Finite Group Databasebeta

← #13324620

Subgroups — #13324620

Order 1792.

566 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11740790C211yesmaximal, characteristic
2#11740776C211yesmaximal, characteristic, complemented
3#11736498C211yesmaximal, characteristic
4C7×#1493C211yesmaximal, characteristic, complemented
5#11728246C211yesmaximal, characteristic, complemented
6#11727490C211yesmaximal, characteristic
7#11727479C211yesmaximal, characteristic, complemented
8#11725977C211yesmaximal, characteristic, complemented
9#11725976C211yesmaximal, characteristic, complemented
10#11725975C211yesmaximal, characteristic, complemented
11#11725974C211yesmaximal, characteristic, complemented
12#11725973C211yesmaximal, characteristic, complemented
13#11725972C211yesmaximal, characteristic, complemented
14#11725971C211yesmaximal, characteristic, complemented
15#11725970C211yesmaximal, characteristic, complemented
16C7×#533C2211yescharacteristic
17#90170C2211yescharacteristic
18C7×#423C2211yescharacteristic
19C2×C4×C7×C8C2211yescharacteristic
20#89900—21no—
21#89899—21no—
22#89861C411yescharacteristic
23#89858C411yescharacteristic
24#89854C411yescharacteristic
25#89852C411yescharacteristic
26#89824C411yescharacteristic
27#89824C411yescharacteristic
28#89821C411yescharacteristic
29#89821C411yescharacteristic
30C4×#1144C2211yescharacteristic
31C4×#1144C2211yescharacteristic
32C4×#1143C2211yescharacteristic
33C4×#1143C2211yescharacteristic
34#89796—21no—
35#89796—21no—
36#89796C2211yescharacteristic
37#89796C2211yescharacteristic
38Q8×C7⋊C8C2211yescharacteristic
39Q8×C7⋊C8C2211yescharacteristic
40#89772—21no—
41#89772—21no—
42#89698C2211yescharacteristic
43#89697C2211yescharacteristic
44C4×#1136C2211yescharacteristic
45#89612—21no—
46#89611—21no—
47#89610C2211yescharacteristic
48#89606C2211yescharacteristic
49#89603C2211yescharacteristic
50#89602C2211yescharacteristic
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#89250C2211yescharacteristic
65#89249C2211yescharacteristic
66#89249C2211yescharacteristic
67#17988—71nomaximal, Sylow
68C2×C7×M16—21no—
69C22×C7×C8—21no—
70C7×C4⋊Q8C2×C411yescharacteristic
71C7×C4⋊Q8C2×C411yescharacteristic
72C7×#125—21no—
73C7×C22⋊Q8—21no—
74C7×C22⋊Q8C2×C411yescharacteristic
75C7×C22⋊Q8C2×C411yescharacteristic
76C4×C7×Q8—21no—
77C4×C7×Q8C2311yescharacteristic
78C4×C7×Q8C2311yescharacteristic
79C7×#117—21no—
80C2×C42×C7C2311yescharacteristic
81C2×#1144C2×C411yescharacteristic
82C2×#1144C2×C411yescharacteristic
83C2×#1143C2×C411yescharacteristic
84C2×#1143C2×C411yescharacteristic
85#6493C2×C411yescharacteristic
86#6492—21no—
87C4×C22⋊D7—21no—
88#6487C2×C411yescharacteristic
89C2×#1136C2×C411yescharacteristic
90C2×#1136C2×C411yescharacteristic
91C2×#1131—21no—
92C2×C8×D7—21no—
93#6439—21no—
94#6438C2×C411yescharacteristic
95C4×D28C2311yescharacteristic
96#6435—21no—
97#6433C2×C411yescharacteristic
98C4×Dic14C2311yescharacteristic
99C7×C4⋊C8—21no—
100C7×C4⋊C8C2311yescharacteristic
101C7×C4⋊C8C2311yescharacteristic
