Finite Group Databasebeta

← #49170276

Subgroups — #49170276

Order 37504.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627650C211yesmaximal, characteristic, complemented
2C22×#17989790C211yesmaximal, characteristic, complemented
3#34036788C211yesmaximal, characteristic, complemented
4#34036516C211yesmaximal, characteristic, complemented
5#34036373C211yesmaximal, characteristic, complemented
6#34036363C211yesmaximal, characteristic, complemented
7#34036344C211yesmaximal, characteristic, complemented
8#34036326C211yesmaximal, characteristic, complemented
9#34036280C211yesmaximal, characteristic, complemented
10#34036272C211yesmaximal, characteristic, complemented
11#34036267C211yesmaximal, characteristic, complemented
12#34036263C211yesmaximal, characteristic, complemented
13#34036229C211yesmaximal, characteristic, complemented
14#34036201C211yesmaximal, characteristic, complemented
15D42×C293C211yesmaximal, characteristic, complemented
16C2×#17989802C2211yescharacteristic, complemented
17C22×Dic586C2211yescharacteristic, complemented
18#22627650—24no—
19C2×#17989790—24no—
20C2×#17989790C2211yescharacteristic
21C2×#17989790C2211yescharacteristic
22C2×#17989790C2211yescharacteristic, complemented
23C2×#17989790C2211yescharacteristic, complemented
24C2×#17989790C2211yescharacteristic, complemented
25C2×#17989790C2211yescharacteristic, complemented
26C2×#17989787C2211yescharacteristic
27C2×#17989787C2211yescharacteristic, complemented
28C2×#17989787C2211yescharacteristic, complemented
29C2×#17989786C2211yescharacteristic, complemented
30C22×#14556873C2211yescharacteristic, complemented
31#22627612C2211yescharacteristic, complemented
32#22627610—21no—
33#22627603C2211yescharacteristic, complemented
34#22627602—21no—
35#22627598C2211yescharacteristic, complemented
36#22627596—21no—
37C4×Dic586C2211yescharacteristic, complemented
38#22627584—21no—
39#22627557C2211yescharacteristic, complemented
40C4⋊#14556873C2211yescharacteristic, complemented
41#22627547C2211yescharacteristic, complemented
42#22627547C2211yescharacteristic, complemented
43#22627545C2211yescharacteristic
44#22627545C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic, complemented
46#22627544C2211yescharacteristic, complemented
47C22⋊#14556873C2211yescharacteristic, complemented
48C22⋊#14556873C2211yescharacteristic, complemented
49#22627535C2211yescharacteristic, complemented
50C22×D4×C293—21no—
51C22×D4×C293C2211yescharacteristic
52C22×D4×C293C2211yescharacteristic
53#127×C293C2211yescharacteristic
54#121×C293—21no—
55#121×C293C2211yescharacteristic
56#121×C293C2211yescharacteristic
57#120×C293—21no—
58#120×C293—21no—
59C4×D4×C293C2211yescharacteristic
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#17989790—22no—
74#17989790—22no—
75#17989790—22no—
76#17989790—22no—
77#17989790—41no—
78#17989790D414yescomplemented
79#17989787—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—
96C24×C293—21no—
97C24×C293—21no—
98C2×D4×C293—22no—
99C2×D4×C293—22no—
100C2×D4×C293—21no—
101C2×D4×C293—21no—
102C2×D4×C293—21no—
103C2×D4×C293—21no—
104C2×D4×C293—21no—
105C2×D4×C293—21no—
106C2×D4×C293—41no—
107C2×D4×C293—41no—
108C2×D4×C293—44no—
109C2×D4×C293D411yescharacteristic
110C2×D4×C293C2311yescharacteristic
111C2×D4×C293C2311yescharacteristic
112C2×D4×C293C2311yescharacteristic
113C22×C4×C293—21no—
114C22×C4×C293C2311yescharacteristic
115C22×C4×C293C2311yescharacteristic
116C4⋊C4×C293D411yescharacteristic
117C4⋊C4×C293C2311yescharacteristic
118C22⋊C4×C293—21no—
119C22⋊C4×C293—21no—
120C22⋊C4×C293—21no—
121C22⋊C4×C293D411yescharacteristic
122C22⋊C4×C293D411yescharacteristic
