Finite Group Databasebeta

← #49170342

Subgroups — #49170342

Order 37504.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627653C211yesmaximal, characteristic, complemented
2C2×#22627645C211yesmaximal, characteristic, complemented
3#34036791C211yesmaximal, characteristic, complemented
4#34036783C211yesmaximal, characteristic, complemented
5#34036523C211yesmaximal, characteristic, complemented
6#34036376C211yesmaximal, characteristic, complemented
7#34036371C211yesmaximal, characteristic, complemented
8#34036344C211yesmaximal, characteristic, complemented
9#34036339C211yesmaximal, characteristic, complemented
10#34036294C211yesmaximal, characteristic, complemented
11#34036292C211yesmaximal, characteristic, complemented
12#34036286C211yesmaximal, characteristic, complemented
13#34036275C211yesmaximal, characteristic, complemented
14#34036202C211yesmaximal, characteristic, complemented
15#440×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989801C2211yescharacteristic
18C2×#17989801C2211yescharacteristic
19C2×Q8×D293C2211yescharacteristic
20#22627653—24no—
21#22627645—24no—
22C2×Dic1172C2211yescharacteristic
23C2×Dic1172C2211yescharacteristic
24C2×#17989792C2211yescharacteristic
25C2×#17989792C2211yescharacteristic
26C2×#17989791C2211yescharacteristic
27C2×#17989791C2211yescharacteristic
28C2×#17989790C2211yescharacteristic
29C2×#17989787C2211yescharacteristic
30C2×#17989785C2211yescharacteristic
31C2×C8×D293C2211yescharacteristic
32#22627624C2211yescharacteristic
33#22627612—21no—
34#22627612C2211yescharacteristic
35#22627608—21no—
36#22627608—21no—
37#22627604—21no—
38#22627604C2211yescharacteristic
39#22627604C2211yescharacteristic
40#22627604C2211yescharacteristic
41#22627599—21no—
42#22627599C2211yescharacteristic
43#22627598—21no—
44C4×D1172—21no—
45C4×D1172C2211yescharacteristic
46C2×C4⋊Dic293—21no—
47C4⋊#14556873C2211yescharacteristic
48#22627547C2211yescharacteristic
49#22627547C2211yescharacteristic
50#22627547C2211yescharacteristic
51#22627544C2211yescharacteristic
52#22627536C2211yescharacteristic
53#22627536C2211yescharacteristic
54C2×SD16×C293C2211yescharacteristic
55C4×Q8×C293C2211yescharacteristic
56C4×D4×C293C2211yescharacteristic
57#107×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59#102×C293C2211yescharacteristic
60#97×C293C2211yescharacteristic
61#17989803—22no—
62#17989803—41no—
63#17989801—22no—
64#17989801—22no—
65#17989801—41no—
66#17989801—41no—
67C2×Dic586—21no—
68C2×Dic586C2311yescharacteristic
69C2×Dic586C2311yescharacteristic
70C2×Dic586C2311yescharacteristic
71Q8×D293—22no—
72Q8×D293—41no—
73C2×D1172—21no—
74C2×D1172—21no—
75C2×D1172D411yescharacteristic
76C2×D1172C2311yescharacteristic
77C2×C22⋊D293—21no—
78C2×C22⋊D293—21no—
79C22×Dic293—21no—
80C22×Dic293—21no—
81C2×C4×D293—21no—
82C2×C4×D293—21no—
83C2×C4×D293C2311yescharacteristic
84C2×C4×D293C2311yescharacteristic
85Dic1172—22no—
86Dic1172—41no—
87#17989792—22no—
88#17989792—22no—
89#17989791—22no—
90#17989791—41no—
91#17989790—22no—
92#17989787—22no—
93#17989785—22no—
94C2×#14556873C2311yescharacteristic
95C2×#14556873C2311yescharacteristic
96C8×D293—22no—
97C4⋊Dic293—21no—
98C4⋊Dic293—21no—
99C4⋊Dic293—21no—
100C4⋊Dic293—21no—
101C4⋊Dic293—21no—
102C4⋊Dic293D411yescharacteristic
103#17989779—21no—
104#17989779—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779—21no—
