Finite Group Databasebeta

← #13360506

Subgroups — #13360506

Order 1792.

1002 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C7×C22⋊Q8C211yesmaximal, characteristic
2C2×#89824C211yesmaximal, characteristic
3C2×#89802C211yesmaximal, characteristic, complemented
4C4×#6487C211yesmaximal, characteristic
5C2×C4×#1136C211yesmaximal, characteristic
6#11729451C211yesmaximal, characteristic
7#11729385C211yesmaximal, characteristic, complemented
8#11727431C211yesmaximal, characteristic, complemented
9#11727428C211yesmaximal, characteristic, complemented
10#11727372C211yesmaximal, characteristic, complemented
11#11727368C211yesmaximal, characteristic, complemented
12#11727270C211yesmaximal, characteristic
13#11727267C211yesmaximal, characteristic
14#11727235C211yesmaximal, characteristic, complemented
15#11727229C211yesmaximal, characteristic, complemented
16C2×C7×C22⋊Q8C2211yescharacteristic
17C2×C4×C7×Q8C2211yescharacteristic
18C22×C42×C7C2211yescharacteristic
19C22×#1144C2211yescharacteristic
20C2×#6487C2211yescharacteristic
21C22×#1136C2211yescharacteristic
22C22×#1136C2211yescharacteristic
23C2×C4×Dic14C2211yescharacteristic
24C7×#391C2211yescharacteristic
25C7×#389C2211yescharacteristic
26C7×#387—21no—
27C7×#385—21no—
28C7×#380C2211yescharacteristic
29C4×C7×C4⋊C4—21no—
30C4×C7×C4⋊C4C2211yescharacteristic
31C4×C7×C22⋊C4—21no—
32C2×#6409C2211yescharacteristic
33C2×#6409C2211yescharacteristic
34C2×#6409C2211yescharacteristic
35#89984C2211yescharacteristic
36#89982—21no—
37C4×C22⋊Dic7—21no—
38#89824C418yescomplemented
39#89802—24no—
40C2×#6384C2211yescharacteristic
41C2×#6384C2211yescharacteristic
42C2×#6384C2211yescharacteristic
43C2×#6382C2211yescharacteristic
44C2×#6382C2211yescharacteristic
45C2×#6381C2211yescharacteristic
46C4×C4⋊Dic7C2211yescharacteristic
47#89705—21no—
48C4×Dic7⋊C4—21no—
49#89701C2211yescharacteristic
50#89700C2211yescharacteristic
51C4×#1136—24no—
52C2×#6377C2211yescharacteristic
53C2×#6377C2211yescharacteristic
54C2×C4×C7⋊C8C2211yescharacteristic
55C2×C4×C7⋊C8C2211yescharacteristic
56#89324C2211yescharacteristic
57#89324C2211yescharacteristic
58#89324C2211yescharacteristic
59#89324C2211yescharacteristic
60#89324C2211yescharacteristic
61#89324C2211yescharacteristic
62#21539—71nomaximal, Sylow
63C22×C7×Q8C2311yescharacteristic
64C23×C4×C7D411yescharacteristic
65C23×C4×C7D411yescharacteristic
66C23×C4×C7C2311yescharacteristic
67C22×Dic14C2311yescharacteristic
68C7×C22⋊Q8—22no—
69C7×C22⋊Q8C2×C414yes—
70C4×C7×Q8—22no—
71C4×C7×Q8—22no—
72C2×C7×C4⋊C4—21no—
73C2×C7×C4⋊C4—21no—
74C2×C7×C4⋊C4—21no—
75C2×C7×C4⋊C4C2311yescharacteristic
76C2×C7×C4⋊C4C2311yescharacteristic
77C2×C7×C4⋊C4C2311yescharacteristic
78C2×C7×C22⋊C4—21no—
79C2×C7×C22⋊C4—21no—
80C2×C42×C7—22no—
81C2×C42×C7—22no—
82C2×C42×C7—21no—
83C2×C42×C7—21no—
