Finite Group Databasebeta

← #49170345

Subgroups — #49170345

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×#22627657C211yesmaximal, characteristic, complemented
2C2×#22627646C211yesmaximal, characteristic, complemented
3#34036788C211yesmaximal, characteristic, complemented
4#34036784C211yesmaximal, characteristic, complemented
5#34036523C211yesmaximal, characteristic, complemented
6#34036375C211yesmaximal, characteristic, complemented
7#34036370C211yesmaximal, characteristic, complemented
8#34036345C211yesmaximal, characteristic, complemented
9#34036340C211yesmaximal, characteristic, complemented
10#34036293C211yesmaximal, characteristic, complemented
11#34036293C211yesmaximal, characteristic, complemented
12#34036287C211yesmaximal, characteristic, complemented
13#34036276C211yesmaximal, characteristic, complemented
14#34036231C211yesmaximal, characteristic, complemented
15#435×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989802C2211yescharacteristic
18C2×#17989802C2211yescharacteristic
19C22×Dic586C2211yescharacteristic
20#22627657—24no—
21#22627646—24no—
22C2×Dic1172C2211yescharacteristic
23C2×Dic1172C2211yescharacteristic
24C2×Dic1172C2211yescharacteristic
25C2×Dic1172C2211yescharacteristic
26C2×#17989791C2211yescharacteristic
27C2×#17989791C2211yescharacteristic
28C2×#17989791C2211yescharacteristic
29C2×#17989791C2211yescharacteristic
30C2×D2344C2211yescharacteristic
31#22627624C2211yescharacteristic
32#22627612C2211yescharacteristic
33#22627610—21no—
34#22627606—21no—
35#22627606—21no—
36#22627603C2211yescharacteristic
37#22627603C2211yescharacteristic
38#22627603C2211yescharacteristic
39#22627602—21no—
40#22627598C2211yescharacteristic
41#22627596—21no—
42#22627595—21no—
43C4×Dic586C2211yescharacteristic
44C4×D1172C2211yescharacteristic
45#22627584—21no—
46C4⋊C4×D293—21no—
47#22627558C2211yescharacteristic
48#22627549C2211yescharacteristic
49#22627549C2211yescharacteristic
50#22627549C2211yescharacteristic
51#22627549C2211yescharacteristic
52#22627546C2211yescharacteristic
53#22627546C2211yescharacteristic
54C2×M16×C293C2211yescharacteristic
55C22×C8×C293C2211yescharacteristic
56C4×D4×C293C2211yescharacteristic
57C4⋊C8×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C22⋊C8×C293C2211yescharacteristic
60#97×C293C2211yescharacteristic
61#17989802—22no—
62#17989802—22no—
63#17989802—22no—
64#17989802—41no—
65#17989802—41no—
66#17989802—41no—
67C2×Dic586—22no—
68C2×Dic586—21no—
69C2×Dic586—41no—
70C2×Dic586C2311yescharacteristic
71C2×Dic586C2311yescharacteristic
72C2×Dic586C2311yescharacteristic
73C2×Dic586C2311yescharacteristic
74C2×D1172C2311yescharacteristic
75C2×D1172C2311yescharacteristic
76C2×C22⋊D293—21no—
77C2×C22⋊D293—21no—
78C2×C22⋊D293—21no—
79C2×C22⋊D293—21no—
80C22×Dic293—21no—
81C2×C4×D293—21no—
82C2×C4×D293—21no—
83C2×C4×D293—21no—
84C2×C4×D293—21no—
85Dic1172—22no—
86Dic1172—22no—
87Dic1172—22no—
88Dic1172—41no—
89#17989791—22no—
90#17989791—22no—
91#17989791—41no—
92#17989791D414yescomplemented
93D2344—22no—
94C4⋊Dic293—21no—
95C4⋊Dic293—21no—
