Finite Group Databasebeta

← #49170340

Subgroups — #49170340

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
2#34036786C211yesmaximal, characteristic, complemented
3#34036778C211yesmaximal, characteristic, complemented
4#34036520C211yesmaximal, characteristic, complemented
5#34036372C211yesmaximal, characteristic, complemented
6#34036370C211yesmaximal, characteristic, complemented
7#34036342C211yesmaximal, characteristic, complemented
8#34036337C211yesmaximal, characteristic, complemented
9#34036291C211yesmaximal, characteristic, complemented
10#34036291C211yesmaximal, characteristic, complemented
11#34036283C211yesmaximal, characteristic, complemented
12#34036271C211yesmaximal, characteristic, complemented
13#34036230C211yesmaximal, characteristic, complemented
14#34036200C211yesmaximal, characteristic, complemented
15C2×#135×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×Q8×D293C2211yescharacteristic
18#22627653—24no—
19C2×Dic1172C2211yescharacteristic
20C2×#17989792C2211yescharacteristic
21C2×#17989792C2211yescharacteristic
22C2×#17989790C2211yescharacteristic
23C2×#17989790C2211yescharacteristic
24C2×#17989785C2211yescharacteristic
25#22627622C2211yescharacteristic
26#22627611—21no—
27#22627611C2211yescharacteristic
28#22627607—21no—
29#22627605—21no—
30#22627603—21no—
31#22627603C2211yescharacteristic
32#22627603C2211yescharacteristic
33#22627600C2211yescharacteristic
34#22627596—21no—
35#22627595—21no—
36#22627595C2211yescharacteristic
37Q8×Dic293C2211yescharacteristic
38D4×Dic293C2211yescharacteristic
39C4×C22⋊D293—21no—
40C4×C22⋊D293C2211yescharacteristic
41C2×#17989781—21no—
42#22627558C2211yescharacteristic
43#22627553C2211yescharacteristic
44#22627549C2211yescharacteristic
45#22627549C2211yescharacteristic
46#22627548C2211yescharacteristic
47#22627548C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627545C2211yescharacteristic
50C22⋊#14556873C2211yescharacteristic
51#22627536C2211yescharacteristic
52#22627534C2211yescharacteristic
53C2×#41×C293C2211yescharacteristic
54C2×#41×C293C2211yescharacteristic
55#135×C293—24no—
56C2×Q16×C293C2211yescharacteristic
57C2×SD16×C293C2211yescharacteristic
58C2×SD16×C293C2211yescharacteristic
59C2×D8×C293C2211yescharacteristic
60C22×C8×C293C2211yescharacteristic
61#17989801—22no—
62#17989801—41no—
63C2×Dic586—21no—
64C2×Dic586C2311yescharacteristic
65C2×Dic586C2311yescharacteristic
66Q8×D293—22no—
67Q8×D293—41no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C22⋊D293D411yescharacteristic
71C22×Dic293—21no—
72C22×Dic293—21no—
73C2×C4×D293—21no—
74C2×C4×D293C2311yescharacteristic
75Dic1172—22no—
76#17989792—22no—
77#17989792—41no—
78#17989790—22no—
79#17989790—41no—
80#17989785—22no—
81C2×#14556873C2311yescharacteristic
82C2×#14556873C2311yescharacteristic
83C4⋊Dic293—21no—
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86#17989781—21no—
87#17989781—21no—
88#17989781—21no—
89#17989781—21no—
90#17989781—21no—
91#17989781D411yescharacteristic
92C22⋊Dic293—21no—
93C22⋊Dic293—21no—
94C22⋊Dic293—21no—
95C22⋊Dic293—21no—
96C22⋊Dic293—21no—
97C22⋊Dic293—21no—
98C22⋊Dic293D411yescharacteristic
99#17989779—21no—
