Finite Group Databasebeta

← #13324966

Subgroups — #13324966

Order 1792.

640 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737038C211yesmaximal, characteristic
2#11736991C211yesmaximal, characteristic, complemented
3#11736851C211yesmaximal, characteristic, complemented
4C7×#1586C211yesmaximal, characteristic, complemented
5D8×C7⋊C8C211yesmaximal, characteristic, complemented
6#11728620C211yesmaximal, characteristic, complemented
7C8×#1141C211yesmaximal, characteristic, complemented
8#11726289C211yesmaximal, characteristic, complemented
9#11726277C211yesmaximal, characteristic, complemented
10#11725930C211yesmaximal, characteristic, complemented
11#11725919C211yesmaximal, characteristic, complemented
12#11725911C211yesmaximal, characteristic, complemented
13#11725910C211yesmaximal, characteristic, complemented
14#11725834C211yesmaximal, characteristic, complemented
15#11725822C211yesmaximal, characteristic, complemented
16#90239C2211yescharacteristic
17C4×#1159C2211yescharacteristic
18C4×C7×D8C2211yescharacteristic
19C7×#436C2211yescharacteristic
20C7×C8×D4C2211yescharacteristic
21#89930C411yescharacteristic
22#89922C411yescharacteristic
23#89901—21no—
24#89900—21no—
25#89883—21no—
26C2×Dic7⋊C8—21no—
27C4×#1142C2211yescharacteristic
28C4×#1141C2211yescharacteristic
29D4×C7⋊C8C2211yescharacteristic
30D4×C7⋊C8C2211yescharacteristic
31#89657C411yescharacteristic
32#89647C411yescharacteristic
33#89610C2211yescharacteristic
34#89609C2211yescharacteristic
35#89605C2211yescharacteristic
36#89603C2211yescharacteristic
37#89553C411yescharacteristic
38#89551C411yescharacteristic
39#89534C411yescharacteristic
40#89533C411yescharacteristic
41#89502—21no—
42#89499—21no—
43(C22⋊D7)⋊C8—21no—
44#89491—21no—
45C4×#1132C2211yescharacteristic
46C8×D28C2211yescharacteristic
47#89457C2211yescharacteristic
48#89457C2211yescharacteristic
49C4×C8×D7C2211yescharacteristic
50#89451C2211yescharacteristic
51C7×#334C2211yescharacteristic
52C7×D4⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×#322C2211yescharacteristic
55D4⋊(C7⋊C8)C2211yescharacteristic
56D4⋊(C7⋊C8)C2211yescharacteristic
57#89279C2211yescharacteristic
58#89278C2211yescharacteristic
59#89275C2211yescharacteristic
60#89274C2211yescharacteristic
61#89254C2211yescharacteristic
62#89253C2211yescharacteristic
63#89251C2211yescharacteristic
64#89250C2211yescharacteristic
65C8×C7⋊C8C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18015—71nomaximal, Sylow
68C2×#1159C2×C411yescharacteristic
69C2×#1157—21no—
70C2×C7×D8C2×C411yescharacteristic
71C2×C7×M16—21no—
72C22×C7×C8—21no—
73C4×C7×D4C2311yescharacteristic
74C4×C7×D4C2311yescharacteristic
75#6503C2×C411yescharacteristic
76#6501C2×C411yescharacteristic
77D4×Dic7C2×C411yescharacteristic
