Finite Group Databasebeta

← #34047844

Subgroups — #34047844

Order 19072.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011884C211yesmaximal, characteristic
2#23749527C211yesmaximal, characteristic, complemented
3#23749525C211yesmaximal, characteristic, complemented
4#23749517C211yesmaximal, characteristic, complemented
5#23749512C211yesmaximal, characteristic, complemented
6#23749509C211yesmaximal, characteristic, complemented
7#23749503C211yesmaximal, characteristic, complemented
8#23749502C211yesmaximal, characteristic, complemented
9#23749502C211yesmaximal, characteristic, complemented
10#23749501C211yesmaximal, characteristic, complemented
11#23749500C211yesmaximal, characteristic, complemented
12#23749496C211yesmaximal, characteristic, complemented
13#23749487C211yesmaximal, characteristic, complemented
14#23749482C211yesmaximal, characteristic, complemented
15#388×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C22×C22⋊D149C2211yescharacteristic
18C22×C22⋊D149C2211yescharacteristic
19C23×Dic149C2211yescharacteristic
20C22×C4×D149C2211yescharacteristic
21C22×C4×D149C2211yescharacteristic
22#18011884C418yescomplemented
23C2×C4⋊Dic149C2211yescharacteristic
24C2×C4⋊Dic149C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×C22⋊Dic149C2211yescharacteristic
28C2×#14558713C2211yescharacteristic
29C2×#14558713C2211yescharacteristic
30C2×#14558713C2211yescharacteristic
31C2×#14558713C2211yescharacteristic
32C2×#14558713C2211yescharacteristic
33C2×#14558713C2211yescharacteristic
34C2×#14558713C2211yescharacteristic
35C2×#14558713C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46C2×C22⋊C4×C149C2211yescharacteristic
47C2×C22⋊C4×C149C2211yescharacteristic
48C2×C22⋊C4×C149C2211yescharacteristic
49C2×C42×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C23×D149C2311yescharacteristic
53C23×D149C2311yescharacteristic
54C2×D596—41no—
55C2×D596—41no—
56C2×D596C2×C414yescomplemented
57C2×C22⋊D149—41no—
58C2×C22⋊D149—41no—
59C2×C22⋊D149—41no—
60C2×C22⋊D149—41no—
61C2×C22⋊D149C2×C414yes—
62C2×C22⋊D149C2×C414yescomplemented
63C22×Dic149—41no—
64C22×Dic149—41no—
65C22×Dic149—41no—
66C22×Dic149C2311yescharacteristic
67C22×Dic149C2311yescharacteristic
68C22×Dic149C2311yescharacteristic
69C22×Dic149C2311yescharacteristic
70C22×Dic149C2311yescharacteristic
71C22×Dic149C2311yescharacteristic
72C2×C4×D149—41no—
73C2×C4×D149—41no—
74C2×C4×D149—41no—
75C2×C4×D149—41no—
76C2×C4×D149—41no—
77C2×C4×D149C2×C414yescomplemented
78C4⋊Dic149—41no—
79C4⋊Dic149—41no—
80#14558715—41no—
81#14558715C2×C414yescomplemented
82C22⋊Dic149—41no—
83#14558713—41no—
84#14558713—41no—
85#14558713—41no—
86#14558713—41no—
87#14558713—41no—
88#14558713—41no—
89#14558713—41no—
90#14558713C2×C414yescomplemented
91C4×Dic149—41no—
92C24×C149C2311yescharacteristic
93C22×C4×C149C2311yescharacteristic
94C22×C4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96C22×C4×C149C2311yescharacteristic
97C22×C4×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C4⋊C4×C149—41no—
100C22⋊C4×C149—41no—
101C22⋊C4×C149—41no—
102C22⋊C4×C149C2×C414yescomplemented
103C42×C149—41no—
104C22×D149—21no—
105C22×D149—21no—
106C22×D149—21no—
107C22×D149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—21no—
111C22×D149—21no—
112C22×D149—21no—
113C22×D149—21no—
114C22×D149—21no—
115C22×D149—21no—
116C22×D149C22×C412yes—
117C22×D149C22×C412yes—
118D596—44no—