102C4×C7×C8—21no—
103C4×C7×C8C2311yescharacteristic
104C4×C7×C8C2311yescharacteristic
105#6409C2×C411yescharacteristic
106#6409C2×C411yescharacteristic
107#6409C2×C411yescharacteristic
108#6409C2×C411yescharacteristic
109C22⋊(C7⋊C8)—21no—
110C22⋊(C7⋊C8)D411yescharacteristic
111C22⋊(C7⋊C8)D411yescharacteristic
112(C2×D7)⋊C8—21no—
113(C2×D7)⋊C8—21no—
114#6389—21no—
115Dic7⋊C8—21no—
116Dic7⋊C8—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)D411yescharacteristic
131C4⋊(C7⋊C8)D411yescharacteristic
132C4⋊(C7⋊C8)C2311yescharacteristic
133C4⋊(C7⋊C8)C2311yescharacteristic
134#6377—21no—
135#6377—21no—
136#6377—21no—
137#6377C2×C411yescharacteristic
138#6377C2×C411yescharacteristic
139C4×C7⋊C8—21no—
140C4×C7⋊C8—21no—
141C4×C7⋊C8C2311yescharacteristic
142C4×C7⋊C8C2311yescharacteristic
143C4×C7⋊C8C2311yescharacteristic
144C4×C7⋊C8C2311yescharacteristic
145#3172—71no—
146#2993—71no—
147#2985—71no—
148#1588—71no—
149#1587—71no—
150#1587—71no—
151#1585—71no—
152#1584—71no—
153#1584—71no—
154#1583—71no—
155#1582—71no—
156#1569—71no—
157#1494—71no—
158#1493D711yescharacteristic, complemented
159#1451—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—
167C2×D28C22×C411yescharacteristic
168C2×C4×D7—21no—
169C2×Dic14C22×C411yescharacteristic
170C7×M16—81no—
171C2×C7×C8—21no—
172C2×C7×C8—21no—
173C2×C7×C8—21no—
174C2×C7×C8—21no—
175C2×C7×C8—42no—
176C7×C4⋊C4—21no—
177C7×C4⋊C4—21no—
178C7×C4⋊C4—21no—
179C7×C4⋊C4—21no—
180C7×C4⋊C4—21no—
181C7×C4⋊C4—21no—
182C7×C4⋊C4—21no—
183C7×C4⋊C4C22×C411yescharacteristic
184C7×C4⋊C4C22×C411yescharacteristic
185C7×C22⋊C4—21no—
186C7×C22⋊C4—21no—
187C42×C7—21no—
188C42×C7—21no—
189C42×C7C22×C411yescharacteristic
190C42×C7C2×D411yescharacteristic
191C42×C7#4111yescharacteristic
192C42×C7C2411yescharacteristic
193C22⋊Dic7—21no—
194#1144—41no—
195#1144—41no—
196#1143—41no—
197#1143—41no—
198(C2×D7)⋊C4—21no—
199(C2×D7)⋊C4—21no—
200(C2×D7)⋊C4—21no—
201(C2×D7)⋊C4—21no—
202C4⋊Dic7C22×C411yescharacteristic
203C4⋊Dic7C22×C411yescharacteristic
204Dic7⋊C4—21no—
205Dic7⋊C4—21no—
206Dic7⋊C4—21no—
207Dic7⋊C4—21no—
208C4×Dic7—21no—
209#1136—41no—
210#1136—41no—
211C2×C7⋊C8—21no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8C22×C411yescharacteristic
214C2×C7⋊C8C22×C411yescharacteristic
215C2×C7⋊C8C22×C411yescharacteristic
216C2×C7⋊C8C22×C411yescharacteristic
217C2×C7⋊C8C2×D411yescharacteristic
218C2×C7⋊C8C2×D411yescharacteristic
219C2×C7⋊C8C2×D411yescharacteristic
220C2×C7⋊C8C2×D411yescharacteristic
221#1131—81no—
222C8×D7—81no—
223#533C2×D711yescharacteristic
224#529—71no—
225#501—71no—
226#497—71no—
227#491—71no—
228#489—71no—
229#470—71no—
230#470—71no—
231#468—71no—
232#468—71no—
233#446—71no—
234#446—71no—
235#446—71no—
236#446—141no—
237#446—141no—
238C8×Q8—71no—
239C8×Q8—71no—
240C8×Q8—71no—
241C4×Q16—71no—
242C4×Q16—71no—
243C4×SD16—71no—
244C4×SD16—71no—
245#436—71no—
246#436—141no—
247#435—141no—
248C8×D4—71no—
249#433—141no—
250#433—141no—
251#433—141no—
252#432—71no—
253#431—71no—
254#424—141no—
