Finite Group Databasebeta

← #49170366

Subgroups — #49170366

Order 37504.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627654C211yesmaximal, characteristic, complemented
2C2×#22627644C211yesmaximal, characteristic, complemented
3#34036788C211yesmaximal, characteristic, complemented
4#34036516C211yesmaximal, characteristic, complemented
5#34036380C211yesmaximal, characteristic, complemented
6#34036356C211yesmaximal, characteristic, complemented
7#34036351C211yesmaximal, characteristic, complemented
8#34036326C211yesmaximal, characteristic, complemented
9#34036291C211yesmaximal, characteristic, complemented
10#34036274C211yesmaximal, characteristic, complemented
11#34036272C211yesmaximal, characteristic, complemented
12#34036267C211yesmaximal, characteristic, complemented
13#34036234C211yesmaximal, characteristic, complemented
14#34036201C211yesmaximal, characteristic, complemented
15#550×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C22×Dic586C2211yescharacteristic
18#22627654—24no—
19#22627644—24no—
20C2×#17989792C2211yescharacteristic
21C2×#17989792C2211yescharacteristic
22C2×#17989790C2211yescharacteristic
23C2×#17989790C2211yescharacteristic
24C2×#17989790C2211yescharacteristic
25C2×#17989790C2211yescharacteristic
26C2×#17989789C2211yescharacteristic
27C2×#17989787C2211yescharacteristic
28C2×#17989787C2211yescharacteristic
29C2×#17989786C2211yescharacteristic
30C22×#14556873C2211yescharacteristic
31#22627612C2211yescharacteristic
32#22627610—21no—
33#22627603C2211yescharacteristic
34#22627602—21no—
35#22627598C2211yescharacteristic
36#22627596—21no—
37C4×Dic586C2211yescharacteristic
38#22627584—21no—
39#22627555C2211yescharacteristic
40C4⋊#14556873C2211yescharacteristic
41#22627548C2211yescharacteristic
42#22627547C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627545C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627544C2211yescharacteristic
47C22⋊#14556873C2211yescharacteristic
48C22⋊#14556873C2211yescharacteristic
49#22627535C2211yescharacteristic
50C2×#41×C293C2211yescharacteristic
51C2×#41×C293C2211yescharacteristic
52#127×C293—21no—
53#127×C293C2211yescharacteristic
54#121×C293—21no—
55#121×C293—21no—
56#121×C293C2211yescharacteristic
57#121×C293C2211yescharacteristic
58C4×Q8×C293C2211yescharacteristic
59C4×D4×C293—21no—
60C4×D4×C293C2211yescharacteristic
61#17989802—22no—
62#17989802—41no—
63C2×Dic586—22no—
64C2×Dic586—21no—
65C2×Dic586—41no—
66C2×Dic586C2311yescharacteristic
67C2×Dic586C2311yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C22×Dic293—21no—
72C2×C4×D293—21no—
73#17989792—22no—
74#17989792D414yescomplemented
75#17989790—22no—
76#17989790—22no—
77#17989790—22no—
78#17989790—41no—
79#17989789—22no—
80#17989787—22no—
81#17989787—41no—
82#17989786—22no—
83C2×#14556873—22no—
84C2×#14556873C2311yescharacteristic
85C2×#14556873C2311yescharacteristic
86C2×#14556873C2311yescharacteristic
87C2×#14556873C2311yescharacteristic
88C4⋊Dic293C2311yescharacteristic
89#17989781—21no—
90#17989781—21no—
91C22⋊Dic293—21no—
92#17989779—21no—
93#17989779—21no—
94#17989779—21no—
95C4×Dic293—21no—
96#41×C293—22no—
97#41×C293—22no—
98#41×C293—41no—
99#41×C293—41no—
100C2×Q8×C293C2311yescharacteristic
101C2×D4×C293—21no—
102C2×D4×C293—21no—
103C2×D4×C293—21no—
104C2×D4×C293—21no—
105C2×D4×C293—21no—