119C22⋊D149—44no—
120C22⋊D149—44no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—44no—
138C2×Dic149C22×C412yes—
139C2×Dic149C22×C412yes—
140C4×D149—44no—
141C4×D149—44no—
142C23×C149—21no—
143C23×C149—21no—
144C23×C149—21no—
145C23×C149—21no—
146C23×C149—21no—
147C23×C149—21no—
148C23×C149C22×C412yes—
149C23×C149C2411yescharacteristic
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149—21no—
154C2×C4×C149—21no—
155C2×C4×C149—21no—
156C2×C4×C149—21no—
157C2×C4×C149—21no—
158C2×C4×C149—21no—
159C2×C4×C149—21no—
160C2×C4×C149—21no—
161C2×C4×C149—21no—
162C2×C4×C149—21no—
163C2×C4×C149—21no—
164C2×C4×C149—21no—
165C2×C4×C149—21no—
166C2×C4×C149C22×C412yes—
167C2×C4×C149C22×C412yes—
168C22×C149—22no—
169C22×C149—22no—
170C22×C149—22no—
171C22×C149—41no—
172C22×C149—41no—
173C22×C149—41no—
174C22×C149—41no—
175C22×C149C23×C411yescharacteristic
176C22×C149H(5,𝔽2)11yescharacteristic
177C22×C149H(5,𝔽2)11yescharacteristic
178C22×C149H(5,𝔽2)11yescharacteristic
179C22×C149H(5,𝔽2)11yescharacteristic
180C22×C149H(5,𝔽2)11yescharacteristic
181C22×C1492−1+411yescharacteristic
182C2×D149—22no—
183C2×D149—22no—
184C2×D149—22no—
185C2×D149—22no—
186C2×D149—22no—
187C2×D149—22no—
188C2×D149—41no—
189C2×D149—41no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—41no—
194C2×D149—41no—
195C2×D149—41no—
196C4×C149—22no—
197C4×C149—22no—
198C4×C149—41no—
199C4×C149—41no—
200C4×C149—41no—
201C4×C149—41no—
202Dic149—22no—
203Dic149—22no—
204Dic149—41no—
205Dic149—41no—
206Dic149—41no—
207Dic149—41no—
208C2×C149—42no—
209C2×C149#51811yescharacteristic
210C2×C149#51811yescharacteristic
211C2×C149#52011yescharacteristic
212C2×C149#56011yescharacteristic
213C2×C149#56011yescharacteristic
214C2×C149#56211yescharacteristic
215C2×C149#56211yescharacteristic
216D149—42no—
217D149—42no—
218C149#237711yescharacteristic, complemented, Sylow
219#2377—1491nomaximal, Sylow
220C2×#121—1491no—
221#390—1491no—
222#390—1491no—
223#388—1491no—
224#388D14911yescharacteristic, complemented
225#387—1491no—
226#387—1491no—
227#386—1491no—
228#386—1491no—
229#386—1491no—
230#386—1491no—
231#385—1491no—
232#385—1491no—
233#381—1491no—
234#380—1491no—
235C22×D4—1491no—
236C22×D4—1491no—
237C22×D4—1491no—
238C23×C4—1491no—
239C23×C4—1491no—
240C23×C4—1491no—
241#121—1498no—
242C2×C4⋊C4—1491no—
243C2×C4⋊C4—1491no—
244C2×C4⋊C4—1491no—
245C2×C4⋊C4—1491no—
246C2×C4⋊C4C2×D14911yescharacteristic
247C2×C22⋊C4—1491no—
248C2×C22⋊C4—1491no—
249C2×C22⋊C4—1491no—
250C2×C22⋊C4—1491no—
251C2×C22⋊C4—1491no—
252C2×C22⋊C4—1491no—
253C2×C22⋊C4—1491no—
254C2×C22⋊C4—1491no—
255C2×C22⋊C4—1491no—
256C2×C22⋊C4C2×D14911yescharacteristic
257C2×C22⋊C4C2×D14911yescharacteristic
258C2×C22⋊C4C2×D14911yescharacteristic
259C2×C42—1491no—
260C2×C42C2×D14911yescharacteristic
261#95—1491no—
262#95—1491no—
263#95—1491no—
264#95—1491no—
265#95—1491no—
266#95—1491no—
267#95—1491no—
268#95—1491no—
269#95C2×D14911yescharacteristic
270#95C2×D14911yescharacteristic
271C24—1491no—
272C24—1491no—
273C24C22×D14911yescharacteristic
274C2×D4—5961no—
275C2×D4—5961no—
276C2×D4—5961no—
277C2×D4—5961no—
278C2×D4—5961no—
279C2×D4—5961no—
280C2×D4—1494no—
281C2×D4—1494no—
282C2×D4—1494no—
283C22×C4—5961no—
284C22×C4—5961no—
285C22×C4—5961no—
286C22×C4—5961no—
287C22×C4—5961no—
288C22×C4—5961no—
289C22×C4—5961no—
290C22×C4—5961no—
291C22×C4—1491no—
292C22×C4—1491no—
293C22×C4—1491no—
294C22×C4—1491no—