96C4⋊Dic293C2311yescharacteristic
97C4⋊Dic293C2311yescharacteristic
98#17989781—21no—
99#17989781—21no—
100#17989781—21no—
101#17989781—21no—
102C22⋊Dic293—21no—
103C22⋊Dic293—21no—
104C22⋊Dic293—21no—
105#17989779—21no—
106#17989779—21no—
107#17989779—21no—
108#17989779—21no—
109C4×Dic293—21no—
110C2×D4×C293D411yescharacteristic
111C22×C4×C293C2311yescharacteristic
112C22×C4×C293C2311yescharacteristic
113M16×C293—22no—
114C2×C8×C293—22no—
115C2×C8×C293C2311yescharacteristic
116C2×C8×C293C2311yescharacteristic
117C2×C8×C293C2311yescharacteristic
118C2×C8×C293C2311yescharacteristic
119C4⋊C4×C293D411yescharacteristic
120C22⋊C4×C293D411yescharacteristic
121C22⋊C4×C293D411yescharacteristic
122C42×C293C2311yescharacteristic
123C22×D293—21no—
124C22×D293—21no—
125Dic586—21no—
126Dic586—21no—
127Dic586—21no—
128Dic586—21no—
129Dic586—21no—
130Dic586—21no—
131Dic586—21no—
132Dic586—42no—
133Dic586C2×D412yes—
134D1172—21no—
135D1172—21no—
136D1172—21no—
137D1172C2×D412yes—
138C22⋊D293—42no—
139C22⋊D293—42no—
140C22⋊D293—42no—
141C22⋊D293—42no—
142C2×Dic293—21no—
143C2×Dic293—21no—
144C2×Dic293—21no—
145C2×Dic293—21no—
146C2×Dic293—21no—
147C2×Dic293—21no—
148C2×Dic293—42no—
149C4×D293—42no—
150C4×D293—42no—
151C4×D293—42no—
152C4×D293—42no—
153C23×C293C2×D411yescharacteristic
154C23×C293C2×D411yescharacteristic
155D4×C293—41no—
156C2×C4×C293—21no—
157C2×C4×C293—21no—
158C2×C4×C293—21no—
159C2×C4×C293—21no—
160C2×C4×C293C2×D411yescharacteristic
161C2×C4×C293C2×D411yescharacteristic
162C2×C4×C293C2×D411yescharacteristic
163C2×C4×C293C2×D411yescharacteristic
164C2×C4×C293C2411yescharacteristic
165C8×C293—21no—
166C8×C293—21no—
167C8×C293—21no—
168C8×C293C2×D412yes—
169C22×C293—21no—
170C22×C293—21no—
171C22×C293—21no—
172C22×C293—21no—
173C22×C293—21no—
174C22×C293—21no—
175C22×C293C22×D411yescharacteristic
176C2×D293—22no—
177C2×D293—41no—
178C2×D293—41no—
179C2×D293—41no—
180C2×D293—41no—
181C2×D293—41no—
182C4×C293—21no—
183C4×C293—21no—
184C4×C293—21no—
185C4×C293—21no—
186C4×C293C22×D411yescharacteristic
187C4×C293H(5,𝔽2)11yescharacteristic
188Dic293—22no—
189Dic293—41no—
190Dic293—41no—
191Dic293—41no—
192Dic293—41no—
193Dic293—41no—
194C2×C293—41no—
195C2×C293—41no—
196C2×C293D4211yescharacteristic
197C2×C293#57511yescharacteristic
198C2×C293#57811yescharacteristic
199D293—42no—
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#440—2931no—
217#435D29311yescharacteristic, complemented
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×SD16—2931no—
232C2×D8—2931no—
233C2×M16C2×D29311yescharacteristic
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—5861no—
250C4×D4C2×D29311yescharacteristic
251C2×C4⋊C4—5861no—
252#107—2931no—
253C4⋊C8C2×D29311yescharacteristic
254#103—2931no—
255#103—2931no—
256#103—2931no—
257#103—2931no—
258#102—2931no—
259#102—2931no—
260C22⋊C8C2×D29311yescharacteristic
261C22⋊C8C2×D29311yescharacteristic
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—2931no—
273C2×Q8—5862no—
274C2×Q8—5861no—
275C2×Q8—11721no—
276C2×D4—2931no—
277C2×D4—2931no—