78C2×#1142C2×C411yescharacteristic
79C2×#1141C2×C411yescharacteristic
80C4×C22⋊D7—21no—
81C4×C22⋊D7—21no—
82C2×C4×Dic7—21no—
83C22×C7⋊C8—21no—
84C22×C7⋊C8—21no—
85C2×#1132C2×C411yescharacteristic
86C2×#1131—21no—
87C2×#1131—21no—
88C2×C8×D7—21no—
89C2×C8×D7—21no—
90#6458C2×C411yescharacteristic
91#6455C2×C411yescharacteristic
92#6451C2×C411yescharacteristic
93#6450C2×C411yescharacteristic
94#6448—21no—
95#6447—21no—
96(C22⋊D7)⋊C4—21no—
97#6440—21no—
98C4×D28C2311yescharacteristic
99C42×D7C2311yescharacteristic
100C4×Dic14C2311yescharacteristic
101C7×#107C2×C411yescharacteristic
102C7×C4⋊C8C2311yescharacteristic
103C7×C4⋊C8C2311yescharacteristic
104C7×#102C2×C411yescharacteristic
105C7×#102C2×C411yescharacteristic
106C7×C22⋊C8—21no—
107C7×C22⋊C8—21no—
108C4×C7×C8C2311yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111#6406C2×C411yescharacteristic
112#6406C2×C411yescharacteristic
113C22⋊(C7⋊C8)—21no—
114C22⋊(C7⋊C8)—21no—
115#6395C2×C411yescharacteristic
116(C2×D7)⋊C8—21no—
117(C2×D7)⋊C8—21no—
118(C2×D7)⋊C8—21no—
119(C2×D7)⋊C8C2×C411yescharacteristic
120(C2×D7)⋊C8C2×C411yescharacteristic
121(C2×D7)⋊C8D411yescharacteristic
122(C2×D7)⋊C8D411yescharacteristic
123#6391C2×C411yescharacteristic
124#6390C2×C411yescharacteristic
125#6389—21no—
126#6389—21no—
127Dic7⋊C8—21no—
128Dic7⋊C8—21no—
129Dic7⋊C8—21no—
130Dic7⋊C8C2×C411yescharacteristic
131Dic7⋊C8C2×C411yescharacteristic
132Dic7⋊C8D411yescharacteristic
133Dic7⋊C8D411yescharacteristic
134C8×Dic7—21no—
135C8×Dic7—21no—
136#6384C2×C411yescharacteristic
137#6383C2×C411yescharacteristic
138#6382C2×C411yescharacteristic
139#6381C2×C411yescharacteristic
140C4⋊(C7⋊C8)C2311yescharacteristic
141C4⋊(C7⋊C8)C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3106—71no—
146#2990—71no—
147#2979—71no—
148#1590—71no—
149#1590—71no—
150#1586—71no—
151#1586D711yescharacteristic, complemented
152#1585—71no—
153#1585—71no—
154C8×D8—71no—
155C8×D8—71no—
156#1574—71no—
157#1492—71no—
158#1476—71no—
159#1450—71no—
160C2×C7×D4C22×C411yescharacteristic
161C2×C7×D4C22×C411yescharacteristic
162C22×C4×C7—21no—
163C22×C4×C7—21no—
164C2×C22⋊D7—21no—
165C2×C22⋊D7—21no—
166C2×C22⋊D7—21no—
167C2×C22⋊D7—21no—
168C22×Dic7—21no—
169C22×Dic7—21no—
170#1159—22no—
171#1159—41no—
172#1157—81no—
173#1157—81no—
174C2×D28—21no—
175C2×D28C22×C411yescharacteristic
176C2×C4×D7—21no—
177C2×C4×D7C22×C411yescharacteristic
178C2×C4×D7C2×D411yescharacteristic
179C2×C4×D7#4111yescharacteristic
180C2×Dic14—21no—
181C2×Dic14C22×C411yescharacteristic
182C7×D8—22no—
183C7×M16—81no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8—21no—
187C2×C7×C8—81no—
188C2×C7×C8C22×C411yescharacteristic
189C2×C7×C8C22×C411yescharacteristic
190C2×C7×C8C2×D411yescharacteristic
191C2×C7×C8C2×D411yescharacteristic
