Finite Group Databasebeta

← #27187631

Subgroups — #27187631

Order 12928.

532 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20266129C211yesmaximal, characteristic
2#20266128C211yesmaximal, characteristic, complemented
3#20266127C211yesmaximal, characteristic, complemented
4#20266127C211yesmaximal, characteristic, complemented
5#20266127C211yesmaximal, characteristic, complemented
6#20266127C211yesmaximal, characteristic, complemented
7#20266126C211yesmaximal, characteristic, complemented
8#20266126C211yesmaximal, characteristic, complemented
9#20266125C211yesmaximal, characteristic
10#20266124C211yesmaximal, characteristic, complemented
11#20266119C211yesmaximal, characteristic, complemented
12C4⋊C4×#87938C211yesmaximal, characteristic, complemented
13C22⋊C4×#87938C211yesmaximal, characteristic, complemented
14C4×C22⋊#87938C211yesmaximal, characteristic, complemented
15#123×D101C211yesmaximal, characteristic
16C23×#87938C2211yescharacteristic
17C2×C4⋊#87938C2211yescharacteristic
18C2×C4⋊#87938C2211yescharacteristic
19C2×C4⋊#87938C2211yescharacteristic
20C2×C4⋊#87938C2211yescharacteristic
21C2×C4⋊#87938C2211yescharacteristic
22C2×C22⋊#87938C2211yescharacteristic
23C2×C22⋊#87938C2211yescharacteristic
24C2×C22⋊#87938C2211yescharacteristic
25C2×C22⋊#87938C2211yescharacteristic
26C2×C22⋊#87938C2211yescharacteristic
27C2×C22⋊#87938C2211yescharacteristic
28C2×C22⋊#87938C2211yescharacteristic
29C2×C4×#87938C2211yescharacteristic
30C2×C4×#87938C2211yescharacteristic
31C2×C4×#87938C2211yescharacteristic
32C2×C4×#87938C2211yescharacteristic
33C2×C4×#87938C2211yescharacteristic
34(C2×#87938)⋊C4C2211yescharacteristic
35(C2×#87938)⋊C4C2211yescharacteristic
36(C2×#87938)⋊C4C2211yescharacteristic
37(C2×#87938)⋊C4C2211yescharacteristic
38(C2×#87938)⋊C4C2211yescharacteristic
39(C2×#87938)⋊C4C2211yescharacteristic
40(C2×#87938)⋊C4C2211yescharacteristic
41(C2×#87938)⋊C4C2211yescharacteristic
42(C2×#87938)⋊C4C2211yescharacteristic
43(C2×#87938)⋊C4C2211yescharacteristic
44C2×D4×D101C2211yescharacteristic
45C22×C4×D101C2211yescharacteristic
46#15692240C411yescharacteristic, complemented
47#15692240C411yescharacteristic, complemented
48#15692239C411yescharacteristic, complemented
49#15692238C411yescharacteristic, complemented
50#15692237C411yescharacteristic, complemented
51#15692237C411yescharacteristic, complemented
52#15692236C411yescharacteristic, complemented
53C4⋊C4×D101C2211yescharacteristic
54C4⋊C4×D101C2211yescharacteristic
55C22⋊C4×D101C2211yescharacteristic
56C22⋊C4×D101C2211yescharacteristic
57C22⋊C4×D101C2211yescharacteristic
58#123×C101C411yescharacteristic, complemented
59C22×#87938—22no—
60C22×#87938—41no—
61C22×#87938—41no—
62C22×#87938C2311yescharacteristic
63C22×#87938C2311yescharacteristic
64C22×#87938C2311yescharacteristic