278C2×D4—5861no—
279C2×D4—5861no—
280C2×D4—5861no—
281C2×D4—5861no—
282C2×D4D117211yescharacteristic
283C22×C4—5861no—
284C22×C4—5861no—
285C22×C4—5861no—
286C22×C4—5861no—
287C22×C4—5861no—
288C22×C4C22×D29311yescharacteristic
289C22×C4C22×D29311yescharacteristic
290Q16—5862no—
291Q16—5862no—
292Q16—5862no—
293Q16—11721no—
294SD16—2934no—
295SD16—5862no—
296SD16—5862no—
297SD16—11721no—
298D8—5862no—
299M16—22no—
300C2×C8—22no—
301C2×C8C22×D29311yescharacteristic
302C2×C8C22×D29311yescharacteristic
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⋊C4D117211yescharacteristic
314C22⋊C4—5861no—
315C22⋊C4—5861no—
316C22⋊C4—5861no—
317C22⋊C4—5861no—
318C22⋊C4—5861no—
319C22⋊C4—5861no—
320C22⋊C4—5861no—
321C22⋊C4D117211yescharacteristic
322C22⋊C4D117211yescharacteristic
323C42—5861no—
324C42C22×D29311yescharacteristic
325C23—5861no—
326C23—5861no—
327C23C2×D117211yescharacteristic
328C23C2×D117211yescharacteristic
329Q8—2932no—
330Q8—5861no—
331Q8—5861no—
332Q8—5861no—
333Q8—5861no—
334Q8—5861no—
335Q8—5861no—
336Q8—5861no—
337Q8—11722no—
338D4—41no—
339D4—2932no—
340D4—5861no—
341D4—5861no—
342D4—5861no—
343D4—11722no—
344D4—11722no—
345D4—11722no—
346D4—11722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—5861no—
352C2×C4—5861no—
353C2×C4—5861no—
354C2×C4—5861no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—11722no—
358C2×C4—11722no—
359C2×C4—11722no—
360C2×C4—11722no—
361C2×C4—11722no—
362C2×C4C2×D117211yescharacteristic
363C2×C4C2×D117211yescharacteristic
364C2×C4C2×D117211yescharacteristic
365C2×C4C2×D117211yescharacteristic
366C2×C4C23×D29311yescharacteristic
367C8—21no—
368C8—21no—
369C8—21no—
370C8D4×D29312yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—5862no—
378C22—11721no—
379C22—11721no—
380C22—11721no—
381C22—11721no—
382C22—11721no—
383C22C22×D117211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—5862no—
389C4—11721no—
390C4—11721no—
391C4—11721no—
392C4—11721no—
393C4—11721no—
394C4C2×D4×D29311yescharacteristic
395C4#2262767011yescharacteristic
396C2—41no—
397C2—41no—
398C2—23441no—
399C2—11722no—
400C2D4×D117211yescharacteristic
401C2#3403692911yescharacteristic
402C2#3403694611yescharacteristic
subgroupG/H
centerC22C22×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#435×C293C2
socleC22×C293C22×D4
hypercenter#435D293
hypocenterC293#3269
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#22627657C2semidirect
2. C2×#22627646C2semidirect
3. #34036788C2semidirect
4. #34036784C2semidirect
5. #34036523C2semidirect
6. #34036375C2semidirect
7. #34036370C2semidirect
8. #34036345C2semidirect
9. #34036340C2semidirect
10. #34036293C2semidirect
11. #34036293C2semidirect
12. #34036287C2semidirect
13. #34036276C2semidirect
14. #34036231C2semidirect
15. #435×C293C2semidirect
92. #17989791D4semidirect
201. C293#3269semidirect
217. #435D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276572
C2×#226276462
#340367882
#340367842
#340365232
#340363752
#340363702
#340363452
#340363402
#340362932
#340362872
#340362762
#340362312
#435×C2932
#3269293