Finite Group Databasebeta

← #32985335

Subgroups — #32985335

Order 18688.

428 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620254C211yesmaximal, characteristic
2#22608679C211yesmaximal, characteristic, complemented
3#22608429C211yesmaximal, characteristic, complemented
4#22608425C211yesmaximal, characteristic
5#22608333C211yesmaximal, characteristic, complemented
6#22608329C211yesmaximal, characteristic
7C8×C4⋊C4×C73C211yesmaximal, characteristic, complemented
8#17989144C2211yescharacteristic
9#17989137C2211yescharacteristic
10#17988942—21no—
11#17988942—21no—
12#17988938C411yescharacteristic, complemented
13#17988938C411yescharacteristic, complemented
14#17988934C411yescharacteristic, complemented
15#17988934C411yescharacteristic, complemented
16#17988640C2211yescharacteristic
17#17988640C2211yescharacteristic
18#17988584—21no—
19#17988584—21no—
20#17988340—21no—
21#17988338—21no—
22#17988323—22no—
23#17988320—22no—
24#17988317—22no—
25#17988314—22no—
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×C4×C8×C73—21no—
28C2×C4×C8×C73C2211yescharacteristic
29C4×C4⋊C4×C73C2211yescharacteristic
30#336×C73—21no—
31C2×#11924028—21no—
32#14556591C2×C411yescharacteristic
33#14556591C2×C411yescharacteristic
34#14556591C2×C411yescharacteristic
35#14556588C2×C411yescharacteristic
36#14556583—21no—
37#14556579—21no—
38#14556570—21no—
39#14556570—21no—
40#14556565—21no—
41#14556565—21no—
42C4×Dic146—21no—
43C4×Dic146—21no—
44C4×D292—21no—
45C4×D292—21no—
46#14556550—21no—
47C4⋊#10596831—21no—
48C4⋊#10596831—21no—
49#14556516—21no—
50#14556516—21no—
51#14556516—21no—
52#14556516—21no—
53#14556513—21no—
54#14556513—21no—
55#14556513—21no—
56#14556513—21no—
57C22⋊#10596831—21no—
58C22⋊#10596831—21no—
59C4×#10596831—21no—
60C4×#10596831—21no—
61C22×C8×C73—21no—
62C22×C8×C73D411yescharacteristic
63C22×C8×C73D411yescharacteristic
64C2×C4⋊C4×C73—21no—
65C2×C42×C73—21no—
66C2×C42×C73C2311yescharacteristic
67C4⋊C8×C73—21no—
68C4⋊C8×C73D412yes—
69C4×C8×C73—42no—
70C4×C8×C73C2×C411yescharacteristic
71C4×C8×C73C2×C411yescharacteristic
72C4×C8×C73D411yescharacteristic
73C4×C8×C73D411yescharacteristic
74#95×C73D412yes—
75#11924028—41no—
76#11924028—41no—
77#11924028—41no—
78#11924028—41no—
79C2×Dic146—21no—
80C2×Dic146—21no—
81C2×Dic146—21no—
82C2×D292—21no—
83C2×D292—21no—
84C2×D292—21no—
85C2×C22⋊D73—41no—
86C2×C4×D73—41no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C4⋊Dic73—21no—
90C4⋊Dic73—21no—
91C4⋊Dic73—21no—
92C4⋊Dic73—21no—
93C4⋊Dic73—21no—
94C4⋊Dic73—21no—
95#11924007—41no—
96#11924007—41no—
97C22⋊Dic73—41no—
98#11924005—41no—
99#11924005—41no—
100C4×Dic73—41no—
101C22×C4×C73—22no—
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73#4111yescharacteristic
105C2×C8×C73—21no—
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—22no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73C22⋊C411yescharacteristic
113C2×C8×C73C22⋊C411yescharacteristic
114C2×C8×C73C22⋊C411yescharacteristic
115C2×C8×C73C22⋊C411yescharacteristic
116C4⋊C4×C73—24no—
117C42×C73—41no—
118C42×C73—41no—