65C22×#87938C2311yescharacteristic
66C22×#87938C2311yescharacteristic
67C22×#87938C2311yescharacteristic
68C22×#87938C2311yescharacteristic
69C22×#87938C2311yescharacteristic
70C4⋊#87938—22no—
71C4⋊#87938—41no—
72C4⋊#87938—41no—
73C4⋊#87938—41no—
74C4⋊#87938—41no—
75C22⋊#87938—22no—
76C22⋊#87938—22no—
77C22⋊#87938—22no—
78C22⋊#87938—41no—
79C22⋊#87938—41no—
80C22⋊#87938—41no—
81C22⋊#87938—41no—
82C4×#87938—22no—
83C4×#87938—41no—
84C4×#87938—41no—
85C4×#87938—41no—
86C4×#87938—41no—
87C23×D101C2311yescharacteristic
88C23×D101C2311yescharacteristic
89C2×D404C2×C411yescharacteristic
90C2×C22⋊D101C2×C411yescharacteristic
91C2×C22⋊D101C2×C411yescharacteristic
92D4×D101—41no—
93D4×D101—41no—
94C22×Dic101C2×C411yescharacteristic, complemented
95C2×C4×D101—41no—
96C2×C4×D101—41no—
97C2×C4×D101C2×C411yescharacteristic, complemented
98C2×C4×D101C2×C411yescharacteristic, complemented
99C2×C4×D101C2311yescharacteristic
100C2×C4×D101C2311yescharacteristic
101C2×C4×D101C2311yescharacteristic
102C2×C4×D101C2311yescharacteristic
103C2×C4×D101C2311yescharacteristic
104C4⋊Dic101C2×C411yescharacteristic, complemented
105C4⋊Dic101C2×C411yescharacteristic, complemented
106#13108053C2×C411yescharacteristic, complemented
107#13108053C2×C411yescharacteristic, complemented
108#13108053C2×C411yescharacteristic, complemented
109#13108053C2×C411yescharacteristic, complemented
110C22⋊Dic101C2×C411yescharacteristic
111C22⋊Dic101C2×C411yescharacteristic
112C22⋊Dic101C2×C411yescharacteristic, complemented
113#13108051C2×C411yescharacteristic
114#13108051C2×C411yescharacteristic
115#13108051C2×C411yescharacteristic
116#13108051C2×C411yescharacteristic
117#13108051C2×C411yescharacteristic, complemented
118#13108051C2×C411yescharacteristic, complemented
119C2×D4×C101C2×C411yescharacteristic
120C22×C4×C101C2×C411yescharacteristic, complemented
121C4⋊C4×C101C2×C411yescharacteristic, complemented
122C4⋊C4×C101C2×C411yescharacteristic, complemented
123C22⋊C4×C101C2×C411yescharacteristic
124C22⋊C4×C101C2×C411yescharacteristic
125C22⋊C4×C101C2×C411yescharacteristic, complemented
126C23×C101C22×C411yescharacteristic
127C23×C101C22×C411yescharacteristic
128C22×D101—21no—
129C22×D101—21no—
130C22×D101—21no—
131C22×D101—21no—
132C22×D101—21no—
133C22×D101—21no—
134C22×D101—21no—
135C22×D101—21no—
136C22×D101—21no—
137C22×D101—21no—
138C22×D101—21no—
139C22×D101—21no—
140C22×D101C22×C411yescharacteristic
141C22×D101C22×C411yescharacteristic
142C22×D101C2411yescharacteristic
143C2×#87938—21no—
144C2×#87938—21no—
145C2×#87938—21no—
146C2×#87938—21no—
147C2×#87938—21no—
148C2×#87938—21no—
149C2×#87938—21no—
150C2×#87938—21no—
151C2×#87938—21no—
152C2×#87938—21no—
153C2×#87938—21no—
154C2×#87938—21no—
155C2×#87938—21no—
156C2×#87938—21no—
157C2×#87938—21no—