84C2×C42×C7D411yescharacteristic
85C2×C42×C7D411yescharacteristic
86C2×C42×C7C2311yescharacteristic
87C2×C42×C7C2311yescharacteristic
88C2×C22⋊Dic7—21no—
89C2×C22⋊Dic7—21no—
90C2×#1144—22no—
91C2×#1144—22no—
92C2×#1144C2×C414yescomplemented
93C2×C4⋊Dic7C2311yescharacteristic
94C2×C4⋊Dic7C2311yescharacteristic
95C2×C4⋊Dic7C2311yescharacteristic
96#6487—22no—
97#6487C2×C414yes—
98C2×Dic7⋊C4—21no—
99C2×Dic7⋊C4—21no—
100C2×Dic7⋊C4—21no—
101C2×C4×Dic7—21no—
102C2×C4×Dic7—21no—
103C2×#1136—22no—
104C2×#1136—22no—
105C2×#1136—22no—
106C2×#1136—22no—
107C2×#1136—22no—
108C2×#1136C2×C414yes—
109C22×C7⋊C8C2311yescharacteristic
110C22×C7⋊C8C2311yescharacteristic
111C22×C7⋊C8C2311yescharacteristic
112C22×C7⋊C8C2311yescharacteristic
113C4×Dic14—22no—
114C4×Dic14—22no—
115C7×#95—21no—
116C7×#95—21no—
117C7×#95—21no—
118C7×#95—21no—
119C7×#95—21no—
120#6409—22no—
121#6409—22no—
122#6409C2×C414yescomplemented
123C7⋊#95—21no—
124C7⋊#95—21no—
125C7⋊#95—21no—
126C7⋊#95—21no—
127C7⋊#95—21no—
128#6384—22no—
129#6384—22no—
130#6384C2×C414yescomplemented
131#6382—22no—
132#6382C2×C414yescomplemented
133#6381—22no—
134#6377—22no—
135#6377D414yes—
136C4×C7⋊C8—22no—
137C4×C7⋊C8—22no—
138C2×#470—71no—
139C2×#441—71no—
140C2×C4×M16—71no—
141C4×C22⋊Q8—71no—
142C4×C22⋊Q8D711yescharacteristic
143#1969—71no—
144#1941—71no—
145#1933—71no—
146#1933—71no—
147#1894—71no—
148#1894—71no—
149#1809—71no—
150#1776—71no—
151#1763—71no—
152#1763—71no—
153C24×C7C2×D411yescharacteristic
154C2×C7×Q8—21no—
155C2×C7×Q8—21no—
156C2×C7×Q8—21no—
157C2×C7×Q8—21no—
158C2×C7×Q8—21no—
159C2×C7×Q8C22×C412yes—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C22×C4×C7—21no—
165C22×C4×C7—21no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—21no—
171C22×C4×C7—21no—
172C22×C4×C7—41no—
173C22×C4×C7—41no—
174C22×C4×C7C22×C412yes—
175C22×C4×C7C2×D411yescharacteristic
176C22×C4×C7C2×D411yescharacteristic
177C22×C4×C7C2×D411yescharacteristic
178C22×C4×C7C2×D411yescharacteristic
179C22×C4×C7C2×D411yescharacteristic
180C22×C4×C7#4112yes—
181C22×C4×C7C2411yescharacteristic
182C22×Dic7—21no—
183C22×Dic7—21no—
184C22×Dic7—21no—
185C22×Dic7—21no—
186C2×Dic14—21no—
187C2×Dic14—21no—
188C2×Dic14—21no—
189C2×Dic14—21no—
190C2×Dic14—21no—
191C2×Dic14C22×C412yes—
192C7×C4⋊C4—24no—
193C7×C4⋊C4—21no—
194C7×C4⋊C4—21no—
195C7×C4⋊C4—21no—
196C7×C4⋊C4—21no—
197C7×C4⋊C4—21no—
198C7×C4⋊C4—42no—
199C7×C4⋊C4—42no—
200C7×C4⋊C4C22×C412yes—
201C7×C22⋊C4—24no—
202C7×C22⋊C4—42no—
203C42×C7—22no—
204C42×C7—22no—
205C42×C7—21no—
206C42×C7—21no—
207C42×C7—42no—
208C42×C7—42no—
209C42×C7C2×D412yes—
210C42×C7#4112yes—
211C22⋊Dic7—24no—
212C22⋊Dic7—42no—
213#1144—28no—
214C4⋊Dic7—21no—
215C4⋊Dic7—21no—
216C4⋊Dic7—21no—
217C4⋊Dic7—21no—
218C4⋊Dic7—21no—
219C4⋊Dic7C22×C412yes—
220Dic7⋊C4—24no—
221Dic7⋊C4—42no—
222Dic7⋊C4—42no—
