Dic14—41no—
349Dic14—41no—
350Dic14—41no—
351C7⋊C8—22no—
352C7⋊C8—22no—
353C7⋊C8—41no—
354C7⋊C8—41no—
355C22×Q8—71no—
356C22×Q8—71no—
357C22×D4C22×D711yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C2×SD16—74no—
362C2×SD16—74no—
363C2×SD16—142no—
364C2×SD16—142no—
365C2×SD16—142no—
366C2×SD16—142no—
367C22×C8—71no—
368C22×C8—71no—
369C22×C8—71no—
370C22×C8—71no—
371C4⋊Q8—74no—
372C4⋊Q8—142no—
373C4×Q8—142no—
374C4×Q8—142no—
375C4×Q8—142no—
376C4×Q8—142no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4C4×D714yes—
382C4×D4D2814yes—
383C2×C4⋊C4—71no—
384C2×C4⋊C4—71no—
385C2×C4⋊C4—141no—
386C2×C4⋊C4—141no—
387C2×C4⋊C4—141no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4C22×D711yescharacteristic
390C2×C4⋊C4C22×D711yescharacteristic
391C2×C4⋊C4C22×D711yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—141no—
399C2×C42—141no—
400C2×C42C22×D711yescharacteristic
401C2×C42C22×D711yescharacteristic
402C2×C42C22×D711yescharacteristic
403#107—142no—
404#106—142no—
405C4⋊C8—74no—
406C4⋊C8—142no—
407#103—74no—
408#103—74no—
409#103—142no—
410#103—142no—
411#103—142no—
412#103—142no—
413#102—142no—
414#102—142no—
415#97—142no—
416C4×C8—142no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—141no—
421#95—141no—
422#95—141no—
423#95—141no—
424#95—141no—
425#95—141no—
426#95C22⋊D711yescharacteristic
427#95C22⋊D711yescharacteristic
428#95C22⋊D711yescharacteristic
429#95C22⋊D711yescharacteristic
430C22×C7—24no—
431C22×C7—42no—
432C22×C7—42no—
433C22×C7—42no—
434C22×C7—42no—
435C22×C7—42no—
436C22×C7—42no—
437C22×C7C2×C4×D411yescharacteristic
438C22×C7C2×#12111yescharacteristic
439C22×C7#52511yescharacteristic
440C22×C7#57711yescharacteristic
441C22×C7#57711yescharacteristic
442C22×C7#57711yescharacteristic
443C22×C7#57811yescharacteristic
444C4×C7—22no—
445C4×C7—22no—
446C4×C7—22no—
447C4×C7—22no—
448C4×C7—41no—
449C4×C7—41no—
450C4×C7—42no—
451C4×C7—42no—
452C4×C7—42no—
453C4×C7C2×C4×D411yescharacteristic
454C4×C7C4×#4111yescharacteristic
455C4×C7#52911yescharacteristic
456C4×C7#53211yescharacteristic
457Dic7—42no—
458Dic7—42no—
459Dic7—81no—
460Dic7—81no—
461C24—21no—
462C2×Q8—72no—
463C2×Q8—72no—
464C2×Q8—141no—
465C2×Q8—141no—
466C2×Q8—141no—
467C2×Q8—141no—
468C2×Q8—141no—
469C2×Q8—141no—
470C2×Q8—141no—
471C2×Q8—141no—
472C2×Q8—141no—
473C2×Q8—141no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4C2×C4×D712yes—
478C2×D4C2×D2812yes—
479C2×D4#115712yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4—81no—
492C22×C4—141no—
493C22×C4—141no—
494C22×C4—141no—
495C22×C4—141no—
496C22×C4C2×C22⋊D711yescharacteristic
497C22×C4C2×C22⋊D711yescharacteristic
498C22×C4C2×C22⋊D711yescharacteristic
499C22×C4C2×C22⋊D711yescharacteristic
500C22×C4C2×C22⋊D711yescharacteristic
501C22×C4C2×C22⋊D711yescharacteristic
502C22×C4C23×D711yescharacteristic
503SD16—148no—
504SD16—148no—
505C2×C8—72no—
506C2×C8—72no—
507C2×C8—141no—
508C2×C8—141no—
509C2×C8—141no—
510C2×C8—141no—
511C2×C8—141no—
512C2×C8—141no—
513C2×C8—141no—
514C2×C8—141no—
515C2×C8—141no—
516C2×C8—141no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—144no—
521C4⋊C4—144no—
522C4⋊C4—141no—
