Finite Group Databasebeta

← #49170341

Subgroups — #49170341

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×#22627655C211yesmaximal, characteristic, complemented
2C2×#22627644C211yesmaximal, characteristic, complemented
3#34036784C211yesmaximal, characteristic, complemented
4#34036524C211yesmaximal, characteristic, complemented
5#34036373C211yesmaximal, characteristic, complemented
6#34036368C211yesmaximal, characteristic, complemented
7#34036341C211yesmaximal, characteristic, complemented
8#34036339C211yesmaximal, characteristic, complemented
9#34036291C211yesmaximal, characteristic, complemented
10#34036289C211yesmaximal, characteristic, complemented
11#34036285C211yesmaximal, characteristic, complemented
12#34036272C211yesmaximal, characteristic, complemented
13#34036227C211yesmaximal, characteristic, complemented
14#34036201C211yesmaximal, characteristic, complemented
15#548×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic
17C2×#17989802C2211yescharacteristic
18#22627655—24no—
19#22627644—24no—
20C2×#17989792C2211yescharacteristic
21C2×#17989792C2211yescharacteristic
22C2×#17989792C2211yescharacteristic
23C2×#17989792C2211yescharacteristic
24C2×#17989790C2211yescharacteristic
25C2×#17989790C2211yescharacteristic
26C2×#17989789C2211yescharacteristic
27C2×#17989789C2211yescharacteristic
28C2×#17989787C2211yescharacteristic
29C2×#17989786C2211yescharacteristic
30C22×#14556873C2211yescharacteristic
31#22627624C2211yescharacteristic
32#22627606—21no—
33#22627606—21no—
34#22627603C2211yescharacteristic
35#22627603C2211yescharacteristic
36#22627595—21no—
37C4×D1172C2211yescharacteristic
38C4⋊C4×D293—21no—
39#22627557C2211yescharacteristic
40C4⋊#14556873C2211yescharacteristic
41#22627548C2211yescharacteristic
42#22627548C2211yescharacteristic
43#22627547C2211yescharacteristic
44#22627547C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627544C2211yescharacteristic
47C22⋊#14556873C2211yescharacteristic
48C22⋊#14556873C2211yescharacteristic
49#22627535C2211yescharacteristic
50C2×#41×C293C2211yescharacteristic
51C22×Q8×C293C2211yescharacteristic
52#124×C293—21no—
53#124×C293C2211yescharacteristic
54C22⋊Q8×C293—21no—
55C22⋊Q8×C293C2211yescharacteristic
56#121×C293—21no—
57#121×C293C2211yescharacteristic
58C4×Q8×C293C2211yescharacteristic
59C4×D4×C293—21no—
60C4×D4×C293C2211yescharacteristic
61#17989802—22no—
62#17989802—22no—
63#17989802—41no—
64#17989802—41no—
65C2×Dic586C2311yescharacteristic
66C2×Dic586C2311yescharacteristic
67C2×D1172C2311yescharacteristic
68C2×C22⋊D293—21no—
69C2×C22⋊D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73#17989792—22no—
74#17989792—22no—
75#17989792—22no—
76#17989792—41no—
77#17989790—22no—
78#17989790—41no—
79#17989789—22no—
80#17989789D414yescomplemented
81#17989787—22no—
82#17989786—22no—
83C2×#14556873—22no—
84C2×#14556873C2311yescharacteristic
85C2×#14556873C2311yescharacteristic
86C2×#14556873C2311yescharacteristic
87C2×#14556873C2311yescharacteristic
88C4⋊Dic293—21no—
89C4⋊Dic293—21no—
90C4⋊Dic293C2311yescharacteristic
91#17989781—21no—
92#17989781—21no—
93C22⋊Dic293—21no—
94C22⋊Dic293—21no—
95#17989779—21no—
96#41×C293—22no—
97#41×C293—41no—
98C2×Q8×C293—21no—
99C2×Q8×C293—22no—
100C2×Q8×C293—41no—
101C2×Q8×C293C2311yescharacteristic
102C2×Q8×C293C2311yescharacteristic
103C2×D4×C293—21no—
104C2×D4×C293—21no—
105C2×D4×C293D411yescharacteristic
106C2×D4×C293C2311yescharacteristic
107C22×C4×C293—21no—
108C22×C4×C293—21no—
109C22×C4×C293C2311yescharacteristic
110C22×C4×C293C2311yescharacteristic
111C4⋊C4×C293—21no—
112C4⋊C4×C293—21no—
113C4⋊C4×C293D411yescharacteristic
114C4⋊C4×C293C2311yescharacteristic
115C22⋊C4×C293—21no—
116C22⋊C4×C293—21no—
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—21no—
128D1172—21no—
129D1172C2×D412yes—
130C22⋊D293—42no—
131C22⋊D293—42no—
132C2×Dic293—21no—
133C2×Dic293—21no—
134C2×Dic293—21no—
135C4×D293—42no—
136C4×D293—42no—
137C4×D293—42no—
138#14556873—21no—
139#14556873—21no—
140#14556873—21no—
141#14556873C2×D412yes—
142C23×C293—21no—
143C23×C293C2×D411yescharacteristic
144C23×C293C2×D411yescharacteristic
145Q8×C293—21no—
146Q8×C293—21no—
147Q8×C293—21no—
148Q8×C293—42no—
149Q8×C293C2×D412yes—
150D4×C293—21no—
151D4×C293—21no—
152D4×C293—41no—
153D4×C293—42no—
154D4×C293—42no—
155C2×C4×C293—21no—
156C2×C4×C293—21no—
157C2×C4×C293—21no—
158C2×C4×C293—21no—
159C2×C4×C293—21no—
160C2×C4×C293—21no—
161C2×C4×C293—21no—
