Finite Group Databasebeta

← #13324943

Subgroups — #13324943

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740797C211yesmaximal, characteristic
2#11740775C211yesmaximal, characteristic, complemented
3#11736774C211yesmaximal, characteristic
4C7×#1497C211yesmaximal, characteristic, complemented
5#11728551C211yesmaximal, characteristic, complemented
6#11728509C211yesmaximal, characteristic
7#11728497C211yesmaximal, characteristic, complemented
8#11725980C211yesmaximal, characteristic, complemented
9#11725978C211yesmaximal, characteristic, complemented
10#11725977C211yesmaximal, characteristic, complemented
11#11725976C211yesmaximal, characteristic, complemented
12#11725973C211yesmaximal, characteristic, complemented
13#11725971C211yesmaximal, characteristic, complemented
14#11725969C211yesmaximal, characteristic, complemented
15#11725967C211yesmaximal, characteristic, complemented
16C7×#533C2211yescharacteristic
17C4×#1157C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C7×#431C2211yescharacteristic
20#89866C411yescharacteristic
21#89862C411yescharacteristic
22#89859C411yescharacteristic
23#89855C411yescharacteristic
24#89819C411yescharacteristic
25#89819C411yescharacteristic
26#89817C411yescharacteristic
27#89817C411yescharacteristic
28C4×#1144C2211yescharacteristic
29C4×#1144C2211yescharacteristic
30C4×#1143C2211yescharacteristic
31C4×#1143C2211yescharacteristic
32#89796—21no—
33#89796—21no—
34#89796C2211yescharacteristic
35#89796C2211yescharacteristic
36Q8×C7⋊C8C2211yescharacteristic
37Q8×C7⋊C8C2211yescharacteristic
38#89771—21no—
39#89769—21no—
40#89697C2211yescharacteristic
41C2×C4⋊(C7⋊C8)C2211yescharacteristic
42C4×#1136C2211yescharacteristic
43#89610C2211yescharacteristic
44#89610C2211yescharacteristic
45#89602C2211yescharacteristic
46#89602C2211yescharacteristic
47#89501—21no—
48#89501—21no—
49#89479—21no—
50#89477—21no—
51C7×Q8⋊C8C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×Q8⋊C8C2211yescharacteristic
54C7×Q8⋊C8C2211yescharacteristic
55#89275C2211yescharacteristic
56#89275C2211yescharacteristic
57#89274C2211yescharacteristic
58#89274C2211yescharacteristic
59#89254C2211yescharacteristic
60#89254C2211yescharacteristic
61#89251C2211yescharacteristic
62#89251C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18013—71nomaximal, Sylow
68C2×#1157C2×C411yescharacteristic
69C7×C4⋊Q8C2×C411yescharacteristic
70C7×C4⋊Q8C2×C411yescharacteristic
71C7×#125—21no—
72C7×C22⋊Q8—21no—
73C7×C22⋊Q8C2×C411yescharacteristic
74C7×C22⋊Q8C2×C411yescharacteristic
75C4×C7×Q8—21no—
76C4×C7×Q8C2311yescharacteristic
77C4×C7×Q8C2311yescharacteristic
78C7×#117—21no—
79C2×C42×C7C2311yescharacteristic
80C2×#1144C2×C411yescharacteristic
81C2×#1144C2×C411yescharacteristic
82C2×#1143C2×C411yescharacteristic
83C2×#1143C2×C411yescharacteristic
84C4×C22⋊D7—21no—
85C4×C22⋊D7—21no—
86#6489C2×C411yescharacteristic
87C2×#1136D411yescharacteristic
88C2×#1136D411yescharacteristic
89C22×C7⋊C8—21no—
90C2×#1131—21no—
91C2×#1131—21no—
92C4×D28C2×C411yescharacteristic
93C4×D28C2311yescharacteristic
94#6435—21no—
95C42×D7—21no—
96C4×Dic14C2×C411yescharacteristic
97C4×Dic14C2311yescharacteristic
98C7×C4⋊C8—21no—
99C7×C4⋊C8C2311yescharacteristic