123C42×C293C2311yescharacteristic
124C22×D293—21no—
125Dic586—21no—
126Dic586—21no—
127Dic586—21no—
128Dic586—42no—
129Dic586C2×D412yescomplemented
130D1172—21no—
131D1172—21no—
132C22⋊D293—42no—
133C22⋊D293—42no—
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—21no—
137C2×Dic293—42no—
138C4×D293—42no—
139#14556873—21no—
140#14556873—21no—
141#14556873—21no—
142#14556873C2×D412yescomplemented
143C23×C293—21no—
144C23×C293—21no—
145C23×C293—21no—
146C23×C293—42no—
147C23×C293—42no—
148C23×C293—42no—
149C23×C293—42no—
150C23×C293—81no—
151C23×C293—81no—
152C23×C293C2×D411yescharacteristic
153C23×C293C2×D411yescharacteristic
154D4×C293—22no—
155D4×C293—21no—
156D4×C293—21no—
157D4×C293—21no—
158D4×C293—21no—
159D4×C293—21no—
160D4×C293—42no—
161D4×C293—42no—
162D4×C293—42no—
163D4×C293—42no—
164D4×C293—42no—
165D4×C293—81no—
166D4×C293C2×D412yes—
167C2×C4×C293—21no—
168C2×C4×C293—21no—
169C2×C4×C293—21no—
170C2×C4×C293—21no—
171C2×C4×C293—21no—
172C2×C4×C293—42no—
173C2×C4×C293C2×D411yescharacteristic
174C2×C4×C293C2×D411yescharacteristic
175C2×C4×C293C2×D411yescharacteristic
176C2×C4×C293C2×D411yescharacteristic
177C2×C4×C293C2411yescharacteristic
178C22×C293—21no—
179C22×C293—21no—
180C22×C293—21no—
181C22×C293—22no—
182C22×C293—21no—
183C22×C293—21no—
184C22×C293—41no—
185C22×C293—41no—
186C22×C293—41no—
187C22×C293—41no—
188C22×C293—41no—
189C22×C293—41no—
190C22×C293—41no—
191C22×C293—41no—
192C22×C293—84no—
193C22×C293—84no—
194C22×C293AGL(1,ℤ/8)12yescomplemented
195C22×C293C22×D411yescharacteristic
196C2×D293—41no—
197C2×D293—41no—
198C2×D293—41no—
199C4×C293—21no—
200C4×C293—21no—
201C4×C293—21no—
202C4×C293—21no—
203C4×C293—41no—
204C4×C293C22×D411yescharacteristic
205C4×C293H(5,𝔽2)11yescharacteristic
206Dic293—22no—
207Dic293—41no—
208Dic293—41no—
209C2×C293—22no—
210C2×C293—41no—
211C2×C293—42no—
212C2×C293—81no—
213C2×C293—81no—
214C2×C293D4211yescharacteristic
215C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C293#57711yescharacteristic
217D293—81no—
218C293#326511yescharacteristic, complemented, Sylow
219#3265—2931nomaximal, Sylow
220C2×AGL(1,ℤ/8)—2931no—
221C22×SD16—2931no—
222#548—2931no—
223D42D29311yescharacteristic, complemented
224#496—2931no—
225#468—2931no—
226#466—2931no—
227#463—2931no—
228#460—2931no—
229#450—2931no—
230#449—2931no—
231#448—2931no—
232#447—2931no—
233#440—2931no—
234#435—2931no—
235C2×#41—2931no—
236C22×Q8—2931no—
237C22×D4—21no—
238C22×D4C2×D29311yescharacteristic
239C22×D4C2×D29311yescharacteristic
240AGL(1,ℤ/8)—5864no—
241C2×SD16—2931no—
242C2×SD16—2931no—
243C2×SD16—2931no—
244C2×SD16—2931no—
245C2×SD16—2931no—
246C2×SD16—2931no—
247C2×SD16—5864no—
248C2×D8—2931no—
249C2×D8—2931no—
250C2×D8—2931no—
251C2×M16—2931no—
252C22×C8—2931no—
253#127C2×D29311yescharacteristic
254#124—2931no—
255#124—5861no—
256C22⋊Q8—2931no—
257C22⋊Q8—5861no—
258#121—21no—
259#121—2931no—
260#121—5861no—
261#121C2×D29311yescharacteristic
262#121C2×D29311yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—2931no—
266C4×D4—5861no—
267C4×D4C2×D29311yescharacteristic
268C4×D4C2×D29311yescharacteristic
269#107—2931no—
270C4⋊C8—2931no—
271#103—2931no—
272#103—2931no—
273#102—2931no—
274#102—2931no—
275#102—2931no—
276#102—2931no—
277C22⋊C8—2931no—
278C22⋊C8—2931no—
279#97—2931no—
280C24—21no—
281C24—21no—
282#41—5862no—
283#41—11721no—
284C2×Q8—2931no—
285C2×Q8—2931no—
286C2×Q8—5862no—
287C2×Q8—5861no—
288C2×Q8—11721no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—2931no—
301C2×D4—5861no—
302C2×D4—5861no—
303C2×D4C22⋊D29311yescharacteristic
304C2×D4C22×D29311yescharacteristic
305C2×D4C22×D29311yescharacteristic
306C2×D4C22×D29311yescharacteristic