162C2×C4×C293—42no—
163C2×C4×C293—42no—
164C2×C4×C293C2×D411yescharacteristic
165C2×C4×C293C2×D411yescharacteristic
166C2×C4×C293C2×D411yescharacteristic
167C2×C4×C293C2×D411yescharacteristic
168C2×C4×C293C2411yescharacteristic
169C22×C293—21no—
170C22×C293—21no—
171C22×C293—21no—
172C22×C293—21no—
173C22×C293—21no—
174C22×C293—21no—
175C22×C293—41no—
176C22×C293—41no—
177C22×C293—41no—
178C22×C293C22×D411yescharacteristic
179C2×D293—22no—
180C2×D293—41no—
181C2×D293—41no—
182C4×C293—21no—
183C4×C293—21no—
184C4×C293—22no—
185C4×C293—21no—
186C4×C293—21no—
187C4×C293—41no—
188C4×C293—41no—
189C4×C293C22×D411yescharacteristic
190C4×C293H(5,𝔽2)11yescharacteristic
191Dic293—41no—
192Dic293—41no—
193Dic293—41no—
194C2×C293—41no—
195C2×C293—41no—
196C2×C293—81no—
197C2×C293D4211yescharacteristic
198C2×C293#57511yescharacteristic
199C2×C293#57811yescharacteristic
200D293—42no—
201C293#326911yescharacteristic, complemented, Sylow
202#3269—2931nomaximal, Sylow
203C2×#137—2931no—
204C2×#135—2931no—
205#548D29311yescharacteristic, complemented
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×#41—2931no—
220C2×#41C2×D29311yescharacteristic
221C22×Q8C2×D29311yescharacteristic
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×M16—2931no—
234C22×C8—2931no—
235C4⋊Q8—2931no—
236#124—21no—
237#124C2×D29311yescharacteristic
238#123—5861no—
239#123—5861no—
240C22⋊Q8—21no—
241C22⋊Q8—2931no—
242C22⋊Q8—2931no—
243C22⋊Q8C2×D29311yescharacteristic
244#121—21no—
245#121—5861no—
246#121C2×D29311yescharacteristic
247C4×Q8C2×D29311yescharacteristic
248C4×D4—21no—
249C4×D4—2931no—
250C4×D4C2×D29311yescharacteristic
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—41no—
265#41—5862no—
266#41—5862no—
267#41—11721no—
268#41—11721no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2931no—
273C2×Q8—2931no—
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—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—5862no—
300C2×C8—2931no—
301C2×C8—2931no—
302C2×C8—2931no—
303C2×C8—2931no—
304C2×C8—5862no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—2931no—
308C4⋊C4—5861no—
309C4⋊C4—5861no—
310C4⋊C4—5861no—
311C4⋊C4—5861no—
312C4⋊C4C22⋊D29311yescharacteristic
313C4⋊C4C22×D29311yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—21no—
318C22⋊C4—5861no—
319C22⋊C4—5861no—
320C22⋊C4—5861no—
321C22⋊C4C22⋊D29311yescharacteristic
322C22⋊C4C22⋊D29311yescharacteristic
323C42—21no—
324C42C22×D29311yescharacteristic
325C23—21no—
326C23—5861no—
327C23C2×C22⋊D29311yescharacteristic
328C23C2×C22⋊D29311yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—42no—
333Q8—5861no—
334Q8—5861no—
335Q8—5861no—
336Q8—5861no—
337Q8D4×D29312yes—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—2932no—
344D4—5861no—
345D4—11722no—
346D4—11722no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—11722no—
360C2×C4—11722no—
361C2×C4—11722no—
362C2×C4C2×C22⋊D29311yescharacteristic
363C2×C4C2×C22⋊D29311yescharacteristic
364C2×C4C2×C22⋊D29311yescharacteristic
365C2×C4C2×C22⋊D29311yescharacteristic
366C2×C4C23×D29311yescharacteristic
367C8—2932no—
368C8—5861no—
369C8—5861no—
370C8—5861no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5862no—
381C22—11721no—
382C22—11721no—
383C22C22×C22⋊D29311yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—41no—
390C4—41no—
391C4—11721no—
392C4—11721no—
393C4—11721no—
394C4C2×D4×D29311yescharacteristic
395C4#2262766911yescharacteristic
396C2—41no—
397C2—41no—
398C2—81no—
399C2—11722no—
400C2D4×C22⋊D29311yescharacteristic
401C2#3403692711yescharacteristic
402C2#3403694411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#548×C293C2
socleC22×C293C22×D4
hypercenter#548D293
hypocenterC293#3269
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#22627655C2semidirect
2. C2×#22627644C2semidirect
3. #34036784C2semidirect
4. #34036524C2semidirect
5. #34036373C2semidirect
6. #34036368C2semidirect
7. #34036341C2semidirect
8. #34036339C2semidirect
9. #34036291C2semidirect
10. #34036289C2semidirect
11. #34036285C2semidirect
12. #34036272C2semidirect
13. #34036227C2semidirect
14. #34036201C2semidirect
15. #548×C293C2semidirect
80. #17989789D4semidirect
201. C293#3269semidirect
205. #548D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276552
C2×#226276442
#340367842
#340365242
#340363732
#340363682
#340363412
#340363392
#340362912
#340362892
#340362852
#340362722
#340362272
#340362012
#548×C2932
#3269293