Finite Group Databasebeta

← #13325519

Subgroups — #13325519

Order 1792.

618 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11737409C211yesmaximal, characteristic
2#11737366C211yesmaximal, characteristic
3C4×D7×Q16C211yesmaximal, characteristic
4C7×#1584C211yesmaximal, characteristic, complemented
5#11728706C211yesmaximal, characteristic, complemented
6#11728686C211yesmaximal, characteristic, complemented
7#11728657C211yesmaximal, characteristic, complemented
8#11726324C211yesmaximal, characteristic
9#11726314C211yesmaximal, characteristic, complemented
10#11725993C211yesmaximal, characteristic
11#11725993C211yesmaximal, characteristic
12#11725981C211yesmaximal, characteristic, complemented
13#11725969C211yesmaximal, characteristic, complemented
14#11725840C211yesmaximal, characteristic, complemented
15#11725824C211yesmaximal, characteristic
16C2×D7×Q16C411yescharacteristic
17C4×Q8×D7C2211yescharacteristic
18C4×Q8×D7C2211yescharacteristic
19C7×#446C2211yescharacteristic
20C7×C8×Q8C2211yescharacteristic
21C4×C7×Q16C2211yescharacteristic
22Q16×Dic7C411yescharacteristic
23C4×#1144C2211yescharacteristic
24C4×#1144C2211yescharacteristic
25#89796C2211yescharacteristic
26Q8×C7⋊C8C2211yescharacteristic
27D7×#107C411yescharacteristic
28#89645C411yescharacteristic
29#89607—21no—
30#89607C2211yescharacteristic
31#89607C2211yescharacteristic
32#89605—21no—
33#89603—21no—
34#89603C2211yescharacteristic
35#89602C2211yescharacteristic
36#89600—21no—
37D7×#103C411yescharacteristic
38D7×#103C411yescharacteristic
39#89562C411yescharacteristic
40#89562C411yescharacteristic
41#89477—21no—
42#89473—21no—
43C4×Dic28C2211yescharacteristic
44C4×#1131C2211yescharacteristic
45#89457—21no—
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#89275C2211yescharacteristic
60#89275C2211yescharacteristic
61#89253C2211yescharacteristic
62#89251C2211yescharacteristic
63#89251C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66#89249C2211yescharacteristic
67#18062—71nomaximal, Sylow
68C2×Q8×D7C2×C411yescharacteristic
69C2×Q8×D7C2×C411yescharacteristic
70C2×C7×Q16C2×C411yescharacteristic
71C4×C7×Q8C2311yescharacteristic
72C4×C7×Q8C2311yescharacteristic
73Q8×Dic7C2×C411yescharacteristic
74Q8×Dic7C2×C411yescharacteristic
75C2×#1144C2×C411yescharacteristic
76C2×#1144C2×C411yescharacteristic
77D7×Q16—24no—
78C2×Dic28C2×C411yescharacteristic
79C2×#1131—21no—
80C2×C8×D7C2×C411yescharacteristic
81C2×C8×D7C2×C411yescharacteristic
82D7×C4⋊C4—21no—
83D7×C4⋊C4—21no—
84D7×C4⋊C4C2×C411yescharacteristic
85D7×C4⋊C4C2×C411yescharacteristic
86#6450—21no—
87#6450—21no—
88#6450C2×C411yescharacteristic
89#6450C2×C411yescharacteristic
90C42×D7—21no—
91C42×D7—21no—
92C42×D7C2311yescharacteristic
93C4×Dic14—21no—
94C4×Dic14—21no—
95C4×Dic14C2311yescharacteristic
96C4×Dic14C2311yescharacteristic
97C7×#107C2×C411yescharacteristic
98C7×C4⋊C8—21no—
99C7×C4⋊C8—21no—
100C7×C4⋊C8C2311yescharacteristic
101C7×C4⋊C8C2311yescharacteristic
102C7×#103C2×C411yescharacteristic
103C7×#103C2×C411yescharacteristic
104C7×#97—21no—
105C4×C7×C8—21no—
