Finite Group Databasebeta

← #49169341

Subgroups — #49169341

Order 37504.

412 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036683C211yesmaximal, characteristic, complemented
2#34036676C211yesmaximal, characteristic
3#34036526C211yesmaximal, characteristic, complemented
4#34036500C211yesmaximal, characteristic, complemented
5#34036478C211yesmaximal, characteristic, complemented
6#34036474C211yesmaximal, characteristic, complemented
7#34036361C211yesmaximal, characteristic, complemented
8#34036359C211yesmaximal, characteristic, complemented
9#34036357C211yesmaximal, characteristic, complemented
10#34036355C211yesmaximal, characteristic, complemented
11C4×#17989791C211yesmaximal, characteristic, complemented
12C4×#17989789C211yesmaximal, characteristic, complemented
13C4×#17989790C211yesmaximal, characteristic, complemented
14C4×C8×D293C211yesmaximal, characteristic, complemented
15C4×SD16×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C2×#17989791C2211yescharacteristic
18C2×#17989790C2211yescharacteristic
19C2×#17989789C2211yescharacteristic
20C2×C8×D293C2211yescharacteristic
21C2×C8×D293C2211yescharacteristic
22#22627623C2211yescharacteristic
23#22627623C2211yescharacteristic
24#22627622C2211yescharacteristic
25#22627620C2211yescharacteristic
26#22627614—21no—
27#22627610—21no—
28#22627604C2211yescharacteristic
29#22627602—21no—
30#22627600C2211yescharacteristic
31#22627599C2211yescharacteristic
32#22627597—21no—
33#22627595C2211yescharacteristic
34C4×Dic586—21no—
35C4×Dic586C2211yescharacteristic
36C4×D1172C2211yescharacteristic
37C4×C22⋊D293—21no—
38#22627581—21no—
39C42×D293C2211yescharacteristic
40#22627556C2211yescharacteristic
41#22627555C2211yescharacteristic
42#22627555C2211yescharacteristic
43#22627549C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627547C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627544C2211yescharacteristic
49C4×#14556873C2211yescharacteristic
50C8×Dic293C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×SD16×C293C2211yescharacteristic
53C4×Q8×C293C2211yescharacteristic
54C4×D4×C293C2211yescharacteristic
55#106×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C4×C8×C293C2211yescharacteristic
59#17989802—44no—
60C2×Dic586—21no—
61C2×Dic586—21no—
62C2×Dic586C2311yescharacteristic
63C2×D1172—21no—
64C2×D1172C2311yescharacteristic
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293D411yescharacteristic
70C2×C4×D293D411yescharacteristic
71C2×C4×D293C2311yescharacteristic
72#17989791—22no—
73#17989790—22no—
74#17989789—22no—
75C2×#14556873C2311yescharacteristic
76C2×#14556873C2311yescharacteristic
77C8×D293—22no—
78C8×D293—22no—
79C4⋊Dic293—21no—
80C4⋊Dic293C2311yescharacteristic
81C4⋊Dic293C2311yescharacteristic
82#17989781—21no—
83#17989781—21no—
84#17989781—21no—
85#17989781—21no—
86#17989781—21no—
87#17989781—21no—
88C22⋊Dic293—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93C4×Dic293—21no—
94C4×Dic293D411yescharacteristic
95C4×Dic293D411yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C2×D4×C293C2311yescharacteristic
99C22×C4×C293—21no—
100SD16×C293—22no—
101C2×C8×C293C2311yescharacteristic
102C2×C8×C293C2311yescharacteristic
103C4⋊C4×C293—21no—
104C4⋊C4×C293C2311yescharacteristic
105C4⋊C4×C293C2311yescharacteristic
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C42×C293C2311yescharacteristic
109C22×D293—21no—
110C22×D293C2×D411yescharacteristic
111Dic586—21no—
112Dic586—21no—
113Dic586—42no—
114Dic586—42no—
115D1172—21no—
116D1172—21no—
117D1172—42no—
118C22⋊D293—42no—
119C22⋊D293—42no—
120C22⋊D293—42no—
121C2×Dic293—21no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C4×D293—21no—
128C4×D293—21no—
129C4×D293—22no—
130C4×D293—42no—
131C4×D293SD1614yescomplemented
132#14556873—21no—
133#14556873#4112yescomplemented
134C23×C293—21no—
135Q8×C293—21no—
136Q8×C293—21no—
137D4×C293—21no—
138D4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—42no—
143C2×C4×C293C2×D411yescharacteristic
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293#4112yescomplemented
148C22×C293—41no—
149C22×C293—41no—
150C22×C293—41no—
151C22×C293C22×D411yescharacteristic
152C2×D293—21no—
153C2×D293—21no—
154C2×D293—41no—
155C2×D293—41no—
156C2×D293—41no—
157C2×D293C2×SD1612yes—
158C4×C293—21no—
159C4×C293—41no—
160C4×C293—41no—
161C4×C293—41no—
162C4×C293C2×SD1612yes—
163C4×C293C2×#4111yescharacteristic
164C4×C293C2×#4111yescharacteristic
165Dic293—21no—
166Dic293—41no—
167Dic293—41no—
168Dic293—41no—
169Dic293C2×SD1612yes—
170Dic293#13512yes—
171C2×C293—81no—
172C2×C293#53211yescharacteristic
