Finite Group Databasebeta

← #49170338

Subgroups — #49170338

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×#22627654C211yesmaximal, characteristic, complemented
2C2×#22627643C211yesmaximal, characteristic, complemented
3#34036785C211yesmaximal, characteristic, complemented
4#34036778C211yesmaximal, characteristic, complemented
5#34036520C211yesmaximal, characteristic, complemented
6#34036373C211yesmaximal, characteristic, complemented
7#34036369C211yesmaximal, characteristic, complemented
8#34036342C211yesmaximal, characteristic, complemented
9#34036338C211yesmaximal, characteristic, complemented
10#34036292C211yesmaximal, characteristic, complemented
11#34036288C211yesmaximal, characteristic, complemented
12#34036287C211yesmaximal, characteristic, complemented
13#34036226C211yesmaximal, characteristic, complemented
14#34036203C211yesmaximal, characteristic, complemented
15#449×C293C211yesmaximal, characteristic, complemented
16C2×#17989801C2211yescharacteristic
17C2×#17989801C2211yescharacteristic
18C22×Dic586C2211yescharacteristic
19#22627654—24no—
20#22627643—24no—
21C2×Dic1172C2211yescharacteristic
22C2×Dic1172C2211yescharacteristic
23C2×#17989792C2211yescharacteristic
24C2×#17989792C2211yescharacteristic
25C2×#17989790C2211yescharacteristic
26C2×#17989790C2211yescharacteristic
27C2×#17989790C2211yescharacteristic
28C2×#17989786C2211yescharacteristic
29C2×C8×D293C2211yescharacteristic
30#22627622C2211yescharacteristic
31#22627611C2211yescharacteristic
32#22627610—21no—
33#22627607—21no—
34#22627605—21no—
35#22627604C2211yescharacteristic
36#22627603C2211yescharacteristic
37#22627601—21no—
38#22627600C2211yescharacteristic
39#22627596—21no—
40#22627596—21no—
41#22627589C2211yescharacteristic
42D4×Dic293—21no—
43D4×Dic293C2211yescharacteristic
44C4×C22⋊D293C2211yescharacteristic
45C2×#17989781—21no—
46#22627557C2211yescharacteristic
47#22627553C2211yescharacteristic
48#22627549C2211yescharacteristic
49#22627549C2211yescharacteristic
50#22627547C2211yescharacteristic
51#22627545C2211yescharacteristic
52#22627536C2211yescharacteristic
53#22627534C2211yescharacteristic
54C2×#41×C293C2211yescharacteristic
55C2×SD16×C293C2211yescharacteristic
56C2×D8×C293C2211yescharacteristic
57#121×C293C2211yescharacteristic
58#103×C293C2211yescharacteristic
59#102×C293C2211yescharacteristic
60C22⋊C8×C293C2211yescharacteristic
61#17989801—22no—
62#17989801—22no—
63#17989801—41no—
64#17989801—41no—
65C2×Dic586—22no—
66C2×Dic586—21no—
67C2×Dic586—41no—
68C2×Dic586C2311yescharacteristic
69C2×Dic586C2311yescharacteristic
70C2×Dic586C2311yescharacteristic
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C2×C22⋊D293D411yescharacteristic
74C22×Dic293—21no—
75C22×Dic293—21no—
76C22×Dic293—21no—
77C22×Dic293—21no—
78C2×C4×D293C2311yescharacteristic
79Dic1172—22no—
80Dic1172—41no—
81#17989792—22no—
82#17989792—22no—
83#17989790—22no—
84#17989790—22no—
85#17989790D414yescomplemented
86#17989786—22no—
87C2×#14556873C2311yescharacteristic
88C2×#14556873C2311yescharacteristic
89C8×D293—22no—
90C4⋊Dic293—21no—
91C4⋊Dic293C2311yescharacteristic
92#17989781—21no—
93#17989781—21no—
94#17989781—21no—
95#17989781—21no—
96#17989781—21no—
97#17989781D411yescharacteristic
98C22⋊Dic293—21no—
99C22⋊Dic293—21no—
100C22⋊Dic293—21no—
101C22⋊Dic293—21no—
102C22⋊Dic293D411yescharacteristic
103#17989779—21no—
104#17989779—21no—
105#17989779D411yescharacteristic
106C4×Dic293—21no—
107C4×Dic293C2311yescharacteristic
108#41×C293—22no—
109#41×C293—41no—
110C2×Q8×C293C2311yescharacteristic
111C2×D4×C293—21no—
112C2×D4×C293—21no—
113C2×D4×C293C2311yescharacteristic
114C2×D4×C293C2311yescharacteristic
115C22×C4×C293—21no—
116C22×C4×C293C2311yescharacteristic
117SD16×C293—41no—
118D8×C293—22no—
119C2×C8×C293C2311yescharacteristic
120C2×C8×C293C2311yescharacteristic
121C4⋊C4×C293C2311yescharacteristic
122C22⋊C4×C293—21no—
123C22×D293C2×D411yescharacteristic
124Dic586—21no—
125Dic586—21no—
126Dic586—21no—
127Dic586—21no—
128Dic586—21no—
129Dic586—42no—
130Dic586C2×D412yes—
131C22⋊D293—41no—
132C22⋊D293—42no—
133C22⋊D293—42no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—21no—
137C2×Dic293—21no—
138C2×Dic293—42no—
139C2×Dic293—42no—
140C2×Dic293—42no—
141C2×Dic293—42no—
