Finite Group Databasebeta

← #13324749

Subgroups — #13324749

Order 1792.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740585C211yesmaximal, characteristic
2#11740574C211yesmaximal, characteristic, complemented
3#11736774C211yesmaximal, characteristic, complemented
4C7×#1494C211yesmaximal, characteristic, complemented
5#11728550C211yesmaximal, characteristic, complemented
6#11727488C211yesmaximal, characteristic, complemented
7C8×#1136C211yesmaximal, characteristic, complemented
8#11725978C211yesmaximal, characteristic, complemented
9#11725973C211yesmaximal, characteristic, complemented
10#11725971C211yesmaximal, characteristic, complemented
11#11725967C211yesmaximal, characteristic, complemented
12#11725914C211yesmaximal, characteristic, complemented
13#11725909C211yesmaximal, characteristic, complemented
14#11725906C211yesmaximal, characteristic, complemented
15#11725903C211yesmaximal, characteristic, complemented
16C7×#529C2211yescharacteristic
17C4×#1157C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C2×C4×C7×C8C2211yescharacteristic
20#89838C411yescharacteristic
21#89835C411yescharacteristic
22#89829C411yescharacteristic
23#89826C411yescharacteristic
24#89819C411yescharacteristic
25#89817C411yescharacteristic
26#89809C411yescharacteristic
27#89807C411yescharacteristic
28C4×#1144C2211yescharacteristic
29C4×#1143C2211yescharacteristic
30#89796C2211yescharacteristic
31Q8×C7⋊C8C2211yescharacteristic
32C4×#1142C2211yescharacteristic
33C4×#1141C2211yescharacteristic
34#89784—21no—
35#89784C2211yescharacteristic
36#89783—21no—
37D4×C7⋊C8C2211yescharacteristic
38#89772—21no—
39#89769—21no—
40#89697C2211yescharacteristic
41#89697C2211yescharacteristic
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×D4⋊C8C2211yescharacteristic
54C7×D4⋊C8C2211yescharacteristic
55#89275C2211yescharacteristic
56#89275C2211yescharacteristic
57#89274C2211yescharacteristic
58#89274C2211yescharacteristic
59#89254C2211yescharacteristic
60#89254C2211yescharacteristic
61#89251C2211yescharacteristic
62#89251C2211yescharacteristic
63#89249C2211yescharacteristic
64#89249C2211yescharacteristic
65C8×C7⋊C8C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#17999—71nomaximal, Sylow
68C2×#1157C2×C411yescharacteristic
69C22×C7×C8—21no—
70C7×#126—21no—
71C7×#125C2×C411yescharacteristic
72C7×#124C2×C411yescharacteristic
73C7×#123—21no—
74C7×C22⋊Q8C2×C411yescharacteristic
75C7×#121C2×C411yescharacteristic
76C4×C7×Q8C2311yescharacteristic
77C4×C7×D4—21no—
78C4×C7×D4C2311yescharacteristic
79C7×#117—21no—
80C2×C42×C7C2311yescharacteristic
81C2×#1144C2×C411yescharacteristic
82C2×#1143C2×C411yescharacteristic
83C2×#1142C2×C411yescharacteristic
84C2×#1141C2×C411yescharacteristic
85C4×C22⋊D7—21no—
86C4×C22⋊D7—21no—
87#6489C2×C411yescharacteristic
88C2×#1136—21no—
89C2×#1136D411yescharacteristic
90C2×#1136D411yescharacteristic
91C22×C7⋊C8—21no—
92C2×#1131—21no—
93C2×#1131—21no—
94C4×D28C2×C411yescharacteristic
95C4×D28C2311yescharacteristic
96#6435—21no—
97C42×D7—21no—
98C4×Dic14C2×C411yescharacteristic
99C4×Dic14C2311yescharacteristic
100C7×C4⋊C8C2311yescharacteristic
101C7×C4⋊C8C2311yescharacteristic
102C7×C22⋊C8—21no—
103C7×#97—21no—
104C4×C7×C8—21no—
105C4×C7×C8C2311yescharacteristic
106C4×C7×C8C2311yescharacteristic
