Finite Group Databasebeta

← #13360189

Subgroups — #13360189

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×#2327C211yesmaximal, characteristic, complemented
2C2×#89855C211yesmaximal, characteristic
3C2×#89798C211yesmaximal, characteristic
4C2×C4×#1143C211yesmaximal, characteristic
5#11730857C211yesmaximal, characteristic
6#11729532C211yesmaximal, characteristic, complemented
7#11729385C211yesmaximal, characteristic, complemented
8C4×#6409C211yesmaximal, characteristic, complemented
9#11727441C211yesmaximal, characteristic
10#11727441C211yesmaximal, characteristic
11#11727421C211yesmaximal, characteristic, complemented
12#11727420C211yesmaximal, characteristic, complemented
13#11727310C211yesmaximal, characteristic
14#11727294C211yesmaximal, characteristic, complemented
15#11727190C211yesmaximal, characteristic, complemented
16C2×C7×C4⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C2×C4×C7×Q8C2211yescharacteristic
19C22×#1143C2211yescharacteristic
20C22×#1143C2211yescharacteristic
21C2×C4×D28C2211yescharacteristic
22C2×C4×D28C2211yescharacteristic
23C2×C4×D28C2211yescharacteristic
24C7×#391C2211yescharacteristic
25C7×#391C2211yescharacteristic
26C7×#387—21no—
27C7×#387—21no—
28C7×#387—21no—
29C7×#387—21no—
30C7×#382C2211yescharacteristic
31C7×#376C2211yescharacteristic
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35C2×#6409C2211yescharacteristic
36C2×#6409C2211yescharacteristic
37C2×#6409C2211yescharacteristic
38#89855C418yescomplemented
39#89798—24no—
40C4×#1143—24no—
41C2×#6383C2211yescharacteristic
42C2×#6383C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6381C2211yescharacteristic
45C4×C4⋊Dic7C2211yescharacteristic
46C4×C4⋊Dic7C2211yescharacteristic
47C4×C4⋊Dic7C2211yescharacteristic
48C2×C4⋊(C7⋊C8)C2211yescharacteristic
49C2×C4⋊(C7⋊C8)C2211yescharacteristic
50C2×#6377C2211yescharacteristic
51C2×C4×C7⋊C8C2211yescharacteristic
52#89438—21no—
53#89438—21no—
54#89438—21no—
55D7×#95—21no—
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89319C2211yescharacteristic
61#89319C2211yescharacteristic
62#21514—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C22×C7×Q8C2311yescharacteristic
65C22×D28C2311yescharacteristic
66C22×C4×D7—21no—
67C22×C4×D7—21no—
68C22×C4×D7—21no—
69C7×C4⋊Q8—22no—
70C7×C4⋊Q8C2×C414yescomplemented
71C4×C7×Q8—22no—
72C4×C7×Q8—22no—
73C4×C7×Q8—22no—
74C4×C7×Q8—22no—
75C2×C7×C4⋊C4—21no—
76C2×C7×C4⋊C4—21no—
77C2×C7×C4⋊C4—21no—
78C2×C7×C4⋊C4—21no—
79C2×C7×C4⋊C4C2311yescharacteristic
80C2×C7×C4⋊C4C2311yescharacteristic
81C2×C42×C7—21no—
82C2×C42×C7—21no—
83C2×C42×C7C2311yescharacteristic
84C2×C42×C7C2311yescharacteristic
85C2×C42×C7C2311yescharacteristic
86C2×#1143—22no—
87C2×#1143—22no—
88C2×#1143—22no—
89C2×#1143—22no—
90C2×#1143C2×C414yes—
91C2×#1143C2×C414yes—
92C2×(C2×D7)⋊C4—21no—
93C2×(C2×D7)⋊C4—21no—
94C2×(C2×D7)⋊C4—21no—
95C2×C4⋊Dic7C2311yescharacteristic
96C2×C4⋊Dic7C2311yescharacteristic
97C2×C4⋊Dic7C2311yescharacteristic
98C2×C4×Dic7—21no—
99C2×C4×Dic7—21no—
100C2×C4×Dic7—21no—
101C22×C7⋊C8C2311yescharacteristic
102C22×C7⋊C8C2311yescharacteristic
103C22×C7⋊C8C2311yescharacteristic
104C22×C7⋊C8C2311yescharacteristic
105C4×D28—22no—
