Finite Group Databasebeta

← #27187655

Subgroups — #27187655

Order 12928.

652 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#87938C211yesmaximal, characteristic
2C2×#15692334C211yesmaximal, characteristic, complemented
3#20266128C211yesmaximal, characteristic, complemented
4#20266127C211yesmaximal, characteristic, complemented
5#20266127C211yesmaximal, characteristic, complemented
6#20266126C211yesmaximal, characteristic, complemented
7#20266126C211yesmaximal, characteristic, complemented
8#20266125C211yesmaximal, characteristic
9#20266124C211yesmaximal, characteristic, complemented
10#20266124C211yesmaximal, characteristic, complemented
11C4⋊C4×#87938C211yesmaximal, characteristic, complemented
12C22⋊C4×#87938C211yesmaximal, characteristic, complemented
13C22⋊C4×#87938C211yesmaximal, characteristic, complemented
14C2×(C2×#87938)⋊C4C211yesmaximal, characteristic, complemented
15#123×D101C211yesmaximal, characteristic
16C23×#87938C2211yescharacteristic
17C23×#87938C2211yescharacteristic
18C23×#87938C2211yescharacteristic
19D4×#87938—24no—
20#15692334—24no—
21C2×C4⋊#87938C2211yescharacteristic
22C2×C4⋊#87938C2211yescharacteristic
23C2×C4⋊#87938C2211yescharacteristic
24C2×C4⋊#87938C2211yescharacteristic
25C2×C4⋊#87938C2211yescharacteristic
26C2×C22⋊#87938C2211yescharacteristic
27C2×C22⋊#87938C2211yescharacteristic
28C2×C22⋊#87938C2211yescharacteristic
29C2×C22⋊#87938C2211yescharacteristic
30C2×C22⋊#87938C2211yescharacteristic
31C2×C4×#87938C2211yescharacteristic
32C2×C4×#87938C2211yescharacteristic
33C2×C4×#87938C2211yescharacteristic
34C2×C4×#87938C2211yescharacteristic
35C2×C4×#87938C2211yescharacteristic
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
44(C2×#87938)⋊C4C2211yescharacteristic
45(C2×#87938)⋊C4C2211yescharacteristic
46C2×D4×D101C2211yescharacteristic
47C22×C4×D101C2211yescharacteristic
48#15692240C411yescharacteristic, complemented
49#15692240C411yescharacteristic, complemented
50#15692239C411yescharacteristic, complemented
51#15692238C411yescharacteristic, complemented
52#15692237C411yescharacteristic, complemented
53#15692237C411yescharacteristic, complemented
54#15692236C411yescharacteristic, complemented
55C4⋊C4×D101C2211yescharacteristic
56C4⋊C4×D101C2211yescharacteristic
57C22⋊C4×D101C2211yescharacteristic
58C22⋊C4×D101C2211yescharacteristic
59C22⋊C4×D101C2211yescharacteristic
60#123×C101C411yescharacteristic, complemented
61C22×#87938—22no—
62C22×#87938—22no—
63C22×#87938—22no—
64C22×#87938—22no—
65C22×#87938—22no—
66C22×#87938—22no—
67C22×#87938—41no—
68C22×#87938—41no—
69C22×#87938—41no—
70C22×#87938C2311yescharacteristic
71C22×#87938C2311yescharacteristic
72C22×#87938C2311yescharacteristic
73C22×#87938C2311yescharacteristic
74C22×#87938C2311yescharacteristic
75C22×#87938C2311yescharacteristic
76C22×#87938C2311yescharacteristic
