Finite Group Databasebeta

← #49161466

Subgroups — #49161466

Order 37504.

556 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627602C211yesmaximal, characteristic
2C2×C4×Dic586C211yesmaximal, characteristic, complemented
3C2×#22627582C211yesmaximal, characteristic
4#34036033C211yesmaximal, characteristic, complemented
5#34036028C211yesmaximal, characteristic, complemented
6#34036026C211yesmaximal, characteristic, complemented
7#34036026C211yesmaximal, characteristic, complemented
8#34036021C211yesmaximal, characteristic
9#34036021C211yesmaximal, characteristic
10#34036020C211yesmaximal, characteristic
11#34036018C211yesmaximal, characteristic
12#34036010C211yesmaximal, characteristic, complemented
13#34035988C211yesmaximal, characteristic
14#34035980C211yesmaximal, characteristic, complemented
15#387×C293C211yesmaximal, characteristic, complemented
16C22×Dic586C2211yescharacteristic
17C22×C4×D293C2211yescharacteristic
18#22627602C418yescomplemented
19C4×Dic586—24no—
20#22627582—24no—
21C2×C4⋊Dic293C2211yescharacteristic
22C2×C4⋊Dic293C2211yescharacteristic
23C2×C4⋊Dic293C2211yescharacteristic
24C2×#17989781C2211yescharacteristic
25C2×#17989781C2211yescharacteristic
26C2×#17989781C2211yescharacteristic
27C2×#17989781C2211yescharacteristic
28C2×#17989781C2211yescharacteristic
29C2×#17989781C2211yescharacteristic
30C2×#17989779C2211yescharacteristic
31C2×#17989779C2211yescharacteristic
32C2×#17989779C2211yescharacteristic
33C2×#17989779C2211yescharacteristic
34C2×#17989779C2211yescharacteristic
35C2×#17989779C2211yescharacteristic
36C2×C4×Dic293C2211yescharacteristic
37C2×C4×Dic293C2211yescharacteristic
38C2×C4×Dic293C2211yescharacteristic
39C2×C4×Dic293C2211yescharacteristic
40C2×C4×Dic293C2211yescharacteristic
41#22627531C2211yescharacteristic
42#22627531C2211yescharacteristic
43#22627531C2211yescharacteristic
44#22627531C2211yescharacteristic
45#22627531C2211yescharacteristic
46#22627531C2211yescharacteristic
47C2×C4⋊C4×C293C2211yescharacteristic
48C2×C4⋊C4×C293C2211yescharacteristic
49C2×C42×C293C2211yescharacteristic
50#95×C293C2211yescharacteristic
51#95×C293C2211yescharacteristic
52#95×C293C2211yescharacteristic
53#95×C293C2211yescharacteristic
54C23×D293C2311yescharacteristic
55C2×Dic586—22no—
56C2×Dic586—22no—
57C2×Dic586C2×C414yes—
58C22×Dic293C2311yescharacteristic
59C22×Dic293C2311yescharacteristic
60C22×Dic293C2311yescharacteristic
61C22×Dic293C2311yescharacteristic
62C22×Dic293C2311yescharacteristic
63C22×Dic293C2311yescharacteristic
64C22×Dic293C2311yescharacteristic
65C2×C4×D293—22no—
66C2×C4×D293—22no—
67C2×C4×D293C2×C414yes—
68C4⋊Dic293—22no—
69C4⋊Dic293—22no—
70C4⋊Dic293—41no—
71#17989781—22no—
72#17989781—22no—
73#17989781—22no—
74#17989781—41no—
75#17989781C2×C414yes—
76#17989781C2×C414yes—
77#17989779—22no—
78#17989779—22no—
79#17989779—41no—
80#17989779—41no—
81#17989779C2×C414yes—
82#17989779C2×C414yes—
83C4×Dic293—22no—
84C4×Dic293—22no—
85C4×Dic293—41no—
86C4×Dic293—41no—
87C4×Dic293D414yes—
88C22×C4×C293C2311yescharacteristic
89C22×C4×C293C2311yescharacteristic
90C22×C4×C293C2311yescharacteristic
91C22×C4×C293C2311yescharacteristic