106C4×D28—22no—
107C4×D28—22no—
108C4×D28—22no—
109C4×D28C2×C414yes—
110C4×D28D414yes—
111C7×#95—21no—
112C7×#95—21no—
113C7×#95—21no—
114C7×#95—21no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95D411yescharacteristic
118C7×#95D411yescharacteristic
119C7×#95D411yescharacteristic
120C7×#95D411yescharacteristic
121#6409—22no—
122#6409—22no—
123#6409—22no—
124#6409—22no—
125#6409C2×C414yescomplemented
126#6409C2×C414yescomplemented
127C7⋊#95—21no—
128C7⋊#95—21no—
129C7⋊#95—21no—
130#6383—22no—
131#6383—22no—
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#2327D711yescharacteristic, complemented
142#2275—71no—
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—
153C23×D7—21no—
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8—21no—
160C2×C7×Q8—21no—
161C2×C7×Q8—21no—
162C2×C7×Q8—21no—
163C2×C7×Q8—21no—
164C2×C7×Q8C22×C412yes—
165C2×C7×Q8C22×C412yes—
166C22×C4×C7—21no—
167C22×C4×C7—21no—
168C22×C4×C7—21no—
169C22×C4×C7—21no—
170C22×C4×C7C2×D411yescharacteristic
171C22×C4×C7C2×D411yescharacteristic
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7C2×D411yescharacteristic
174C22×C4×C7C2×D411yescharacteristic
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2411yescharacteristic
177C22×Dic7—21no—
178C22×Dic7—21no—
179C22×Dic7—21no—
180C2×D28—21no—
181C2×D28—21no—
182C2×D28—21no—
183C2×D28C22×C412yes—
184C2×D28C2×D412yes—
185C2×D28#4112yes—
186C2×C4×D7—24no—
187C2×C4×D7—24no—
188C2×C4×D7—24no—
189C2×C4×D7—81no—
190C2×C4×D7—81no—
191C2×C4×D7—81no—
192C2×C4×D7—81no—
193C2×C4×D7—81no—
194C2×C4×D7—81no—
195C7×C4⋊C4—24no—
196C7×C4⋊C4—24no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—21no—
199C7×C4⋊C4—21no—
200C7×C4⋊C4—21no—
201C7×C4⋊C4—42no—
202C7×C4⋊C4—42no—
203C42×C7—21no—
204C42×C7—21no—
205C42×C7—42no—
206C42×C7—42no—
207C42×C7C22×C412yes—
208C42×C7C2×D412yes—
209C42×C7#4112yes—
210C42×C7#4112yes—
211#1143—28no—
212#1143—28no—
213(C2×D7)⋊C4—24no—
214(C2×D7)⋊C4—24no—
215(C2×D7)⋊C4—24no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7C22×C412yes—
220C4⋊Dic7C2×D412yes—
221C4⋊Dic7#4112yes—
222C4×Dic7—81no—
223C4×Dic7—81no—
224C4×Dic7—81no—
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⋊Q8C2×D711yescharacteristic
240C2×C4×Q8C2×D711yescharacteristic
241C2×C4×Q8C2×D711yescharacteristic
242C2×C4×D4—71no—
243C2×C4×D4—71no—
244C2×C4×D4—71no—
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#391C2×D711yescharacteristic
263#391C2×D711yescharacteristic
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#382C2×D711yescharacteristic
269C4×C4⋊C4—71no—
270C4×C4⋊C4—71no—
271C4×C4⋊C4—71no—
272C4×C22⋊C4—141no—
273C4×C22⋊C4—141no—
274C4×C22⋊C4—141no—
275#376C2×D711yescharacteristic
276C2×#95—141no—
277#340—71no—
278#340—71no—
279#340—71no—
280#340—71no—
281#336—71no—
282#336—71no—
283C23×C7C22×D411yescharacteristic
284C22×D7—22no—
285C22×D7—22no—
286C22×D7—22no—
287C22×D7—41no—
288C22×D7—41no—
289C22×D7—41no—
290C22×D7—41no—
291C7×Q8—22no—
292C7×Q8—22no—
293C7×Q8—22no—
294C7×Q8—22no—
295C7×Q8—41no—
296C7×Q8—41no—
297C7×Q8—41no—
298C7×Q8—41no—
299C2×C4×C7—21no—
300C2×C4×C7—21no—
301C2×C4×C7—21no—
302C2×C4×C7—21no—
303C2×C4×C7—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—21no—
