Finite Group Databasebeta

← #13325167

Subgroups — #13325167

Order 1792.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737409C211yesmaximal, characteristic, complemented
2#11737098C211yesmaximal, characteristic
3#11736991C211yesmaximal, characteristic
4C7×#1592C211yesmaximal, characteristic, complemented
5#11728707C211yesmaximal, characteristic, complemented
6#11728651C211yesmaximal, characteristic, complemented
7#11728618C211yesmaximal, characteristic, complemented
8#11726327C211yesmaximal, characteristic, complemented
9#11726316C211yesmaximal, characteristic, complemented
10#11725985C211yesmaximal, characteristic, complemented
11#11725978C211yesmaximal, characteristic, complemented
12#11725933C211yesmaximal, characteristic
13#11725903C211yesmaximal, characteristic, complemented
14#11725830C211yesmaximal, characteristic, complemented
15#11725828C211yesmaximal, characteristic, complemented
16C4×Q8×D7C2211yescharacteristic
17#90239C2211yescharacteristic
18C7×#446C2211yescharacteristic
19C4×C7×SD16C2211yescharacteristic
20C7×#436C2211yescharacteristic
21#89942C411yescharacteristic
22#89935C411yescharacteristic
23#89901—21no—
24#89900—21no—
25C4×#1143C2211yescharacteristic
26#89796C2211yescharacteristic
27C4×#1142C2211yescharacteristic
28D4×C7⋊C8C2211yescharacteristic
29#89635C411yescharacteristic
30#89626C411yescharacteristic
31#89610C2211yescharacteristic
32#89607C2211yescharacteristic
33#89605—21no—
34#89605C2211yescharacteristic
35#89602C2211yescharacteristic
36#89600—21no—
37#89578C411yescharacteristic
38#89563C411yescharacteristic
39#89549C411yescharacteristic
40#89534C411yescharacteristic
41#89499—21no—
42(C22⋊D7)⋊C8—21no—
43#89477—21no—
44#89473—21no—
45C4×#1132C2211yescharacteristic
46C8×D28C2211yescharacteristic
47#89457C2211yescharacteristic
48#89457C2211yescharacteristic
49#89457C2211yescharacteristic
50C8×Dic14C2211yescharacteristic
51C7×#335C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×#322C2211yescharacteristic
55Q8⋊(C7⋊C8)C2211yescharacteristic
56D4⋊(C7⋊C8)C2211yescharacteristic
57#89279C2211yescharacteristic
58#89278C2211yescharacteristic
59#89275C2211yescharacteristic
60#89275C2211yescharacteristic
61#89254C2211yescharacteristic
62#89253C2211yescharacteristic
63#89251C2211yescharacteristic
64#89250C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18030—71nomaximal, Sylow
68C2×Q8×D7C2×C411yescharacteristic
69C2×#1157—21no—
70C2×C7×SD16C2×C411yescharacteristic
71C2×C7×M16—21no—
72C4×C7×Q8C2311yescharacteristic
73C4×C7×D4C2311yescharacteristic
74Q8×Dic7C2×C411yescharacteristic
75C2×#1143C2×C411yescharacteristic
76#6503C2×C411yescharacteristic
77#6501C2×C411yescharacteristic
78C2×#1142C2×C411yescharacteristic
79C4×C22⋊D7—21no—
80C22×C7⋊C8—21no—
81C2×#1132C2×C411yescharacteristic
82C2×#1131—21no—
83C2×C8×D7—21no—
84#6458C2×C411yescharacteristic
85D7×C4⋊C4—21no—
86D7×C4⋊C4C2×C411yescharacteristic
87#6451C2×C411yescharacteristic
88#6450—21no—
89#6450C2×C411yescharacteristic
90#6448—21no—
91#6447—21no—
92C4×D28C2311yescharacteristic
93C42×D7—21no—
94C42×D7C2311yescharacteristic
95C4×Dic14—21no—
96C4×Dic14C2311yescharacteristic
97C7×#106C2×C411yescharacteristic
98C7×C4⋊C8—21no—
99C7×C4⋊C8C2311yescharacteristic
100C7×C4⋊C8C2311yescharacteristic
101C7×#103C2×C411yescharacteristic
102C7×#102C2×C411yescharacteristic
103C7×C22⋊C8—21no—
104C7×#97—21no—
