Finite Group Databasebeta

← #13325570

Subgroups — #13325570

Order 1792.

586 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737405C211yesmaximal, characteristic
2#11737363C211yesmaximal, characteristic
3#11737170C211yesmaximal, characteristic
4C7×#1584C211yesmaximal, characteristic, complemented
5#11728705C211yesmaximal, characteristic, complemented
6C8×#1144C211yesmaximal, characteristic, complemented
7#11728657C211yesmaximal, characteristic, complemented
8D7×#335C211yesmaximal, characteristic
9#11726314C211yesmaximal, characteristic, complemented
10#11725986C211yesmaximal, characteristic
11#11725986C211yesmaximal, characteristic
12#11725979C211yesmaximal, characteristic, complemented
13#11725967C211yesmaximal, characteristic, complemented
14#11725840C211yesmaximal, characteristic, complemented
15#11725821C211yesmaximal, characteristic
16#90269C2211yescharacteristic
17#90269C2211yescharacteristic
18C7×#446C2211yescharacteristic
19C7×C8×Q8C2211yescharacteristic
20C4×C7×Q16C2211yescharacteristic
21#89960C411yescharacteristic
22#89953C411yescharacteristic
23C4×#1144C2211yescharacteristic
24C4×#1144C2211yescharacteristic
25#89796C2211yescharacteristic
26Q8×C7⋊C8C2211yescharacteristic
27#89659C411yescharacteristic
28#89646C411yescharacteristic
29#89611—21no—
30#89611—21no—
31D7×C4⋊C8C2211yescharacteristic
32D7×C4⋊C8C2211yescharacteristic
33#89603—21no—
34#89603C2211yescharacteristic
35#89602C2211yescharacteristic
36#89600—21no—
37#89585C411yescharacteristic
38#89585C411yescharacteristic
39#89564C411yescharacteristic
40#89564C411yescharacteristic
41#89480—21no—
42#89473—21no—
43C4×Dic28C2211yescharacteristic
44#89461—21no—
45C4×#1131C2211yescharacteristic
46#89457C2211yescharacteristic
47C4×C8×D7C2211yescharacteristic
48#89451—21no—
49#89451C2211yescharacteristic
50C8×Dic14C2211yescharacteristic
51C7×#335C2211yescharacteristic
52C7×Q8⋊C8C2211yescharacteristic
53C7×Q8⋊C8C2211yescharacteristic
54C7×#322C2211yescharacteristic
55Q8⋊(C7⋊C8)C2211yescharacteristic
56Q8⋊(C7⋊C8)C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89274C2211yescharacteristic
60#89274C2211yescharacteristic
61#89253C2211yescharacteristic
62#89251C2211yescharacteristic
63#89251C2211yescharacteristic
64#89249C2211yescharacteristic
65C8×C7⋊C8C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18068—71nomaximal, Sylow
68C2×C7×Q16C2×C411yescharacteristic
69C4×C7×Q8C2311yescharacteristic
70C4×C7×Q8C2311yescharacteristic
71#6509C2×C411yescharacteristic
72#6509C2×C411yescharacteristic
73#6507C2×C411yescharacteristic
74#6507C2×C411yescharacteristic
75C2×#1144C2×C411yescharacteristic
76C2×#1144C2×C411yescharacteristic
77C2×Dic28C2×C411yescharacteristic
78C2×#1131D411yescharacteristic
79C2×#1131D411yescharacteristic
80C2×C8×D7—21no—
81C2×C8×D7—21no—
82C2×C8×D7C2×C411yescharacteristic
83C2×C8×D7C2×C411yescharacteristic
84#6460C2×C411yescharacteristic
85#6460C2×C411yescharacteristic
86#6459—21no—
87#6459—21no—
88#6452—21no—
89#6452—21no—
90#6451C2×C411yescharacteristic
91#6451C2×C411yescharacteristic
92#6435—21no—
93#6435—21no—
94C42×D7C2311yescharacteristic
95C4×Dic14—21no—
96C4×Dic14—21no—
97C4×Dic14C2311yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×#107C2×C411yescharacteristic