223C4×Dic7—42no—
224C4×Dic7—42no—
225#1136—28no—
226#1136—28no—
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⋊C8C22×C412yes—
234C2×C7⋊C8C22×C412yes—
235C2×C7⋊C8C2×D412yes—
236C2×C7⋊C8C2×D412yes—
237C2×C7⋊C8#4112yes—
238C2×C7⋊C8#4112yes—
239C22×Q16—71no—
240C22×M16—71no—
241C22×M16—71no—
242C2×C22⋊Q8—71no—
243C2×C22⋊Q8C2×D711yescharacteristic
244C2×C4×Q8—71no—
245C2×C4×Q8C2×D711yescharacteristic
246C22×C42C2×D711yescharacteristic
247#470—78no—
248#441—144no—
249C2×#107—71no—
250C2×#106—71no—
251C2×#106—71no—
252C2×#103—71no—
253C2×#103—71no—
254C2×#103—71no—
255C2×#103—71no—
256C2×#103—71no—
257C2×#103—71no—
258C4×M16—144no—
259C2×#97—71no—
260C2×#97—71no—
261C2×C4×C8—71no—
262C2×C4×C8—71no—
263#391—71no—
264#391C2×D711yescharacteristic
265#389—71no—
266#389C2×D711yescharacteristic
267#387—21no—
268#387—141no—
269#385—21no—
270#385—141no—
271#380—71no—
272#380C2×D711yescharacteristic
273C4×C4⋊C4—21no—
274C4×C4⋊C4—71no—
275C4×C4⋊C4—141no—
276C4×C4⋊C4C2×D711yescharacteristic
277C4×C22⋊C4—21no—
278C4×C22⋊C4—141no—
279#340—71no—
280#340—71no—
281#340—71no—
282#340—71no—
283#340—71no—
284#340—71no—
285C23×C7—21no—
286C23×C7—21no—
287C23×C7—21no—
288C23×C7—21no—
289C23×C7—21no—
290C23×C7—21no—
291C23×C7C4×D412yes—
292C23×C7C22×D411yescharacteristic
293C7×Q8—22no—
294C7×Q8—22no—
295C7×Q8—41no—
296C7×Q8—41no—
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—21no—
304C2×C4×C7—21no—
305C2×C4×C7—21no—
306C2×C4×C7—21no—
307C2×C4×C7—22no—
308C2×C4×C7—22no—
309C2×C4×C7—22no—
310C2×C4×C7—22no—
311C2×C4×C7—22no—
312C2×C4×C7—22no—
313C2×C4×C7—44no—
314C2×C4×C7—44no—
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×C7#12112yes—
327C2×C4×C7#12112yes—
328C2×C4×C7#13712yes—
329C2×C4×C7#13712yes—
330C2×C4×C7C23×C411yescharacteristic
331C2×C4×C7C22×D411yescharacteristic
332C2×C4×C7C2×#4111yescharacteristic
333C2×C4×C7C2×#4111yescharacteristic
334C2×C4×C7C2×#4111yescharacteristic
335C2×C4×C7C2×#4111yescharacteristic
336C2×Dic7—22no—
337C2×Dic7—22no—
338C2×Dic7—41no—
339C2×Dic7—41no—
340C2×Dic7—41no—
341C2×Dic7—41no—
342C2×Dic7—41no—
343C2×Dic7—41no—
344C2×Dic7—41no—
345C2×Dic7—41no—
346C2×Dic7—41no—
347C2×Dic7—41no—
348Dic14—22no—
349Dic14—22no—
350Dic14—41no—
351Dic14—41no—
352C7⋊C8—22no—
353C7⋊C8—22no—
354C7⋊C8—22no—
355C7⋊C8C4×D414yes—
356C22×Q8—71no—
357C22×Q8C22×D711yescharacteristic
358C23×C4C22⋊D711yescharacteristic
359C23×C4C22⋊D711yescharacteristic
360C23×C4C22×D711yescharacteristic
361C2×Q16—74no—
362C2×Q16—142no—
363C2×Q16—142no—
364C2×M16—74no—
365C2×M16—142no—
366C2×M16—142no—
367C2×M16—142no—
368C2×M16—142no—
369C2×M16—142no—
370C22×C8—71no—
371C22×C8—71no—
372C22×C8—71no—
373C22×C8—71no—
374C22⋊Q8—22no—
375C22⋊Q8—74no—
376C22⋊Q8—142no—
377C22⋊Q8C4×D714yes—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—142no—