255#423C2×D711yescharacteristic
256C4×M16—71no—
257C2×C4×C8C2×D711yescharacteristic
258#335—71no—
259#335—71no—
260#334—71no—
261#334—71no—
262Q8⋊C8—71no—
263Q8⋊C8—71no—
264Q8⋊C8C2×D711yescharacteristic
265Q8⋊C8C2×D711yescharacteristic
266Q8⋊C8C2×D711yescharacteristic
267Q8⋊C8C2×D711yescharacteristic
268D4⋊C8—71no—
269D4⋊C8—71no—
270#322—71no—
271#322—71no—
272#322—71no—
273#322—71no—
274C23×C7C4×D411yescharacteristic
275C22×D7—21no—
276C7×Q8—21no—
277C7×Q8—21no—
278C7×Q8—21no—
279C7×Q8—21no—
280C7×Q8—81no—
281C2×C4×C7—21no—
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—41no—
290C2×C4×C7C4×D411yescharacteristic
291C2×C4×C7C4×D411yescharacteristic
292C2×C4×C7C4×D411yescharacteristic
293C2×C4×C7C23×C411yescharacteristic
294C2×C4×C7C22×D411yescharacteristic
295C2×C4×C7C2×#4111yescharacteristic
296C22⋊D7—81no—
297C2×Dic7—21no—
298C2×Dic7—21no—
299C2×Dic7—21no—
300D28—21no—
301D28—21no—
302C4×D7—41no—
303C4×D7—41no—
304Dic14—21no—
305Dic14—21no—
306C7×C8—22no—
307C7×C8—41no—
308C7×C8—41no—
309C7×C8—41no—
310C7⋊C8—21no—
311C7⋊C8—21no—
312C7⋊C8—21no—
313C7⋊C8—21no—
314C7⋊C8—21no—
315C7⋊C8—21no—
316C7⋊C8—21no—
317C7⋊C8—21no—
318C7⋊C8—41no—
319C7⋊C8—41no—
320C2×Q16—71no—
321C2×Q16—71no—
322C2×SD16—71no—
323C2×SD16—71no—
324C2×M16—21no—
325C2×M16—71no—
326C2×M16—71no—
327C2×M16—141no—
328C22×C8—21no—
329C22×C8—141no—
330C4⋊Q8C4×D711yescharacteristic
331C4⋊Q8C4×D711yescharacteristic
332#126—141no—
333#125—21no—
334#125—71no—
335#124—71no—
336#123—141no—
337C22⋊Q8—21no—
338C22⋊Q8—71no—
339C22⋊Q8C4×D711yescharacteristic
340C22⋊Q8C4×D711yescharacteristic
341#121—71no—
342C4×Q8—21no—
343C4×Q8—71no—
344C4×Q8C22×D711yescharacteristic
345C4×Q8C22×D711yescharacteristic
346C4×D4—71no—
347C4×D4—141no—
348#117—21no—
349#117—141no—
350C2×C42C22×D711yescharacteristic
351#107—71no—
352#107—71no—
353#106—71no—
354#106—71no—
355C4⋊C8—21no—
356C4⋊C8—71no—
357C4⋊C8—71no—
358C4⋊C8—71no—
359C4⋊C8—71no—
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#102—71no—
375#102—71no—
376C22⋊C8—71no—
377C22⋊C8—71no—
378C22⋊C8—141no—
379C22⋊C8—141no—
380C22⋊C8—141no—
381#97—71no—
382#97—71no—
383#97—141no—
384#97—141no—
385#97—141no—
386#97—141no—
387C4×C8—21no—
388C4×C8—71no—
389C4×C8—71no—
390C4×C8—71no—
391C4×C8—71no—
392C4×C8—141no—
393C4×C8—141no—
394C4×C8—141no—
395C4×C8C22×D711yescharacteristic
396C4×C8C22×D711yescharacteristic
397C22×C7—21no—
398C22×C7—21no—
399C22×C7—21no—
400C22×C7C2×C4×D411yescharacteristic
401C2×D7—41no—
402C2×D7—41no—
403C2×D7—41no—
404C4×C7—21no—
405C4×C7—21no—
406C4×C7—21no—
407C4×C7—21no—
408C4×C7—41no—
409C4×C7—41no—
410C4×C7—41no—
411C4×C7—41no—
412C4×C7#56811yescharacteristic
413C4×C7#56811yescharacteristic
414C4×C7#57711yescharacteristic
415C4×C7#57811yescharacteristic
416Dic7—41no—
417Dic7—41no—
418Dic7—41no—
419C2×Q8—21no—
420C2×Q8—71no—
421C2×Q8C2×C4×D711yescharacteristic
422C2×Q8C2×C4×D711yescharacteristic
423C2×D4—71no—
424C2×D4—141no—
425C22×C4—141no—
426C22×C4C2×C4×D711yescharacteristic
427C22×C4D4×D711yescharacteristic