173C2×C293C22×SD1611yescharacteristic
174C2×C293C2×#13511yescharacteristic
175D293—22no—
176D293—81no—
177C293#316711yescharacteristic, complemented, Sylow
178#3167—2931nomaximal, Sylow
179#533—2931no—
180#532—2931no—
181#498—2931no—
182#492—2931no—
183#487—2931no—
184#486—2931no—
185#465—2931no—
186#465—2931no—
187#465—2931no—
188#465—2931no—
189C4×SD16—2931no—
190C4×SD16—2931no—
191C4×SD16—2931no—
192C4×SD16D29311yescharacteristic, complemented
193C2×C4×C8—2931no—
194C2×#41—5861no—
195C2×SD16—2931no—
196C2×SD16—2931no—
197C2×SD16—2931no—
198C2×SD16C2×D29311yescharacteristic
199C22×C8—2931no—
200C22×C8—2931no—
201C4⋊Q8—2931no—
202C4⋊Q8—2931no—
203C4⋊Q8—2931no—
204#127—2931no—
205#125—5861no—
206#124—5861no—
207C22⋊Q8—2931no—
208C22⋊Q8—2931no—
209C22⋊Q8—5861no—
210#121—2931no—
211#121—2931no—
212#121—5861no—
213C4×Q8—2931no—
214C4×Q8—5861no—
215C4×Q8C2×D29311yescharacteristic
216C4×D4—2931no—
217C4×D4—5861no—
218C4×D4C2×D29311yescharacteristic
219#117—5861no—
220C2×C42—2931no—
221#106—2931no—
222#106—2931no—
223#106—2931no—
224#106C2×D29311yescharacteristic
225#103—2931no—
226#103—2931no—
227#103—2931no—
228#103C2×D29311yescharacteristic
229#102—2931no—
230#102—2931no—
231#102—2931no—
232#102C2×D29311yescharacteristic
233C4×C8—2931no—
234C4×C8—2931no—
235C4×C8—2931no—
236C4×C8C2×D29311yescharacteristic
237#41—11724no—
238C2×Q8—2931no—
239C2×Q8—5861no—
240C2×Q8—5861no—
241C2×Q8C22×D29311yescharacteristic
242C2×D4—2931no—
243C2×D4—5861no—
244C2×D4—5861no—
245C2×D4—5861no—
246C2×D4—5861no—
247C2×D4C22×D29311yescharacteristic
248C22×C4—21no—
249C22×C4—2931no—
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—5861no—
253SD16—22no—
254SD16—5862no—
255SD16—5862no—
256SD16—5862no—
257C2×C8—2931no—
258C2×C8—2931no—
259C2×C8—5862no—
260C2×C8—5862no—
261C2×C8C22×D29311yescharacteristic
262C2×C8C22×D29311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—2931no—
265C4⋊C4—2931no—
266C4⋊C4—5861no—
267C4⋊C4—5861no—
268C4⋊C4—5861no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4—5861no—
272C4⋊C4—5861no—
273C4⋊C4C22×D29311yescharacteristic
274C4⋊C4C22×D29311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—5861no—
277C22⋊C4—5861no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C42—21no—
282C42—2931no—
283C42—2931no—
284C42—2931no—
285C42—5861no—
286C42C22×D29311yescharacteristic
287C23—21no—
288C23—2931no—
289C23—5861no—
290Q8—21no—
291Q8—21no—
292Q8—5861no—
293Q8—5861no—
294Q8—11722no—
295Q8—11722no—
296D4—21no—
297D4—21no—
298D4—5861no—
299D4—5861no—
300D4—11722no—
301D4—11722no—
302D4—11722no—
303D4—11722no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—2931no—
309C2×C4—2931no—
310C2×C4—2934no—
311C2×C4—2931no—
312C2×C4—5862no—
313C2×C4—5861no—
314C2×C4—5861no—
315C2×C4—5861no—
316C2×C4—5861no—
317C2×C4—5861no—
318C2×C4—11722no—
319C2×C4D4×D29311yescharacteristic
320C2×C4D4×D29311yescharacteristic
321C2×C4C23×D29311yescharacteristic
322C8—21no—
323C8—2932no—
324C8—5861no—
325C8#1798980212yescomplemented
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2932no—
330C22—5861no—
331C22—5861no—
332C22—11721no—
333C22—11721no—
334C22—11721no—
335C22C2×D4×D29311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2932no—
341C4—2932no—
342C4—5861no—
343C4—11721no—
344C4—11721no—
345C4—11721no—
346C4SD16×D29312yes—
347C4#41×D29311yescharacteristic
348C4C2×#1798980211yescharacteristic
349C2—81no—
350C2—23441no—
351C2—5862no—
352C2#3403667611yescharacteristic
353C2C2×SD16×D29311yescharacteristic
354C2#135×D29311yescharacteristic
subgroupG/H
centerC2×C4D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC4×SD16×C293C2
socleC22×C293C22×D4
prime radical#34036676C2
hypercenterC4×SD16D293
hypocenterC293#3167
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #34036683C2semidirect
3. #34036526C2semidirect
4. #34036500C2semidirect
5. #34036478C2semidirect
6. #34036474C2semidirect
7. #34036361C2semidirect
8. #34036359C2semidirect
9. #34036357C2semidirect
10. #34036355C2semidirect
11. C4×#17989791C2semidirect
12. C4×#17989789C2semidirect
13. C4×#17989790C2semidirect
14. C4×C8×D293C2semidirect
15. C4×SD16×C293C2semidirect
131. C4×D293SD16semidirect
133. #14556873#41semidirect
147. C8×C293#41semidirect
177. C293#3167semidirect
192. C4×SD16D293semidirect
325. C8#17989802semidirect

Maximal subgroups

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

subgroupindex
#340366832
#340366762
#340365262
#340365002
#340364782
#340364742
#340363612
#340363592
#340363572
#340363552
C4×#179897912
C4×#179897892
C4×#179897902
C4×C8×D2932
C4×SD16×C2932
#3167293