381C4×Q8—142no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—71no—
386C2×C4⋊C4—71no—
387C2×C4⋊C4—71no—
388C2×C4⋊C4—141no—
389C2×C4⋊C4—141no—
390C2×C4⋊C4—141no—
391C2×C4⋊C4C22×D711yescharacteristic
392C2×C4⋊C4C22×D711yescharacteristic
393C2×C4⋊C4C22×D711yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—141no—
397C2×C22⋊C4—141no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—141no—
403C2×C42—141no—
404C2×C42C22⋊D711yescharacteristic
405C2×C42C22⋊D711yescharacteristic
406C2×C42C22×D711yescharacteristic
407C2×C42C22×D711yescharacteristic
408#107—142no—
409#106—74no—
410#106—142no—
411#103—74no—
412#103—74no—
413#103—142no—
414#103—142no—
415#103—142no—
416#103—142no—
417#97—74no—
418#97—142no—
419C4×C8—142no—
420C4×C8—142no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—141no—
427#95—141no—
428#95—141no—
429#95—141no—
430#95—141no—
431C22×C7—22no—
432C22×C7—22no—
433C22×C7—22no—
434C22×C7—41no—
435C22×C7—41no—
436C22×C7—41no—
437C22×C7—41no—
438C22×C7C2×C4×D411yescharacteristic
439C22×C7C2×#12111yescharacteristic
440C22×C7#53211yescharacteristic
441C22×C7C2×#13711yescharacteristic
442C22×C7C2×#13711yescharacteristic
443C22×C7#57511yescharacteristic
444C22×C7#57511yescharacteristic
445C4×C7—22no—
446C4×C7—22no—
447C4×C7—22no—
448C4×C7—22no—
449C4×C7—22no—
450C4×C7—42no—
451C4×C7—42no—
452C4×C7—81no—
453C4×C7—81no—
454C4×C7C2×C4×D411yescharacteristic
455C4×C7C4×#4111yescharacteristic
456C4×C7#52511yescharacteristic
457C4×C7#52911yescharacteristic
458Dic7—42no—
459Dic7—42no—
460Dic7—81no—
461Dic7—81no—
462C24C2×C22⋊D711yescharacteristic
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—72no—
469C2×Q8—141no—
470C2×Q8—141no—
471C2×Q8—141no—
472C2×Q8—141no—
473C2×Q8—141no—
474C2×Q8C2×C4×D712yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—141no—
490C22×C4—141no—
491C22×C4—141no—
492C22×C4—141no—
493C22×C4C2×C4×D712yes—
494C22×C4#115712yes—
495C22×C4C2×C22⋊D711yescharacteristic
496C22×C4C2×C22⋊D711yescharacteristic
497C22×C4C2×C22⋊D711yescharacteristic
498C22×C4C2×C22⋊D711yescharacteristic
499C22×C4C2×C22⋊D711yescharacteristic
500C22×C4C23×D711yescharacteristic
501Q16—148no—
502M16—148no—
503M16—148no—
504C2×C8—72no—
505C2×C8—72no—
506C2×C8—72no—
507C2×C8—72no—
508C2×C8—72no—
509C2×C8—72no—
510C2×C8—141no—
511C2×C8—141no—
512C2×C8—141no—
513C2×C8—141no—
514C2×C8—141no—
515C2×C8—141no—
516C4⋊C4—24no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—72no—
525C4⋊C4—144no—
526C4⋊C4—141no—
527C4⋊C4—141no—
528C4⋊C4—141no—
529C4⋊C4—141no—
530C4⋊C4—141no—
531C4⋊C4—282no—
532C4⋊C4—282no—
533C4⋊C4C2×C4×D712yes—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—144no—
537C22⋊C4—282no—
538C42—22no—
539C42—22no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—42no—
544C42—282no—
545C42—282no—
546C42D4×D712yes—
547C42#115912yes—
548C2×C7—42no—