109#17989779D411yescharacteristic
110#17989779D411yescharacteristic
111C2×Q8×C293C2311yescharacteristic
112C2×D4×C293C2311yescharacteristic
113C22×C4×C293—21no—
114SD16×C293D414yescomplemented
115C2×C8×C293C2311yescharacteristic
116C2×C8×C293C2311yescharacteristic
117C4⋊C4×C293—21no—
118C4⋊C4×C293C2311yescharacteristic
119C4⋊C4×C293C2311yescharacteristic
120C22⋊C4×C293—21no—
121C42×C293—21no—
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124C22×D293C2×D411yescharacteristic
125C22×D293C2×D411yescharacteristic
126Dic586—21no—
127Dic586—21no—
128Dic586—21no—
129Dic586—21no—
130Dic586—21no—
131Dic586—21no—
132Dic586—42no—
133D1172—21no—
134D1172—21no—
135D1172—41no—
136D1172—42no—
137D1172—42no—
138C22⋊D293—42no—
139C22⋊D293—42no—
140C2×Dic293—21no—
141C2×Dic293—21no—
142C2×Dic293—21no—
143C2×Dic293—42no—
144C2×Dic293—42no—
145C2×Dic293C2×D411yescharacteristic
146C2×Dic293C2×D411yescharacteristic
147C4×D293—21no—
148C4×D293—21no—
149C4×D293—21no—
150C4×D293—21no—
151C4×D293—42no—
152C4×D293—42no—
153#14556873—21no—
154#14556873—21no—
155C23×C293—21no—
156Q8×C293—21no—
157Q8×C293C2×D412yes—
158D4×C293—21no—
159D4×C293C2×D412yes—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293—42no—
164C2×C4×C293C2×D411yescharacteristic
165C2×C4×C293C2×D411yescharacteristic
166C2×C4×C293C2411yescharacteristic
167C8×C293—21no—
168C8×C293C2×D412yes—
169C22×C293—22no—
170C22×C293—41no—
171C22×C293—41no—
172C22×C293C22×D411yescharacteristic
173C2×D293—21no—
174C2×D293—21no—
175C2×D293—21no—
176C2×D293—21no—
177C2×D293—21no—
178C2×D293—21no—
179C2×D293—41no—
180C2×D293—41no—
181C2×D293—41no—
182C4×C293—22no—
183C4×C293—21no—
184C4×C293—21no—
185C4×C293—41no—
186C4×C293—41no—
187C4×C293C22×D411yescharacteristic
188C4×C293H(5,𝔽2)11yescharacteristic
189Dic293—21no—
190Dic293—21no—
191Dic293—41no—
192Dic293—41no—
193Dic293—41no—
194C2×C293—42no—
195C2×C293D4211yescharacteristic
196C2×C293#57511yescharacteristic
197C2×C293#57811yescharacteristic
198D293—41no—
199D293—41no—
200D293—81no—
201C293#326911yescharacteristic, complemented, Sylow
202#3269—2931nomaximal, Sylow
203C2×#137—2931no—
204C2×#135—2931no—
205#548—2931no—
206#547—2931no—
207#497—2931no—
208#468—2931no—
209#467—2931no—
210#463—2931no—
211#462—2931no—
212#452—2931no—
213#452—2931no—
214#451—2931no—
215#449—2931no—
216#440D29311yescharacteristic, complemented
217#435—2931no—
218C2×#41—2931no—
219C2×#41—2931no—
220C2×#41—2931no—
221C22×Q8—2931no—
222#137—5864no—
223#135—5864no—
224C2×Q16—2931no—
225C2×Q16—2931no—
226C2×Q16—2931no—
227C2×Q16—2931no—
228C2×SD16—2931no—
229C2×SD16—2931no—
230C2×SD16—2931no—
231C2×SD16C2×D29311yescharacteristic
232C2×D8—2931no—
233C2×M16—2931no—
234C22×C8—2931no—
235C4⋊Q8—2931no—
236#124—2931no—
237#124—5861no—
238#123—5861no—
239#123—5861no—
240C22⋊Q8—2931no—
241C22⋊Q8—2931no—
242C22⋊Q8—2931no—
243C22⋊Q8—5861no—
244#121—2931no—
245#121—5861no—
246#121—5861no—
247C4×Q8C2×D29311yescharacteristic
248C4×D4—2931no—
249C4×D4—5861no—
250C4×D4C2×D29311yescharacteristic
251C2×C4⋊C4—5861no—
252#107C2×D29311yescharacteristic
253C4⋊C8—2931no—
254#103—2931no—
255#103—2931no—
256#103—2931no—
257#103C2×D29311yescharacteristic
258#102—2931no—
259#102C2×D29311yescharacteristic
260C22⋊C8—2931no—
261C22⋊C8—2931no—
262#97C2×D29311yescharacteristic
263#41—5862no—
264#41—5862no—
265#41—5862no—
266#41—11721no—
267#41—11721no—