107#6409C2×C411yescharacteristic
108#6409C2×C411yescharacteristic
109#6406C2×C411yescharacteristic
110#6406C2×C411yescharacteristic
111C22⋊(C7⋊C8)—21no—
112C22⋊(C7⋊C8)—21no—
113C22⋊(C7⋊C8)—21no—
114C22⋊(C7⋊C8)C2×C411yescharacteristic
115C22⋊(C7⋊C8)C2×C411yescharacteristic
116(C2×D7)⋊C8—21no—
117(C2×D7)⋊C8—21no—
118Dic7⋊C8—21no—
119Dic7⋊C8—21no—
120C8×Dic7—21no—
121C8×Dic7—21no—
122#6384C2×C411yescharacteristic
123#6384C2×C411yescharacteristic
124#6383C2×C411yescharacteristic
125#6383C2×C411yescharacteristic
126#6382C2×C411yescharacteristic
127#6382C2×C411yescharacteristic
128#6381C2×C411yescharacteristic
129#6381C2×C411yescharacteristic
130C4⋊(C7⋊C8)—21no—
131C4⋊(C7⋊C8)—21no—
132C4⋊(C7⋊C8)C2×C411yescharacteristic
133C4⋊(C7⋊C8)C2×C411yescharacteristic
134C4⋊(C7⋊C8)C2311yescharacteristic
135C4⋊(C7⋊C8)C2311yescharacteristic
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#3102—71no—
146#2971—71no—
147#2969—71no—
148#1590—71no—
149#1589—71no—
150#1584—71no—
151#1583—71no—
152#1583—71no—
153#1581—71no—
154C8×Q16—71no—
155C8×SD16—71no—
156#1572—71no—
157#1494D711yescharacteristic, complemented
158#1476—71no—
159C8×M16—71no—
160C2×C7×Q8C22×C411yescharacteristic
161C2×C7×D4—21no—
162C2×C7×D4C22×C411yescharacteristic
163C22×C4×C7—21no—
164C22×C4×C7C22×C411yescharacteristic
165C22×C4×C7C2×D411yescharacteristic
166C22×C4×C7#4111yescharacteristic
167C2×C22⋊D7—21no—
168#1157—22no—
169#1157—41no—
170C2×D28C22×C411yescharacteristic
171C2×C4×D7—21no—
172C2×C4×D7—21no—
173C2×C4×D7—21no—
174C2×Dic14C22×C411yescharacteristic
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—21no—
179C2×C7×C8—42no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4—21no—
184C7×C4⋊C4C22×C411yescharacteristic
185C7×C4⋊C4C22×C411yescharacteristic
186C7×C22⋊C4—21no—
187C7×C22⋊C4—21no—
188C7×C22⋊C4—21no—
189C7×C22⋊C4—21no—
190C7×C22⋊C4—21no—
191C42×C7—21no—
192C42×C7C22×C411yescharacteristic
193C42×C7C2×D411yescharacteristic
194C42×C7#4111yescharacteristic
195C42×C7C2411yescharacteristic
196C22⋊Dic7—21no—
197#1144—22no—
198#1143—41no—
199#1142—22no—
200#1141—41no—
201(C2×D7)⋊C4—21no—
202(C2×D7)⋊C4—21no—
203C4⋊Dic7C22×C411yescharacteristic
204C4⋊Dic7C22×C411yescharacteristic
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207C4×Dic7—21no—
208C4×Dic7—21no—
209C4×Dic7—21no—
210#1136—22no—
211#1136—22no—
212#1136—42no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8—21no—
215C2×C7⋊C8—42no—
216C2×C7⋊C8C22×C411yescharacteristic
217C2×C7⋊C8C22×C411yescharacteristic
218C2×C7⋊C8C22×C411yescharacteristic
219C2×C7⋊C8C22×C411yescharacteristic
220C2×C7⋊C8C2×D411yescharacteristic
221C2×C7⋊C8C2×D411yescharacteristic
222C2×C7⋊C8C2×D411yescharacteristic
223C2×C7⋊C8C2×D411yescharacteristic
224#1131—42no—
225#1131—42no—
226#529C2×D711yescharacteristic
227C4×#41—71no—
228#485—71no—
229#482—71no—
230#479—71no—
231#478—71no—
232#464—71no—
233#463—71no—
234#452—71no—
235#449—71no—
236#446—71no—
237C8×Q8—71no—
238C8×Q8—71no—
239C8×Q8—71no—
240C4×Q16—71no—
241C4×SD16—71no—
242C4×SD16—71no—
243C4×D8—71no—
244#436—71no—
245#436—71no—
246#436—71no—
247#436—141no—
248#436—141no—
249#436—141no—
250#435—141no—
251C8×D4—71no—
252#433—141no—
253#432—141no—
254#432C2×D711yescharacteristic
255#431—71no—
256#431—71no—
257#405—141no—
258C4×M16—71no—