523C4⋊C4—141no—
524C4⋊C4—141no—
525C4⋊C4—141no—
526C4⋊C4—282no—
527C4⋊C4—282no—
528C4⋊C4C2×C4×D712yes—
529C4⋊C4C2×D2812yes—
530C4⋊C4#115712yes—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C42—21no—
535C42—21no—
536C42—81no—
537C42—81no—
538C42—81no—
539C42—282no—
540C42—282no—
541C42C2×C4×D712yes—
542C42C2×D2812yes—
543C42#115712yes—
544C42#115712yes—
545C2×C7—44no—
546C2×C7C4×#12111yescharacteristic
547C2×C7#294711yescharacteristic
548C2×C7#294911yescharacteristic
549C2×C7#304211yescharacteristic
550C2×C7#304611yescharacteristic
551C2×C7#312011yescharacteristic
552C2×C7#312311yescharacteristic
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23C22×C22⋊D711yescharacteristic
561Q8—142no—
562Q8—142no—
563Q8—142no—
564Q8—142no—
565Q8—281no—
566Q8—281no—
567Q8—281no—
568Q8—281no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4C4×D2814yes—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—281no—
602C2×C4—281no—
603C2×C4—281no—
604C2×C4—281no—
605C2×C4—281no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—281no—
609C2×C4—281no—
610C2×C4—281no—
611C2×C4C4×C22⋊D712yes—
612C2×C4C4×C22⋊D712yes—
613C2×C4#649312yes—
614C2×C4#649312yes—
615C2×C4C22×C4×D711yescharacteristic
616C2×C4C22×D2811yescharacteristic
617C2×C4C2×#115711yescharacteristic
618C2×C4C2×#115711yescharacteristic
619C2×C4C2×#115711yescharacteristic
620C2×C4C2×#115711yescharacteristic
621C8—142no—
622C8—142no—
623C8—281no—
624C8—281no—
625C7#2151411yescharacteristic, complemented, Sylow
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C2×C4×C22⋊D711yescharacteristic
634C22C2×#649311yescharacteristic
635C22#9048211yescharacteristic
636C22#9052711yescharacteristic
637C22#9052711yescharacteristic
638C22#9052711yescharacteristic
639C22#9052911yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—42no—
645C4—42no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—282no—
650C4—282no—
651C4—561no—
652C4—561no—
653C4C2×C4×D2811yescharacteristic
654C4C4×#115711yescharacteristic
655C4#9016811yescharacteristic
656C4#9017011yescharacteristic
657C2—44no—
658C2C4×#649311yescharacteristic
659C2#1173998811yescharacteristic
660C2#1173998911yescharacteristic
661C2#1173999011yescharacteristic
662C2#1174001611yescharacteristic
663C2#1174001711yescharacteristic
664C2#1174002011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2275C2
socleC23×C7C22×D4
prime radicalC22×C7×D4C23
cosocleC22×C4×C7C24
hypercenter#2275D7
hypocenterC7#21514
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
5. #11730833C2semidirect
9. #11727240C2semidirect
10. #11727229C2semidirect
11. C4×#6384C2semidirect
12. #11727222C2semidirect
13. #11727219C2semidirect
14. #11727218C2semidirect
15. #11727190C2semidirect
34. #89791C4semidirect
106. #6432C2×C4semidirect
130. #6384C2×C4semidirect
131. #6384C2×C4semidirect
135. C4⋊(C7⋊C8)C2×C4semidirect
625. C7#21514semidirect

Maximal subgroups

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

subgroupindex
C7×#22752
C2×#897912
C2×C4×#11422
C2×#897902
#117308332
#117293662
#117293592
#117272402
#117272292
C4×#63842
#117272222
#117272192
#117272182
#117271902
#215147