Finite Group Databasebeta

← #13325166

Subgroups — #13325166

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#11740760C211yesmaximal, characteristic
2#11740723C211yesmaximal, characteristic
3#11736760C211yesmaximal, characteristic, complemented
4C7×#1496C211yesmaximal, characteristic
5#11728550C211yesmaximal, characteristic, complemented
6#11728521C211yesmaximal, characteristic, complemented
7#11728498C211yesmaximal, characteristic, complemented
8#11725916C211yesmaximal, characteristic, complemented
9#11725915C211yesmaximal, characteristic, complemented
10#11725913C211yesmaximal, characteristic, complemented
11#11725910C211yesmaximal, characteristic, complemented
12#11725909C211yesmaximal, characteristic, complemented
13#11725908C211yesmaximal, characteristic, complemented
14#11725904C211yesmaximal, characteristic, complemented
15#11725903C211yesmaximal, characteristic, complemented
16C7×#532C2211yescharacteristic
17C2×C4×Dic14C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C7×#431C2211yescharacteristic
20#90006—21no—
21#90006—21no—
22#89866C411yescharacteristic
23#89866C411yescharacteristic
24#89847C411yescharacteristic
25#89847C411yescharacteristic
26#89812C411yescharacteristic
27#89812C411yescharacteristic
28#89806C411yescharacteristic
29#89806C411yescharacteristic
30C4×#1142C2211yescharacteristic
31C4×#1142C2211yescharacteristic
32C4×#1142C2211yescharacteristic
33C4×#1142C2211yescharacteristic
34#89784—21no—
35#89784C2211yescharacteristic
36#89784C2211yescharacteristic
37D4×C7⋊C8—21no—
38D4×C7⋊C8C2211yescharacteristic
39D4×C7⋊C8C2211yescharacteristic
40#89697C2211yescharacteristic
41#89697C2211yescharacteristic
42#89697C2211yescharacteristic
43#89603C2211yescharacteristic
44#89603C2211yescharacteristic
45#89602C2211yescharacteristic
46#89602C2211yescharacteristic
47#89491—21no—
48#89490—21no—
49#89473—21no—
50#89473—21no—
51C7×D4⋊C8C2211yescharacteristic
52C7×D4⋊C8C2211yescharacteristic
53C7×D4⋊C8C2211yescharacteristic
54C7×D4⋊C8C2211yescharacteristic
55#89275C2211yescharacteristic
56#89275C2211yescharacteristic
57#89274C2211yescharacteristic
58#89274C2211yescharacteristic
59#89251C2211yescharacteristic
60#89251C2211yescharacteristic
61#89251C2211yescharacteristic
62#89251C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18030—71nomaximal, Sylow
68C2×C7×#41—21no—
69C22×Dic14C2×C411yescharacteristic
70C7×C4⋊Q8C2×C411yescharacteristic
71C7×#127C2×C411yescharacteristic
72C7×#124—21no—
73C7×#121—21no—
74C7×#121C2×C411yescharacteristic
75C7×#121C2×C411yescharacteristic
76C4×C7×D4—21no—
77C4×C7×D4C2311yescharacteristic
78C4×C7×D4C2311yescharacteristic
79C2×C42×C7C2311yescharacteristic
80C2×#1142C2×C411yescharacteristic
81C2×#1142C2×C411yescharacteristic
82C2×#1142C2×C411yescharacteristic
83C2×#1142C2×C411yescharacteristic
84C2×C4⋊Dic7C2×C411yescharacteristic
85C2×Dic7⋊C4—21no—
86C2×C4×Dic7—21no—
87C2×#1136—21no—
88C2×#1136—21no—
89C22×C7⋊C8—21no—
90C22×C7⋊C8—21no—
91C4×Dic14—21no—
92C4×Dic14—21no—
93C4×Dic14C2×C411yescharacteristic
94C4×Dic14C2×C411yescharacteristic
95C4×Dic14C2311yescharacteristic
96C4×Dic14C2311yescharacteristic
97C7×C4⋊C8—21no—
