Finite Group Databasebeta

← #27173958

Subgroups — #27173958

Order 12928.

928 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13108073C211yesmaximal, characteristic
2C2×C4×C22⋊D101C211yesmaximal, characteristic, complemented
3C2×#15692215C211yesmaximal, characteristic, complemented
4#20265081C211yesmaximal, characteristic, complemented
5#20265081C211yesmaximal, characteristic, complemented
6#20265057C211yesmaximal, characteristic, complemented
7#20265053C211yesmaximal, characteristic, complemented
8#20265053C211yesmaximal, characteristic, complemented
9#20265039C211yesmaximal, characteristic, complemented
10#20265038C211yesmaximal, characteristic, complemented
11#20265035C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic101C211yesmaximal, characteristic, complemented
13C2×#15692162C211yesmaximal, characteristic, complemented
14#95×D101C211yesmaximal, characteristic, complemented
15#386×C101C211yesmaximal, characteristic, complemented
16C2×#13108073—24no—
17C2×#13108073—24no—
18C2×#13108073C418yescomplemented
19C22×Dic202C2211yescharacteristic
20C22×C22⋊D101C2211yescharacteristic
21C22×C22⋊D101C2211yescharacteristic
22C23×Dic101C2211yescharacteristic
23C23×Dic101C2211yescharacteristic
24C23×Dic101C2211yescharacteristic
25C22×C4×D101C2211yescharacteristic
26C22×C4×D101C2211yescharacteristic
27C22×C4×D101C2211yescharacteristic
28C4×C22⋊D101—24no—
29#15692215—24no—
30C2×#13108053C2211yescharacteristic
31C2×#13108053C2211yescharacteristic
32C2×C22⋊Dic101C2211yescharacteristic
33C2×C22⋊Dic101C2211yescharacteristic
34C2×C22⋊Dic101C2211yescharacteristic
35C2×#13108051C2211yescharacteristic
36C2×#13108051C2211yescharacteristic
37C2×C4×Dic101C2211yescharacteristic
38C2×C4×Dic101C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45#15692162C2211yescharacteristic
46#15692162C2211yescharacteristic
47#15692162C2211yescharacteristic
48#15692162C2211yescharacteristic
49C22×D4×C101C2211yescharacteristic
50C23×C4×C101C2211yescharacteristic
51C2×C22⋊C4×C101C2211yescharacteristic
52C2×C22⋊C4×C101C2211yescharacteristic
53C2×C22⋊C4×C101C2211yescharacteristic
54#95×C101C2211yescharacteristic
55#95×C101C2211yescharacteristic
56C23×D101C2311yescharacteristic
57#13108073—232no—
58C2×Dic202—22no—
59C2×Dic202—22no—
60C2×Dic202C2×C414yescomplemented
61C2×C22⋊D101—22no—
62C2×C22⋊D101—22no—
63C2×C22⋊D101C2×C414yes—
64C2×C22⋊D101C2×C414yescomplemented
65C2×C22⋊D101D414yes—
66C2×C22⋊D101D414yes—
67C22×Dic101—22no—
68C22×Dic101—22no—
69C22×Dic101—22no—
70C22×Dic101—22no—
71C22×Dic101—22no—
72C22×Dic101—22no—
73C22×Dic101—41no—
74C22×Dic101C2×C414yescomplemented
75C22×Dic101C2×C414yescomplemented
76C22×Dic101C2311yescharacteristic
77C22×Dic101C2311yescharacteristic
78C22×Dic101C2311yescharacteristic
79C22×Dic101C2311yescharacteristic
80C22×Dic101C2311yescharacteristic
81C22×Dic101C2311yescharacteristic
82C22×Dic101C2311yescharacteristic
83C2×C4×D101—22no—
