Finite Group Databasebeta

← #13324935

Subgroups — #13324935

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#11736774C211yesmaximal, characteristic
2#11736747C211yesmaximal, characteristic
3#11736453C211yesmaximal, characteristic, complemented
4C7×#1573C211yesmaximal, characteristic, complemented
5#11728557C211yesmaximal, characteristic, complemented
6#11728497C211yesmaximal, characteristic, complemented
7#11728179C211yesmaximal, characteristic
8#11726319C211yesmaximal, characteristic, complemented
9#11726316C211yesmaximal, characteristic, complemented
10#11726314C211yesmaximal, characteristic, complemented
11#11726311C211yesmaximal, characteristic, complemented
12#11726277C211yesmaximal, characteristic, complemented
13#11726276C211yesmaximal, characteristic, complemented
14#11726274C211yesmaximal, characteristic, complemented
15#11726271C211yesmaximal, characteristic, complemented
16C4×#1157C2211yescharacteristic
17#90161C2211yescharacteristic
18C7×#432C2211yescharacteristic
19C7×#431C2211yescharacteristic
20C2×C7×C4⋊C8C2211yescharacteristic
21#89874—21no—
22#89873—21no—
23#89697C2211yescharacteristic
24C4×#1136C2211yescharacteristic
25#89623C411yescharacteristic
26#89621C411yescharacteristic
27#89618C411yescharacteristic
28#89613C411yescharacteristic
29#89610C2211yescharacteristic
30#89610C2211yescharacteristic
31#89603C2211yescharacteristic
32#89603C2211yescharacteristic
33#89602C2211yescharacteristic
34#89602C2211yescharacteristic
35#89602C2211yescharacteristic
36#89602C2211yescharacteristic
37#89600—21no—
38#89600—21no—
39#89505C411yescharacteristic
40#89505C411yescharacteristic
41#89501—21no—
42#89501—21no—
43#89495C411yescharacteristic
44#89495C411yescharacteristic
45#89479—21no—
46#89477—21no—
47C4×Dic28C2211yescharacteristic
48C4×Dic28C2211yescharacteristic
49C4×#1132C2211yescharacteristic
50C4×#1132C2211yescharacteristic
51C7×#335C2211yescharacteristic
52C7×#335C2211yescharacteristic
53C7×#334C2211yescharacteristic
54C7×#334C2211yescharacteristic
55#89279C2211yescharacteristic
56#89279C2211yescharacteristic
57#89279C2211yescharacteristic
58#89279C2211yescharacteristic
59#89279C2211yescharacteristic
60#89279C2211yescharacteristic
61#89278C2211yescharacteristic
62#89278C2211yescharacteristic
63#89250C2211yescharacteristic
64#89249C2211yescharacteristic
65#89249C2211yescharacteristic
66C8×C7⋊C8C2211yescharacteristic
67#18013—71nomaximal, Sylow
68C2×#1157C2×C411yescharacteristic
69C22×C7×C8—21no—
70C2×C42×C7C2311yescharacteristic
71C4×C22⋊D7—21no—
72C4×C22⋊D7—21no—
73#6489—21no—
74#6489C2×C411yescharacteristic
75#6487—21no—
76#6487C2×C411yescharacteristic
77#6487C2×C411yescharacteristic
78C2×#1136D411yescharacteristic
79C2×#1136D411yescharacteristic
80C2×Dic28C2×C411yescharacteristic
81C2×Dic28C2×C411yescharacteristic
82C2×#1132C2×C411yescharacteristic