106C2×D4×C293—21no—
107C2×D4×C293D411yescharacteristic
108C2×D4×C293C2311yescharacteristic
109C2×D4×C293C2311yescharacteristic
110C22×C4×C293—21no—
111C22×C4×C293—21no—
112C22×C4×C293C2311yescharacteristic
113C22×C4×C293C2311yescharacteristic
114C4⋊C4×C293—21no—
115C4⋊C4×C293D411yescharacteristic
116C4⋊C4×C293C2311yescharacteristic
117C22⋊C4×C293—21no—
118C22⋊C4×C293—21no—
119C22⋊C4×C293D411yescharacteristic
120C22⋊C4×C293D411yescharacteristic
121C42×C293—21no—
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124Dic586—21no—
125Dic586—21no—
126Dic586—21no—
127Dic586—42no—
128Dic586C2×D412yes—
129D1172—21no—
130D1172—21no—
131C22⋊D293—42no—
132C22⋊D293—42no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—42no—
137C4×D293—42no—
138#14556873—21no—
139#14556873—21no—
140#14556873—21no—
141#14556873C2×D412yes—
142C23×C293—21no—
143C23×C293—21no—
144C23×C293C2×D411yescharacteristic
145C23×C293C2×D411yescharacteristic
146Q8×C293—21no—
147Q8×C293C2×D412yes—
148D4×C293—21no—
149D4×C293—21no—
150D4×C293—21no—
151D4×C293—21no—
152D4×C293—41no—
153D4×C293—42no—
154D4×C293—42no—
155D4×C293—42no—
156D4×C293—81no—
157D4×C293—81no—
158D4×C293—81no—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293—21no—
164C2×C4×C293—21no—
165C2×C4×C293—42no—
166C2×C4×C293—42no—
167C2×C4×C293C2×D411yescharacteristic
168C2×C4×C293C2×D411yescharacteristic
169C2×C4×C293C2×D411yescharacteristic
170C2×C4×C293C2×D411yescharacteristic
171C2×C4×C293C2411yescharacteristic
172C22×C293—21no—
173C22×C293—21no—
174C22×C293—21no—
175C22×C293—21no—
176C22×C293—21no—
177C22×C293—21no—
178C22×C293—41no—
179C22×C293—41no—
180C22×C293—41no—
181C22×C293—41no—
182C22×C293—41no—
183C22×C293—41no—
184C22×C293C22×D411yescharacteristic
185C2×D293—41no—
186C2×D293—41no—
187C2×D293—41no—
188C4×C293—21no—
189C4×C293—21no—
190C4×C293—22no—
191C4×C293—21no—
192C4×C293—21no—
193C4×C293—41no—
194C4×C293C22×D411yescharacteristic
195C4×C293H(5,𝔽2)11yescharacteristic
196Dic293—22no—
197Dic293—41no—
198Dic293—41no—
199C2×C293—41no—
200C2×C293—41no—
201C2×C293—81no—
202C2×C293—81no—
203C2×C293D4211yescharacteristic
204C2×C293#57511yescharacteristic
205C2×C293#57711yescharacteristic
206D293—81no—
207C293#327111yescharacteristic, complemented, Sylow
208#3271—2931nomaximal, Sylow
209C2×#137—2931no—
210C2×#135—2931no—
211#550D29311yescharacteristic, complemented
212#548—2931no—
213#496—2931no—
214#469—2931no—
215#465—2931no—
216#464—2931no—
217#460—2931no—
218#452—2931no—
219#449—2931no—
220#449—2931no—
221#448—2931no—
222#441—2931no—
223#435—2931no—
224C2×#41—2931no—
225C2×#41C2×D29311yescharacteristic
226C2×#41C2×D29311yescharacteristic
227C22×Q8—2931no—
228#137—5864no—
229#135—5864no—
230C2×Q16—2931no—
231C2×Q16—2931no—
232C2×SD16—2931no—
233C2×SD16—2931no—
234C2×SD16—2931no—
235C2×SD16—2931no—
236C2×SD16—2931no—
237C2×D8—2931no—
238C2×D8—2931no—
239C2×M16—2931no—
240C22×C8—2931no—
241#127—21no—
242#127C2×D29311yescharacteristic
243#124—2931no—
244#124—5861no—
245C22⋊Q8—2931no—
246C22⋊Q8—5861no—
247#121—21no—
248#121—21no—
249#121—2931no—
250#121—5861no—
251#121C2×D29311yescharacteristic
252#121C2×D29311yescharacteristic
253C4×Q8—2931no—
254C4×Q8C2×D29311yescharacteristic
255C4×D4—21no—
256C4×D4—5861no—
257C4×D4C2×D29311yescharacteristic
258#106—2931no—
259C4⋊C8—2931no—