84C2×C4×D101—22no—
85C2×C4×D101—22no—
86C2×C4×D101—22no—
87C2×C4×D101—22no—
88C2×C4×D101—22no—
89C2×C4×D101—41no—
90C2×C4×D101—41no—
91C2×C4×D101C2×C414yescomplemented
92#13108053—22no—
93#13108053—22no—
94C22⋊Dic101—22no—
95C22⋊Dic101—22no—
96C22⋊Dic101—41no—
97#13108051—22no—
98#13108051—22no—
99C4×Dic101—22no—
100C4×Dic101—22no—
101C24×C101C2311yescharacteristic
102C24×C101C2311yescharacteristic
103C2×D4×C101—22no—
104C2×D4×C101—22no—
105C2×D4×C101C2×C414yescomplemented
106C22×C4×C101—22no—
107C22×C4×C101—22no—
108C22×C4×C101—41no—
109C22×C4×C101C2311yescharacteristic
110C22×C4×C101C2311yescharacteristic
111C22×C4×C101C2311yescharacteristic
112C22×C4×C101C2311yescharacteristic
113C22×C4×C101C2311yescharacteristic
114C22⋊C4×C101—22no—
115C22⋊C4×C101—22no—
116C22⋊C4×C101—41no—
117C23×C101—21no—
118C23×C101—21no—
119C23×C101—21no—
120C23×C101—21no—
121C23×C101—21no—
122C23×C101—21no—
123C23×C101—21no—
124C23×C101—21no—
125C23×C101—21no—
126C23×C101—21no—
127C23×C101C22×C412yes—
128C23×C101C22×C412yes—
129C23×C101C2×D412yes—
130C23×C101C2×D412yes—
131C23×C101C2411yescharacteristic
132C22×D101—21no—
133C22×D101—21no—
134C22×D101—21no—
135C22×D101—21no—
136C22×D101C22×C412yes—
137C22×D101C2×D412yes—
138C22×D101C2×D412yes—
139D4×C101—28no—
140C2×C4×C101—21no—
141C2×C4×C101—21no—
142C2×C4×C101—21no—
143C2×C4×C101—21no—
144C2×C4×C101—21no—
145C2×C4×C101—21no—
146C2×C4×C101—21no—
147C2×C4×C101—21no—
148C2×C4×C101—21no—
149C2×C4×C101—21no—
150C2×C4×C101—21no—
151C2×C4×C101—21no—
152C2×C4×C101—21no—
153C2×C4×C101—44no—
154C2×C4×C101C22×C412yes—
155C2×C4×C101#4112yescomplemented
156C22⋊D101—28no—
157C22⋊D101C22⋊C4116yescomplemented
158C2×Dic101—28no—
159C2×Dic101—21no—
160C2×Dic101—21no—
161C2×Dic101—21no—
162C2×Dic101—21no—
163C2×Dic101—21no—
164C2×Dic101—21no—
165C2×Dic101—28no—
166C2×Dic101—21no—
167C2×Dic101—21no—
168C2×Dic101—21no—
169C2×Dic101—21no—
170C2×Dic101—21no—
171C2×Dic101—21no—
172C2×Dic101—21no—
173C2×Dic101—21no—
174C2×Dic101—21no—
175C2×Dic101—44no—
176C2×Dic101C22×C412yes—
177C2×Dic101C22×C412yes—
178C2×Dic101C22×C412yes—
179C2×Dic101C2×D412yes—
180C2×Dic101C2×D412yes—
181C2×Dic101#4112yescomplemented
182C4×D101—28no—
183C4×D101—44no—
184C4×D101—44no—
185Dic202—28no—
186C22×C101—22no—
187C22×C101—22no—
188C22×C101—22no—
189C22×C101—22no—
190C22×C101—22no—
191C22×C101—22no—
192C22×C101—22no—
193C22×C101—22no—
194C22×C101—22no—
195C22×C101—41no—
196C22×C101—41no—
197C22×C101—41no—
198C22×C101—41no—
199C22×C101C2×C22⋊C414yes—
200C22×C101C23×C411yescharacteristic
201C22×C101C22×D411yescharacteristic
202C22×C101C22×D411yescharacteristic
203C22×C101C2×#4111yescharacteristic
204C22×C101C2×#4111yescharacteristic
205C22×C101H(5,𝔽2)11yescharacteristic
206C22×C1012−1+411yescharacteristic
207C2×D101—22no—
208C2×D101—22no—
209C2×D101—22no—
210C2×D101—22no—
211C2×D101—22no—
212C2×D101—22no—
213C2×D101C2×C22⋊C414yes—
214C4×C101—22no—
215C4×C101—22no—
216C4×C101—41no—