100C7×C4⋊C8C2311yescharacteristic
101C7×C22⋊C8—21no—
102C7×C22⋊C8—21no—
103C7×#97—21no—
104C4×C7×C8C2311yescharacteristic
105C4×C7×C8C2311yescharacteristic
106#6409C2×C411yescharacteristic
107#6409C2×C411yescharacteristic
108#6409C2×C411yescharacteristic
109#6409C2×C411yescharacteristic
110C22⋊(C7⋊C8)C2×C411yescharacteristic
111C22⋊(C7⋊C8)C2×C411yescharacteristic
112(C2×D7)⋊C8—21no—
113(C2×D7)⋊C8—21no—
114Dic7⋊C8—21no—
115Dic7⋊C8—21no—
116C8×Dic7—21no—
117C8×Dic7—21no—
118#6384C2×C411yescharacteristic
119#6384C2×C411yescharacteristic
120#6383C2×C411yescharacteristic
121#6383C2×C411yescharacteristic
122#6382C2×C411yescharacteristic
123#6382C2×C411yescharacteristic
124#6381C2×C411yescharacteristic
125#6381C2×C411yescharacteristic
126C4⋊(C7⋊C8)—21no—
127C4⋊(C7⋊C8)—21no—
128C4⋊(C7⋊C8)—21no—
129C4⋊(C7⋊C8)—21no—
130C4⋊(C7⋊C8)—21no—
131C4⋊(C7⋊C8)C2×C411yescharacteristic
132C4⋊(C7⋊C8)C2×C411yescharacteristic
133C4⋊(C7⋊C8)C2311yescharacteristic
134C4⋊(C7⋊C8)C2311yescharacteristic
135#6377—21no—
136#6377—21no—
137#6377D411yescharacteristic
138#6377D411yescharacteristic
139C4×C7⋊C8—21no—
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3107—71no—
146#2971—71no—
147#2962—71no—
148#1592—71no—
149#1590—71no—
150#1588—71no—
151#1587—71no—
152#1584—71no—
153#1583—71no—
154#1579—71no—
155C8×Q16—71no—
156#1573—71no—
157#1497D711yescharacteristic, complemented
158#1477—71no—
159#1453—71no—
160C2×C7×Q8—21no—
161C2×C7×Q8C22×C411yescharacteristic
162C2×C7×Q8C22×C411yescharacteristic
163C22×C4×C7C22×C411yescharacteristic
164C22×C4×C7C2×D411yescharacteristic
165C22×C4×C7#4111yescharacteristic
166C2×C22⋊D7—21no—
167#1157—22no—
168#1157—41no—
169C2×D28C22×C411yescharacteristic
170C2×C4×D7—21no—
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×Dic14C22×C411yescharacteristic
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4—21no—
185C7×C4⋊C4C22×C411yescharacteristic
186C7×C4⋊C4C22×C411yescharacteristic
187C7×C22⋊C4—21no—
188C7×C22⋊C4—21no—
189C42×C7—21no—
190C42×C7—21no—
191C42×C7C22×C411yescharacteristic
192C42×C7C2×D411yescharacteristic
193C42×C7#4111yescharacteristic
194C42×C7C2411yescharacteristic
195C22⋊Dic7—21no—
196#1144—22no—
197#1144—22no—
198#1143—41no—
199#1143—41no—
200(C2×D7)⋊C4—21no—
201(C2×D7)⋊C4—21no—
202C4⋊Dic7C22×C411yescharacteristic
203C4⋊Dic7C22×C411yescharacteristic
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206C4×Dic7—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209#1136—22no—
210#1136—41no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—42no—
214C2×C7⋊C8C22×C411yescharacteristic
215C2×C7⋊C8C22×C411yescharacteristic
216C2×C7⋊C8C22×C411yescharacteristic
217C2×C7⋊C8C22×C411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219C2×C7⋊C8C2×D411yescharacteristic
220C2×C7⋊C8C2×D411yescharacteristic
221C2×C7⋊C8C2×D411yescharacteristic
222#1131—42no—
223#1131—42no—
224#533C2×D711yescharacteristic
225C4×#41—71no—
226#485—71no—
227#485—71no—
228#475—71no—
229#474—71no—
230#462—71no—
231#461—71no—
232#452—71no—
233#452—71no—
234#446—71no—
235#446—71no—
236#446—141no—
237#446—141no—
238C8×Q8—71no—
239C8×Q8—71no—
240C8×Q8—71no—
241C8×Q8—71no—
242C4×Q16—71no—
243C4×Q16—71no—
244C4×SD16—71no—
245C4×SD16—71no—
246#436—71no—