77C22×#87938C2311yescharacteristic
78C4⋊#87938—22no—
79C4⋊#87938—22no—
80C4⋊#87938—22no—
81C4⋊#87938—22no—
82C4⋊#87938—41no—
83C22⋊#87938—22no—
84C22⋊#87938—22no—
85C22⋊#87938—22no—
86C22⋊#87938—41no—
87C22⋊#87938D414yes—
88C4×#87938—22no—
89C4×#87938—22no—
90C4×#87938—22no—
91C4×#87938—22no—
92C4×#87938—41no—
93C23×D101C2311yescharacteristic
94C23×D101C2311yescharacteristic
95C2×D404C2×C411yescharacteristic
96C2×C22⋊D101C2×C411yescharacteristic
97C2×C22⋊D101C2×C411yescharacteristic
98D4×D101—22no—
99D4×D101—22no—
100C22×Dic101C2×C411yescharacteristic, complemented
101C2×C4×D101—22no—
102C2×C4×D101—22no—
103C2×C4×D101C2×C411yescharacteristic, complemented
104C2×C4×D101C2×C411yescharacteristic, complemented
105C2×C4×D101C2311yescharacteristic
106C2×C4×D101C2311yescharacteristic
107C2×C4×D101C2311yescharacteristic
108C2×C4×D101C2311yescharacteristic
109C2×C4×D101C2311yescharacteristic
110C4⋊Dic101C2×C411yescharacteristic, complemented
111C4⋊Dic101C2×C411yescharacteristic, complemented
112#13108053C2×C411yescharacteristic, complemented
113#13108053C2×C411yescharacteristic, complemented
114#13108053C2×C411yescharacteristic, complemented
115#13108053C2×C411yescharacteristic, complemented
116C22⋊Dic101C2×C411yescharacteristic, complemented
117C22⋊Dic101C2×C411yescharacteristic, complemented
118C22⋊Dic101C2×C411yescharacteristic, complemented
119#13108051C2×C411yescharacteristic, complemented
120#13108051C2×C411yescharacteristic, complemented
121#13108051C2×C411yescharacteristic, complemented
122#13108051C2×C411yescharacteristic, complemented
123#13108051C2×C411yescharacteristic, complemented
124#13108051C2×C411yescharacteristic, complemented
125C2×D4×C101C2×C411yescharacteristic
126C22×C4×C101C2×C411yescharacteristic, complemented
127C4⋊C4×C101C2×C411yescharacteristic, complemented
128C4⋊C4×C101C2×C411yescharacteristic, complemented
129C22⋊C4×C101C2×C411yescharacteristic, complemented
130C22⋊C4×C101C2×C411yescharacteristic, complemented
131C22⋊C4×C101C2×C411yescharacteristic, complemented
132C23×C101C22×C411yescharacteristic
133C23×C101C22×C411yescharacteristic
134C22×D101—21no—
135C22×D101—21no—
136C22×D101—21no—
137C22×D101—21no—
138C22×D101—21no—
139C22×D101—21no—
140C22×D101—21no—
141C22×D101—21no—
142C22×D101—21no—
143C22×D101—21no—
144C22×D101C22×C411yescharacteristic
145C22×D101C22×C411yescharacteristic
146C22×D101C2×D412yes—
147C22×D101#4112yes—
148C22×D101C2411yescharacteristic
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—21no—
166C2×#87938—21no—
167C2×#87938—21no—
168C2×#87938—21no—
169C2×#87938—44no—
170C2×#87938—44no—
171C2×#87938—44no—
172C2×#87938C2×D412yes—
173C2×#87938C2×D412yes—
174C2×#87938#4112yes—
175C2×#87938#4112yes—
176D4×C101—22no—
177C2×C4×C101—22no—
178C2×C4×C101C22×C411yescharacteristic
179C2×C4×C101C22×C411yescharacteristic