549C2×C7C4×#12111yescharacteristic
550C2×C7C4×#13711yescharacteristic
551C2×C7C4×#13711yescharacteristic
552C2×C7#305611yescharacteristic
553C2×C7#305611yescharacteristic
554C2×C7#318311yescharacteristic
555C2×C7#318511yescharacteristic
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23C4×C22⋊D712yes—
563C23C22×C22⋊D711yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—142no—
569Q8—142no—
570Q8—281no—
571Q8—281no—
572C2×C4—21no—
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—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—44no—
589C2×C4—44no—
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—41no—
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—281no—
609C2×C4—281no—
610C2×C4—281no—
611C2×C4—281no—
612C2×C4C4×C22⋊D712yes—
613C2×C4#650212yes—
614C2×C4#650212yes—
615C2×C4#650512yes—
616C2×C4#651412yes—
617C2×C4C22×C4×D711yescharacteristic
618C2×C4C2×#115711yescharacteristic
619C2×C4C2×D4×D711yescharacteristic
620C2×C4C2×#115911yescharacteristic
621C2×C4D7×#4111yescharacteristic
622C2×C4D7×#4111yescharacteristic
623C8—74no—
624C8—142no—
625C8—142no—
626C8—142no—
627C7#2153911yescharacteristic, complemented, Sylow
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×C4×C22⋊D711yescharacteristic
636C22C2×#650211yescharacteristic
637C22C2×#650511yescharacteristic
638C22#9051311yescharacteristic
639C22#9051311yescharacteristic
640C22C2×#651411yescharacteristic
641C22#9052311yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—42no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—282no—
652C4—282no—
653C4—561no—
654C4—561no—
655C4C4×#115911yescharacteristic
656C4#9022911yescharacteristic
657C4C4×D4×D711yescharacteristic
658C4#9023811yescharacteristic
659C2—42no—
660C2C4×#650211yescharacteristic
661C2C4×#650511yescharacteristic
662C2C4×#651411yescharacteristic
663C2#1174017711yescharacteristic
664C2#1174037011yescharacteristic
665C2#1174058411yescharacteristic
666C2#1174079311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutatorC2×C4×C7C23×C4
FrattiniC22×C4C23×D7
FittingC4×C7×C22⋊Q8C2
socleC23×C7C22×D4
prime radicalC24×C7C2×D4
cosocleC22×C4×C7C24
hypercenterC4×C22⋊Q8D7
hypocenterC7#21539
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#89802C2semidirect
7. #11729385C2semidirect
8. #11727431C2semidirect
9. #11727428C2semidirect
10. #11727372C2semidirect
11. #11727368C2semidirect
14. #11727235C2semidirect
15. #11727229C2semidirect
38. #89824C4semidirect
92. C2×#1144C2×C4semidirect
122. #6409C2×C4semidirect
130. #6384C2×C4semidirect
132. #6382C2×C4semidirect
627. C7#21539semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C22⋊Q82
C2×#898242
C2×#898022
C4×#64872
C2×C4×#11362
#117294512
#117293852
#117274312
#117274282
#117273722
#117273682
#117272702
#117272672
#117272352
#117272292
#215397