106C4×C7×C8C2311yescharacteristic
107C4×C7×C8C2311yescharacteristic
108C4×C7×C8C2311yescharacteristic
109#6409C2×C411yescharacteristic
110#6409C2×C411yescharacteristic
111(C2×D7)⋊C8—21no—
112(C2×D7)⋊C8—21no—
113(C2×D7)⋊C8D411yescharacteristic
114(C2×D7)⋊C8D411yescharacteristic
115#6392C2×C411yescharacteristic
116#6390C2×C411yescharacteristic
117#6390C2×C411yescharacteristic
118#6389—21no—
119#6389—21no—
120#6389—21no—
121#6389—21no—
122#6389—21no—
123Dic7⋊C8—21no—
124Dic7⋊C8—21no—
125Dic7⋊C8—21no—
126Dic7⋊C8—21no—
127Dic7⋊C8D411yescharacteristic
128Dic7⋊C8D411yescharacteristic
129C8×Dic7—21no—
130C8×Dic7—21no—
131C8×Dic7C2×C411yescharacteristic
132C8×Dic7C2×C411yescharacteristic
133#6384C2×C411yescharacteristic
134#6384C2×C411yescharacteristic
135#6381C2×C411yescharacteristic
136#6381C2×C411yescharacteristic
137C4⋊(C7⋊C8)—21no—
138C4⋊(C7⋊C8)—21no—
139C4⋊(C7⋊C8)C2311yescharacteristic
140C4⋊(C7⋊C8)C2311yescharacteristic
141#6377—21no—
142C4×C7⋊C8—21no—
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145C4×C7⋊C8C2311yescharacteristic
146#2984—71no—
147#2984—71no—
148C2×C4×Q16—71no—
149#1593—71no—
150#1593—71no—
151#1584—71no—
152#1584—71no—
153#1584—71no—
154#1584D711yescharacteristic, complemented
155#1579—71no—
156#1579—71no—
157#1568—71no—
158#1491—71no—
159#1491—71no—
160#1451—71no—
161C2×C7×Q8C22×C411yescharacteristic
162C2×C7×Q8C22×C411yescharacteristic
163Q8×D7—22no—
164Q8×D7—22no—
165Q8×D7—41no—
166Q8×D7—41no—
167C2×C4×D7—21no—
168C2×C4×D7—21no—
169C2×C4×D7—21no—
170C2×C4×D7—21no—
171C2×C4×D7C22×C411yescharacteristic
172C2×C4×D7C2×D411yescharacteristic
173C2×C4×D7#4111yescharacteristic
174C2×Dic14—21no—
175C2×Dic14—21no—
176C2×Dic14C22×C411yescharacteristic
177C2×Dic14C22×C411yescharacteristic
178C7×Q16—22no—
179C2×C7×C8—21no—
180C2×C7×C8—21no—
181C2×C7×C8—21no—
182C2×C7×C8C22×C411yescharacteristic
183C2×C7×C8C22×C411yescharacteristic
184C2×C7×C8C2×D411yescharacteristic
185C2×C7×C8C2×D411yescharacteristic
186C7×C4⋊C4—21no—
187C7×C4⋊C4—21no—
188C7×C4⋊C4C22×C411yescharacteristic
189C7×C4⋊C4C22×C411yescharacteristic
190C42×C7—21no—
191C42×C7—21no—
192C42×C7C2411yescharacteristic
193#1144—22no—
194#1144M1614yescomplemented
195C4⋊Dic7—21no—
196C4⋊Dic7—21no—
197C4⋊Dic7C22×C411yescharacteristic
198C4⋊Dic7C22×C411yescharacteristic
199Dic7⋊C4—21no—
200Dic7⋊C4—21no—
201Dic7⋊C4—21no—
202Dic7⋊C4—21no—
203Dic7⋊C4—21no—
204Dic7⋊C4—21no—
205C4×Dic7—21no—
206C4×Dic7—21no—
207C4×Dic7—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⋊C8C22×C411yescharacteristic
218C2×C7⋊C8C22×C411yescharacteristic
219C2×C7⋊C8C2×D411yescharacteristic
220C2×C7⋊C8C2×D411yescharacteristic
221Dic28—22no—
222#1131—42no—
223C8×D7—22no—
224C8×D7—41no—
225C22×Q16—71no—
226C2×C4×Q8—71no—
227C2×C4×Q8—71no—
228#446—71no—
229#446—71no—
230#446—71no—
231#446—141no—
232#446—141no—
233#446—141no—
234#446—141no—
235#446C2×D711yescharacteristic
236C8×Q8—71no—
237C8×Q8—71no—
238C8×Q8—71no—
239C8×Q8C2×D711yescharacteristic
240C4×Q16—71no—
241C4×Q16—71no—
242C4×Q16—71no—
243C4×Q16—71no—
244C4×Q16—71no—
245C4×Q16—71no—
246C4×Q16—71no—