268#41—11721no—
269C2×Q8—2931no—
270C2×Q8—2931no—
271C2×Q8—2931no—
272C2×Q8—5861no—
273C2×Q8—5862no—
274C2×Q8—11721no—
275C2×Q8C22×D29311yescharacteristic
276C2×D4—2931no—
277C2×D4—2931no—
278C2×D4—5861no—
279C2×D4—5861no—
280C2×D4—5861no—
281C2×D4—5861no—
282C2×D4C22×D29311yescharacteristic
283C22×C4—21no—
284C22×C4—2931no—
285C22×C4—2931no—
286C22×C4—5861no—
287C22×C4—5861no—
288C22×C4—5861no—
289C22×C4—5861no—
290Q16—5862no—
291Q16—5862no—
292Q16—5862no—
293Q16—11721no—
294SD16—5862no—
295SD16—5862no—
296SD16—11721no—
297SD16D117214yescomplemented
298D8—5862no—
299M16—5862no—
300C2×C8—2931no—
301C2×C8—2931no—
302C2×C8—5862no—
303C2×C8C22×D29311yescharacteristic
304C2×C8C22×D29311yescharacteristic
305C4⋊C4—21no—
306C4⋊C4—2931no—
307C4⋊C4—5861no—
308C4⋊C4—5861no—
309C4⋊C4—5861no—
310C4⋊C4—5861no—
311C4⋊C4—5861no—
312C4⋊C4C22×D29311yescharacteristic
313C4⋊C4C22×D29311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—2931no—
316C22⋊C4—2931no—
317C22⋊C4—5861no—
318C22⋊C4—5861no—
319C22⋊C4—5861no—
320C22⋊C4—5861no—
321C22⋊C4—5861no—
322C22⋊C4—5861no—
323C42—21no—
324C42C22×D29311yescharacteristic
325C23—21no—
326C23—2931no—
327C23—2931no—
328C23—5861no—
329Q8—21no—
330Q8—5861no—
331Q8—5861no—
332Q8—5861no—
333Q8—5861no—
334Q8—5861no—
335Q8—5861no—
336Q8—11722no—
337Q8C2×D117212yes—
338D4—21no—
339D4—5861no—
340D4—5861no—
341D4—11721no—
342D4—11722no—
343D4—11722no—
344D4—11722no—
345D4—11722no—
346D4C2×D117212yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—42no—
351C2×C4—2931no—
352C2×C4—2931no—
353C2×C4—5861no—
354C2×C4—5861no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—5861no—
360C2×C4—11722no—
361C2×C4—11722no—
362C2×C4—11722no—
363C2×C4—11722no—
364C2×C4D4×D29311yescharacteristic
365C2×C4D4×D29311yescharacteristic
366C2×C4C23×D29311yescharacteristic
367C8—21no—
368C8—5861no—
369C8—5861no—
370C8C2×D117212yes—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—5861no—
375C22—5861no—
376C22—5861no—
377C22—5861no—
378C22—5861no—
379C22—5861no—
380C22—11721no—
381C22—11721no—
382C22—11721no—
383C22C2×D4×D29311yescharacteristic
384C4—22no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—5861no—
390C4—5861no—
391C4—11721no—
392C4—11721no—
393C4—11721no—
394C4C22×D117211yescharacteristic
395C4#2262767011yescharacteristic
396C2—42no—
397C2—23441no—
398C2—11721no—
399C2—11721no—
400C2D4×D117211yescharacteristic
401C2#3403692511yescharacteristic
402C2#3403694511yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#440×C293C2
socleC22×C293C22×D4
hypercenter#440D293
hypocenterC293#3269
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#22627653C2semidirect
2. C2×#22627645C2semidirect
3. #34036791C2semidirect
4. #34036783C2semidirect
5. #34036523C2semidirect
6. #34036376C2semidirect
7. #34036371C2semidirect
8. #34036344C2semidirect
9. #34036339C2semidirect
10. #34036294C2semidirect
11. #34036292C2semidirect
12. #34036286C2semidirect
13. #34036275C2semidirect
14. #34036202C2semidirect
15. #440×C293C2semidirect
114. SD16×C293D4semidirect
201. C293#3269semidirect
216. #440D293semidirect
297. SD16D1172semidirect

Maximal subgroups

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

subgroupindex
C2×#226276532
C2×#226276452
#340367912
#340367832
#340365232
#340363762
#340363712
#340363442
#340363392
#340362942
#340362922
#340362862
#340362752
#340362022
#440×C2932
#3269293