158C2×#87938—21no—
159C2×#87938—21no—
160C2×#87938—21no—
161C2×#87938—21no—
162C2×#87938—21no—
163C2×#87938—21no—
164C2×#87938—21no—
165C2×#87938—44no—
166C2×#87938#4112yes—
167C2×#87938#4112yes—
168D4×C101—41no—
169C2×C4×C101—41no—
170C2×C4×C101C22×C411yescharacteristic
171C2×C4×C101C22×C411yescharacteristic
172C2×C4×C101C22×C411yescharacteristic
173C2×C4×C101C22×C411yescharacteristic
174C2×C4×C101C22×C411yescharacteristic
175C22⋊D101—41no—
176C22⋊D101—41no—
177C2×Dic101—41no—
178C2×Dic101C22×C411yescharacteristic
179C2×Dic101C22×C411yescharacteristic
180C2×Dic101C22×C411yescharacteristic
181C2×Dic101C22×C411yescharacteristic
182C2×Dic101C22×C411yescharacteristic
183D404—41no—
184C4×D101—21no—
185C4×D101—21no—
186C4×D101—21no—
187C4×D101—21no—
188C4×D101—21no—
189C4×D101—21no—
190C4×D101—21no—
191C4×D101—21no—
192C4×D101—21no—
193C4×D101—21no—
194C4×D101—41no—
195C4×D101—41no—
196C22×C101—21no—
197C22×C101—21no—
198C22×C101—21no—
199C22×C101—21no—
200C22×C101—21no—
201C22×C101—21no—
202C22×C101C23×C411yescharacteristic
203C2×D101—21no—
204C2×D101—21no—
205C2×D101—21no—
206C2×D101—21no—
207C2×D101—21no—
208C2×D101—21no—
209C2×D101—41no—
210C2×D101—41no—
211C2×D101—41no—
212C2×D101—41no—
213C2×D101—41no—
214C2×D101—41no—
215C2×D101—41no—
216C2×D101—41no—
217C2×D101C2×#4111yescharacteristic
218C2×D101C2×#4111yescharacteristic
219C2×D101H(5,𝔽2)11yescharacteristic
220C2×D101H(5,𝔽2)11yescharacteristic
221C2×D101H(5,𝔽2)11yescharacteristic
222C2×D1012−1+411yescharacteristic
223#87938—22no—
224#87938—22no—
225#87938—41no—
226#87938—41no—
227#87938—41no—
228#87938—41no—
229#87938—41no—
230#87938—41no—
231C4×C101—21no—
232C4×C101—21no—
233C4×C101—21no—
234C4×C101—21no—
235C4×C101—21no—
236Dic101—21no—
237Dic101—21no—
238Dic101—21no—
239Dic101—21no—
240Dic101—21no—
241C2×C101—41no—
242C2×C101—41no—
243C2×C101C4×#4111yescharacteristic
244C2×C101#51811yescharacteristic
245C2×C101#52011yescharacteristic
246D101—41no—
247D101—41no—
248D101#53811yescharacteristic
249D101#53911yescharacteristic
250D101#54011yescharacteristic
251D101#54211yescharacteristic
252#2335—1011nomaximal, Sylow
253C101#233511yescharacteristic, complemented, Sylow
254C2×#123—1011no—
255#390—1011no—
256#389—1011no—
257#388—1011no—
258#388—1011no—
259#388—1011no—
260#388—1011no—
261#387—1011no—
262#387—1011no—
263#386—1011no—
264#385—1011no—
265#380—1011no—
266C4×C4⋊C4—1011no—
267C4×C22⋊C4—1011no—
268C4×C22⋊C4—1011no—
269C22×D4—1011no—
270C23×C4—1011no—
271C23×C4—1011no—
272#123—1011no—
273#123—1011no—
274#123—1011no—
275#123—1011no—
276#123—1011no—
277#123—1011no—
278#123—1011no—
279#123#8793811yescharacteristic, complemented
280C2×C4⋊C4—1011no—
281C2×C4⋊C4—1011no—
282C2×C4⋊C4—1011no—
283C2×C4⋊C4—1011no—
284C2×C4⋊C4—1011no—
285C2×C4⋊C4—1011no—
286C2×C4⋊C4—1011no—