247#436—71no—
248#436—141no—
249#436—141no—
250#432—141no—
251#432C2×D711yescharacteristic
252#431—71no—
253#431C2×D711yescharacteristic
254#424—141no—
255C2×C4⋊C8—71no—
256#405—141no—
257C4×M16—71no—
258C4×M16—141no—
259#335—71no—
260#335—71no—
261#334—71no—
262#334—71no—
263Q8⋊C8—71no—
264Q8⋊C8—71no—
265Q8⋊C8C2×D711yescharacteristic
266Q8⋊C8C2×D711yescharacteristic
267Q8⋊C8C2×D711yescharacteristic
268Q8⋊C8C2×D711yescharacteristic
269D4⋊C8—71no—
270D4⋊C8—71no—
271#322—71no—
272#322—71no—
273#322—71no—
274C82—71no—
275C23×C7C4×D411yescharacteristic
276C22×D7—21no—
277C7×Q8—21no—
278C7×Q8—21no—
279C7×Q8—21no—
280C7×Q8—21no—
281C7×Q8—81no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—41no—
291C2×C4×C7C4×D411yescharacteristic
292C2×C4×C7C4×D411yescharacteristic
293C2×C4×C7C4×D411yescharacteristic
294C2×C4×C7C23×C411yescharacteristic
295C2×C4×C7C22×D411yescharacteristic
296C2×C4×C7C2×#4111yescharacteristic
297C22⋊D7—42no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300C2×Dic7—21no—
301D28—21no—
302D28—21no—
303C4×D7—42no—
304C4×D7—41no—
305C4×D7—41no—
306C4×D7—81no—
307Dic14—21no—
308Dic14#13112yes—
309C7×C8—41no—
310C7×C8—41no—
311C7×C8—41no—
312C7×C8—41no—
313C7⋊C8—21no—
314C7⋊C8—21no—
315C7⋊C8—21no—
316C7⋊C8—21no—
317C7⋊C8—21no—
318C7⋊C8—21no—
319C7⋊C8—21no—
320C7⋊C8—41no—
321C7⋊C8—41no—
322C7⋊C8#13712yes—
323C2×#41—71no—
324C2×Q16—71no—
325C2×Q16—71no—
326C2×SD16—71no—
327C2×SD16—71no—
328C2×M16—71no—
329C2×M16—71no—
330C2×M16—141no—
331C2×M16—141no—
332C22×C8—141no—
333C4⋊Q8C4×D711yescharacteristic
334C4⋊Q8C4×D711yescharacteristic
335#125—21no—
336C22⋊Q8—21no—
337C22⋊Q8C4×D711yescharacteristic
338C22⋊Q8C4×D711yescharacteristic
339C4×Q8—21no—
340C4×Q8—71no—
341C4×Q8—71no—
342C4×Q8C22×D711yescharacteristic
343C4×Q8C22×D711yescharacteristic
344C4×D4—71no—
345C4×D4—71no—
346C4×D4—141no—
347C4×D4—141no—
348#117—21no—
349#117—71no—
350#117—141no—
351C2×C42—141no—
352C2×C42C22×D711yescharacteristic
353#107—71no—
354#107—71no—
355#106—71no—
356#106—71no—
357C4⋊C8—21no—
358C4⋊C8—71no—
359C4⋊C8—71no—
360C4⋊C8—71no—
361C4⋊C8—71no—
362C4⋊C8—141no—
363C4⋊C8—141no—
364C4⋊C8—141no—
365C4⋊C8—141no—
366C4⋊C8—141no—
367C4⋊C8—141no—
368C4⋊C8—141no—
369C4⋊C8C22×D711yescharacteristic
370C4⋊C8C22×D711yescharacteristic
371#103—71no—
372#103—71no—
373#103—71no—
374#103—71no—
375#103—71no—
376#103—71no—
377#102—71no—
378#102—71no—
379C22⋊C8—21no—
380C22⋊C8—21no—
381C22⋊C8—71no—
382C22⋊C8—71no—
383C22⋊C8—141no—
384C22⋊C8—141no—
385#97—21no—
386#97—71no—
387#97—71no—
388#97—141no—
389#97—141no—
390C4×C8—71no—
391C4×C8—71no—
392C4×C8—71no—
393C4×C8—71no—
394C4×C8—141no—
395C4×C8—141no—
396C4×C8—141no—
397C4×C8—141no—
398C4×C8C22×D711yescharacteristic
399C4×C8C22×D711yescharacteristic
400C22×C7—21no—
401C22×C7—21no—
402C22×C7—21no—
403C22×C7C2×C4×D411yescharacteristic
404C2×D7—41no—
405C2×D7—41no—
406C2×D7—41no—
407C4×C7—21no—
408C4×C7—21no—
409C4×C7—21no—
410C4×C7—21no—
411C4×C7—41no—
412C4×C7—41no—
413C4×C7—41no—
414C4×C7—41no—
415C4×C7C2×#13111yescharacteristic
416C4×C7#56811yescharacteristic
417C4×C7C2×#13711yescharacteristic
418C4×C7#57511yescharacteristic
419Dic7—22no—
420Dic7—41no—
421Dic7—41no—
422#41—142no—
423#41—281no—
424C2×Q8—21no—