192C7×C4⋊C4C22×C411yescharacteristic
193C7×C4⋊C4C22×C411yescharacteristic
194C7×C22⋊C4—21no—
195C7×C22⋊C4—21no—
196C42×C7C2411yescharacteristic
197C22⋊Dic7—21no—
198C22⋊Dic7—21no—
199#1142—41no—
200#1141—22no—
201(C2×D7)⋊C4—21no—
202(C2×D7)⋊C4—21no—
203(C2×D7)⋊C4—21no—
204C4⋊Dic7C22×C411yescharacteristic
205C4⋊Dic7C22×C411yescharacteristic
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208Dic7⋊C4—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C4×Dic7—21no—
212C4×Dic7C22×C411yescharacteristic
213C4×Dic7C2×D411yescharacteristic
214C4×Dic7#4111yescharacteristic
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—21no—
218C2×C7⋊C8—81no—
219C2×C7⋊C8—81no—
220C2×C7⋊C8C22×C411yescharacteristic
221C2×C7⋊C8C22×C411yescharacteristic
222C2×C7⋊C8C2×D411yescharacteristic
223C2×C7⋊C8C2×D411yescharacteristic
224#1132—41no—
225#1131—81no—
226#1131—81no—
227C8×D7—24no—
228C8×D7—81no—
229#532—71no—
230C4×#41—71no—
231#482—71no—
232#482—71no—
233#477—71no—
234#476—71no—
235#460—71no—
236#459—71no—
237#449—71no—
238#449—71no—
239#446—71no—
240#446—71no—
241C4×SD16—71no—
242C4×SD16—71no—
243C4×D8—71no—
244C4×D8C2×D711yescharacteristic
245#436—71no—
246#436—141no—
247#436C2×D711yescharacteristic
248#435—141no—
249#435—141no—
250C8×D4—71no—
251C8×D4—71no—
252C8×D4—71no—
253C8×D4—141no—
254C8×D4C2×D711yescharacteristic
255#432—141no—
256#431—71no—
257#431—71no—
258#431—71no—
259#423—71no—
260C2×C4⋊C8—141no—
261#408—141no—
262#408—141no—
263C2×C4×C8—71no—
264#335—71no—
265#335—71no—
266#334—71no—
267#334C2×D711yescharacteristic
268Q8⋊C8—71no—
269Q8⋊C8—71no—
270D4⋊C8—71no—
271D4⋊C8—71no—
272D4⋊C8—71no—
273D4⋊C8—71no—
274D4⋊C8C2×D711yescharacteristic
275D4⋊C8C2×D711yescharacteristic
276#322—71no—
277#322C2×D711yescharacteristic
278C82—71no—
279C82—71no—
280C23×C7—21no—
281C23×C7—21no—
282C22×D7—21no—
283C22×D7C4×D411yescharacteristic
284C7×D4—21no—
285C7×D4—21no—
286C7×D4—21no—
287C7×D4#13112yes—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—41no—
291C2×C4×C7—41no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7C23×C411yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C22⋊D7—42no—
298C22⋊D7—42no—
299C22⋊D7—81no—
300C22⋊D7—81no—
301C2×Dic7—21no—
302C2×Dic7—21no—
303C2×Dic7—21no—
304C2×Dic7—42no—
305C2×Dic7—42no—
306C2×Dic7C4×D411yescharacteristic
307C2×Dic7C4×D411yescharacteristic
308C2×Dic7C4×D411yescharacteristic
309D28—21no—
310D28—21no—
311D28—81no—
312C4×D7—21no—
313C4×D7—21no—
314C4×D7—21no—
315C4×D7—21no—
316C4×D7—22no—
317C4×D7—41no—
318C4×D7—41no—
319Dic14—21no—
320Dic14—21no—
321Dic14—81no—
322C7×C8—22no—
323C7×C8—21no—
324C7×C8—21no—
325C7×C8—21no—
326C7×C8—21no—
327C7×C8—41no—
328C7×C8—41no—
329C7⋊C8—22no—
330C7⋊C8—21no—
331C7⋊C8—21no—
332C7⋊C8—21no—
333C7⋊C8—21no—
334C7⋊C8—41no—
335C7⋊C8—41no—