92C22×C4×C293C2311yescharacteristic
93C22×C4×C293C2311yescharacteristic
94C22×C4×C293C2311yescharacteristic
95C4⋊C4×C293—22no—
96C4⋊C4×C293C2×C414yes—
97C42×C293—22no—
98C22×D293—21no—
99C22×D293—21no—
100C22×D293—21no—
101C22×D293—21no—
102C22×D293—21no—
103C22×D293—21no—
104C22×D293C22×C412yes—
105Dic586—28no—
106C2×Dic293—21no—
107C2×Dic293—21no—
108C2×Dic293—21no—
109C2×Dic293—21no—
110C2×Dic293—21no—
111C2×Dic293—21no—
112C2×Dic293—21no—
113C2×Dic293—21no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—21no—
118C2×Dic293—21no—
119C2×Dic293—21no—
120C2×Dic293—21no—
121C2×Dic293C22×C412yes—
122C2×Dic293C22×C412yes—
123C2×Dic293C22×C412yes—
124C2×Dic293C2×D412yes—
125C2×Dic293C2×D412yes—
126C2×Dic293#4112yes—
127C4×D293—28no—
128C23×C293C2411yescharacteristic
129C2×C4×C293—21no—
130C2×C4×C293—21no—
131C2×C4×C293—21no—
132C2×C4×C293—21no—
133C2×C4×C293—21no—
134C2×C4×C293—21no—
135C2×C4×C293—21no—
136C2×C4×C293—21no—
137C2×C4×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293C22×C412yes—
147C2×C4×C293C22×C412yes—
148C2×C4×C293C22×C412yes—
149C2×C4×C293C2×D412yes—
150C22×C293C23×C411yescharacteristic
151C22×C293C22×D411yescharacteristic
152C22×C293C2×#4111yescharacteristic
153C22×C293H(5,𝔽2)11yescharacteristic
154C22×C2932−1+411yescharacteristic
155C22×C2932−1+411yescharacteristic
156C22×C2932−1+411yescharacteristic
157C2×D293—22no—
158C2×D293—22no—
159C2×D293—22no—
160C2×D293—41no—
161C2×D293—41no—
162C2×D293—41no—
163C2×D293—41no—
164C4×C293—22no—
165C4×C293—22no—
166C4×C293—22no—
167C4×C293—22no—
168C4×C293—41no—
169C4×C293—41no—
170C4×C293—41no—
171Dic293—22no—
172Dic293—22no—
173Dic293—22no—
174Dic293—41no—
175Dic293—41no—
176Dic293—41no—
177Dic293C4×D414yes—
178C2×C293C2×C4×D411yescharacteristic
179C2×C293#51911yescharacteristic
180C2×C293#52011yescharacteristic
181C2×C293#53611yescharacteristic
182C2×C293#53711yescharacteristic
183C2×C293#54111yescharacteristic
184C2×C293#54211yescharacteristic
185D293—42no—
186C293#232311yescharacteristic, complemented, Sylow
187#2323—2931nomaximal, Sylow
188C2×C22⋊Q8—2931no—
189C2×C4×Q8—2931no—
190C2×#117—2931no—
191#391—2931no—
192#389—2931no—
193#389—2931no—
194#389—2931no—
195#388—2931no—
196#388—2931no—
197#388—2931no—
198#388—2931no—
199#387—2931no—
200#387D29311yescharacteristic, complemented
201#380—2931no—
202C4×C4⋊C4—2931no—
203C22×Q8—2931no—
204C23×C4—2931no—
205C22⋊Q8—2938no—
206C4×Q8—5864no—
207#117—5864no—
208C2×C4⋊C4—2931no—
209C2×C4⋊C4—2931no—
210C2×C4⋊C4—2931no—
211C2×C4⋊C4—2931no—
212C2×C4⋊C4—2931no—
213C2×C4⋊C4—2931no—
214C2×C4⋊C4—2931no—
215C2×C4⋊C4—2931no—
216C2×C4⋊C4—2931no—
217C2×C4⋊C4C2×D29311yescharacteristic
218C2×C4⋊C4C2×D29311yescharacteristic
219C2×C22⋊C4—2931no—
220C2×C22⋊C4—2931no—
221C2×C22⋊C4—2931no—
222C2×C22⋊C4—2931no—
223C2×C22⋊C4—2931no—
224C2×C22⋊C4—2931no—
225C2×C42—2931no—
226C2×C42—2931no—
227C2×C42—2931no—
228C2×C42—2931no—
229C2×C42—2931no—
230C2×C42C2×D29311yescharacteristic
231#95—2931no—
232#95—2931no—
233#95—2931no—
234#95—2931no—
235#95—2931no—
236#95—2931no—
237#95C2×D29311yescharacteristic
238#95C2×D29311yescharacteristic