98C7×C4⋊C8C2311yescharacteristic
99C7×C4⋊C8C2311yescharacteristic
100C7×C22⋊C8—21no—
101C7×C22⋊C8—21no—
102C7×#97—21no—
103C4×C7×C8C2311yescharacteristic
104C4×C7×C8C2311yescharacteristic
105#6406C2×C411yescharacteristic
106#6406C2×C411yescharacteristic
107#6406C2×C411yescharacteristic
108#6406C2×C411yescharacteristic
109C22⋊(C7⋊C8)—21no—
110C22⋊(C7⋊C8)—21no—
111C22⋊(C7⋊C8)—21no—
112C22⋊(C7⋊C8)—21no—
113C22⋊(C7⋊C8)—21no—
114C22⋊(C7⋊C8)C2×C411yescharacteristic
115C22⋊(C7⋊C8)C2×C411yescharacteristic
116C22⋊(C7⋊C8)D411yescharacteristic
117C22⋊(C7⋊C8)D411yescharacteristic
118#6389—21no—
119#6389—21no—
120Dic7⋊C8—21no—
121Dic7⋊C8—21no—
122Dic7⋊C8—21no—
123Dic7⋊C8—21no—
124C8×Dic7—21no—
125C8×Dic7—21no—
126#6384C2×C411yescharacteristic
127#6384C2×C411yescharacteristic
128#6384C2×C411yescharacteristic
129#6384C2×C411yescharacteristic
130#6382C2×C411yescharacteristic
131#6382C2×C411yescharacteristic
132#6382C2×C411yescharacteristic
133#6382C2×C411yescharacteristic
134C4⋊(C7⋊C8)C2×C411yescharacteristic
135C4⋊(C7⋊C8)C2×C411yescharacteristic
136C4⋊(C7⋊C8)D411yescharacteristic
137C4⋊(C7⋊C8)D411yescharacteristic
138C4⋊(C7⋊C8)C2311yescharacteristic
139C4⋊(C7⋊C8)C2311yescharacteristic
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3103—71no—
146#2984—71no—
147#2979—71no—
148#1592—71no—
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#1496D711yescharacteristic
158#1479—71no—
159#1454—71no—
160C7×#41—81no—
161C7×#41—81no—
162C2×C7×Q8—21no—
163C2×C7×D4—21no—
164C2×C7×D4—21no—
165C2×C7×D4—21no—
166C2×C7×D4—21no—
167C2×C7×D4C22×C411yescharacteristic
168C2×C7×D4C22×C411yescharacteristic
169C22×C4×C7—21no—
170C22×C4×C7—21no—
171C22×C4×C7C22×C411yescharacteristic
172C22×C4×C7C2×D411yescharacteristic
173C22×C4×C7#4111yescharacteristic
174C22×Dic7—21no—
175C22×Dic7—21no—
176C2×Dic14—22no—
177C2×Dic14—21no—
178C2×Dic14—41no—
179C2×Dic14C22×C411yescharacteristic
180C2×Dic14C22×C411yescharacteristic
181C2×C7×C8—21no—
182C2×C7×C8—21no—
183C2×C7×C8—21no—
184C2×C7×C8—21no—
185C7×C4⋊C4—21no—
186C7×C4⋊C4C22×C411yescharacteristic
187C7×C4⋊C4C22×C411yescharacteristic
188C7×C22⋊C4—21no—
189C7×C22⋊C4—21no—
190C7×C22⋊C4—21no—
191C7×C22⋊C4—21no—
192C42×C7C22×C411yescharacteristic
193C42×C7C2×D411yescharacteristic
194C42×C7#4111yescharacteristic
195C42×C7C2411yescharacteristic
196#1142—22no—
197#1142—22no—
198#1142—41no—
199#1142—41no—
200C4⋊Dic7—21no—
201C4⋊Dic7C22×C411yescharacteristic
202C4⋊Dic7C22×C411yescharacteristic
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210C4×Dic7—21no—
211#1136—81no—
212#1136—81no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—81no—
216C2×C7⋊C8—81no—
217C2×C7⋊C8C22×C411yescharacteristic
218C2×C7⋊C8C22×C411yescharacteristic
219C2×C7⋊C8C22×C411yescharacteristic
220C2×C7⋊C8C22×C411yescharacteristic
221C2×C7⋊C8C2×D411yescharacteristic
222C2×C7⋊C8C2×D411yescharacteristic
223C2×C7⋊C8C2×D411yescharacteristic
224C2×C7⋊C8C2×D411yescharacteristic
225#532C2×D711yescharacteristic
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—71no—
237#446—141no—
238#446—141no—
239C8×Q8—71no—
240C8×Q8—71no—
241C4×SD16—71no—
242C4×SD16—71no—
243C4×SD16—71no—