83C2×#1132C2×C411yescharacteristic
84C2×#1131—21no—
85C2×#1131—21no—
86C4×D28C2×C411yescharacteristic
87C4×D28C2311yescharacteristic
88#6435—21no—
89C42×D7—21no—
90#6433—21no—
91#6432C2×C411yescharacteristic
92#6432C2×C411yescharacteristic
93C4×Dic14—21no—
94C4×Dic14C2×C411yescharacteristic
95C4×Dic14C2311yescharacteristic
96C4×Dic14C2311yescharacteristic
97C4×Dic14C2311yescharacteristic
98C7×C4⋊C8—21no—
99C7×C4⋊C8C2×C411yescharacteristic
100C7×C4⋊C8C2×C411yescharacteristic
101C7×C4⋊C8C2311yescharacteristic
102C7×C4⋊C8C2311yescharacteristic
103C7×C4⋊C8C2311yescharacteristic
104C7×C4⋊C8C2311yescharacteristic
105C7×C22⋊C8—21no—
106C7×C22⋊C8C2×C411yescharacteristic
107C7×C22⋊C8C2×C411yescharacteristic
108C7×#97—21no—
109C4×C7×C8C2311yescharacteristic
110C4×C7×C8C2311yescharacteristic
111C22⋊(C7⋊C8)—21no—
112#6395C2×C411yescharacteristic
113#6395C2×C411yescharacteristic
114(C2×D7)⋊C8—21no—
115(C2×D7)⋊C8—21no—
116#6392C2×C411yescharacteristic
117#6392C2×C411yescharacteristic
118#6391C2×C411yescharacteristic
119#6391C2×C411yescharacteristic
120#6390C2×C411yescharacteristic
121#6390C2×C411yescharacteristic
122#6390C2×C411yescharacteristic
123#6390C2×C411yescharacteristic
124#6390C2×C411yescharacteristic
125#6390C2×C411yescharacteristic
126#6389—21no—
127#6389—21no—
128Dic7⋊C8—21no—
129Dic7⋊C8—21no—
130Dic7⋊C8—21no—
131Dic7⋊C8—21no—
132Dic7⋊C8—21no—
133Dic7⋊C8—21no—
134C8×Dic7—21no—
135C8×Dic7—21no—
136C8×Dic7—21no—
137C8×Dic7—21no—
138C4⋊(C7⋊C8)—21no—
139#6377D411yescharacteristic
140#6377D411yescharacteristic
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#1573D711yescharacteristic, complemented
157#1497—71no—
158#1477—71no—
159#1453—71no—
160C22×C4×C7C22×C411yescharacteristic
161C22×C4×C7C2×D411yescharacteristic
162C22×C4×C7#4111yescharacteristic
163C2×C22⋊D7—21no—
164#1157—22no—
165#1157—41no—
166C2×D28C22×C411yescharacteristic
167C2×C4×D7—21no—
168C2×C4×D7—21no—
169C2×C4×D7—21no—
170C2×Dic14—21no—
171C2×Dic14C22×C411yescharacteristic
172C2×Dic14C22×C411yescharacteristic
173C2×Dic14C22×C411yescharacteristic
174C2×C7×C8—21no—
175C2×C7×C8—21no—
176C2×C7×C8—21no—
177C2×C7×C8—21no—
178C2×C7×C8—42no—
179C2×C7×C8C22×C411yescharacteristic
180C2×C7×C8C22×C411yescharacteristic
181C2×C7×C8C22×C411yescharacteristic
182C2×C7×C8C22×C411yescharacteristic
183C42×C7C22×C411yescharacteristic
184C42×C7C2×D411yescharacteristic
185C42×C7#4111yescharacteristic
186C42×C7C2411yescharacteristic
187C22⋊Dic7—21no—
188C22⋊Dic7—21no—
189C22⋊Dic7—21no—
190(C2×D7)⋊C4—21no—
191(C2×D7)⋊C4—21no—
192C4⋊Dic7—21no—
193C4⋊Dic7—21no—
194C4⋊Dic7—21no—
195C4⋊Dic7C22×C411yescharacteristic
196C4⋊Dic7C22×C411yescharacteristic
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—
210#1136—22no—
211#1136—41no—
212C2×C7⋊C8—21no—
213C2×C7⋊C8—21no—
214C2×C7⋊C8C2×D411yescharacteristic