336C2×#41—71no—
337C2×#41—141no—
338C2×SD16—71no—
339C2×SD16—71no—
340C2×D8—71no—
341C2×D8C4×D711yescharacteristic
342C2×M16—21no—
343C2×M16—141no—
344C2×M16—141no—
345C22×C8—21no—
346C22×C8—141no—
347C22×C8—141no—
348C22×C8—141no—
349C22×C8—141no—
350C4⋊Q8—71no—
351#127—71no—
352#124—141no—
353#121—71no—
354#121—71no—
355#121—141no—
356C4×Q8—71no—
357C4×Q8—71no—
358C4×D4—71no—
359C4×D4—71no—
360C4×D4—141no—
361C4×D4—141no—
362C4×D4—141no—
363C4×D4C22×D711yescharacteristic
364C4×D4C22×D711yescharacteristic
365#117—71no—
366#117—141no—
367C2×C42—71no—
368C2×C42—141no—
369#107—71no—
370#107C4×D711yescharacteristic
371#106—71no—
372#106—71no—
373C4⋊C8—71no—
374C4⋊C8—71no—
375C4⋊C8—71no—
376C4⋊C8—71no—
377C4⋊C8—71no—
378C4⋊C8—71no—
379C4⋊C8—141no—
380C4⋊C8—141no—
381C4⋊C8—141no—
382C4⋊C8C22×D711yescharacteristic
383C4⋊C8C22×D711yescharacteristic
384#103—71no—
385#103—71no—
386#102—71no—
387#102—71no—
388#102—71no—
389#102—71no—
390#102C4×D711yescharacteristic
391#102C4×D711yescharacteristic
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—71no—
395C22⋊C8—71no—
396C22⋊C8—71no—
397C22⋊C8—71no—
398C22⋊C8—141no—
399C22⋊C8—141no—
400C22⋊C8—141no—
401C22⋊C8—141no—
402C22⋊C8—141no—
403#97—141no—
404#97—141no—
405C4×C8—71no—
406C4×C8—71no—
407C4×C8—71no—
408C4×C8—141no—
409C4×C8—141no—
410C4×C8C22×D711yescharacteristic
411C4×C8C22×D711yescharacteristic
412C4×C8C22×D711yescharacteristic
413C22×C7—22no—
414C22×C7—41no—
415C22×C7—41no—
416C22×C7—41no—
417C22×C7—41no—
418C22×C7—41no—
419C22×C7C2×C4×D411yescharacteristic
420C2×D7—21no—
421C2×D7—21no—
422C2×D7—21no—
423C2×D7—41no—
424C2×D7—41no—
425C2×D7—41no—
426C4×C7—21no—
427C4×C7—41no—
428C4×C7—41no—
429C4×C7C2×#13111yescharacteristic
430C4×C7#56811yescharacteristic
431C4×C7#57611yescharacteristic
432C4×C7#57711yescharacteristic
433Dic7—21no—
434Dic7—21no—
435Dic7—41no—
436Dic7—41no—
437Dic7—41no—
438Dic7#44312yes—
439#41—142no—
440#41—281no—
441#41—561no—
442#41—561no—
443C2×Q8—71no—
444C2×Q8—141no—
445C2×D4—71no—
446C2×D4—141no—
447C2×D4—141no—
448C2×D4—141no—
449C2×D4—141no—
450C2×D4—141no—
451C2×D4C2×C4×D711yescharacteristic
452C2×D4C2×C4×D711yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—71no—
456C22×C4—71no—
457C22×C4—71no—
458C22×C4—141no—
459C22×C4—141no—
460C22×C4—141no—
461SD16—281no—
462SD16—281no—
463D8—22no—
464D8—142no—
465M16—81no—
466M16—561no—
467M16—561no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—71no—
472C2×C8—71no—
473C2×C8—71no—
474C2×C8—71no—
475C2×C8—81no—
476C2×C8—144no—
477C2×C8—141no—
478C2×C8—141no—
479C2×C8—141no—
480C2×C8—561no—
481C2×C8—561no—
482C2×C8—561no—
483C2×C8C2×C4×D711yescharacteristic
484C2×C8C2×C4×D711yescharacteristic
485C2×C8D4×D711yescharacteristic
486C2×C8D4×D711yescharacteristic
487C4⋊C4—71no—