105C4×C7×C8C2311yescharacteristic
106C4×C7×C8C2311yescharacteristic
107C4×C7×C8C2311yescharacteristic
108#6409C2×C411yescharacteristic
109#6406C2×C411yescharacteristic
110C22⋊(C7⋊C8)—21no—
111#6395C2×C411yescharacteristic
112(C2×D7)⋊C8—21no—
113(C2×D7)⋊C8—21no—
114(C2×D7)⋊C8—21no—
115(C2×D7)⋊C8—21no—
116(C2×D7)⋊C8—21no—
117(C2×D7)⋊C8C2×C411yescharacteristic
118(C2×D7)⋊C8C2×C411yescharacteristic
119(C2×D7)⋊C8D411yescharacteristic
120(C2×D7)⋊C8D411yescharacteristic
121#6391C2×C411yescharacteristic
122#6390C2×C411yescharacteristic
123#6389—21no—
124Dic7⋊C8—21no—
125Dic7⋊C8—21no—
126Dic7⋊C8—21no—
127Dic7⋊C8C2×C411yescharacteristic
128Dic7⋊C8C2×C411yescharacteristic
129Dic7⋊C8D411yescharacteristic
130Dic7⋊C8D411yescharacteristic
131C8×Dic7—21no—
132C8×Dic7—21no—
133C8×Dic7—21no—
134#6384C2×C411yescharacteristic
135#6383C2×C411yescharacteristic
136#6382C2×C411yescharacteristic
137#6382C2×C411yescharacteristic
138C4⋊(C7⋊C8)—21no—
139C4⋊(C7⋊C8)C2311yescharacteristic
140C4⋊(C7⋊C8)C2311yescharacteristic
141#6377—21no—
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3103—71no—
146#2984—71no—
147#2979—71no—
148#1592D711yescharacteristic, complemented
149#1590—71no—
150#1588—71no—
151#1585—71no—
152#1583—71no—
153#1582—71no—
154SD16⋊C8—71no—
155C8×SD16—71no—
156#1572—71no—
157#1496—71no—
158#1479—71no—
159#1454—71no—
160C2×C7×Q8C22×C411yescharacteristic
161C2×C7×D4C22×C411yescharacteristic
162C22×C4×C7—21no—
163C2×C22⋊D7—21no—
164C2×C22⋊D7—21no—
165C2×C22⋊D7—21no—
166Q8×D7—22no—
167Q8×D7—41no—
168#1157—81no—
169#1157—81no—
170C2×D28—21no—
171C2×D28C22×C411yescharacteristic
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×C4×D7—21no—
175C2×C4×D7C22×C411yescharacteristic
176C2×C4×D7C2×D411yescharacteristic
177C2×C4×D7#4111yescharacteristic
178C2×Dic14—21no—
179C2×Dic14—21no—
180C2×Dic14C22×C411yescharacteristic
181C7×SD16—41no—
182C7×M16—81no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C2×C7×C8—21no—
186C2×C7×C8C22×C411yescharacteristic
187C2×C7×C8C22×C411yescharacteristic
188C2×C7×C8C2×D411yescharacteristic
189C2×C7×C8C2×D411yescharacteristic
190C7×C4⋊C4—21no—
191C7×C4⋊C4C22×C411yescharacteristic
192C7×C4⋊C4C22×C411yescharacteristic
193C7×C22⋊C4—21no—
194C42×C7—21no—
195C42×C7C2411yescharacteristic
196C22⋊Dic7—21no—
197#1143—41no—
198#1142—22no—
199(C2×D7)⋊C4—21no—
200(C2×D7)⋊C4—21no—
201C4⋊Dic7—21no—
202C4⋊Dic7C22×C411yescharacteristic
203C4⋊Dic7C22×C411yescharacteristic
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211C4×Dic7C22×C411yescharacteristic
212C4×Dic7C2×D411yescharacteristic
213C4×Dic7#4111yescharacteristic
214C2×C7⋊C8—21no—
215C2×C7⋊C8—21no—
216C2×C7⋊C8—21no—
217C2×C7⋊C8—81no—
218C2×C7⋊C8C22×C411yescharacteristic
219C2×C7⋊C8C22×C411yescharacteristic
220C2×C7⋊C8C2×D411yescharacteristic
221C2×C7⋊C8C2×D411yescharacteristic
222#1132—22no—
223#1131—81no—
224C8×D7—81no—
225#532—71no—
226C2×C4×Q8—71no—
227#481—71no—
228#481—71no—
229#475—71no—
230#475—71no—
231#460—71no—
232#460—71no—
233#448—71no—
234#448—71no—
235#446—71no—
236#446—141no—
237#446—141no—
238#446C2×D711yescharacteristic
239C8×Q8—71no—
240C8×Q8—71no—
241C4×SD16—71no—
242C4×SD16—71no—
243C4×SD16—71no—
244C4×SD16C2×D711yescharacteristic
245#436—71no—
246#436—141no—
247#436C2×D711yescharacteristic
248C8×D4—71no—
249C8×D4—71no—
250C8×D4—141no—
251#432—71no—
252#432—141no—
253#431—71no—