142C2×Dic293C2×D411yescharacteristic
143C2×Dic293C2×D411yescharacteristic
144C2×Dic293C2×D411yescharacteristic
145C4×D293—21no—
146C4×D293—21no—
147#14556873—21no—
148#14556873C2×D412yes—
149C23×C293—21no—
150C23×C293—21no—
151C23×C293C2×D411yescharacteristic
152Q8×C293—21no—
153Q8×C293—21no—
154D4×C293—21no—
155D4×C293—21no—
156D4×C293—21no—
157D4×C293—42no—
158D4×C293—42no—
159D4×C293C2×D412yes—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—21no—
163C2×C4×C293—21no—
164C2×C4×C293—42no—
165C2×C4×C293C2×D411yescharacteristic
166C2×C4×C293C2411yescharacteristic
167C8×C293—21no—
168C8×C293—21no—
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—41no—
184C4×C293—41no—
185C4×C293C22×D411yescharacteristic
186C4×C293H(5,𝔽2)11yescharacteristic
187Dic293—21no—
188Dic293—22no—
189Dic293—21no—
190Dic293—21no—
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×#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#449D29311yescharacteristic, complemented
216#440—2931no—
217#435—2931no—
218C2×#41—2931no—
219C2×#41—2931no—
220C2×#41C2×D29311yescharacteristic
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×D8C2×D29311yescharacteristic
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—5861no—
245#121—5861no—
246#121C2×D29311yescharacteristic
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#103C2×D29311yescharacteristic
258#102—2931no—
259#102C2×D29311yescharacteristic
260C22⋊C8—2931no—
261C22⋊C8C2×D29311yescharacteristic
262#97—2931no—
263#41—22no—
264#41—41no—
265#41—5862no—
266#41—5862no—
267#41—11721no—
268#41—11721no—
269C2×Q8—2931no—
270C2×Q8—2931no—
271C2×Q8—2931no—
272C2×Q8—5862no—
273C2×Q8—5861no—
274C2×Q8—11721no—
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—2931no—
285C22×C4—5861no—
286C22×C4—5861no—
287C22×C4—5861no—
288C22×C4—5861no—
289C22×C4C22×D29311yescharacteristic
290Q16—5862no—
291Q16—5862no—
292Q16—5862no—
293Q16—11721no—
294SD16—41no—
295SD16—2934no—
296SD16—5862no—
297SD16—5862no—
298D8—22no—
299M16—5862no—
300C2×C8—2931no—
301C2×C8—2931no—
302C2×C8—5862no—
303C2×C8C22×D29311yescharacteristic
304C2×C8C22×D29311yescharacteristic
305C4⋊C4—2931no—
306C4⋊C4—2931no—
307C4⋊C4—5861no—
308C4⋊C4—5861no—
309C4⋊C4—5861no—
310C4⋊C4—5861no—
311C4⋊C4—5861no—
312C4⋊C4—5861no—
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—2931no—
324C42—5861no—
325C23—21no—
326C23—21no—
327C23—2931no—
328C23D4×D29311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—2932no—
332Q8—5861no—
333Q8—5861no—
334Q8—5861no—
335Q8—5861no—
336Q8—5861no—
337Q8—11722no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—11721no—
344D4—11722no—
345D4—11722no—
346D4D4×D29312yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—2931no—
353C2×C4—2931no—
354C2×C4—2931no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—5861no—
360C2×C4—5861no—
361C2×C4—11722no—
362C2×C4—11722no—
363C2×C4—11722no—
364C2×C4—11722no—
365C2×C4D4×D29311yescharacteristic
366C2×C4C23×D29311yescharacteristic
367C8—21no—
368C8—21no—
369C8—2932no—
370C8—5861no—
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—41no—
386C4—41no—
387C4—5861no—
388C4—5862no—
389C4—5861no—
390C4—5861no—
391C4—11721no—
392C4—11721no—
393C4—11721no—
394C4C2×D4×D29311yescharacteristic
395C4#2262766911yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—11721no—
400C2#3403676111yescharacteristic
401C2#3403692511yescharacteristic
402C2#3403694311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#449×C293C2
socleC22×C293C22×D4
hypercenter#449D293
hypocenterC293#3269
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#22627654C2semidirect
2. C2×#22627643C2semidirect
3. #34036785C2semidirect
4. #34036778C2semidirect
5. #34036520C2semidirect
6. #34036373C2semidirect
7. #34036369C2semidirect
8. #34036342C2semidirect
9. #34036338C2semidirect
10. #34036292C2semidirect
11. #34036288C2semidirect
12. #34036287C2semidirect
13. #34036226C2semidirect
14. #34036203C2semidirect
15. #449×C293C2semidirect
85. #17989790D4semidirect
201. C293#3269semidirect
215. #449D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276542
C2×#226276432
#340367852
#340367782
#340365202
#340363732
#340363692
#340363422
#340363382
#340362922
#340362882
#340362872
#340362262
#340362032
#449×C2932
#3269293