215C2×C7⋊C8C2×D411yescharacteristic
216C2×C7⋊C8C2×D411yescharacteristic
217C2×C7⋊C8C2×D411yescharacteristic
218Dic28—22no—
219Dic28—22no—
220#1132—41no—
221#1132—41no—
222#1131—42no—
223#1131—42no—
224#533—71no—
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⋊C8C2×D711yescharacteristic
256#405—141no—
257C4×M16—71no—
258C4×M16—141no—
259#335C2×D711yescharacteristic
260#335C2×D711yescharacteristic
261#334C2×D711yescharacteristic
262#334C2×D711yescharacteristic
263Q8⋊C8—71no—
264Q8⋊C8—71no—
265Q8⋊C8—71no—
266Q8⋊C8—71no—
267Q8⋊C8—71no—
268Q8⋊C8—71no—
269D4⋊C8—71no—
270D4⋊C8—71no—
271#322—71no—
272#322—71no—
273#322—71no—
274C82—71no—
275C23×C7C4×D411yescharacteristic
276C22×D7—21no—
277C2×C4×C7—21no—
278C2×C4×C7—21no—
279C2×C4×C7—21no—
280C2×C4×C7—21no—
281C2×C4×C7—41no—
282C2×C4×C7C4×D411yescharacteristic
283C2×C4×C7C4×D411yescharacteristic
284C2×C4×C7C4×D411yescharacteristic
285C2×C4×C7C23×C411yescharacteristic
286C2×C4×C7C22×D411yescharacteristic
287C2×C4×C7C2×#4111yescharacteristic
288C22⋊D7—42no—
289C2×Dic7—21no—
290C2×Dic7—21no—
291C2×Dic7—21no—
292C2×Dic7—21no—
293C2×Dic7—21no—
294C2×Dic7—21no—
295C2×Dic7—21no—
296D28—21no—
297D28—21no—
298C4×D7—42no—
299C4×D7—41no—
300C4×D7—41no—
301C4×D7—81no—
302Dic14—21no—
303Dic14—21no—
304Dic14—21no—
305Dic14—21no—
306Dic14—21no—
307Dic14—81no—
308Dic14#13112yes—
309C7×C8—21no—
310C7×C8—21no—
311C7×C8—21no—
312C7×C8—21no—
313C7×C8—41no—
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#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—21no—
333C4⋊Q8—71no—
334C4⋊Q8—71no—
335#125—141no—
336C22⋊Q8—71no—
337C22⋊Q8—71no—
338C22⋊Q8—141no—
339C4×Q8—71no—
340C4×Q8—71no—
341C4×Q8—71no—
342C4×Q8—71no—
343C4×Q8—141no—
344C4×D4—71no—
345C4×D4—71no—
346C4×D4—141no—
347C4×D4—141no—
348#117—71no—
349#117—141no—
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—141no—
359C4⋊C8—141no—
360C4⋊C8—141no—
361C4⋊C8—141no—
362C4⋊C8—141no—
363C4⋊C8—141no—
364C4⋊C8—141no—
365C4⋊C8C4×D711yescharacteristic
366C4⋊C8C4×D711yescharacteristic
367C4⋊C8C22×D711yescharacteristic
368C4⋊C8C22×D711yescharacteristic
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—141no—
381C22⋊C8—141no—
382C22⋊C8—141no—
383C22⋊C8C4×D711yescharacteristic
384C22⋊C8C4×D711yescharacteristic
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×C7C2×#13111yescharacteristic
412C4×C7#56811yescharacteristic
413C4×C7C2×#13711yescharacteristic
414C4×C7#57511yescharacteristic
415Dic7—22no—
416Dic7—41no—
417Dic7—41no—
418Dic7—41no—
419Dic7—41no—
420Dic7—41no—
421Dic7—41no—
422#41—142no—
423#41—281no—
424C2×Q8—71no—
425C2×Q8—71no—
426C2×Q8—71no—
427C2×Q8—141no—
428C2×D4—71no—
429C2×D4—141no—
430C22×C4—141no—
431C22×C4—141no—
432C22×C4—141no—
433C22×C4C2×C4×D711yescharacteristic
434C22×C4D4×D711yescharacteristic
435C22×C4#116111yescharacteristic