310C2×C4×C7—21no—
311C2×C4×C7—21no—
312C2×C4×C7—21no—
313C2×C4×C7—21no—
314C2×C4×C7—21no—
315C2×C4×C7—41no—
316C2×C4×C7—41no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—41no—
322C2×C4×C7—41no—
323C2×C4×C7—41no—
324C2×C4×C7—41no—
325C2×C4×C7C4×D412yes—
326C2×C4×C7C4×D412yes—
327C2×C4×C7#12112yes—
328C2×C4×C7#12112yes—
329C2×C4×C7C23×C411yescharacteristic
330C2×C4×C7C22×D411yescharacteristic
331C2×C4×C7C2×#4111yescharacteristic
332C2×C4×C7C2×#4111yescharacteristic
333C2×C4×C7C2×#4111yescharacteristic
334C2×C4×C7C2×#4111yescharacteristic
335C2×Dic7—22no—
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—41no—
339C2×Dic7—41no—
340C2×Dic7—41no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343C2×Dic7—41no—
344D28—22no—
345D28—22no—
346D28—22no—
347D28C4×D414yes—
348C4×D7—84no—
349C4×D7—84no—
350C4×D7—84no—
351C7⋊C8—22no—
352C7⋊C8—22no—
353C7⋊C8—41no—
354C7⋊C8—41no—
355C22×Q8C22×D711yescharacteristic
356C22×Q8C22×D711yescharacteristic
357C22×D4—71no—
358C23×C4—141no—
359C23×C4—141no—
360C23×C4—141no—
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—22no—
372C4⋊Q8C4×D714yescomplemented
373C4×Q8—22no—
374C4×Q8—22no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×D4—74no—
378C4×D4—74no—
379C4×D4—142no—
380C4×D4—142no—
381C4×D4—142no—
382C4×D4—142no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—71no—
388C2×C4⋊C4—71no—
389C2×C4⋊C4—71no—
390C2×C4⋊C4C22×D711yescharacteristic
391C2×C4⋊C4C22×D711yescharacteristic
392C2×C22⋊C4—141no—
393C2×C22⋊C4—141no—
394C2×C22⋊C4—141no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—141no—
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—21no—
421#95—21no—
422#95—21no—
423#95—141no—
424#95—141no—
425#95—141no—
426#95C22⋊D711yescharacteristic
427#95C22⋊D711yescharacteristic
428#95C22⋊D711yescharacteristic
429#95C22⋊D711yescharacteristic
430C22×C7C2×C4×D411yescharacteristic
431C22×C7C2×#12111yescharacteristic
432C22×C7#52511yescharacteristic
433C22×C7#57711yescharacteristic
434C22×C7#57711yescharacteristic
435C22×C7#57711yescharacteristic
436C22×C7#57811yescharacteristic
437C2×D7—24no—
438C2×D7—42no—
439C2×D7—42no—
440C2×D7—42no—
441C2×D7—42no—
442C2×D7—42no—
443C2×D7—42no—
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—81no—
453C4×C7—81no—
454C4×C7C2×C4×D411yescharacteristic
455C4×C7C4×#4111yescharacteristic
456C4×C7#52911yescharacteristic
457C4×C7#53211yescharacteristic
458Dic7—42no—
459Dic7—42no—
460Dic7—42no—
461C24—141no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8C2×C4×D712yes—
473C2×Q8C2×C4×D712yes—
474C2×D4—72no—
475C2×D4—72no—
476C2×D4—72no—
477C2×D4—141no—
478C2×D4—141no—
479C2×D4—141no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—144no—
485C22×C4—141no—
486C22×C4—141no—
487C22×C4—141no—
488C22×C4—144no—
489C22×C4—144no—
490C22×C4—561no—
491C22×C4—561no—
492C22×C4—561no—
493C22×C4—561no—
494C22×C4—561no—
495C22×C4—561no—
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—24no—
518C4⋊C4—24no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—42no—
525C4⋊C4—72no—
526C4⋊C4—72no—
527C4⋊C4—72no—
528C4⋊C4—141no—
529C4⋊C4—141no—
530C4⋊C4—141no—
531C22⋊C4—144no—
532C22⋊C4—144no—