254#431—71no—
255#431—71no—
256#431—71no—
257#431—141no—
258#408—141no—
259#408—141no—
260#335—71no—
261#335C2×D711yescharacteristic
262#334—71no—
263#334—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8C2×D711yescharacteristic
268D4⋊C8—71no—
269D4⋊C8—71no—
270D4⋊C8—71no—
271D4⋊C8C2×D711yescharacteristic
272#322—71no—
273#322—71no—
274#322C2×D711yescharacteristic
275C82—71no—
276C23×C7—21no—
277C22×D7—21no—
278C22×D7C4×D411yescharacteristic
279C7×Q8—21no—
280C7×Q8—21no—
281C7×D4—21no—
282C7×D4—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—41no—
287C2×C4×C7—41no—
288C2×C4×C7C23×C411yescharacteristic
289C2×C4×C7C22×D411yescharacteristic
290C2×C4×C7C2×#4111yescharacteristic
291C22⋊D7—42no—
292C22⋊D7—81no—
293C22⋊D7—81no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296C2×Dic7—21no—
297C2×Dic7C4×D411yescharacteristic
298C2×Dic7C4×D411yescharacteristic
299C2×Dic7C4×D411yescharacteristic
300D28—21no—
301D28—21no—
302D28—81no—
303C4×D7—21no—
304C4×D7—21no—
305C4×D7—21no—
306C4×D7—21no—
307C4×D7—41no—
308C4×D7—42no—
309C4×D7—42no—
310C4×D7—41no—
311C4×D7—41no—
312Dic14—21no—
313Dic14—42no—
314Dic14—81no—
315Dic14#13112yes—
316C7×C8—21no—
317C7×C8—21no—
318C7×C8—21no—
319C7×C8—21no—
320C7×C8—41no—
321C7×C8—41no—
322C7×C8—41no—
323C7⋊C8—21no—
324C7⋊C8—21no—
325C7⋊C8—21no—
326C7⋊C8—21no—
327C7⋊C8—41no—
328C7⋊C8—41no—
329C7⋊C8—41no—
330C2×#41—141no—
331C22×Q8—71no—
332C2×SD16—71no—
333C2×SD16—71no—
334C2×SD16—71no—
335C2×SD16C4×D711yescharacteristic
336C2×M16—21no—
337C2×M16—141no—
338C22×C8—141no—
339C22×C8—141no—
340C4⋊Q8—71no—
341#127—71no—
342#124—141no—
343#121—71no—
344#121—71no—
345#121—141no—
346C4×Q8—71no—
347C4×Q8—71no—
348C4×Q8—71no—
349C4×Q8—141no—
350C4×Q8—141no—
351C4×Q8C22×D711yescharacteristic
352C4×D4—71no—
353C4×D4—141no—
354C4×D4C22×D711yescharacteristic
355C2×C4⋊C4—71no—
356C2×C4⋊C4—141no—
357C2×C42—71no—
358C2×C42—141no—
359#106—71no—
360#106—71no—
361#106—71no—
362#106C4×D711yescharacteristic
363C4⋊C8—21no—
364C4⋊C8—71no—
365C4⋊C8—71no—
366C4⋊C8—71no—
367C4⋊C8—71no—
368C4⋊C8—71no—
369C4⋊C8—71no—
370C4⋊C8—141no—
371C4⋊C8—141no—
372C4⋊C8—141no—
373C4⋊C8—141no—
374C4⋊C8C22×D711yescharacteristic
375C4⋊C8C22×D711yescharacteristic
376#103—71no—
377#103—71no—
378#103—71no—
379#103C4×D711yescharacteristic
380#102—71no—
381#102—71no—
382#102—71no—
383#102C4×D711yescharacteristic
384C22⋊C8—21no—
385C22⋊C8—71no—
386C22⋊C8—71no—
387C22⋊C8—71no—
388C22⋊C8—71no—
389C22⋊C8—141no—
390C22⋊C8—141no—
391C22⋊C8—141no—
392C22⋊C8—141no—
393C22⋊C8—141no—
394C22⋊C8—141no—
395#97—21no—
396#97—141no—
397#97—141no—
398C4×C8—71no—
399C4×C8—71no—
400C4×C8—71no—
401C4×C8—141no—
402C4×C8—141no—
403C4×C8—141no—
404C4×C8C22×D711yescharacteristic
405C4×C8C22×D711yescharacteristic
406C4×C8C22×D711yescharacteristic
407C22×C7—41no—
408C22×C7—41no—
409C22×C7—41no—
410C22×C7C2×C4×D411yescharacteristic
411C2×D7—21no—
412C2×D7—21no—
413C2×D7—21no—
414C2×D7—41no—
415C2×D7—41no—
416C2×D7—41no—
417C4×C7—21no—
418C4×C7—41no—
419C4×C7—41no—
420C4×C7—41no—
421C4×C7C2×#13111yescharacteristic
422C4×C7#56811yescharacteristic
423C4×C7#57711yescharacteristic
424C4×C7#57711yescharacteristic
425Dic7—22no—
426Dic7—21no—
427Dic7—21no—
428Dic7—21no—
429Dic7—41no—
430Dic7—41no—
431#41—561no—
432#41—561no—
433C2×Q8—71no—
434C2×Q8—141no—
435C2×Q8—141no—
436C2×Q8—142no—
437C2×Q8—281no—
438C2×Q8C2×C4×D711yescharacteristic