244C4×SD16—71no—
245#436—71no—
246#436—71no—
247#436—141no—
248C8×D4—71no—
249C8×D4—71no—
250C8×D4—141no—
251#432—141no—
252#432C2×D711yescharacteristic
253#431—71no—
254#431—71no—
255#431—71no—
256#431—141no—
257#431C2×D711yescharacteristic
258#408—141no—
259#408—141no—
260#335—71no—
261#335—71no—
262#334—71no—
263#334—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268D4⋊C8C2×D711yescharacteristic
269D4⋊C8C2×D711yescharacteristic
270D4⋊C8C2×D711yescharacteristic
271D4⋊C8C2×D711yescharacteristic
272#322—71no—
273#322—71no—
274#322—71no—
275C82—71no—
276C23×C7—21no—
277C23×C7—21no—
278C23×C7C4×D411yescharacteristic
279C7×Q8—81no—
280C7×D4—21no—
281C7×D4—21no—
282C7×D4—21no—
283C7×D4—21no—
284C7×D4—42no—
285C7×D4—81no—
286C7×D4—81no—
287C7×D4—81no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—21no—
293C2×C4×C7—21no—
294C2×C4×C7—41no—
295C2×C4×C7—41no—
296C2×C4×C7—41no—
297C2×C4×C7—41no—
298C2×C4×C7—41no—
299C2×C4×C7C4×D411yescharacteristic
300C2×C4×C7C4×D411yescharacteristic
301C2×C4×C7C4×D411yescharacteristic
302C2×C4×C7C23×C411yescharacteristic
303C2×C4×C7C22×D411yescharacteristic
304C2×C4×C7C2×#4111yescharacteristic
305C2×Dic7—21no—
306C2×Dic7—21no—
307C2×Dic7—21no—
308C2×Dic7—21no—
309C2×Dic7—42no—
310C2×Dic7—42no—
311Dic14—21no—
312Dic14—21no—
313Dic14—21no—
314Dic14—42no—
315Dic14#13112yes—
316C7×C8—41no—
317C7×C8—41no—
318C7×C8—41no—
319C7×C8—41no—
320C7⋊C8—21no—
321C7⋊C8—21no—
322C7⋊C8—21no—
323C7⋊C8—21no—
324C7⋊C8—21no—
325C7⋊C8—21no—
326C7⋊C8—21no—
327C7⋊C8—21no—
328C7⋊C8—41no—
329C7⋊C8—41no—
330C2×#41—21no—
331C22×Q8—71no—
332C2×SD16—71no—
333C2×SD16—71no—
334C2×SD16—71no—
335C2×SD16—71no—
336C2×M16—141no—
337C2×M16—141no—
338C22×C8—141no—
339C22×C8—141no—
340C4⋊Q8C4×D711yescharacteristic
341#127C4×D711yescharacteristic
342#124—21no—
343#121—21no—
344#121C4×D711yescharacteristic
345#121C4×D711yescharacteristic
346C4×Q8—71no—
347C4×Q8—71no—
348C4×Q8—71no—
349C4×Q8—71no—
350C4×Q8—141no—
351C4×Q8—141no—
352C4×D4—21no—
353C4×D4C22×D711yescharacteristic
354C4×D4C22×D711yescharacteristic
355C2×C4⋊C4—71no—
356C2×C4⋊C4—141no—
357C2×C42—141no—
358C2×C42C22×D711yescharacteristic
359#106—71no—
360#106—71no—
361#106—71no—
362#106—71no—
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#103—71no—
380#102—71no—
381#102—71no—
382#102—71no—
383#102—71no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8—71no—
387C22⋊C8—71no—
388C22⋊C8—71no—
389C22⋊C8—71no—
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—71no—
402C4×C8—141no—
403C4×C8—141no—
404C4×C8—141no—
405C4×C8C22×D711yescharacteristic
406C4×C8C22×D711yescharacteristic
407C22×C7—21no—
408C22×C7—21no—
409C22×C7—21no—
410C22×C7—41no—
411C22×C7—41no—
412C22×C7—41no—
413C22×C7—41no—
414C22×C7—41no—
415C22×C7—41no—
416C22×C7C2×C4×D411yescharacteristic
417C4×C7—21no—
418C4×C7—21no—
419C4×C7—21no—
420C4×C7—21no—
421C4×C7—41no—
422C4×C7—41no—
423C4×C7C2×#13111yescharacteristic
424C4×C7#56811yescharacteristic
425C4×C7#57711yescharacteristic
426C4×C7#57711yescharacteristic
427Dic7—22no—
428Dic7—41no—
429Dic7—41no—
430Dic7—41no—
431#41—81no—
432#41—81no—
433C2×Q8—21no—
434C2×Q8—71no—
435C2×Q8—71no—