425C2×Q8—71no—
426C2×Q8C2×C4×D711yescharacteristic
427C2×Q8C2×C4×D711yescharacteristic
428C2×D4—71no—
429C2×D4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4C2×C4×D711yescharacteristic
434C22×C4D4×D711yescharacteristic
435C22×C4#115911yescharacteristic
436Q16—142no—
437Q16—142no—
438SD16—281no—
439SD16—281no—
440M16—142no—
441M16—282no—
442M16—282no—
443M16—281no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—71no—
449C2×C8—71no—
450C2×C8—71no—
451C2×C8—71no—
452C2×C8—71no—
453C2×C8—71no—
454C2×C8—71no—
455C2×C8—71no—
456C2×C8—141no—
457C2×C8—141no—
458C2×C8—282no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—71no—
467C4⋊C4—71no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4C2×C4×D711yescharacteristic
471C4⋊C4C2×C4×D711yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—141no—
475C22⋊C4—141no—
476C22⋊C4—141no—
477C42—21no—
478C42—21no—
479C42—141no—
480C42—141no—
481C42—141no—
482C42C2×C4×D711yescharacteristic
483C42D4×D711yescharacteristic
484C42#115911yescharacteristic
485C42C23×D711yescharacteristic
486C2×C7—41no—
487C2×C7#293311yescharacteristic
488C2×C7C4×#13711yescharacteristic
489C2×C7#295711yescharacteristic
490D7—81no—
491C23—141no—
492C23(C22⋊D7)⋊C411yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—72no—
498Q8—81no—
499Q8—141no—
500D4—141no—
501D4—141no—
502D4—282no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—141no—
513C2×C4—141no—
514C2×C4—141no—
515C2×C4—282no—
516C2×C4—281no—
517C2×C4—281no—
518C2×C4—561no—
519C2×C4(C22⋊D7)⋊C411yescharacteristic
520C2×C4(C22⋊D7)⋊C411yescharacteristic
521C2×C4(C22⋊D7)⋊C411yescharacteristic
522C2×C4C22×C4×D711yescharacteristic
523C2×C4C2×D4×D711yescharacteristic
524C2×C4C2×#115911yescharacteristic
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—72no—
530C8—141no—
531C8—141no—
532C8—141no—
533C8—141no—
534C8—141no—
535C8—141no—
536C8—141no—
537C8—281no—
538C8—281no—
539C7#1801311yescharacteristic, complemented, Sylow
540C22—21no—
541C22—21no—
542C22—21no—
543C22—281no—
544C22—281no—
545C22—281no—
546C22C2×(C22⋊D7)⋊C411yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—142no—
556C4—281no—
557C4—281no—
558C4D7×#13111yescharacteristic
559C4#9044111yescharacteristic
560C4D7×#13711yescharacteristic
561C4#9046811yescharacteristic
562C2—41no—
563C2—561no—
564C2#1173610411yescharacteristic
565C2#1173639111yescharacteristic
566C2#1173643511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1497C2
socleC22×C7C2×C4×D4
prime radicalC2×#1157C2×C4
cosocleC42×C7C24
hypercenter#1497D7
hypocenterC7#18013
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #11740775C2semidirect
4. C7×#1497C2semidirect
5. #11728551C2semidirect
7. #11728497C2semidirect
8. #11725980C2semidirect
9. #11725978C2semidirect
10. #11725977C2semidirect
11. #11725976C2semidirect
12. #11725973C2semidirect
13. #11725971C2semidirect
14. #11725969C2semidirect
15. #11725967C2semidirect
157. #1497D7semidirect
539. C7#18013semidirect

Maximal subgroups

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

subgroupindex
#117407972
#117407752
#117367742
C7×#14972
#117285512
#117285092
#117284972
#117259802
#117259782
#117259772
#117259762
#117259732
#117259712
#117259692
#117259672
#180137