100C7×C4⋊C8—21no—
101C7×C4⋊C8—21no—
102C7×C4⋊C8C2311yescharacteristic
103C7×C4⋊C8C2311yescharacteristic
104C7×#103C2×C411yescharacteristic
105C7×#103C2×C411yescharacteristic
106C7×#97—21no—
107C4×C7×C8—21no—
108C4×C7×C8C2311yescharacteristic
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111#6409C2×C411yescharacteristic
112#6409C2×C411yescharacteristic
113(C2×D7)⋊C8—21no—
114#6392C2×C411yescharacteristic
115#6390C2×C411yescharacteristic
116#6390C2×C411yescharacteristic
117#6389—21no—
118#6389—21no—
119#6389D411yescharacteristic
120#6389D411yescharacteristic
121Dic7⋊C8—21no—
122Dic7⋊C8—21no—
123Dic7⋊C8—21no—
124Dic7⋊C8—21no—
125Dic7⋊C8—21no—
126Dic7⋊C8—21no—
127Dic7⋊C8—21no—
128C8×Dic7—21no—
129C8×Dic7—21no—
130C8×Dic7C2×C411yescharacteristic
131C8×Dic7C2×C411yescharacteristic
132#6384C2×C411yescharacteristic
133#6384C2×C411yescharacteristic
134#6381C2×C411yescharacteristic
135#6381C2×C411yescharacteristic
136C4⋊(C7⋊C8)—21no—
137C4⋊(C7⋊C8)—21no—
138C4⋊(C7⋊C8)C2311yescharacteristic
139C4⋊(C7⋊C8)C2311yescharacteristic
140#6377—21no—
141C4×C7⋊C8—21no—
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3170—71no—
146#2962—71no—
147#2962—71no—
148#1591—71no—
149#1591—71no—
150#1584—71no—
151#1584—71no—
152#1584—71no—
153#1584D711yescharacteristic, complemented
154C8×Q16—71no—
155C8×Q16—71no—
156C2×#335—71no—
157#1481—71no—
158#1481—71no—
159C8×M16—71no—
160C2×C7×Q8C22×C411yescharacteristic
161C2×C7×Q8C22×C411yescharacteristic
162C2×C4×D7C22×C411yescharacteristic
163C2×C4×D7C2×D411yescharacteristic
164C2×C4×D7#4111yescharacteristic
165C2×Dic14—21no—
166C2×Dic14—21no—
167C2×Dic14C22×C411yescharacteristic
168C2×Dic14C22×C411yescharacteristic
169C7×Q16—41no—
170C2×C7×C8—21no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8C22×C411yescharacteristic
174C2×C7×C8C22×C411yescharacteristic
175C2×C7×C8C2×D411yescharacteristic
176C2×C7×C8C2×D411yescharacteristic
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4C22×C411yescharacteristic
180C7×C4⋊C4C22×C411yescharacteristic
181C42×C7—21no—
182C42×C7—21no—
183C42×C7C2411yescharacteristic
184#1144—22no—
185#1144—22no—
186(C2×D7)⋊C4—21no—
187(C2×D7)⋊C4—21no—
188(C2×D7)⋊C4—21no—
189(C2×D7)⋊C4—21no—
190C4⋊Dic7—21no—
191C4⋊Dic7—21no—
192C4⋊Dic7C22×C411yescharacteristic
193C4⋊Dic7C22×C411yescharacteristic
194Dic7⋊C4—21no—
195Dic7⋊C4—21no—
196Dic7⋊C4—21no—
197Dic7⋊C4—21no—
198Dic7⋊C4—21no—
199Dic7⋊C4—21no—
200Dic7⋊C4—21no—
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204C4×Dic7—21no—
205C4×Dic7—21no—
206C4×Dic7C22×C411yescharacteristic
207C4×Dic7C2×D411yescharacteristic
208C4×Dic7#4111yescharacteristic
209C2×C7⋊C8—21no—
210C2×C7⋊C8—21no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8C22×C411yescharacteristic
213C2×C7⋊C8C22×C411yescharacteristic
214C2×C7⋊C8C2×D411yescharacteristic
215C2×C7⋊C8C2×D411yescharacteristic
216Dic28—41no—
217#1131—22no—
218#1131Q1614yescomplemented
219C8×D7—22no—
220C8×D7—41no—
221C8×D7—42no—
222C8×D7—42no—
223#533—71no—
224#533—71no—
225#500—71no—
226#494—71no—
227#487—71no—
228#487—71no—
229#467—71no—
230#467—71no—
231#467—71no—
232#467—71no—
233#446—71no—
234#446—71no—
235#446—71no—
236#446—141no—