100#17989779D411yescharacteristic
101C4×Dic293—21no—
102C4×Dic293C2311yescharacteristic
103#41×C293—22no—
104#41×C293—22no—
105#41×C293—41no—
106#41×C293—41no—
107C2×Q8×C293C2311yescharacteristic
108C2×Q8×C293C2311yescharacteristic
109C2×D4×C293—21no—
110C2×D4×C293—21no—
111C2×D4×C293C2311yescharacteristic
112C2×D4×C293C2311yescharacteristic
113C22×C4×C293—21no—
114C22×C4×C293—21no—
115C22×C4×C293C2311yescharacteristic
116Q16×C293—22no—
117SD16×C293—22no—
118SD16×C293D414yescomplemented
119D8×C293—22no—
120C2×C8×C293—22no—
121C2×C8×C293C2311yescharacteristic
122C2×C8×C293C2311yescharacteristic
123C22×D293C2×D411yescharacteristic
124Dic586—21no—
125Dic586—21no—
126Dic586—21no—
127Dic586—21no—
128Dic586—42no—
129C22⋊D293—41no—
130C22⋊D293—42no—
131C22⋊D293—42no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—42no—
137C2×Dic293—42no—
138C2×Dic293C2×D411yescharacteristic
139C2×Dic293C2×D411yescharacteristic
140C2×Dic293C2×D411yescharacteristic
141C4×D293—21no—
142C4×D293—21no—
143C4×D293—42no—
144#14556873—21no—
145#14556873—21no—
146C23×C293—21no—
147C23×C293—21no—
148C23×C293C2×D411yescharacteristic
149Q8×C293—21no—
150Q8×C293—21no—
151Q8×C293—21no—
152Q8×C293C2×D412yes—
153D4×C293—21no—
154D4×C293—21no—
155D4×C293—21no—
156D4×C293—42no—
157D4×C293—42no—
158D4×C293C2×D412yes—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293—42no—
164C2×C4×C293—42no—
165C2×C4×C293C2×D411yescharacteristic
166C2×C4×C293C2411yescharacteristic
167C8×C293—21no—
168C8×C293C2×D412yes—
169C22×C293—21no—
170C22×C293—22no—
171C22×C293—21no—
172C22×C293—21no—
173C22×C293—41no—
174C22×C293—41no—
175C22×C293—41no—
176C22×C293—41no—
177C22×C293—41no—
178C22×C293C22×D411yescharacteristic
179C2×D293—21no—
180C2×D293—21no—
181C2×D293—21no—
182C4×C293—21no—
183C4×C293—22no—
184C4×C293—41no—
185C4×C293C22×D411yescharacteristic
186C4×C293H(5,𝔽2)11yescharacteristic
187Dic293—21no—
188Dic293—21no—
189Dic293—21no—
190Dic293—41no—
191Dic293—41no—
192Dic293—41no—
193Dic293—41no—
194C2×C293—41no—
195C2×C293—42no—
196C2×C293—81no—
197C2×C293D4211yescharacteristic
198C2×C293#57511yescharacteristic
199C2×C293#57811yescharacteristic
200D293—41no—
201C293#326911yescharacteristic, complemented, Sylow
202#3269—2931nomaximal, Sylow
203C2×#137—2931no—
204C2×#135D29311yescharacteristic, complemented
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#440—2931no—
217#435—2931no—
218C2×#41—2931no—
219C2×#41C2×D29311yescharacteristic
220C2×#41C2×D29311yescharacteristic
221C22×Q8—2931no—
222#137—5864no—
223#135—24no—
224C2×Q16—2931no—
225C2×Q16—2931no—
226C2×Q16—2931no—
227C2×Q16C2×D29311yescharacteristic
228C2×SD16—2931no—
229C2×SD16—2931no—
230C2×SD16C2×D29311yescharacteristic
231C2×SD16C2×D29311yescharacteristic
232C2×D8C2×D29311yescharacteristic
233C2×M16—2931no—
234C22×C8C2×D29311yescharacteristic
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×Q8—2931no—
248C4×D4—2931no—
249C4×D4—2931no—
250C4×D4—5861no—
251C2×C4⋊C4—5861no—
252#107—2931no—
253C4⋊C8—2931no—
254#103—2931no—
255#103—2931no—
256#103—2931no—
257#103—2931no—
258#102—2931no—
259#102—2931no—
260C22⋊C8—2931no—
261C22⋊C8—2931no—
262#97—2931no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—5862no—