180C2×C4×C101C22×C411yescharacteristic
181C2×C4×C101C22×C411yescharacteristic
182C2×C4×C101C22×C411yescharacteristic
183C22⋊D101—22no—
184C22⋊D101—22no—
185C2×Dic101—22no—
186C2×Dic101C22×C411yescharacteristic
187C2×Dic101C22×C411yescharacteristic
188C2×Dic101C22×C411yescharacteristic
189C2×Dic101C22×C411yescharacteristic
190C2×Dic101C22×C411yescharacteristic
191D404—22no—
192C4×D101—22no—
193C4×D101—22no—
194C4×D101—21no—
195C4×D101—21no—
196C4×D101—21no—
197C4×D101—21no—
198C4×D101—21no—
199C4×D101—21no—
200C4×D101—21no—
201C4×D101—21no—
202C4×D101—21no—
203C4×D101—21no—
204C22×C101—21no—
205C22×C101—21no—
206C22×C101—21no—
207C22×C101—21no—
208C22×C101—21no—
209C22×C101C4×D412yes—
210C22×C101C23×C411yescharacteristic
211C2×D101—21no—
212C2×D101—21no—
213C2×D101—22no—
214C2×D101—22no—
215C2×D101—22no—
216C2×D101—22no—
217C2×D101—21no—
218C2×D101—21no—
219C2×D101—21no—
220C2×D101—41no—
221C2×D101—41no—
222C2×D101—41no—
223C2×D101—41no—
224C2×D101C4×D412yes—
225C2×D101C22×D411yescharacteristic
226C2×D101C2×#4111yescharacteristic
227C2×D101C2×#4111yescharacteristic
228C2×D101C2×#4111yescharacteristic
229C2×D101H(5,𝔽2)11yescharacteristic
230C2×D1012−1+411yescharacteristic
231#87938—22no—
232#87938—22no—
233#87938—22no—
234#87938—22no—
235#87938—41no—
236#87938—41no—
237#87938—41no—
238#87938—41no—
239C4×C101—21no—
240C4×C101—21no—
241C4×C101—21no—
242C4×C101—21no—
243C4×C101—21no—
244Dic101—21no—
245Dic101—21no—
246Dic101—21no—
247Dic101—21no—
248Dic101—21no—
249C2×C101—22no—
250C2×C101—41no—
251C2×C101C2×C4×D411yescharacteristic
252C2×C101C4×#4111yescharacteristic
253C2×C101#52011yescharacteristic
254D101—22no—
255D101—41no—
256D101#54611yescharacteristic
257D101#54711yescharacteristic
258D101#55111yescharacteristic
259D101#55211yescharacteristic
260#2359—1011nomaximal, Sylow
261C101#235911yescharacteristic, complemented, Sylow
262C2×#123—1011no—
263C2×C4×D4—1011no—
264C2×#117—1011no—
265#389—1011no—
266#388—1011no—
267#388—1011no—
268#387—1011no—
269#387—1011no—
270#386—1011no—
271#385—1011no—
272#385—1011no—
273C4×C4⋊C4—1011no—
274C4×C22⋊C4—1011no—
275C4×C22⋊C4—1011no—
276C2×#95—1011no—
277C22×D4—1011no—
278C23×C4—1011no—
279C23×C4—1011no—
280C23×C4—1011no—
281C23×C4—1011no—
282#123—1011no—
283#123—1011no—
284#123—1011no—
285#123—1011no—
286#123—1011no—
287#123—1011no—
288#123—1011no—
289#123#8793811yescharacteristic, complemented
290C4×D4—2024no—
291#117—2024no—
292C2×C4⋊C4—1011no—
293C2×C4⋊C4—1011no—
294C2×C4⋊C4—1011no—
295C2×C4⋊C4—1011no—
296C2×C4⋊C4—1011no—
297C2×C4⋊C4—1011no—
298C2×C4⋊C4—1011no—
299C2×C22⋊C4—1011no—
300C2×C22⋊C4—1011no—
301C2×C22⋊C4—1011no—
302C2×C22⋊C4—1011no—
303C2×C22⋊C4—1011no—
304C2×C22⋊C4—1011no—
305C2×C22⋊C4—1011no—
306C2×C22⋊C4—1011no—
307C2×C42—1011no—
308C2×C42—1011no—
309C2×C42—1011no—
310C2×C42—1011no—