488C4⋊C4—71no—
489C4⋊C4—141no—
490C4⋊C4—141no—
491C4⋊C4—141no—
492C4⋊C4C2×C4×D711yescharacteristic
493C4⋊C4C2×C4×D711yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—141no—
497C22⋊C4—141no—
498C22⋊C4—141no—
499C22⋊C4—141no—
500C22⋊C4—141no—
501C42—71no—
502C42—71no—
503C42—71no—
504C42—141no—
505C42—141no—
506C42—141no—
507C42C23×D711yescharacteristic
508C2×C7—42no—
509C2×C7—81no—
510C2×C7#293311yescharacteristic
511C2×C7#294611yescharacteristic
512C2×C7C2×#44311yescharacteristic
513D7—41no—
514D7—81no—
515C23—21no—
516C23—21no—
517C23—71no—
518C23—141no—
519Q8—141no—
520Q8—141no—
521Q8—561no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—141no—
526D4—141no—
527D4—282no—
528D4—282no—
529D4—561no—
530D4—561no—
531D4—561no—
532D4#647012yes—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—71no—
540C2×C4—71no—
541C2×C4—71no—
542C2×C4—142no—
543C2×C4—141no—
544C2×C4—141no—
545C2×C4—141no—
546C2×C4—141no—
547C2×C4—141no—
548C2×C4—141no—
549C2×C4—141no—
550C2×C4—282no—
551C2×C4—282no—
552C2×C4—281no—
553C2×C4—281no—
554C2×C4C22×C4×D711yescharacteristic
555C2×C4C2×D4×D711yescharacteristic
556C2×C4D7×#4111yescharacteristic
557C8—22no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—142no—
565C8—141no—
566C8—141no—
567C8—141no—
568C8—141no—
569C8—281no—
570C8—281no—
571C7#1801511yescharacteristic, complemented, Sylow
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—141no—
579C22—141no—
580C22—141no—
581C22—281no—
582C22—281no—
583C22—281no—
584C22C4×D4×D711yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—72no—
589C4—141no—
590C4—141no—
591C4—281no—
592C4—281no—
593C4—281no—
594C4C2×#647011yescharacteristic
595C4#9044111yescharacteristic
596C4#9046511yescharacteristic
597C4#9046611yescharacteristic
598C2—42no—
599C2—81no—
600C2—281no—
601C2—561no—
602C2#1173692611yescharacteristic
603C2#1173731111yescharacteristic
604C2D7×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1586C2
socleC22×C7C2×C4×D4
prime radical#11737038C2
cosocleC42×C7C24
hypercenter#1586D7
hypocenterC7#18015
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #11736991C2semidirect
3. #11736851C2semidirect
4. C7×#1586C2semidirect
5. D8×C7⋊C8C2semidirect
6. #11728620C2semidirect
7. C8×#1141C2semidirect
8. #11726289C2semidirect
9. #11726277C2semidirect
10. #11725930C2semidirect
11. #11725919C2semidirect
12. #11725911C2semidirect
13. #11725910C2semidirect
14. #11725834C2semidirect
15. #11725822C2semidirect
151. #1586D7semidirect
571. C7#18015semidirect

Maximal subgroups

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

subgroupindex
#117370382
#117369912
#117368512
C7×#15862
D8×C7⋊C82
#117286202
C8×#11412
#117262892
#117262772
#117259302
#117259192
#117259112
#117259102
#117258342
#117258222
#180157