307C22×C4—21no—
308C22×C4—5861no—
309C22×C4—5861no—
310C22×C4C22×D29311yescharacteristic
311C22×C4C22×D29311yescharacteristic
312SD16—2934no—
313SD16—5862no—
314SD16—5862no—
315SD16—5862no—
316SD16—5862no—
317SD16—11721no—
318D8—5862no—
319D8—5862no—
320D8—11721no—
321M16—5862no—
322C2×C8—2931no—
323C2×C8—2931no—
324C2×C8—2931no—
325C2×C8—2931no—
326C2×C8—5862no—
327C4⋊C4—2931no—
328C4⋊C4—5861no—
329C4⋊C4—5861no—
330C4⋊C4C22⋊D29311yescharacteristic
331C4⋊C4C22×D29311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—5861no—
336C22⋊C4—5861no—
337C22⋊C4—5861no—
338C22⋊C4—5861no—
339C22⋊C4C22⋊D29311yescharacteristic
340C22⋊C4C22⋊D29311yescharacteristic
341C42—5861no—
342C42C22×D29311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—5861no—
353C23C2×C22⋊D29311yescharacteristic
354C23C2×C22⋊D29311yescharacteristic
355Q8—2932no—
356Q8—5861no—
357Q8—5861no—
358Q8—5861no—
359Q8—11722no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—5861no—
373D4—5861no—
374D4—11722no—
375D4—11722no—
376D4D4×D29312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—5861no—
384C2×C4—5861no—
385C2×C4—5861no—
386C2×C4—11722no—
387C2×C4—11722no—
388C2×C4C2×C22⋊D29311yescharacteristic
389C2×C4C2×C22⋊D29311yescharacteristic
390C2×C4C2×C22⋊D29311yescharacteristic
391C2×C4C2×C22⋊D29311yescharacteristic
392C2×C4C23×D29311yescharacteristic
393C8—2932no—
394C8—5861no—
395C8—5861no—
396C8—5861no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—21no—
402C22—21no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—11721no—
414C22—11721no—
415C22—11721no—
416C22#2262765012yescomplemented
417C22C22×C22⋊D29311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—5862no—
424C4—11721no—
425C4—11721no—
426C4C2×D4×D29311yescharacteristic
427C4#2262766911yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—23441no—
434C2D4×C22⋊D29311yescharacteristic
435C2C2×#2262765011yescharacteristic
436C2#3403694011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
FittingD42×C293C2
socleC22×C293C22×D4
hypercenterD42D293
hypocenterC293#3265
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#22627650C2semidirect
2. C22×#17989790C2semidirect
3. #34036788C2semidirect
4. #34036516C2semidirect
5. #34036373C2semidirect
6. #34036363C2semidirect
7. #34036344C2semidirect
8. #34036326C2semidirect
9. #34036280C2semidirect
10. #34036272C2semidirect
11. #34036267C2semidirect
12. #34036263C2semidirect
13. #34036229C2semidirect
14. #34036201C2semidirect
15. D42×C293C2semidirect
16. C2×#17989802C22semidirect
17. C22×Dic586C22semidirect
22. C2×#17989790C22semidirect
23. C2×#17989790C22semidirect
24. C2×#17989790C22semidirect
25. C2×#17989790C22semidirect
27. C2×#17989787C22semidirect
28. C2×#17989787C22semidirect
29. C2×#17989786C22semidirect
30. C22×#14556873C22semidirect
31. #22627612C22semidirect
33. #22627603C22semidirect
35. #22627598C22semidirect
37. C4×Dic586C22semidirect
39. #22627557C22semidirect
40. C4⋊#14556873C22semidirect
41. #22627547C22semidirect
42. #22627547C22semidirect
44. #22627545C22semidirect
45. #22627545C22semidirect
46. #22627544C22semidirect
47. C22⋊#14556873C22semidirect
48. C22⋊#14556873C22semidirect
49. #22627535C22semidirect
78. #17989790D4semidirect
129. Dic586C2×D4semidirect
142. #14556873C2×D4semidirect
194. C22×C293AGL(1,ℤ/8)semidirect
218. C293#3265semidirect
223. D42D293semidirect
416. C22#22627650semidirect

Maximal subgroups

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

subgroupindex
C2×#226276502
C22×#179897902
#340367882
#340365162
#340363732
#340363632
#340363442
#340363262
#340362802
#340362722
#340362672
#340362632
#340362292
#340362012
D42×C2932
#3265293