436C2×Q8—142no—
437C2×Q8—141no—
438C2×Q8—281no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4C2×C4×D711yescharacteristic
444C2×D4C2×C4×D711yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—141no—
448C22×C4—141no—
449C22×C4C2×C4×D711yescharacteristic
450C22×C4D4×D711yescharacteristic
451C22×C4#115911yescharacteristic
452SD16—142no—
453SD16—142no—
454SD16—281no—
455SD16—281no—
456M16—561no—
457M16—561no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—71no—
463C2×C8—71no—
464C2×C8—71no—
465C2×C8—71no—
466C2×C8—71no—
467C2×C8—71no—
468C2×C8—71no—
469C2×C8—71no—
470C2×C8—141no—
471C2×C8—141no—
472C2×C8—561no—
473C2×C8—561no—
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—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C42—141no—
489C42—141no—
490C42—141no—
491C42—141no—
492C42C2×C4×D711yescharacteristic
493C42D4×D711yescharacteristic
494C42#115911yescharacteristic
495C42C23×D711yescharacteristic
496C2×C7—41no—
497C2×C7—81no—
498C2×C7—81no—
499C2×C7#293311yescharacteristic
500C2×C7#294911yescharacteristic
501C2×C7#295511yescharacteristic
502C23—21no—
503C23—21no—
504C23(C22⋊D7)⋊C411yescharacteristic
505Q8—72no—
506Q8—81no—
507Q8—141no—
508Q8—141no—
509Q8—141no—
510Q8—282no—
511D4—21no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—81no—
517D4—81no—
518D4—81no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—141no—
531C2×C4—141no—
532C2×C4—141no—
533C2×C4—141no—
534C2×C4—282no—
535C2×C4—282no—
536C2×C4(C22⋊D7)⋊C411yescharacteristic
537C2×C4(C22⋊D7)⋊C411yescharacteristic
538C2×C4(C22⋊D7)⋊C411yescharacteristic
539C2×C4C22×C4×D711yescharacteristic
540C2×C4C2×D4×D711yescharacteristic
541C2×C4C2×#115911yescharacteristic
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—141no—
547C8—141no—
548C8—141no—
549C8—141no—
550C8—141no—
551C8—141no—
552C8—141no—
553C8—141no—
554C8—281no—
555C8—281no—
556C7#1803011yescharacteristic, complemented, Sylow
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×(C22⋊D7)⋊C411yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—142no—
574C4—281no—
575C4—281no—
576C4—281no—
577C4D7×#13111yescharacteristic
578C4#9044111yescharacteristic
579C4#9046611yescharacteristic
580C4#9046611yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1173610411yescharacteristic
585C2#1173636111yescharacteristic
586C2#1173643411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1496C2
socleC22×C7C2×C4×D4
prime radicalC7×#532C22
cosocleC42×C7C24
hypercenter#1496D7
hypocenterC7#18030
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
3. #11736760C2semidirect
5. #11728550C2semidirect
6. #11728521C2semidirect
7. #11728498C2semidirect
8. #11725916C2semidirect
9. #11725915C2semidirect
10. #11725913C2semidirect
11. #11725910C2semidirect
12. #11725909C2semidirect
13. #11725908C2semidirect
14. #11725904C2semidirect
15. #11725903C2semidirect
556. C7#18030semidirect

Maximal subgroups

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

subgroupindex
#117407602
#117407232
#117367602
C7×#14962
#117285502
#117285212
#117284982
#117259162
#117259152
#117259132
#117259102
#117259092
#117259082
#117259042
#117259032
#180307