287C2×C22⋊C4—1011no—
288C2×C22⋊C4—1011no—
289C2×C22⋊C4—1011no—
290C2×C22⋊C4—1011no—
291C2×C22⋊C4—1011no—
292C2×C22⋊C4—1011no—
293C2×C22⋊C4—1011no—
294C2×C22⋊C4—1011no—
295C2×C22⋊C4—1011no—
296C2×C22⋊C4—1011no—
297C2×C42—1011no—
298C2×C42—1011no—
299C2×C42—1011no—
300C2×C42—1011no—
301C2×C42—1011no—
302#95—1011no—
303#95—1011no—
304#95—1011no—
305#95—1011no—
306#95—1011no—
307#95—1011no—
308#95—1011no—
309#95—1011no—
310#95—1011no—
311#95—1011no—
312C24—1011no—
313C24—1011no—
314C2×D4—1011no—
315C2×D4—1011no—
316C2×D4—1011no—
317C2×D4—4041no—
318C2×D4—4041no—
319C2×D4C2×#8793811yescharacteristic
320C22×C4—1011no—
321C22×C4—1011no—
322C22×C4—1011no—
323C22×C4—1011no—
324C22×C4—1011no—
325C22×C4—1011no—
326C22×C4—1011no—
327C22×C4—1011no—
328C22×C4—1011no—
329C22×C4—1011no—
330C22×C4—1011no—
331C22×C4—1011no—
332C22×C4—1011no—
333C22×C4—1011no—
334C22×C4—1011no—
335C22×C4—1011no—
336C22×C4—4041no—
337C22×C4—4041no—
338C22×C4—4041no—
339C22×C4—4041no—
340C22×C4—2022no—
341C22×C4C2×#8793811yescharacteristic, complemented
342C4⋊C4—1011no—
343C4⋊C4—1011no—
344C4⋊C4—1011no—
345C4⋊C4—1011no—
346C4⋊C4—1011no—
347C4⋊C4—1011no—
348C4⋊C4—4041no—
349C4⋊C4—4041no—
350C4⋊C4—4041no—
351C4⋊C4—4041no—
352C4⋊C4—2022no—
353C4⋊C4C2×#8793811yescharacteristic, complemented
354C4⋊C4C2×#8793811yescharacteristic, complemented
355C22⋊C4—1011no—
356C22⋊C4—1011no—
357C22⋊C4—1011no—
358C22⋊C4—1011no—
359C22⋊C4—1011no—
360C22⋊C4—1011no—
361C22⋊C4—1011no—
362C22⋊C4—1011no—
363C22⋊C4—1011no—
364C22⋊C4—4041no—
365C22⋊C4—4041no—
366C22⋊C4—4041no—
367C22⋊C4—4041no—
368C22⋊C4—2022no—
369C22⋊C4—2022no—
370C22⋊C4—2022no—
371C22⋊C4C2×#8793811yescharacteristic
372C22⋊C4C2×#8793811yescharacteristic
373C22⋊C4C2×#8793811yescharacteristic, complemented
374C42—4041no—
375C42—4041no—
376C42—4041no—
377C42—4041no—
378C42—2022no—
379C23—1011no—
380C23—1011no—
381C23—1011no—
382C23—2021no—
383C23—2021no—
384C23—2021no—
385C23—2021no—
386C23—2021no—
387C23—2021no—
388C23—2021no—
389C23—2021no—
390C23—2021no—
391C23—2021no—
392C23—2021no—
393C23—2021no—
394C23C22×#8793811yescharacteristic
395C23C22×#8793811yescharacteristic
396D4—41no—
397D4—4041no—
398D4—4041no—
399D4—4041no—
400C2×C4—41no—
401C2×C4—1012no—
402C2×C4—1012no—
403C2×C4—1011no—
404C2×C4—1011no—
405C2×C4—1011no—
406C2×C4—1011no—
407C2×C4—1011no—
408C2×C4—4041no—
409C2×C4—4041no—
410C2×C4—4044no—
411C2×C4—4041no—
412C2×C4—2021no—
413C2×C4—2021no—
414C2×C4—2021no—
415C2×C4—2021no—
416C2×C4—2021no—
417C2×C4—2021no—
418C2×C4—2021no—
419C2×C4—2021no—
420C2×C4—2021no—
421C2×C4—2021no—
422C2×C4—2021no—
423C2×C4—2021no—
424C2×C4—2021no—
425C2×C4—2021no—
426C2×C4—2021no—
427C2×C4—2021no—
428C2×C4—2021no—
429C2×C4—2021no—
430C2×C4—2021no—
431C2×C4—2021no—
432C2×C4—2021no—
433C2×C4—2021no—
434C2×C4—2021no—