268#41—11721no—
269C2×Q8—2931no—
270C2×Q8—2931no—
271C2×Q8—5861no—
272C2×Q8—5862no—
273C2×Q8—11721no—
274C2×Q8C22×D29311yescharacteristic
275C2×Q8C22×D29311yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—2931no—
279C2×D4—5861no—
280C2×D4—5861no—
281C2×D4C22×D29311yescharacteristic
282C2×D4C22×D29311yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2931no—
286C22×C4—5861no—
287C22×C4—5861no—
288C22×C4—5861no—
289C22×C4C22×D29311yescharacteristic
290Q16—22no—
291Q16—5862no—
292Q16—5862no—
293Q16—11721no—
294SD16—22no—
295SD16—5862no—
296SD16—11721no—
297SD16C22⋊D29314yescomplemented
298D8—22no—
299M16—5862no—
300C2×C8—22no—
301C2×C8—2931no—
302C2×C8—2931no—
303C2×C8C22×D29311yescharacteristic
304C2×C8C22×D29311yescharacteristic
305C4⋊C4—2931no—
306C4⋊C4—2931no—
307C4⋊C4—2931no—
308C4⋊C4—5861no—
309C4⋊C4—5861no—
310C4⋊C4—5861no—
311C4⋊C4—5861no—
312C4⋊C4—5861no—
313C4⋊C4—5861no—
314C22⋊C4—2931no—
315C22⋊C4—2931no—
316C22⋊C4—5861no—
317C22⋊C4—5861no—
318C22⋊C4—5861no—
319C22⋊C4—5861no—
320C22⋊C4—5861no—
321C22⋊C4—5861no—
322C22⋊C4—5861no—
323C42—2931no—
324C42—5861no—
325C23—21no—
326C23—21no—
327C23—2931no—
328C23D4×D29311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—5861no—
333Q8—5861no—
334Q8—5861no—
335Q8—5861no—
336Q8—11722no—
337Q8C2×C22⋊D29312yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—11721no—
344D4—11722no—
345D4—11722no—
346D4C2×C22⋊D29312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—2931no—
354C2×C4—2931no—
355C2×C4—2931no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—5861no—
360C2×C4—5861no—
361C2×C4—5861no—
362C2×C4—11722no—
363C2×C4—11722no—
364C2×C4—11722no—
365C2×C4D4×D29311yescharacteristic
366C2×C4C23×D29311yescharacteristic
367C8—21no—
368C8—5861no—
369C8—5861no—
370C8C2×C22⋊D29312yes—
371C22—21no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5861no—
381C22—5861no—
382C22—5861no—
383C22C2×D4×D29311yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—5861no—
388C4—5861no—
389C4—5861no—
390C4—11721no—
391C4—11721no—
392C4—11721no—
393C4—11721no—
394C4C22×C22⋊D29311yescharacteristic
395C4#2262766911yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—11721no—
400C2D4×C22⋊D29311yescharacteristic
401C2#3403692611yescharacteristic
402C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingC2×#135×C293C2
socleC22×C293C22×D4
hypercenterC2×#135D293
hypocenterC293#3269
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22627653C2semidirect
2. #34036786C2semidirect
3. #34036778C2semidirect
4. #34036520C2semidirect
5. #34036372C2semidirect
6. #34036370C2semidirect
7. #34036342C2semidirect
8. #34036337C2semidirect
9. #34036291C2semidirect
10. #34036291C2semidirect
11. #34036283C2semidirect
12. #34036271C2semidirect
13. #34036230C2semidirect
14. #34036200C2semidirect
15. C2×#135×C293C2semidirect
118. SD16×C293D4semidirect
201. C293#3269semidirect
204. C2×#135D293semidirect
297. SD16C22⋊D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276532
#340367862
#340367782
#340365202
#340363722
#340363702
#340363422
#340363372
#340362912
#340362832
#340362712
#340362302
#340362002
C2×#135×C2932
#3269293