217C4×C101—41no—
218C4×C101—41no—
219Dic101—22no—
220Dic101—22no—
221Dic101—22no—
222Dic101—41no—
223Dic101—41no—
224Dic101—41no—
225Dic101C2×C22⋊C414yes—
226C2×C101—24no—
227C2×C101—42no—
228C2×C101C22×C22⋊C411yescharacteristic
229C2×C101C4×#4111yescharacteristic
230C2×C101#52011yescharacteristic
231C2×C101#54611yescharacteristic
232C2×C101#54611yescharacteristic
233C2×C101#54711yescharacteristic
234C2×C101#54711yescharacteristic
235D101—24no—
236#2339—1011nomaximal, Sylow
237C101#233911yescharacteristic, complemented, Sylow
238C22×#41—1011no—
239C2×C4×D4—1011no—
240C2×C4×D4—1011no—
241#391—1011no—
242#391—1011no—
243#386—1011no—
244#386—1011no—
245#386—1011no—
246#386D10111yescharacteristic, complemented
247#381—1011no—
248#381—1011no—
249#380—1011no—
250C4×C22⋊C4—1011no—
251C2×#95—1011no—
252C2×#95—1011no—
253C2×#41—1018no—
254C2×#41—2024no—
255C2×#41—2024no—
256C22×Q8—1011no—
257C22×D4—1011no—
258C22×D4—1011no—
259C22×D4C2×D10111yescharacteristic
260C23×C4—1011no—
261C23×C4—1011no—
262C23×C4—1011no—
263C23×C4—1011no—
264C23×C4—1011no—
265C23×C4—1011no—
266C23×C4C2×D10111yescharacteristic
267C4×D4—2024no—
268C4×D4—2024no—
269C2×C4⋊C4—1011no—
270C2×C4⋊C4—1011no—
271C2×C22⋊C4—1011no—
272C2×C22⋊C4—1011no—
273C2×C22⋊C4—1011no—
274C2×C22⋊C4—1011no—
275C2×C22⋊C4—1011no—
276C2×C22⋊C4C2×D10111yescharacteristic
277C2×C22⋊C4C2×D10111yescharacteristic
278C2×C22⋊C4C2×D10111yescharacteristic
279C2×C42—1011no—
280C2×C42—1011no—
281#95—1011no—
282#95—1011no—
283#95—1011no—
284#95—1011no—
285#95—1011no—
286#95—1011no—
287#95—1011no—
288#95—1011no—
289#95—1011no—
290#95—1011no—
291#95C2×D10111yescharacteristic
292#95C2×D10111yescharacteristic
293C24—1011no—
294C24C22×D10111yescharacteristic
295C24C22×D10111yescharacteristic
296#41—20232no—
297C2×Q8—1014no—
298C2×Q8—2022no—
299C2×Q8—2022no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—1014no—
303C2×D4—1014no—
304C2×D4—1014no—
305C2×D4—1014no—
306C2×D4—2022no—
307C2×D4—2022no—
308C2×D4C4×D10114yescomplemented
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4—1011no—
313C22×C4—1014no—
314C22×C4—1014no—
315C22×C4—1011no—
316C22×C4—1011no—
317C22×C4—1011no—
318C22×C4—1014no—
319C22×C4—1011no—
320C22×C4—1011no—
321C22×C4—1011no—
322C22×C4—4041no—
323C22×C4—4041no—
324C22×C4—4041no—
325C22×C4—2022no—
326C22×C4—2022no—
327C22×C4—2022no—
328C22×C4—2022no—
329C22×C4—2022no—
330C22×C4—2022no—
331C22×C4—2022no—
332C22×C4—2022no—
333C22×C4—2022no—
334C22×C4—2022no—
335C22×C4—2022no—
336C22×C4—2022no—
337C22×C4C22×D10111yescharacteristic
338C22×C4C22×D10111yescharacteristic
339C22×C4C22×D10111yescharacteristic
340C22×C4C22×D10111yescharacteristic
341C22×C4C22×D10111yescharacteristic
342C4⋊C4—2022no—
343C4⋊C4—2022no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—41no—
347C22⋊C4—4041no—
348C22⋊C4—2022no—
349C22⋊C4—2022no—
350C22⋊C4—2022no—
351C22⋊C4—2022no—
352C42—2022no—