247C4×Q16C2×D711yescharacteristic
248#432—71no—
249#432—71no—
250#432—141no—
251#432—141no—
252#431—71no—
253#431—141no—
254#431—141no—
255C2×#107—71no—
256C2×#103—71no—
257C2×#103—71no—
258C4×M16—71no—
259C2×C4×C8—71no—
260#335—71no—
261#335C2×D711yescharacteristic
262#334—71no—
263#334—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268Q8⋊C8—71no—
269Q8⋊C8—71no—
270Q8⋊C8C2×D711yescharacteristic
271Q8⋊C8C2×D711yescharacteristic
272#322—71no—
273#322—71no—
274#322—71no—
275#322C2×D711yescharacteristic
276C22×D7C4×D411yescharacteristic
277C7×Q8—21no—
278C7×Q8—21no—
279C7×Q8—21no—
280C7×Q8C2×M1612yes—
281C2×C4×C7—21no—
282C2×C4×C7—21no—
283C2×C4×C7—21no—
284C2×C4×C7—21no—
285C2×C4×C7C23×C411yescharacteristic
286C2×C4×C7C22×D411yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C2×Dic7—21no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7C4×D411yescharacteristic
293C2×Dic7C4×D411yescharacteristic
294C2×Dic7C4×D411yescharacteristic
295C4×D7—22no—
296C4×D7—21no—
297C4×D7—21no—
298C4×D7—21no—
299C4×D7—21no—
300C4×D7—42no—
301C4×D7—42no—
302C4×D7—42no—
303C4×D7—42no—
304Dic14—21no—
305Dic14—21no—
306Dic14—21no—
307Dic14—42no—
308Dic14—42no—
309Dic14C2×M1612yes—
310C7×C8—21no—
311C7×C8—21no—
312C7×C8—21no—
313C7×C8—21no—
314C7×C8—41no—
315C7×C8—41no—
316C7×C8—41no—
317C7⋊C8—21no—
318C7⋊C8—21no—
319C7⋊C8—21no—
320C7⋊C8—41no—
321C7⋊C8—41no—
322C7⋊C8—41no—
323C7⋊C8C2×M1612yes—
324C22×Q8—71no—
325C22×Q8—71no—
326C2×Q16—71no—
327C2×Q16—71no—
328C2×Q16—71no—
329C2×Q16—144no—
330C2×Q16C4×D711yescharacteristic
331C2×M16—141no—
332C22×C8—71no—
333C22×C8—71no—
334C4×Q8—71no—
335C4×Q8—71no—
336C4×Q8—71no—
337C4×Q8—71no—
338C4×Q8—71no—
339C4×Q8—71no—
340C4×Q8—141no—
341C4×Q8—141no—
342C4×Q8—141no—
343C4×Q8—141no—
344C4×Q8C22×D711yescharacteristic
345C4×Q8C22×D711yescharacteristic
346C2×C4⋊C4—71no—
347C2×C4⋊C4—71no—
348C2×C4⋊C4—141no—
349C2×C4⋊C4—141no—
350C2×C42—71no—
351C2×C42—141no—
352C2×C42—141no—
353#107—71no—
354#107—71no—
355#107—71no—
356#107C4×D711yescharacteristic
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—71no—
360C4⋊C8—71no—
361C4⋊C8—71no—
362C4⋊C8—71no—
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#103C4×D711yescharacteristic
378#103C4×D711yescharacteristic
379C22⋊C8—71no—
380C22⋊C8—71no—
381C22⋊C8—141no—
382C22⋊C8—141no—
383#97—21no—
384#97—141no—
385#97—141no—
386#97—141no—
387#97—141no—
388#97—141no—
389#97—141no—
390C4×C8—21no—
391C4×C8—71no—
392C4×C8—71no—
393C4×C8—71no—
394C4×C8—71no—
395C4×C8—71no—
396C4×C8—141no—
397C4×C8—141no—
398C4×C8—141no—
399C4×C8C22×D711yescharacteristic
400C4×C8C22×D711yescharacteristic
401C4×C8C22×D711yescharacteristic
402C22×C7C2×C4×D411yescharacteristic
403C2×D7—21no—
404C2×D7—21no—
405C2×D7#44412yes—
406C4×C7—22no—
407C4×C7—21no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7—41no—
411C4×C7C22×M1611yescharacteristic
412C4×C7#56811yescharacteristic
413C4×C7#57811yescharacteristic
414C4×C7#57811yescharacteristic
415Dic7—22no—
416Dic7—21no—
417Dic7—21no—
418Dic7—21no—
419Dic7—41no—
420Dic7—41no—
421Dic7—41no—
422C2×Q8—71no—
