Finite Group Databasebeta

← #34004817

Subgroups — #34004817

Order 18688.

588 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625864C211yesmaximal, characteristic
2C4×#14556658C211yesmaximal, characteristic
3C2×#17989437C212yesmaximal
4#22624767C212yesmaximal
5C4×#14556556C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×#14556658—21no—
8C2×#14556658—21no—
9C2×C4⋊#10596833C2212yes—
10C2×C4×#10596833C2212yes—
11#17989453—21no—
12#17989437—24no—
13C2×C4×Dic146C411yescharacteristic
14C2×#14556556C411yescharacteristic
15C2×#14556556C2211yescharacteristic
16C4⋊C4×Dic73C411yescharacteristic
17C4⋊C4×Dic73C2211yescharacteristic
18C4×#11924007—21no—
19#17988438—21no—
20#17988438—21no—
21C42×Dic73—21no—
22C42×Dic73C2211yescharacteristic
23C4×C4⋊C4×C73C411yescharacteristic
24C22×#10596833—22no—
25C22×#10596833—22no—
26#14556658—24no—
27#14556658—42no—
28#14556658—42no—
29C4⋊#10596833—22no—
30C4⋊#10596833—22no—
31C4×#10596833—22no—
32C4×#10596833—22no—
33C22×Dic146C2×C411yescharacteristic
34C4×Dic146—22no—
35C4×Dic146—22no—
36#14556556—22no—
37#14556556—21no—
38#14556556—21no—
39#14556556C814yescomplemented
40#14556556D412yes—
41#14556556Q812yes—
42C2×C4⋊Dic73C2×C411yescharacteristic
43C2×#11924007—21no—
44C2×#11924007—21no—
45C2×#11924007—21no—
46C2×C4×Dic73—21no—
47C2×C4×Dic73—21no—
48C2×C4×Dic73—21no—
49C2×C4×Dic73—21no—
50C2×C4×Dic73—21no—
51C2×C4×Dic73C2×C411yescharacteristic
52C2×C4×Dic73D411yescharacteristic
53C2×C4×Dic73D411yescharacteristic
54C2×C4×Dic73D411yescharacteristic
55C2×C4×Dic73D411yescharacteristic
56C2×C4×Dic73C2311yescharacteristic
57#14556498—21no—
58#14556498—21no—
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C4⋊C4×C73C2×C411yescharacteristic
61C2×C42×C73—21no—
62C2×C42×C73C2×C411yescharacteristic
63#95×C73—21no—
64C2×#10596833—24no—
65C2×#10596833—42no—
66C2×#10596833—42no—
67C2×#10596833—42no—
68C2×#10596833—42no—
69C2×#10596833—42no—
70C2×Dic146—21no—
71C2×Dic146—21no—
72C2×Dic146—21no—
73C2×Dic146C4⋊C412yes—
74C2×Dic146C2×C812yes—
75C2×Dic146M1612yes—
76C22×Dic73—21no—
77C22×Dic73—21no—
78C22×Dic73C22⋊C411yescharacteristic
79C22×Dic73C22⋊C411yescharacteristic
80C22×Dic73C2×D411yescharacteristic
81C22×Dic73C2×D411yescharacteristic
82C4⋊Dic73—21no—
83C4⋊Dic73M1612yes—
84#11924007—24no—
85#11924007—24no—
86#11924007—22no—
87#11924007—22no—
88C4×Dic73—24no—
89C4×Dic73—24no—
90C4×Dic73—22no—
91C4×Dic73—22no—
92C4×Dic73—22no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—41no—
96C4×Dic73—42no—
97C4×Dic73—41no—
98C4×Dic73—41no—
99C4×Dic73C2×C812yes—
100C4×Dic73M1612yes—
101C4×Dic73SD1612yes—
102C4×Dic73Q1612yes—
103C4×Dic73C2×D411yescharacteristic
104C4×Dic73C2×Q811yescharacteristic
105C4×Dic73#4111yescharacteristic
106C4×Dic73#4111yescharacteristic
107C22×C4×C73—21no—
108C22×C4×C73—21no—
109C22×C4×C73C22⋊C411yescharacteristic
110C22×C4×C73C22⋊C411yescharacteristic
111C22×C4×C73C22×C411yescharacteristic
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73C4⋊C412yes—
115C4⋊C4×C73C2×C812yes—
116C42×C73—21no—
117C42×C73—21no—
118C42×C73—42no—