295C22×C4—1491no—
296C22×C4—1491no—
297C22×C4—1494no—
298C22×C4C22×D14911yescharacteristic
299C22×C4C22×D14911yescharacteristic
300C22×C4C22×D14911yescharacteristic
301C22×C4C22×D14911yescharacteristic
302C22×C4C22×D14911yescharacteristic
303C22×C4C22×D14911yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—5961no—
306C4⋊C4—5961no—
307C4⋊C4—5961no—
308C4⋊C4—1494no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—5961no—
312C22⋊C4—5961no—
313C22⋊C4—5961no—
314C22⋊C4—5961no—
315C22⋊C4—5961no—
316C22⋊C4—5961no—
317C22⋊C4—5961no—
318C22⋊C4—5961no—
319C22⋊C4—1494no—
320C22⋊C4C4×D14914yescomplemented
321C42—41no—
322C42—5961no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—2981no—
330C23—2981no—
331C23—2981no—
332C23—2981no—
333C23—2981no—
334C23—2981no—
335C23—2981no—
336C23—2981no—
337C23—2981no—
338C23—2981no—
339C23—2981no—
340C23—2981no—
341C23—1492no—
342C23—1492no—
343C23C2×C4×D14912yes—
344C23C23×D14911yescharacteristic
345D4—5964no—
346D4—5964no—
347D4—5964no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—2981no—
365C2×C4—2981no—
366C2×C4—2981no—
367C2×C4—2981no—
368C2×C4—2981no—
369C2×C4—2981no—
370C2×C4—2981no—
371C2×C4—2981no—
372C2×C4—2981no—
373C2×C4—2981no—
374C2×C4—2981no—
375C2×C4—2981no—
376C2×C4—2981no—
377C2×C4—2981no—
378C2×C4—2981no—
379C2×C4—2981no—
380C2×C4—5964no—
381C2×C4—5964no—
382C2×C4—5964no—
383C2×C4—1492no—
384C2×C4—1492no—
385C2×C4C2×C4×D14912yes—
386C2×C4C2×C4×D14912yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—2982no—
395C22—2982no—
396C22—2982no—
397C22—2982no—
398C22—2982no—
399C22—2982no—
400C22—5961no—
401C22—5961no—
402C22—5961no—
403C22—5961no—
404C22—5961no—
405C22—5961no—
406C22—5961no—
407C22—5961no—
408C22C22×C4×D14911yescharacteristic
409C22#1801195611yescharacteristic
410C22#1801195611yescharacteristic
411C22#1801195711yescharacteristic
412C22#1801195711yescharacteristic
413C22#1801195711yescharacteristic
414C22#1801195811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—2982no—
422C4—2982no—
423C4—5961no—
424C4—5961no—
425C4—5961no—
426C4—5961no—
427C2—42no—
428C2—5962no—
429C2—5962no—
430C2#2375009711yescharacteristic
431C2#2375009711yescharacteristic
432C2#2375010511yescharacteristic
433C2#2375036311yescharacteristic
434C2#2375036611yescharacteristic
435C2#2375036911yescharacteristic
436C2#2375037211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#388×C149C2
socle, cosocleC23×C149C24
prime radicalC2×#18011884C2
hypercenter#388D149
hypocenterC149#2377
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #23749527C2semidirect
3. #23749525C2semidirect
4. #23749517C2semidirect
5. #23749512C2semidirect
6. #23749509C2semidirect
7. #23749503C2semidirect
8. #23749502C2semidirect
9. #23749502C2semidirect
10. #23749501C2semidirect
11. #23749500C2semidirect
12. #23749496C2semidirect
13. #23749487C2semidirect
14. #23749482C2semidirect
15. #388×C149C2semidirect
22. #18011884C4semidirect
56. C2×D596C2×C4semidirect
62. C2×C22⋊D149C2×C4semidirect
77. C2×C4×D149C2×C4semidirect
81. #14558715C2×C4semidirect
90. #14558713C2×C4semidirect
102. C22⋊C4×C149C2×C4semidirect
218. C149#2377semidirect
224. #388D149semidirect
320. C22⋊C4C4×D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118842
#237495272
#237495252
#237495172
#237495122
#237495092
#237495032
#237495022
#237495012
#237495002
#237494962
#237494872
#237494822
#388×C1492
#2377149