259C4×M16—141no—
260C2×C4×C8C2×D711yescharacteristic
261#335—71no—
262#335—71no—
263#334—71no—
264#334—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8C2×D711yescharacteristic
268Q8⋊C8C2×D711yescharacteristic
269D4⋊C8—71no—
270D4⋊C8—71no—
271D4⋊C8C2×D711yescharacteristic
272D4⋊C8C2×D711yescharacteristic
273#322—71no—
274#322—71no—
275C82—71no—
276C82—71no—
277C23×C7—21no—
278C23×C7C4×D411yescharacteristic
279C22×D7—21no—
280C7×Q8—21no—
281C7×Q8—21no—
282C7×D4—21no—
283C7×D4—21no—
284C7×D4—81no—
285C2×C4×C7—21no—
286C2×C4×C7—21no—
287C2×C4×C7—21no—
288C2×C4×C7—21no—
289C2×C4×C7—21no—
290C2×C4×C7—21no—
291C2×C4×C7—21no—
292C2×C4×C7—41no—
293C2×C4×C7—41no—
294C2×C4×C7—41no—
295C2×C4×C7C4×D411yescharacteristic
296C2×C4×C7C4×D411yescharacteristic
297C2×C4×C7C4×D411yescharacteristic
298C2×C4×C7C23×C411yescharacteristic
299C2×C4×C7C22×D411yescharacteristic
300C2×C4×C7C2×#4111yescharacteristic
301C22⋊D7—42no—
302C2×Dic7—21no—
303C2×Dic7—21no—
304C2×Dic7—21no—
305D28—21no—
306D28—21no—
307C4×D7—42no—
308C4×D7—41no—
309C4×D7—41no—
310C4×D7—81no—
311Dic14—21no—
312Dic14#13112yes—
313C7×C8—22no—
314C7×C8—41no—
315C7×C8—41no—
316C7×C8—41no—
317C7⋊C8—21no—
318C7⋊C8—21no—
319C7⋊C8—21no—
320C7⋊C8—21no—
321C7⋊C8—21no—
322C7⋊C8—21no—
323C7⋊C8—41no—
324C7⋊C8—41no—
325C7⋊C8#13512yes—
326C7⋊C8#13512yes—
327C2×#41—71no—
328C2×Q16—71no—
329C2×SD16—71no—
330C2×SD16—71no—
331C2×D8—71no—
332C2×M16—71no—
333C2×M16—71no—
334C2×M16—141no—
335C2×M16—141no—
336C2×M16—141no—
337C22×C8—21no—
338C22×C8—141no—
339#126—21no—
340#125C4×D711yescharacteristic
341#124C4×D711yescharacteristic
342#123—21no—
343C22⋊Q8C4×D711yescharacteristic
344#121C4×D711yescharacteristic
345C4×Q8—71no—
346C4×Q8—71no—
347C4×Q8C22×D711yescharacteristic
348C4×D4—21no—
349C4×D4—71no—
350C4×D4—71no—
351C4×D4—141no—
352C4×D4—141no—
353C4×D4C22×D711yescharacteristic
354#117—21no—
355#117—71no—
356#117—141no—
357C2×C42—141no—
358C2×C42C22×D711yescharacteristic
359#107—71no—
360#107—71no—
361#106—71no—
362#106—71no—
363C4⋊C8—71no—
364C4⋊C8—71no—
365C4⋊C8—71no—
366C4⋊C8—71no—
367C4⋊C8—141no—
368C4⋊C8—141no—
369C4⋊C8—141no—
370C4⋊C8—141no—
371C4⋊C8C22×D711yescharacteristic
372C4⋊C8C22×D711yescharacteristic
373#103—71no—
374#103—71no—
375#103—71no—
376#103—71no—
377#102—71no—
378#102—71no—
379#102—71no—
380#102—71no—
381C22⋊C8—21no—
382C22⋊C8—71no—
383C22⋊C8—71no—
384C22⋊C8—141no—
385C22⋊C8—141no—
386C22⋊C8—141no—
387C22⋊C8—141no—
388C22⋊C8—141no—
389#97—21no—
390#97—71no—
391#97—71no—
392#97—141no—
393C4×C8—21no—
394C4×C8—71no—
395C4×C8—71no—
396C4×C8—71no—
397C4×C8—71no—
398C4×C8—141no—
399C4×C8—141no—
400C4×C8—141no—
401C4×C8—141no—
402C4×C8C22×D711yescharacteristic
403C4×C8C22×D711yescharacteristic
404C22×C7—21no—
405C22×C7—21no—
406C22×C7—21no—
407C22×C7—41no—
408C22×C7—41no—
409C22×C7—41no—
410C22×C7C2×C4×D411yescharacteristic
411C2×D7—41no—
412C2×D7—41no—
413C2×D7—41no—
414C4×C7—21no—
415C4×C7—21no—
416C4×C7—21no—
417C4×C7—21no—
418C4×C7—41no—
419C4×C7—41no—
420C4×C7—41no—
421C4×C7C2×#13111yescharacteristic
422C4×C7#56811yescharacteristic
423C4×C7C2×#13511yescharacteristic
424C4×C7C2×#13511yescharacteristic
425Dic7—22no—
426Dic7—41no—
427Dic7—41no—
428#41—142no—
429#41—281no—
430C2×Q8—71no—
431C2×Q8C2×C4×D711yescharacteristic
432C2×D4—21no—
433C2×D4—71no—