119C23×C73C2×C22⋊C411yescharacteristic
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—22no—
123C2×C4×C73—22no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73#10312yes—
132C2×C4×C73C2×C4⋊C411yescharacteristic
133C2×C4×C73#11711yescharacteristic
134C2×C4×C73C22×C811yescharacteristic
135C2×C4×C73C2×M1611yescharacteristic
136C2×C4×C73C2×M1611yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×Dic73—22no—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—22no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73C22⋊C812yes—
149C2×Dic73C22⋊C812yes—
150C2×Dic73#10312yes—
151C2×Dic73#10412yes—
152C2×Dic73#12111yescharacteristic
153C2×Dic73#12111yescharacteristic
154C2×Dic73C22⋊Q811yescharacteristic
155C2×Dic73C22⋊Q811yescharacteristic
156C2×Dic73C2×SD1611yescharacteristic
157C2×Dic73C2×Q1611yescharacteristic
158C2×Dic73AGL(1,ℤ/8)11yescharacteristic
159C2×Dic73#13711yescharacteristic
160Dic146—22no—
161Dic146—22no—
162Dic146—22no—
163Dic146C4⋊C814yescomplemented
164#10596833—44no—
165#10596833—82no—
166C22×C73#38011yescharacteristic
167C22×C73C2×C22⋊C811yescharacteristic
168C22×C73#40711yescharacteristic
169C22×C73C2×#10311yescharacteristic
170C22×C73#41711yescharacteristic
171C22×C73C2×#10411yescharacteristic
172C22×C73#42111yescharacteristic
173C4×C73—22no—
174C4×C73—42no—
175C4×C73—42no—
176C4×C73—41no—
177C4×C73C2×C4⋊C811yescharacteristic
178C4×C73#42311yescharacteristic
179C4×C73#43111yescharacteristic
180C4×C73#43211yescharacteristic
181Dic73—24no—
182Dic73—21no—
183Dic73—21no—
184Dic73—22no—
185Dic73—42no—
186Dic73Q8⋊C814yescomplemented
187Dic73#46011yescharacteristic
188Dic73#46211yescharacteristic
189Dic73#47511yescharacteristic
190Dic73#47711yescharacteristic
191#8564—731nomaximal, Sylow
192C2×C73C2×Q8⋊C811yescharacteristic
193C2×C73#147711yescharacteristic
194C2×C73#148711yescharacteristic
195C2×C73#148911yescharacteristic
196C2×C73#179711yescharacteristic
197C2×C73#180311yescharacteristic
198C2×C73#180611yescharacteristic
199C42×Q8—731no—
200#1842—731no—
201C4×C4⋊C8—731no—
202C2×Q8⋊C8—732no—
203#1279—732no—
204C73#856411yescharacteristic, complemented, Sylow
205C2×C4×Q8—731no—
206C2×C4×Q8—731no—
207C2×C4×Q8—731no—
208C2×C4⋊C8—732no—
209C2×C4⋊C8—1461no—
210C2×C4⋊C8—1461no—
211C2×C4⋊C8—1461no—
212C2×C4×C8—732no—
213C4×C4⋊C4—731no—
214C4×C4⋊C4—731no—
215C4×C4⋊C4—1461no—
216C4×C4⋊C4—1461no—
217C4×C4⋊C4—1461no—
218C4×C4⋊C4#6440811yescharacteristic
219C43—731no—
220C43—1461no—
221#336—1461no—
222Q8⋊C8—1464no—
223C22×Q8—731no—
224C22×C8—1462no—
225C22×C8—1462no—
226C4×Q8—732no—
227C4×Q8—732no—
228C4×Q8—734no—
229C4×Q8—1462no—
230C4×Q8—1462no—
231C4×Q8—1462no—
232C4×Q8—1461no—
233C4×Q8—1461no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4—1461no—
237C2×C4⋊C4—1461no—
238C2×C4⋊C4C2×#6440811yescharacteristic
239C2×C4⋊C4C2×#6440811yescharacteristic
240C2×C42—21no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42—731no—
244C2×C42—731no—
245C2×C42—731no—
246C2×C42—731no—
247C2×C42—1461no—
248C2×C42—1461no—
249C2×C42—1461no—
250C2×C42—1461no—
251C2×C42—1461no—