533C22⋊C4—144no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—42no—
538C42—561no—
539C42—561no—
540C42—561no—
541C42C2×C4×D712yes—
542C42#115712yes—
543C42D4×D712yes—
544C42#115912yes—
545C2×C7C4×#12111yescharacteristic
546C2×C7#294711yescharacteristic
547C2×C7#294911yescharacteristic
548C2×C7#304211yescharacteristic
549C2×C7#304611yescharacteristic
550C2×C7#312011yescharacteristic
551C2×C7#312311yescharacteristic
552D7—44no—
553C23—142no—
554C23—142no—
555C23—142no—
556C23—281no—
557C23—281no—
558C23—281no—
559C23—281no—
560C23C22×C22⋊D711yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569D4—74no—
570D4—142no—
571D4—142no—
572D4—142no—
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—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—142no—
600C2×C4—142no—
601C2×C4—142no—
602C2×C4—281no—
603C2×C4—281no—
604C2×C4—281no—
605C2×C4—281no—
606C2×C4—281no—
607C2×C4—281no—
608C2×C4—564no—
609C2×C4—564no—
610C2×C4—564no—
611C2×C4C4×C22⋊D712yes—
612C2×C4C4×C22⋊D712yes—
613C2×C4#650112yes—
614C2×C4#650112yes—
615C2×C4C22×C4×D711yescharacteristic
616C2×C4C2×#115711yescharacteristic
617C2×C4C2×D4×D711yescharacteristic
618C2×C4C2×#115911yescharacteristic
619C2×C4D7×#4111yescharacteristic
620C2×C4D7×#4111yescharacteristic
621C8—142no—
622C8—142no—
623C8—281no—
624C8—281no—
625C7#2151411yescharacteristic, complemented, Sylow
626C22—144no—
627C22—282no—
628C22—282no—
629C22—282no—
630C22—282no—
631C22—282no—
632C22—282no—
633C22C2×C4×C22⋊D711yescharacteristic
634C22C2×#650111yescharacteristic
635C22#9051911yescharacteristic
636C22#9052811yescharacteristic
637C22#9052811yescharacteristic
638C22#9052811yescharacteristic
639C22#9052911yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—42no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—282no—
651C4—282no—
652C4—282no—
653C4C4×#115911yescharacteristic
654C4C4×D4×D711yescharacteristic
655C4#9023911yescharacteristic
656C4#9024811yescharacteristic
657C2—284no—
658C2C4×#650111yescharacteristic
659C2#1173999211yescharacteristic
660C2#1173999311yescharacteristic
661C2#1174085011yescharacteristic
662C2#1174085111yescharacteristic
663C2#1174089111yescharacteristic
664C2#1174089211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC7×#2327C2
socleC23×C7C22×D4
prime radicalC22×D28C23
cosocleC22×C4×C7C24
hypercenter#2327D7
hypocenterC7#21514
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ #376 ◁ #2327

Complements

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

NH ≅ G/Ntype
1. C7×#2327C2semidirect
6. #11729532C2semidirect
7. #11729385C2semidirect
8. C4×#6409C2semidirect
11. #11727421C2semidirect
12. #11727420C2semidirect
14. #11727294C2semidirect
15. #11727190C2semidirect
38. #89855C4semidirect
70. C7×C4⋊Q8C2×C4semidirect
125. #6409C2×C4semidirect
126. #6409C2×C4semidirect
135. C4⋊(C7⋊C8)C2×C4semidirect
141. #2327D7semidirect
372. C4⋊Q8C4×D7semidirect
625. C7#21514semidirect

Maximal subgroups

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

subgroupindex
C7×#23272
C2×#898552
C2×#897982
C2×C4×#11432
#117308572
#117295322
#117293852
C4×#64092
#117274412
#117274212
#117274202
#117273102
#117272942
#117271902
#215147