435C2×C4—2021no—
436C2×C4—2021no—
437C2×C4—2021no—
438C2×C4—2021no—
439C2×C4—2021no—
440C2×C4—2021no—
441C2×C4—2021no—
442C2×C4—2021no—
443C2×C4—2021no—
444C2×C4C22×#8793811yescharacteristic
445C2×C4C22×#8793811yescharacteristic
446C2×C4C22×#8793811yescharacteristic
447C2×C4C22×#8793811yescharacteristic
448C2×C4C22×#8793811yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—1011no—
456C22—1011no—
457C22—1011no—
458C22—1011no—
459C22—1011no—
460C22—1011no—
461C22—4041no—
462C22—4041no—
463C22—4041no—
464C22—4041no—
465C22—4041no—
466C22—4041no—
467C22—4041no—
468C22—4041no—
469C22—2021no—
470C22—2021no—
471C22—2021no—
472C22—2021no—
473C22—2021no—
474C22—2021no—
475C22C23×#8793811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—4041no—
482C4—4041no—
483C4—4041no—
484C4—4041no—
485C4—4041no—
486C4—4041no—
487C4—2022no—
488C4—2022no—
489C4—2021no—
490C4—2021no—
491C4—2021no—
492C4—2021no—
493C4—2021no—
494C2—41no—
495C2—41no—
496C2—1011no—
497C2—1011no—
498C2—1011no—
499C2—1011no—
500C2—4041no—
501C2—4041no—
502C2#41×#8793811yescharacteristic
503C2#2026624411yescharacteristic
504C2#2026624611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#87938
commutator, socleC22×C101C23×C4
Fitting#123×C101C4
prime radicalC2×D4×D101C22
cosocleC22×D101C24
hypercenter#123#87938
hypocenterC101#2335
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #20266128C2semidirect
3. #20266127C2semidirect
4. #20266127C2semidirect
5. #20266127C2semidirect
6. #20266127C2semidirect
7. #20266126C2semidirect
8. #20266126C2semidirect
10. #20266124C2semidirect
11. #20266119C2semidirect
12. C4⋊C4×#87938C2semidirect
13. C22⋊C4×#87938C2semidirect
14. C4×C22⋊#87938C2semidirect
46. #15692240C4semidirect
47. #15692240C4semidirect
48. #15692239C4semidirect
49. #15692238C4semidirect
50. #15692237C4semidirect
51. #15692237C4semidirect
52. #15692236C4semidirect
58. #123×C101C4semidirect
94. C22×Dic101C2×C4semidirect
97. C2×C4×D101C2×C4semidirect
98. C2×C4×D101C2×C4semidirect
104. C4⋊Dic101C2×C4semidirect
105. C4⋊Dic101C2×C4semidirect
106. #13108053C2×C4semidirect
107. #13108053C2×C4semidirect
108. #13108053C2×C4semidirect
109. #13108053C2×C4semidirect
112. C22⋊Dic101C2×C4semidirect
117. #13108051C2×C4semidirect
118. #13108051C2×C4semidirect
120. C22×C4×C101C2×C4semidirect
121. C4⋊C4×C101C2×C4semidirect
122. C4⋊C4×C101C2×C4semidirect
125. C22⋊C4×C101C2×C4semidirect
253. C101#2335semidirect
279. #123#87938semidirect
341. C22×C4C2×#87938semidirect
353. C4⋊C4C2×#87938semidirect
354. C4⋊C4C2×#87938semidirect
373. C22⋊C4C2×#87938semidirect

Maximal subgroups

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

subgroupindex
#202661292
#202661282
#202661272
#202661262
#202661252
#202661242
#202661192
C4⋊C4×#879382
C22⋊C4×#879382
C4×C22⋊#879382
#123×D1012
#2335101