252C2×C42C2×#6440811yescharacteristic
253C4⋊C8—2922no—
254C4⋊C8—2922no—
255C4⋊C8—1462no—
256C4⋊C8—1462no—
257C4⋊C8—1464no—
258C4×C8—1462no—
259C4×C8—1462no—
260#95—21no—
261#95—1461no—
262#95—1461no—
263C2×Q8—732no—
264C2×Q8—732no—
265C2×Q8—732no—
266C2×Q8—1461no—
267C2×Q8—1461no—
268C2×Q8—1461no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4C22⋊#6440811yescharacteristic
278C22×C4C22⋊#6440811yescharacteristic
279C22×C4C22×#6440811yescharacteristic
280C2×C8—2922no—
281C2×C8—2922no—
282C2×C8—2922no—
283C2×C8—2922no—
284C2×C8—2922no—
285C2×C8—1464no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—732no—
289C4⋊C4—1462no—
290C4⋊C4—1462no—
291C4⋊C4—1464no—
292C4⋊C4—1464no—
293C4⋊C4—1461no—
294C4⋊C4C4⋊#6440812yes—
295C4⋊C4#1192403612yes—
296C42—21no—
297C42—21no—
298C42—42no—
299C42—2921no—
300C42—2921no—
301C42—2921no—
302C42—2922no—
303C42—732no—
304C42—732no—
305C42—732no—
306C42—732no—
307C42—731no—
308C42—731no—
309C42—731no—
310C42—731no—
311C42—1461no—
312C42—1462no—
313C42—1461no—
314C42—1462no—
315C42—1462no—
316C42—1464no—
317C42—1464no—
318C23C2×C22⋊#6440811yescharacteristic
319Q8—734no—
320Q8—1462no—
321Q8—1462no—
322Q8—1462no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—731no—
337C2×C4—731no—
338C2×C4—732no—
339C2×C4—731no—
340C2×C4—732no—
341C2×C4—731no—
342C2×C4—731no—
343C2×C4—731no—
344C2×C4—732no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—732no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4—1462no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4#1455665412yes—
357C2×C4C2×C4⋊#6440811yescharacteristic
358C2×C4#1455667011yescharacteristic
359C2×C4C2×#1192403611yescharacteristic
360C2×C4D73⋊M1611yescharacteristic
361C2×C4D73⋊M1611yescharacteristic
362C2×C4D73⋊M1611yescharacteristic
363C8—2924no—
364C8—5842no—
365C22#1798952911yescharacteristic
366C22#1798955511yescharacteristic
367C22#1798955911yescharacteristic
368C22C2×#1455665411yescharacteristic
369C22#1798957811yescharacteristic
370C22D73⋊#10411yescharacteristic
371C22#1798958511yescharacteristic
372C4—22no—
373C4—42no—
374C4—42no—
375C4—41no—
376C4—2922no—
377C4—731no—
378C4—731no—
379C4—731no—
380C4—731no—
381C4—734no—
382C4—1461no—
383C4—1461no—
384C4—1462no—
385C4—1464no—
386C4#1798958811yescharacteristic
387C4#1798959211yescharacteristic
388C4#1798960511yescharacteristic
389C4#1798961011yescharacteristic
390C2#2262522011yescharacteristic
391C2#2262522711yescharacteristic
392C2#2262526111yescharacteristic
393C2#2262526811yescharacteristic
394C2#2262578811yescharacteristic
395C2#2262580011yescharacteristic
396C2#2262580511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC4×C4⋊C4×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C4⋊C4#64408
hypocenterC73#8564
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
39. #14556556C8semidirect
163. Dic146C4⋊C8semidirect
186. Dic73Q8⋊C8semidirect
204. C73#8564semidirect

Maximal subgroups

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

subgroupindex
#226258642
C4×#145566582
C2×#179894372
#226247672
C4×#145565562
#856473