353C42—2022no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—1012no—
365C23—1012no—
366C23—1012no—
367C23—2021no—
368C23—2021no—
369C23—2021no—
370C23—2021no—
371C23C2×C4×D10112yes—
372C23C2×C4×D10112yes—
373C23D4×D10112yes—
374C23D4×D10112yes—
375C23C23×D10111yescharacteristic
376Q8—2028no—
377D4—28no—
378D4—10116no—
379D4—2028no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—44no—
394C2×C4—1012no—
395C2×C4—1012no—
396C2×C4—1012no—
397C2×C4—1012no—
398C2×C4—1012no—
399C2×C4—1012no—
400C2×C4—4044no—
401C2×C4—4044no—
402C2×C4—4044no—
403C2×C4—2028no—
404C2×C4—2028no—
405C2×C4—2021no—
406C2×C4—2021no—
407C2×C4—2021no—
408C2×C4—2021no—
409C2×C4—2021no—
410C2×C4—2021no—
411C2×C4—2021no—
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—2028no—
421C2×C4C2×C4×D10112yes—
422C2×C4#1310807312yescomplemented
423C22—22no—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—1014no—
437C22—2022no—
438C22—2022no—
439C22—2022no—
440C22—2022no—
441C22—2022no—
442C22—2022no—
443C22C22⋊C4×D10114yes—
444C22C22×C4×D10111yescharacteristic
445C22C2×D4×D10111yescharacteristic
446C22C2×D4×D10111yescharacteristic
447C22#41×D10111yescharacteristic
448C22C2×#1310807311yescharacteristic
449C22#1569230011yescharacteristic
450C22#1569230211yescharacteristic
451C4—22no—
452C4—22no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—1014no—
457C4—4041no—
458C4—4041no—
459C4—4041no—
460C4—2022no—
461C4—2022no—
462C4—2022no—
463C2—24no—
464C2—42no—
465C2—2024no—
466C2C2×C22⋊C4×D10111yescharacteristic
467C2C4×#1310807311yescharacteristic
468C2#2026565611yescharacteristic
469C2#2026581411yescharacteristic
470C2#2026581611yescharacteristic
471C2#2026582511yescharacteristic
472C2#2026582711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#386×C101C2
socle, cosocleC23×C101C24
prime radicalC22×#13108073C2
hypercenter#386D101
hypocenterC101#2339
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D101C2semidirect
3. C2×#15692215C2semidirect
4. #20265081C2semidirect
5. #20265081C2semidirect
6. #20265057C2semidirect
7. #20265053C2semidirect
8. #20265053C2semidirect
9. #20265039C2semidirect
10. #20265038C2semidirect
11. #20265035C2semidirect
12. C22⋊C4×Dic101C2semidirect
13. C2×#15692162C2semidirect
14. #95×D101C2semidirect
15. #386×C101C2semidirect
18. C2×#13108073C4semidirect
60. C2×Dic202C2×C4semidirect
64. C2×C22⋊D101C2×C4semidirect
74. C22×Dic101C2×C4semidirect
75. C22×Dic101C2×C4semidirect
91. C2×C4×D101C2×C4semidirect
105. C2×D4×C101C2×C4semidirect
155. C2×C4×C101#41semidirect
157. C22⋊D101C22⋊C4semidirect
181. C2×Dic101#41semidirect
237. C101#2339semidirect
246. #386D101semidirect
308. C2×D4C4×D101semidirect
422. C2×C4#13108073semidirect

Maximal subgroups

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

subgroupindex
C22×#131080732
C2×C4×C22⋊D1012
C2×#156922152
#202650812
#202650572
#202650532
#202650392
#202650382
#202650352
C22⋊C4×Dic1012
C2×#156921622
#95×D1012
#386×C1012
#2339101