311C2×C42—1011no—
312#95—1011no—
313#95—1011no—
314#95—1011no—
315#95—1011no—
316#95—1011no—
317#95—1011no—
318#95—1011no—
319#95—1011no—
320#95—1011no—
321#95—1011no—
322C24—1011no—
323C24—1011no—
324C2×D4—1011no—
325C2×D4—1011no—
326C2×D4—1011no—
327C2×D4—2022no—
328C2×D4—2022no—
329C2×D4C2×#8793811yescharacteristic
330C22×C4—1011no—
331C22×C4—1011no—
332C22×C4—1011no—
333C22×C4—1011no—
334C22×C4—1011no—
335C22×C4—1011no—
336C22×C4—1011no—
337C22×C4—1011no—
338C22×C4—1011no—
339C22×C4—1011no—
340C22×C4—1011no—
341C22×C4—1011no—
342C22×C4—1011no—
343C22×C4—1011no—
344C22×C4—1011no—
345C22×C4—1011no—
346C22×C4—4041no—
347C22×C4—4041no—
348C22×C4—4041no—
349C22×C4—2022no—
350C22×C4—2022no—
351C22×C4—2022no—
352C22×C4—2022no—
353C22×C4—2022no—
354C22×C4—2022no—
355C22×C4—2022no—
356C22×C4—2022no—
357C22×C4C2×#8793811yescharacteristic, complemented
358C4⋊C4—1011no—
359C4⋊C4—1011no—
360C4⋊C4—1011no—
361C4⋊C4—1011no—
362C4⋊C4—1011no—
363C4⋊C4—1011no—
364C4⋊C4—4041no—
365C4⋊C4—2022no—
366C4⋊C4—2022no—
367C4⋊C4—2022no—
368C4⋊C4—2022no—
369C4⋊C4C2×#8793811yescharacteristic, complemented
370C4⋊C4C2×#8793811yescharacteristic, complemented
371C22⋊C4—1014no—
372C22⋊C4—1011no—
373C22⋊C4—1011no—
374C22⋊C4—1011no—
375C22⋊C4—1011no—
376C22⋊C4—1011no—
377C22⋊C4—1011no—
378C22⋊C4—1011no—
379C22⋊C4—1011no—
380C22⋊C4—1011no—
381C22⋊C4—4041no—
382C22⋊C4—2022no—
383C22⋊C4—2022no—
384C22⋊C4—2022no—
385C22⋊C4C2×#8793811yescharacteristic, complemented
386C22⋊C4C2×#8793811yescharacteristic, complemented
387C22⋊C4C2×#8793811yescharacteristic, complemented
388C42—4041no—
389C42—2022no—
390C42—2022no—
391C42—2022no—
392C42—2022no—
393C23—1011no—
394C23—1012no—
395C23—1012no—
396C23—1011no—
397C23—1011no—
398C23—2021no—
399C23—2021no—
400C23—2021no—
401C23—2021no—
402C23—2021no—
403C23—2021no—
404C23—2021no—
405C23—2021no—
406C23—2021no—
407C23—2021no—
408C23C22×#8793811yescharacteristic
409C23C22×#8793811yescharacteristic
410D4—22no—
411D4—2022no—
412D4—2022no—
413D4—2022no—
414C2×C4—22no—
415C2×C4—1012no—
416C2×C4—1012no—
417C2×C4—1012no—
418C2×C4—1012no—
419C2×C4—1011no—
420C2×C4—1011no—
421C2×C4—1011no—
422C2×C4—1011no—
423C2×C4—1011no—
424C2×C4—4044no—
425C2×C4—4044no—
426C2×C4—4044no—
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—2022no—
436C2×C4—2022no—
437C2×C4—2021no—
438C2×C4—2021no—
439C2×C4—2021no—
440C2×C4—2021no—
441C2×C4—2021no—
442C2×C4—2021no—
443C2×C4—2021no—
444C2×C4—2021no—
445C2×C4—2021no—
446C2×C4—2021no—
447C2×C4—2021no—
448C2×C4—2021no—
449C2×C4—2021no—
450C2×C4—2021no—
451C2×C4—2021no—
452C2×C4—2021no—
453C2×C4—2021no—
454C2×C4—2021no—
455C2×C4—2021no—
456C2×C4—2021no—
457C2×C4—2021no—
458C2×C4—2021no—
459C2×C4—2022no—
460C2×C4C22×#8793811yescharacteristic
461C2×C4C22×#8793811yescharacteristic
462C2×C4C22×#8793811yescharacteristic
463C2×C4C22×#8793811yescharacteristic