239#95C2×D29311yescharacteristic
240#95C2×D29311yescharacteristic
241C24—2931no—
242C2×Q8—2934no—
243C2×Q8—5862no—
244C2×Q8—5862no—
245C22×C4—2931no—
246C22×C4—2931no—
247C22×C4—2931no—
248C22×C4—2931no—
249C22×C4—2934no—
250C22×C4—2931no—
251C22×C4—2931no—
252C22×C4—2931no—
253C22×C4—5862no—
254C22×C4—5862no—
255C22×C4C22×D29311yescharacteristic
256C22×C4C22×D29311yescharacteristic
257C22×C4C22×D29311yescharacteristic
258C22×C4C22×D29311yescharacteristic
259C22×C4C22×D29311yescharacteristic
260C22×C4C22×D29311yescharacteristic
261C22×C4C22×D29311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—2934no—
264C4⋊C4—2934no—
265C4⋊C4—5862no—
266C4⋊C4—5862no—
267C4⋊C4—5862no—
268C4⋊C4—5862no—
269C4⋊C4—5862no—
270C4⋊C4—11721no—
271C4⋊C4—11721no—
272C4⋊C4C4×D29314yes—
273C22⋊C4—2934no—
274C22⋊C4—2934no—
275C22⋊C4—5862no—
276C22⋊C4—5862no—
277C22⋊C4—11721no—
278C22⋊C4—11721no—
279C42—22no—
280C42—2934no—
281C42—5862no—
282C42—5862no—
283C42—11721no—
284C42—11721no—
285C23—2932no—
286C23—5861no—
287C23—5861no—
288C23—5861no—
289C23—5861no—
290C23—5861no—
291C23—5861no—
292C23C23×D29311yescharacteristic
293Q8—5868no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—2932no—
312C2×C4—2932no—
313C2×C4—2932no—
314C2×C4—2932no—
315C2×C4—2932no—
316C2×C4—2932no—
317C2×C4—5868no—
318C2×C4—5861no—
319C2×C4—5861no—
320C2×C4—5861no—
321C2×C4—5861no—
322C2×C4—5861no—
323C2×C4—5861no—
324C2×C4—5861no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—5861no—
329C2×C4—5861no—
330C2×C4—5861no—
331C2×C4—5861no—
332C2×C4—5861no—
333C2×C4C2×C4×D29312yes—
334C2×C4C2×C4×D29312yes—
335C2×C4C2×C4×D29312yes—
336C2×C4D4×D29312yes—
337C22—5862no—
338C22—5862no—
339C22—5862no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22—11721no—
344C22C22×C4×D29311yescharacteristic
345C22C2×D4×D29311yescharacteristic
346C22#41×D29311yescharacteristic
347C22#2262767011yescharacteristic
348C22#2262767111yescharacteristic
349C22#2262767111yescharacteristic
350C22#2262767211yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—2934no—
359C4—5862no—
360C4—5862no—
361C4—5862no—
362C4—11721no—
363C4—11721no—
364C4—11721no—
365C2—11722no—
366C2C4×D4×D29311yescharacteristic
367C2#3403660511yescharacteristic
368C2#3403660911yescharacteristic
369C2#3403670111yescharacteristic
370C2#3403670911yescharacteristic
371C2#3403673811yescharacteristic
372C2#3403674511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D293
commutatorC22×C293C23×C4
Fitting#387×C293C2
socle, cosocleC23×C293C24
prime radicalC23×D293C23
hypercenter#387D293
hypocenterC293#2323
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic586C2semidirect
4. #34036033C2semidirect
5. #34036028C2semidirect
6. #34036026C2semidirect
7. #34036026C2semidirect
12. #34036010C2semidirect
14. #34035980C2semidirect
15. #387×C293C2semidirect
18. #22627602C4semidirect
186. C293#2323semidirect
200. #387D293semidirect

Maximal subgroups

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

subgroupindex
C2×#226276022
C2×C4×Dic5862
C2×#226275822
#340360332
#340360282
#340360262
#340360212
#340360202
#340360182
#340360102
#340359882
#340359802
#387×C2932
#2323293