237#446—141no—
238#446—141no—
239#446—141no—
240#446C2×D711yescharacteristic
241C8×Q8—71no—
242C8×Q8—71no—
243C8×Q8—71no—
244C8×Q8C2×D711yescharacteristic
245C4×Q16—71no—
246C4×Q16—71no—
247C4×Q16—71no—
248C4×Q16C2×D711yescharacteristic
249#431—71no—
250#424—141no—
251#424—141no—
252C2×C4⋊C8—71no—
253C2×C4⋊C8—71no—
254#405—141no—
255#405—141no—
256C4×M16—71no—
257C2×C4×C8—71no—
258#335—71no—
259#335—71no—
260#335—71no—
261#335C2×D711yescharacteristic
262Q8⋊C8—71no—
263Q8⋊C8—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268Q8⋊C8C2×D711yescharacteristic
269Q8⋊C8C2×D711yescharacteristic
270#322—71no—
271#322C2×D711yescharacteristic
272C82—71no—
273C82—71no—
274C22×D7C4×D411yescharacteristic
275C7×Q8—21no—
276C7×Q8—21no—
277C7×Q8—21no—
278C7×Q8—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7C23×C411yescharacteristic
284C2×C4×C7C22×D411yescharacteristic
285C2×C4×C7C2×#4111yescharacteristic
286C2×Dic7—21no—
287C2×Dic7—21no—
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7C4×D411yescharacteristic
291C2×Dic7C4×D411yescharacteristic
292C2×Dic7C4×D411yescharacteristic
293C4×D7—21no—
294C4×D7—21no—
295C4×D7—41no—
296C4×D7C2×Q1612yes—
297C4×D7#13512yes—
298Dic14—21no—
299Dic14—21no—
300Dic14—21no—
301Dic14—21no—
302Dic14—81no—
303Dic14—81no—
304C7×C8—21no—
305C7×C8—21no—
306C7×C8—21no—
307C7×C8—41no—
308C7×C8—41no—
309C7×C8—41no—
310C7×C8C2×Q1612yes—
311C7⋊C8—21no—
312C7⋊C8—21no—
313C7⋊C8—41no—
314C7⋊C8—41no—
315C7⋊C8—41no—
316C7⋊C8#13112yes—
317C7⋊C8C2×Q1612yes—
318C2×Q16—71no—
319C2×Q16—71no—
320C2×Q16—71no—
321C2×Q16C4×D711yescharacteristic
322C2×M16—71no—
323C2×M16—71no—
324C22×C8—71no—
325C22×C8—71no—
326C22×C8—141no—
327C22×C8—141no—
328C4⋊Q8—71no—
329C4⋊Q8—71no—
330C4⋊Q8—71no—
331C4⋊Q8—71no—
332#125—141no—
333#125—141no—
334C22⋊Q8—71no—
335C22⋊Q8—71no—
336C22⋊Q8—71no—
337C22⋊Q8—71no—
338C22⋊Q8—141no—
339C22⋊Q8—141no—
340C4×Q8—71no—
341C4×Q8—71no—
342C4×Q8—141no—
343C4×Q8—141no—
344C4×Q8C22×D711yescharacteristic
345C4×Q8C22×D711yescharacteristic
346#117—141no—
347#117—141no—
348C2×C42—71no—
349#107—71no—
350#107—71no—
351#107—71no—
352#107C4×D711yescharacteristic
353C4⋊C8—21no—
354C4⋊C8—21no—
355C4⋊C8—71no—
356C4⋊C8—71no—
357C4⋊C8—141no—
358C4⋊C8—141no—
359C4⋊C8—141no—
360C4⋊C8—141no—
361C4⋊C8—141no—
362C4⋊C8—141no—
363C4⋊C8—141no—
364C4⋊C8—141no—
365C4⋊C8—141no—
366C4⋊C8C22×D711yescharacteristic
367C4⋊C8C22×D711yescharacteristic
368#103—71no—
369#103—71no—
370#103—71no—
371#103—71no—
372#103—71no—
373#103—71no—
374#103C4×D711yescharacteristic
375#103C4×D711yescharacteristic
376C22⋊C8—141no—
377#97—21no—
378#97—71no—
379#97—71no—
380#97—141no—
381#97—141no—
382#97—141no—
383C4×C8—21no—
384C4×C8—71no—
385C4×C8—71no—
386C4×C8—71no—
387C4×C8—71no—
388C4×C8—71no—
389C4×C8—141no—
390C4×C8—141no—
391C4×C8—141no—
392C4×C8C22×D711yescharacteristic
393C4×C8C22×D711yescharacteristic
394C4×C8C22×D711yescharacteristic
395C22×C7C2×C4×D411yescharacteristic
396C2×D7—21no—
397C2×D7—21no—
398C2×D7C4×Q1612yes—
399C4×C7—21no—
400C4×C7—41no—
401C4×C7—41no—
402C4×C7—41no—
403C4×C7—41no—
404C4×C7C2×#13111yescharacteristic
405C4×C7#56811yescharacteristic
406C4×C7C22×Q1611yescharacteristic
407C4×C7C2×#13511yescharacteristic