464C2×C4C22×#8793811yescharacteristic
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—1011no—
471C22—1011no—
472C22—1011no—
473C22—1011no—
474C22—1011no—
475C22—1011no—
476C22—1012no—
477C22—4041no—
478C22—4041no—
479C22—4041no—
480C22—4041no—
481C22—2022no—
482C22—2022no—
483C22—2022no—
484C22—2022no—
485C22—2021no—
486C22—2021no—
487C22—2021no—
488C22—2021no—
489C22—2021no—
490C22D4×#8793812yes—
491C22C23×#8793811yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—4041no—
498C4—4041no—
499C4—4041no—
500C4—4041no—
501C4—2022no—
502C4—2022no—
503C4—2022no—
504C4—2022no—
505C4—2021no—
506C4—2021no—
507C4—2021no—
508C4—2021no—
509C4—2021no—
510C2—22no—
511C2—41no—
512C2—1011no—
513C2—1011no—
514C2—1011no—
515C2—1011no—
516C2—4041no—
517C2—2022no—
518C2C2×D4×#8793811yescharacteristic
519C2#41×#8793811yescharacteristic
520C2#2026624611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#87938
commutator, socleC22×C101C23×C4
Fitting#123×C101C4
prime radicalC2×D4×D101C22
cosocleC22×D101C24
hypercenter#123#87938
hypocenterC101#2359
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C2×#15692334C2semidirect
3. #20266128C2semidirect
4. #20266127C2semidirect
5. #20266127C2semidirect
6. #20266126C2semidirect
7. #20266126C2semidirect
9. #20266124C2semidirect
10. #20266124C2semidirect
11. C4⋊C4×#87938C2semidirect
12. C22⋊C4×#87938C2semidirect
13. C22⋊C4×#87938C2semidirect
14. C2×(C2×#87938)⋊C4C2semidirect
48. #15692240C4semidirect
49. #15692240C4semidirect
50. #15692239C4semidirect
51. #15692238C4semidirect
52. #15692237C4semidirect
53. #15692237C4semidirect
54. #15692236C4semidirect
60. #123×C101C4semidirect
100. C22×Dic101C2×C4semidirect
103. C2×C4×D101C2×C4semidirect
104. C2×C4×D101C2×C4semidirect
110. C4⋊Dic101C2×C4semidirect
111. C4⋊Dic101C2×C4semidirect
112. #13108053C2×C4semidirect
113. #13108053C2×C4semidirect
114. #13108053C2×C4semidirect
115. #13108053C2×C4semidirect
116. C22⋊Dic101C2×C4semidirect
117. C22⋊Dic101C2×C4semidirect
118. C22⋊Dic101C2×C4semidirect
119. #13108051C2×C4semidirect
120. #13108051C2×C4semidirect
121. #13108051C2×C4semidirect
122. #13108051C2×C4semidirect
123. #13108051C2×C4semidirect
124. #13108051C2×C4semidirect
126. C22×C4×C101C2×C4semidirect
127. C4⋊C4×C101C2×C4semidirect
128. C4⋊C4×C101C2×C4semidirect
129. C22⋊C4×C101C2×C4semidirect
130. C22⋊C4×C101C2×C4semidirect
131. C22⋊C4×C101C2×C4semidirect
261. C101#2359semidirect
289. #123#87938semidirect
357. C22×C4C2×#87938semidirect
369. C4⋊C4C2×#87938semidirect
370. C4⋊C4C2×#87938semidirect
385. C22⋊C4C2×#87938semidirect
386. C22⋊C4C2×#87938semidirect
387. C22⋊C4C2×#87938semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#879382
C2×#156923342
#202661282
#202661272
#202661262
#202661252
#202661242
C4⋊C4×#879382
C22⋊C4×#879382
C2×(C2×#87938)⋊C42
#123×D1012
#2359101