428C22×C4#115911yescharacteristic
429Q16—281no—
430Q16—281no—
431SD16—281no—
432SD16—281no—
433M16—81no—
434M16—281no—
435M16—281no—
436M16—561no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—42no—
442C2×C8—71no—
443C2×C8—71no—
444C2×C8—71no—
445C2×C8—71no—
446C2×C8—71no—
447C2×C8—71no—
448C2×C8—71no—
449C2×C8—71no—
450C2×C8—141no—
451C2×C8—141no—
452C2×C8—561no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—71no—
461C4⋊C4—71no—
462C4⋊C4—141no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4C2×C4×D711yescharacteristic
467C4⋊C4C2×C4×D711yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—141no—
471C22⋊C4—141no—
472C22⋊C4—141no—
473C22⋊C4—141no—
474C22⋊C4—141no—
475C42—21no—
476C42—21no—
477C42—141no—
478C42C2×C4×D711yescharacteristic
479C42D4×D711yescharacteristic
480C42#115911yescharacteristic
481C42C23×D711yescharacteristic
482C2×C7—41no—
483C2×C7#293211yescharacteristic
484C2×C7#294711yescharacteristic
485C2×C7#295611yescharacteristic
486D7—81no—
487C23—141no—
488C23(C22⋊D7)⋊C411yescharacteristic
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—81no—
494Q8—141no—
495Q8—141no—
496D4—141no—
497D4—141no—
498D4—561no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—141no—
509C2×C4—141no—
510C2×C4—141no—
511C2×C4—281no—
512C2×C4—281no—
513C2×C4(C22⋊D7)⋊C411yescharacteristic
514C2×C4(C22⋊D7)⋊C411yescharacteristic
515C2×C4(C22⋊D7)⋊C411yescharacteristic
516C2×C4C22×C4×D711yescharacteristic
517C2×C4C2×D4×D711yescharacteristic
518C2×C4C2×#115911yescharacteristic
519C8—22no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—141no—
524C8—141no—
525C8—141no—
526C8—141no—
527C8—141no—
528C8—141no—
529C8—141no—
530C8—141no—
531C8—281no—
532C8—281no—
533C7#1798811yescharacteristic, complemented, Sylow
534C22—21no—
535C22—21no—
536C22—21no—
537C22—281no—
538C22—281no—
539C22—281no—
540C22C2×(C22⋊D7)⋊C411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—281no—
550C4—281no—
551C4—281no—
552C4#9044111yescharacteristic
553C4#9044111yescharacteristic
554C4#9045311yescharacteristic
555C4#9045711yescharacteristic
556C2—41no—
557C2—561no—
558C2#1173610311yescharacteristic
559C2#1173621911yescharacteristic
560C2#1173642511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1493C2
socleC22×C7C2×C4×D4
prime radical#6493C2×C4
cosocleC42×C7C24
hypercenter#1493D7
hypocenterC7#17988
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
2. #11740776C2semidirect
4. C7×#1493C2semidirect
5. #11728246C2semidirect
7. #11727479C2semidirect
8. #11725977C2semidirect
9. #11725976C2semidirect
10. #11725975C2semidirect
11. #11725974C2semidirect
12. #11725973C2semidirect
13. #11725972C2semidirect
14. #11725971C2semidirect
15. #11725970C2semidirect
158. #1493D7semidirect
533. C7#17988semidirect

Maximal subgroups

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

subgroupindex
#117407902
#117407762
#117364982
C7×#14932
#117282462
#117274902
#117274792
#117259772
#117259762
#117259752
#117259742
#117259732
#117259722
#117259712
#117259702
#179887