423C2×Q8—71no—
424C2×Q8—141no—
425C2×Q8—141no—
426C2×Q8—142no—
427C2×Q8—142no—
428C2×Q8—281no—
429C2×Q8—281no—
430C2×Q8C2×C4×D711yescharacteristic
431C2×Q8C2×C4×D711yescharacteristic
432C22×C4—71no—
433C22×C4—71no—
434C22×C4—71no—
435C22×C4—141no—
436C22×C4—141no—
437C22×C4—141no—
438C22×C4—141no—
439Q16—22no—
440Q16—74no—
441Q16—142no—
442Q16—142no—
443M16—282no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—71no—
448C2×C8—71no—
449C2×C8—71no—
450C2×C8—71no—
451C2×C8—142no—
452C2×C8—141no—
453C2×C8—141no—
454C2×C8—141no—
455C2×C8—281no—
456C2×C8C2×C4×D711yescharacteristic
457C2×C8C2×C4×D711yescharacteristic
458C2×C8D4×D711yescharacteristic
459C2×C8D4×D711yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—71no—
463C4⋊C4—71no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4—141no—
467C4⋊C4—141no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C4⋊C4C2×C4×D711yescharacteristic
473C4⋊C4C2×C4×D711yescharacteristic
474C42—21no—
475C42—21no—
476C42—71no—
477C42—71no—
478C42—71no—
479C42—141no—
480C42—141no—
481C42—141no—
482C42—141no—
483C42—141no—
484C42—141no—
485C42C23×D711yescharacteristic
486C2×C7D4×M1611yescharacteristic
487C2×C7#295011yescharacteristic
488C2×C7C2×#44411yescharacteristic
489D7—22no—
490C23—71no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—72no—
495Q8—141no—
496Q8—141no—
497Q8—141no—
498Q8—282no—
499Q8—282no—
500Q8D7×M1612yes—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—71no—
506C2×C4—71no—
507C2×C4—71no—
508C2×C4—142no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—141no—
512C2×C4—141no—
513C2×C4—141no—
514C2×C4—141no—
515C2×C4—141no—
516C2×C4—141no—
517C2×C4—282no—
518C2×C4—282no—
519C2×C4—282no—
520C2×C4—282no—
521C2×C4C22×C4×D711yescharacteristic
522C2×C4C2×D4×D711yescharacteristic
523C2×C4D7×#4111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—72no—
532C8—141no—
533C8—141no—
534C8—141no—
535C8—281no—
536C8—281no—
537C8—281no—
538C7#1806211yescharacteristic, complemented, Sylow
539C22—72no—
540C22—141no—
541C22—141no—
542C22C4×D4×D711yescharacteristic
543C4—22no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—141no—
549C4—141no—
550C4—142no—
551C4—141no—
552C4—281no—
553C4—281no—
554C4—281no—
555C4C2×D7×M1611yescharacteristic
556C4#9044111yescharacteristic
557C4#9045711yescharacteristic
558C4#9046211yescharacteristic
559C2—142no—
560C2#1173692811yescharacteristic
561C2#1173716511yescharacteristic
562C2D7×#44411yescharacteristic
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#18062
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. #11728706C2semidirect
6. #11728686C2semidirect
7. #11728657C2semidirect
9. #11726314C2semidirect
12. #11725981C2semidirect
13. #11725969C2semidirect
14. #11725840C2semidirect
154. #1584D7semidirect
194. #1144M16semidirect
538. C7#18062semidirect

Maximal subgroups

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

subgroupindex
#117374092
#117373662
C4×D7×Q162
C7×#15842
#117287062
#117286862
#117286572
#117263242
#117263142
#117259932
#117259812
#117259692
#117258402
#117258242
#180627