119C42×C73C22×C411yescharacteristic
120C42×C73C2×D411yescharacteristic
121C42×C73C2×D411yescharacteristic
122C42×C73#4111yescharacteristic
123C23×C73#12111yescharacteristic
124C22×D73—41no—
125C2×C4×C73—22no—
126C2×C4×C73—24no—
127C2×C4×C73—41no—
128C2×C4×C73—42no—
129C2×C4×C73—42no—
130C2×C4×C73C2×C22⋊C411yescharacteristic
131C2×C4×C73C4×D411yescharacteristic
132C2×C4×C73C4×D411yescharacteristic
133C2×C4×C73#12111yescharacteristic
134C2×C4×C73#12411yescharacteristic
135C2×C4×C73#12711yescharacteristic
136C2×C4×C73#13511yescharacteristic
137C2×C4×C73#13511yescharacteristic
138C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C73#13711yescharacteristic
140C22⋊D73—81no—
141C22⋊D73—81no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145D292—41no—
146D292—41no—
147D292—42no—
148D292—81no—
149C4×D73—81no—
150C4×D73—81no—
151Dic146—41no—
152Dic146—41no—
153Dic146—42no—
154Dic146—81no—
155C8×C73—21no—
156C8×C73—21no—
157C8×C73—21no—
158C8×C73—21no—
159C8×C73—42no—
160#10596831—81no—
161#10596831—81no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73#39011yescharacteristic
165C22×C73#46311yescharacteristic
166C22×C73#46411yescharacteristic
167C2×D73—81no—
168C2×D73—81no—
169C2×D73—81no—
170C4×C73—21no—
171C4×C73—21no—
172C4×C73—21no—
173C4×C73—44no—
174C4×C73#41611yescharacteristic
175C4×C73#41711yescharacteristic
176C4×C73#44312yes—
177C4×C73#46311yescharacteristic
178C4×C73#46411yescharacteristic
179Dic73—81no—
180Dic73—81no—
181Dic73—81no—
182#9751—731nomaximal, Sylow
183C2×C73—21no—
184C2×C73—21no—
185C2×C73#197411yescharacteristic
186C2×C73#197611yescharacteristic
187C2×C73#198311yescharacteristic
188D73—161no—
189#3131—731no—
190C8×C4⋊C4D7311yescharacteristic, complemented
191#1564—731no—
192#1503—731no—
193#1502—731no—
194#1481—731no—
195#1480—731no—
196C73#975111yescharacteristic, complemented, Sylow
197#533—731no—
198#532—731no—
199#488—1461no—
200#488—1461no—
201#487—731no—
202#487—731no—
203#486—731no—
204#486—731no—
205#431—731no—
206#431—731no—
207C2×C4⋊C8C2×D7311yescharacteristic
208#416—1461no—
209#416—1461no—
210C2×C4×C8—21no—
211C2×C4×C8C2×D7311yescharacteristic
212C4×C4⋊C4C2×D7311yescharacteristic
213#336—21no—
214#335—1461no—
215#334—1461no—
216#328—1462no—
217#327—1462no—
218Q8⋊C8—1462no—
219D4⋊C8—1462no—
220C2×#41—1461no—
221C22×C8—21no—
222C22×C8C22⋊D7311yescharacteristic
223C22×C8C22⋊D7311yescharacteristic
224C4⋊Q8—731no—
225C4⋊Q8—731no—
226C4⋊Q8—731no—
227#127—731no—
228#125—1461no—
229#124—1461no—
230C22⋊Q8—1461no—
231C22⋊Q8—1461no—
232#121—1461no—
233#121—1461no—
234C4×Q8—1461no—
235C4×Q8—1461no—
236C4×D4—1461no—
237C4×D4—1461no—
238#117—1461no—
239C2×C4⋊C4—21no—
240C2×C42—21no—
241C2×C42C22×D7311yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—1461no—
244C4⋊C8—1461no—
245C4⋊C8D29212yes—
246#103—1461no—
247#103—1461no—
248#103—1461no—
249#103—1461no—
250#102—1461no—
251#102—1461no—
252#102—1461no—
253#102—1461no—
254C22⋊C8—1461no—
255C22⋊C8—1461no—
256C4×C8—42no—
257C4×C8—1461no—
258C4×C8—1461no—
259C4×C8C4×D7311yescharacteristic
260C4×C8C4×D7311yescharacteristic