260#103—2931no—
261#103—2931no—
262#103—2931no—
263#102—2931no—
264#102—2931no—
265#102—2931no—
266C22⋊C8—2931no—
267C22⋊C8—2931no—
268#97—2931no—
269#41—22no—
270#41—22no—
271#41—41no—
272#41—41no—
273#41—5862no—
274#41—11721no—
275C2×Q8—2931no—
276C2×Q8—2931no—
277C2×Q8—5862no—
278C2×Q8—5861no—
279C2×Q8—11721no—
280C2×Q8C22×D29311yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—2931no—
288C2×D4—5861no—
289C2×D4—5861no—
290C2×D4C22⋊D29311yescharacteristic
291C2×D4C22×D29311yescharacteristic
292C2×D4C22×D29311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—5861no—
296C22×C4—5861no—
297C22×C4C22×D29311yescharacteristic
298C22×C4C22×D29311yescharacteristic
299Q16—2934no—
300Q16—5862no—
301SD16—5862no—
302SD16—5862no—
303SD16—5862no—
304SD16—5862no—
305SD16—11721no—
306D8—5862no—
307D8—11721no—
308M16—5862no—
309C2×C8—2931no—
310C2×C8—2931no—
311C2×C8—2931no—
312C2×C8—2931no—
313C2×C8—5862no—
314C4⋊C4—21no—
315C4⋊C4—2931no—
316C4⋊C4—5861no—
317C4⋊C4—5861no—
318C4⋊C4C22⋊D29311yescharacteristic
319C4⋊C4C22×D29311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—5861no—
323C22⋊C4—5861no—
324C22⋊C4—5861no—
325C22⋊C4—5861no—
326C22⋊C4C22⋊D29311yescharacteristic
327C22⋊C4C22⋊D29311yescharacteristic
328C42—21no—
329C42—5861no—
330C42C22×D29311yescharacteristic
331C23—21no—
332C23—21no—
333C23—5861no—
334C23C2×C22⋊D29311yescharacteristic
335C23C2×C22⋊D29311yescharacteristic
336Q8—21no—
337Q8—2932no—
338Q8—5861no—
339Q8—5861no—
340Q8—5861no—
341Q8—11722no—
342Q8D4×D29312yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—41no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—5861no—
355D4—5861no—
356D4—11722no—
357D4—11722no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—5861no—
367C2×C4—5861no—
368C2×C4—5861no—
369C2×C4—11722no—
370C2×C4—11722no—
371C2×C4C2×C22⋊D29311yescharacteristic
372C2×C4C2×C22⋊D29311yescharacteristic
373C2×C4C2×C22⋊D29311yescharacteristic
374C2×C4C2×C22⋊D29311yescharacteristic
375C2×C4C23×D29311yescharacteristic
376C8—2932no—
377C8—5861no—
378C8—5861no—
379C8—5861no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—11721no—
393C22—11721no—
394C22—11721no—
395C22C22×C22⋊D29311yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—41no—
402C4—5862no—
403C4—11721no—
404C4—11721no—
405C4C2×D4×D29311yescharacteristic
406C4#2262766911yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—23441no—
412C2D4×C22⋊D29311yescharacteristic
413C2#3403692711yescharacteristic
414C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#550×C293C2
socleC22×C293C22×D4
hypercenter#550D293
hypocenterC293#3271
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#22627654C2semidirect
2. C2×#22627644C2semidirect
3. #34036788C2semidirect
4. #34036516C2semidirect
5. #34036380C2semidirect
6. #34036356C2semidirect
7. #34036351C2semidirect
8. #34036326C2semidirect
9. #34036291C2semidirect
10. #34036274C2semidirect
11. #34036272C2semidirect
12. #34036267C2semidirect
13. #34036234C2semidirect
14. #34036201C2semidirect
15. #550×C293C2semidirect
74. #17989792D4semidirect
207. C293#3271semidirect
211. #550D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276542
C2×#226276442
#340367882
#340365162
#340363802
#340363562
#340363512
#340363262
#340362912
#340362742
#340362722
#340362672
#340362342
#340362012
#550×C2932
#3271293