408Dic7—21no—
409Dic7—21no—
410Dic7—41no—
411Dic7—41no—
412Dic7—41no—
413Dic7—41no—
414Dic7C4×Q1612yes—
415C2×Q8—71no—
416C2×Q8—71no—
417C2×Q8—141no—
418C2×Q8—141no—
419C2×Q8C2×C4×D711yescharacteristic
420C2×Q8C2×C4×D711yescharacteristic
421C22×C4—71no—
422C22×C4—71no—
423C22×C4—71no—
424Q16—41no—
425Q16—142no—
426Q16—142no—
427Q16—281no—
428M16—74no—
429M16—142no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—71no—
434C2×C8—71no—
435C2×C8—71no—
436C2×C8—71no—
437C2×C8—142no—
438C2×C8—141no—
439C2×C8—141no—
440C2×C8—141no—
441C2×C8—281no—
442C2×C8—282no—
443C2×C8—282no—
444C2×C8C2×C4×D711yescharacteristic
445C2×C8C2×C4×D711yescharacteristic
446C2×C8D4×D711yescharacteristic
447C2×C8D4×D711yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—71no—
451C4⋊C4—71no—
452C4⋊C4—141no—
453C4⋊C4—141no—
454C4⋊C4—141no—
455C4⋊C4—141no—
456C4⋊C4—141no—
457C4⋊C4—141no—
458C4⋊C4—141no—
459C4⋊C4—141no—
460C4⋊C4—141no—
461C4⋊C4—141no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4C2×C4×D711yescharacteristic
465C4⋊C4C2×C4×D711yescharacteristic
466C22⋊C4—141no—
467C22⋊C4—141no—
468C22⋊C4—141no—
469C22⋊C4—141no—
470C42—21no—
471C42—21no—
472C42—71no—
473C42—71no—
474C42—71no—
475C42—141no—
476C42—141no—
477C42C23×D711yescharacteristic
478C2×C7#293511yescharacteristic
479C2×C7C2×C4×Q1611yescharacteristic
480C2×C7#295711yescharacteristic
481D7—22no—
482C23—71no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—141no—
488Q8—141no—
489Q8—141no—
490Q8—141no—
491Q8—561no—
492Q8—561no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—71no—
498C2×C4—72no—
499C2×C4—72no—
500C2×C4—71no—
501C2×C4—71no—
502C2×C4—141no—
503C2×C4—141no—
504C2×C4—141no—
505C2×C4—141no—
506C2×C4—141no—
507C2×C4—141no—
508C2×C4—281no—
509C2×C4C22×C4×D711yescharacteristic
510C2×C4C2×D4×D711yescharacteristic
511C2×C4D7×#4111yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—72no—
519C8—72no—
520C8—141no—
521C8—141no—
522C8—281no—
523C8—281no—
524C8—281no—
525C8D7×Q1612yes—
526C7#1806811yescharacteristic, complemented, Sylow
527C22—72no—
528C22—141no—
529C22—141no—
530C22C4×D4×D711yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—72no—
537C4—141no—
538C4—141no—
539C4—281no—
540C4—281no—
541C4—281no—
542C4—281no—
543C4#9043611yescharacteristic
544C4D7×#13111yescharacteristic
545C4C2×D7×Q1611yescharacteristic
546C4D7×#13511yescharacteristic
547C2—142no—
548C2#1173692911yescharacteristic
549C2C4×D7×Q1611yescharacteristic
550C2#1173734411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1584C2
socleC22×C7C2×C4×D4
prime radicalC22×D7C4×D4
cosocleC42×C7C24
hypercenter#1584D7
hypocenterC7#18068
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. C7×#1584C2semidirect
5. #11728705C2semidirect
6. C8×#1144C2semidirect
7. #11728657C2semidirect
9. #11726314C2semidirect
12. #11725979C2semidirect
13. #11725967C2semidirect
14. #11725840C2semidirect
153. #1584D7semidirect
218. #1131Q16semidirect
526. C7#18068semidirect

Maximal subgroups

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

subgroupindex
#117374052
#117373632
#117371702
C7×#15842
#117287052
C8×#11442
#117286572
D7×#3352
#117263142
#117259862
#117259792
#117259672
#117258402
#117258212
#180687