434C2×D4—141no—
435C2×D4C2×C4×D711yescharacteristic
436C22×C4—21no—
437C22×C4—141no—
438C22×C4—141no—
439C22×C4—141no—
440C22×C4C2×C4×D711yescharacteristic
441C22×C4D4×D711yescharacteristic
442C22×C4#115911yescharacteristic
443Q16—142no—
444SD16—142no—
445SD16—281no—
446D8—281no—
447M16—142no—
448M16—142no—
449M16—282no—
450M16—282no—
451M16—282no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8—71no—
458C2×C8—71no—
459C2×C8—71no—
460C2×C8—71no—
461C2×C8—71no—
462C2×C8—71no—
463C2×C8—71no—
464C2×C8—71no—
465C2×C8—141no—
466C2×C8—141no—
467C2×C8—282no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—71no—
473C4⋊C4—71no—
474C4⋊C4—141no—
475C4⋊C4—141no—
476C4⋊C4C2×C4×D711yescharacteristic
477C4⋊C4C2×C4×D711yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—141no—
484C22⋊C4—141no—
485C22⋊C4—141no—
486C42—21no—
487C42—141no—
488C42—141no—
489C42—141no—
490C42C2×C4×D711yescharacteristic
491C42D4×D711yescharacteristic
492C42#115911yescharacteristic
493C42C23×D711yescharacteristic
494C2×C7—41no—
495C2×C7—81no—
496C2×C7#293311yescharacteristic
497C2×C7C4×#13511yescharacteristic
498C2×C7#295611yescharacteristic
499D7—81no—
500C23—21no—
501C23—141no—
502C23(C22⋊D7)⋊C411yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—72no—
506Q8—141no—
507D4—21no—
508D4—21no—
509D4—81no—
510D4—141no—
511D4—141no—
512D4—282no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—141no—
524C2×C4—141no—
525C2×C4—141no—
526C2×C4—282no—
527C2×C4—281no—
528C2×C4—281no—
529C2×C4—561no—
530C2×C4(C22⋊D7)⋊C411yescharacteristic
531C2×C4(C22⋊D7)⋊C411yescharacteristic
532C2×C4(C22⋊D7)⋊C411yescharacteristic
533C2×C4C22×C4×D711yescharacteristic
534C2×C4C2×D4×D711yescharacteristic
535C2×C4C2×#115911yescharacteristic
536C8—22no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—72no—
541C8—72no—
542C8—141no—
543C8—141no—
544C8—141no—
545C8—141no—
546C8—141no—
547C8—141no—
548C8—281no—
549C8—281no—
550C7#1799911yescharacteristic, complemented, Sylow
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—281no—
558C22—281no—
559C22—281no—
560C22C2×(C22⋊D7)⋊C411yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—142no—
569C4—281no—
570C4—281no—
571C4D7×#13111yescharacteristic
572C4#9044111yescharacteristic
573C4D7×#13511yescharacteristic
574C4D7×#13511yescharacteristic
575C2—41no—
576C2—81no—
577C2—561no—
578C2#1173610411yescharacteristic
579C2#1173626311yescharacteristic
580C2#1173642511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1494C2
socleC22×C7C2×C4×D4
prime radical#89809C4
cosocleC42×C7C24
hypercenter#1494D7
hypocenterC7#17999
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #11740574C2semidirect
3. #11736774C2semidirect
4. C7×#1494C2semidirect
5. #11728550C2semidirect
6. #11727488C2semidirect
7. C8×#1136C2semidirect
8. #11725978C2semidirect
9. #11725973C2semidirect
10. #11725971C2semidirect
11. #11725967C2semidirect
12. #11725914C2semidirect
13. #11725909C2semidirect
14. #11725906C2semidirect
15. #11725903C2semidirect
157. #1494D7semidirect
550. C7#17999semidirect

Maximal subgroups

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

subgroupindex
#117405852
#117405742
#117367742
C7×#14942
#117285502
#117274882
C8×#11362
#117259782
#117259732
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