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—42no—
449C2×C8—71no—
450C2×C8—71no—
451C2×C8—71no—
452C2×C8—71no—
453C2×C8—141no—
454C2×C8—141no—
455C2×C8C2×C4×D711yescharacteristic
456C2×C8C2×C4×D711yescharacteristic
457C2×C8C2×C4×D711yescharacteristic
458C2×C8C2×C4×D711yescharacteristic
459C4⋊C4—71no—
460C4⋊C4—71no—
461C4⋊C4—71no—
462C4⋊C4—71no—
463C4⋊C4—141no—
464C4⋊C4—141no—
465C4⋊C4—141no—
466C4⋊C4—141no—
467C4⋊C4—141no—
468C4⋊C4—141no—
469C4⋊C4—141no—
470C4⋊C4—141no—
471C4⋊C4—141no—
472C22⋊C4—141no—
473C22⋊C4—141no—
474C22⋊C4—141no—
475C22⋊C4—141no—
476C22⋊C4—141no—
477C42—141no—
478C42—141no—
479C42—141no—
480C42—141no—
481C42—141no—
482C42C2×C4×D711yescharacteristic
483C42D4×D711yescharacteristic
484C42#116111yescharacteristic
485C42C23×D711yescharacteristic
486C2×C7—41no—
487C2×C7#293311yescharacteristic
488C2×C7C4×#13711yescharacteristic
489C2×C7#295711yescharacteristic
490D7—81no—
491C23—141no—
492C23#645611yescharacteristic
493Q8—72no—
494Q8—141no—
495Q8—141no—
496Q8—141no—
497Q8—141no—
498Q8—141no—
499Q8—561no—
500D4—141no—
501D4—141no—
502D4—282no—
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—141no—
512C2×C4—141no—
513C2×C4—141no—
514C2×C4—141no—
515C2×C4—282no—
516C2×C4—281no—
517C2×C4—281no—
518C2×C4—561no—
519C2×C4#645611yescharacteristic
520C2×C4#645611yescharacteristic
521C2×C4#645611yescharacteristic
522C2×C4C22×C4×D711yescharacteristic
523C2×C4C2×D4×D711yescharacteristic
524C2×C4C2×#116111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—72no—
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×#645611yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—142no—
552C4—281no—
553C4—281no—
554C4—281no—
555C4—281no—
556C4—281no—
557C4—281no—
558C4D7×#13111yescharacteristic
559C4#9044111yescharacteristic
560C4#9046411yescharacteristic
561C4D7×#13711yescharacteristic
562C2—41no—
563C2—561no—
564C2#1173652011yescharacteristic
565C2#1173664511yescharacteristic
566C2#1173669411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D7
commutatorC2×C4×C7C23×C4
FrattiniC42C23×D7
FittingC7×#1573C2
socleC22×C7C2×C4×D4
prime radicalC2×#1157C2×C4
cosocleC42×C7C24
hypercenter#1573D7
hypocenterC7#18013
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #11736453C2semidirect
4. C7×#1573C2semidirect
5. #11728557C2semidirect
6. #11728497C2semidirect
8. #11726319C2semidirect
9. #11726316C2semidirect
10. #11726314C2semidirect
11. #11726311C2semidirect
12. #11726277C2semidirect
13. #11726276C2semidirect
14. #11726274C2semidirect
15. #11726271C2semidirect
156. #1573D7semidirect
539. C7#18013semidirect

Maximal subgroups

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

subgroupindex
#117367742
#117367472
#117364532
C7×#15732
#117285572
#117284972
#117281792
#117263192
#117263162
#117263142
#117263112
#117262772
#117262762
#117262742
#117262712
#180137