261C4×C8D29211yescharacteristic
262C4×C8D29211yescharacteristic
263#95D29212yes—
264#41—2921no—
265#41—2921no—
266#41—2921no—
267#41—2921no—
268C2×Q8—1461no—
269C2×Q8—1461no—
270C2×Q8—1461no—
271C2×D4—2921no—
272C2×D4—1461no—
273C2×D4—1461no—
274C2×D4—1461no—
275C22×C4—22no—
276C22×C4—2921no—
277C22×C4C2×C22⋊D7311yescharacteristic
278C22×C4C2×D29211yescharacteristic
279C22×C4#1192402811yescharacteristic
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—22no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—2921no—
288C2×C8—2921no—
289C2×C8#1192400511yescharacteristic
290C2×C8#1192400511yescharacteristic
291C2×C8#1192400511yescharacteristic
292C2×C8#1192400511yescharacteristic
293C4⋊C4—24no—
294C4⋊C4—2921no—
295C4⋊C4—2921no—
296C4⋊C4—1461no—
297C4⋊C4—1461no—
298C4⋊C4—1461no—
299C4⋊C4—1461no—
300C4⋊C4—1461no—
301C4⋊C4—1461no—
302C22⋊C4—2921no—
303C22⋊C4—2921no—
304C22⋊C4—2921no—
305C42—41no—
306C42—41no—
307C42—2921no—
308C42C2×C4×D7311yescharacteristic
309C42C2×D29211yescharacteristic
310C42C2×D29211yescharacteristic
311C42#1192402811yescharacteristic
312C23—2921no—
313C23#1455656511yescharacteristic
314Q8—2922no—
315Q8—2921no—
316Q8—2921no—
317Q8—5841no—
318D4—2922no—
319D4—2921no—
320D4—2921no—
321D4—5841no—
322D4—5841no—
323D4—5841no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—5841no—
333C2×C4—5841no—
334C2×C4C2×#1192400511yescharacteristic
335C2×C4C4×D29211yescharacteristic
336C2×C4C4×D29211yescharacteristic
337C2×C4#1455656511yescharacteristic
338C2×C4#1455657911yescharacteristic
339C2×C4#1455658811yescharacteristic
340C2×C4#1455661111yescharacteristic
341C2×C4#1455661111yescharacteristic
342C2×C4#1455661711yescharacteristic
343C2×C4#1455662211yescharacteristic
344C8—21no—
345C8—21no—
346C8—21no—
347C8—21no—
348C8—42no—
349C8—5841no—
350C8—5841no—
351C22—21no—
352C22—21no—
353C22—5841no—
354C22—5841no—
355C22—5841no—
356C22#1798848911yescharacteristic
357C22#1798880211yescharacteristic
358C22#1798880911yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—44no—
363C4—5841no—
364C4—5841no—
365C4—5841no—
366C4#1798858111yescharacteristic
367C4#1798858611yescharacteristic
368C4#1798870512yes—
369C4#1798880211yescharacteristic
370C4#1798880911yescharacteristic
371C2—21no—
372C2—21no—
373C2—11681no—
374C2#2261081911yescharacteristic
375C2#2261082911yescharacteristic
376C2#2261086311yescharacteristic
subgroupG/H
centerC2×C4#14556565
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC8×C4⋊C4×C73C2
socleC22×C73#390
prime radical#17989137C22
cosocleC2×C42×C73C23
hypercenterC8×C4⋊C4D73
hypocenterC73#9751
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #22608679C2semidirect
3. #22608429C2semidirect
5. #22608333C2semidirect
7. C8×C4⋊C4×C73C2semidirect
12. #17988938C4semidirect
13. #17988938C4semidirect
14. #17988934C4semidirect
15. #17988934C4semidirect
190. C8×C4⋊C4D73semidirect
196. C73#9751semidirect

Maximal subgroups

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

subgroupindex
#226202542
#226086792
#226084292
#226084252
#226083332
#226083292
C8×C4⋊C4×C732
#975173