439C2×D4—71no—
440C2×D4—141no—
441C2×D4—141no—
442C2×D4—141no—
443C2×D4—141no—
444C2×D4C2×C4×D711yescharacteristic
445C22×C4—21no—
446C22×C4—71no—
447C22×C4—71no—
448C22×C4—71no—
449C22×C4—141no—
450C22×C4—141no—
451C22×C4—141no—
452SD16—41no—
453SD16—142no—
454SD16—142no—
455SD16—281no—
456M16—81no—
457M16—561no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—71no—
462C2×C8—71no—
463C2×C8—71no—
464C2×C8—71no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—141no—
468C2×C8—561no—
469C2×C8—561no—
470C2×C8C2×C4×D711yescharacteristic
471C2×C8C2×C4×D711yescharacteristic
472C2×C8D4×D711yescharacteristic
473C2×C8D4×D711yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—71no—
476C4⋊C4—71no—
477C4⋊C4—141no—
478C4⋊C4—141no—
479C4⋊C4—141no—
480C4⋊C4—141no—
481C4⋊C4—141no—
482C4⋊C4C2×C4×D711yescharacteristic
483C4⋊C4C2×C4×D711yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—141no—
486C22⋊C4—141no—
487C22⋊C4—141no—
488C42—21no—
489C42—71no—
490C42—71no—
491C42—71no—
492C42—141no—
493C42—141no—
494C42—141no—
495C42C23×D711yescharacteristic
496C2×C7—81no—
497C2×C7#293311yescharacteristic
498C2×C7#294911yescharacteristic
499C2×C7#295511yescharacteristic
500D7—41no—
501D7—81no—
502C23—21no—
503C23—71no—
504C23—141no—
505Q8—21no—
506Q8—21no—
507Q8—72no—
508Q8—141no—
509Q8—282no—
510Q8—561no—
511D4—21no—
512D4—21no—
513D4—141no—
514D4—141no—
515D4—282no—
516D4—561no—
517D4—561no—
518D4—561no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—71no—
525C2×C4—71no—
526C2×C4—71no—
527C2×C4—141no—
528C2×C4—141no—
529C2×C4—141no—
530C2×C4—141no—
531C2×C4—141no—
532C2×C4—141no—
533C2×C4—141no—
534C2×C4—281no—
535C2×C4—282no—
536C2×C4—282no—
537C2×C4—281no—
538C2×C4—281no—
539C2×C4C22×C4×D711yescharacteristic
540C2×C4C2×D4×D711yescharacteristic
541C2×C4D7×#4111yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—141no—
550C8—141no—
551C8—141no—
552C8—141no—
553C8—281no—
554C8—281no—
555C8—281no—
556C7#1803011yescharacteristic, complemented, Sylow
557C22—41no—
558C22—41no—
559C22—41no—
560C22—141no—
561C22—141no—
562C22—141no—
563C22—281no—
564C22—281no—
565C22—281no—
566C22C4×D4×D711yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—141no—
572C4—141no—
573C4—142no—
574C4—141no—
575C4—281no—
576C4—281no—
577C4#9043611yescharacteristic
578C4D7×#13111yescharacteristic
579C4#9046611yescharacteristic
580C4#9046911yescharacteristic
581C2—81no—
582C2—281no—
583C2—561no—
584C2#1173698411yescharacteristic
585C2#1173722211yescharacteristic
586C2#1173734211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1592C2
socleC22×C7C2×C4×D4
prime radical#90239C22
cosocleC42×C7C24
hypercenter#1592D7
hypocenterC7#18030
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
1. #11737409C2semidirect
4. C7×#1592C2semidirect
5. #11728707C2semidirect
6. #11728651C2semidirect
7. #11728618C2semidirect
8. #11726327C2semidirect
9. #11726316C2semidirect
10. #11725985C2semidirect
11. #11725978C2semidirect
13. #11725903C2semidirect
14. #11725830C2semidirect
15. #11725828C2semidirect
148. #1592D7semidirect
556. C7#18030semidirect

Maximal subgroups

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

subgroupindex
#117374092
#117370982
#117369912
C7×#15922
#117287072
#117286512
#117286182
#117263272
#117263162
#117259852
#117259782
#117259332
#117259032
#117258302
#117258282
#180307