Finite Group Databasebeta

← #34005204

Subgroups — #34005204

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625785C211yesmaximal, characteristic
2C4×C22⋊#10596833C211yesmaximal, characteristic
3#22624767C212yesmaximal, complemented
4#22624767C212yesmaximal, complemented
5#117×Dic73C211yesmaximal, characteristic
6C2×C4⋊#10596833C2212yes—
7C2×C22⋊#10596833—21no—
8C2×C22⋊#10596833—21no—
9C2×C4×#10596833C2212yes—
10#17989453—21no—
11#17989453—21no—
12C2×#14556550C411yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14C4⋊C4×Dic73C411yescharacteristic
15C4⋊C4×Dic73C411yescharacteristic
16C4⋊C4×Dic73C2211yescharacteristic
17C4⋊C4×Dic73C2211yescharacteristic
18C22⋊C4×Dic73—21no—
19C22⋊C4×Dic73—21no—
20#17988433—21no—
21C42×Dic73—21no—
22C2×#117×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25C4⋊#10596833—22no—
26C4⋊#10596833—22no—
27C22⋊#10596833—24no—
28C22⋊#10596833—42no—
29C4×#10596833—22no—
30C4×#10596833—22no—
31C23×Dic73D411yescharacteristic
32C23×Dic73D411yescharacteristic
33#14556550—22no—
34#14556550—22no—
35C2×C4⋊Dic73C2×C411yescharacteristic
36C2×C4⋊Dic73C2×C411yescharacteristic
37C2×C22⋊Dic73—21no—
38C2×C4×Dic73—22no—
39C2×C4×Dic73—22no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73—21no—
43C2×C4×Dic73—21no—
44C2×C4×Dic73—21no—
45C2×C4×Dic73C2×C411yescharacteristic
46C2×C4×Dic73D411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73C2311yescharacteristic
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52#14556498—21no—
53C23×C4×C73C2×C411yescharacteristic
54#117×C73—22no—
55#117×C73C814yescomplemented
56C2×C4⋊C4×C73C2×C411yescharacteristic
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C22⋊C4×C73—21no—
59C2×C42×C73—21no—
60C2×#10596833—24no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×#10596833—42no—
66C22×Dic73—21no—
67C22×Dic73—21no—
68C22×Dic73—22no—
69C22×Dic73—22no—
70C22×Dic73—22no—
71C22×Dic73—22no—
72C22×Dic73—21no—
73C22×Dic73—21no—
74C22×Dic73—41no—
75C22×Dic73C22⋊C411yescharacteristic
76C22×Dic73C22⋊C411yescharacteristic
77C22×Dic73C2×D411yescharacteristic
78C22×Dic73C2×D411yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73M1612yes—
82C4⋊Dic73M1612yes—
83C22⋊Dic73—24no—
84C4×Dic73—24no—
85C4×Dic73—21no—
86C4×Dic73—21no—
87C4×Dic73—22no—
88C4×Dic73—22no—
89C4×Dic73—42no—
90C4×Dic73—42no—
91C4×Dic73—42no—
92C4×Dic73—41no—
93C4×Dic73—41no—
94C4×Dic73#4112yes—
95C4×Dic73#4112yes—
96C24×C73C22⋊C411yescharacteristic
97C22×C4×C73—21no—
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73C22⋊C411yescharacteristic
104C22×C4×C73C2×C812yes—
105C22×C4×C73M1612yes—
106C22×C4×C73C22×C411yescharacteristic
107C4⋊C4×C73—21no—
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2×C812yes—
110C4⋊C4×C73C2×C812yes—
111C22⋊C4×C73—24no—
112C42×C73—24no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73C22⋊C812yes—
120C23×C73C2×C22⋊C411yescharacteristic
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—22no—
124C2×C4×C73—22no—
125C2×C4×C73—22no—
126C2×C4×C73—22no—
127C2×C4×C73—22no—
128C2×C4×C73—22no—
129C2×C4×C73—41no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73C22⋊C812yes—
134C2×C4×C73#11711yescharacteristic
135C2×C4×C73#11711yescharacteristic
136C2×C4×C73C22×C811yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×C4×C73C2×M1611yescharacteristic
139C2×C4×C73C2×M1611yescharacteristic
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—21no—
148C2×Dic73—21no—
149C2×Dic73—44no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73#10412yes—
157C2×Dic73#12312yes—
158C2×Dic73#12312yes—
159C2×Dic73#13512yes—
160C2×Dic73AGL(1,ℤ/8)11yescharacteristic
161C2×Dic73#13711yescharacteristic
162#10596833—44no—
163#10596833—82no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73#38111yescharacteristic
172C22×C73C2×C22⋊C811yescharacteristic
173C22×C73#40711yescharacteristic
174C22×C73#41611yescharacteristic
175C22×C73#41711yescharacteristic
176C22×C73C2×#10411yescharacteristic
177C22×C73#42111yescharacteristic
178C4×C73—22no—
179C4×C73—42no—
180C4×C73—42no—
181C4×C73#43111yescharacteristic
182C4×C73#43111yescharacteristic
183C4×C73#43211yescharacteristic
184C4×C73#43211yescharacteristic
185Dic73—22no—
186Dic73—22no—
187Dic73—41no—
188Dic73—42no—
189Dic73—42no—
190Dic73#48212yes—
191Dic73#48512yes—
192#8708—731nomaximal, Sylow
193C2×C73—42no—
194C2×C73#147611yescharacteristic
195C2×C73#147711yescharacteristic
196C2×C73#148811yescharacteristic
197C2×C73#148911yescharacteristic
198C2×C73#181711yescharacteristic
199C2×C73#182511yescharacteristic
200C2×C73#182611yescharacteristic
201C4×#117—731no—
202#1797—731no—
203C4×C22⋊C8—731no—
204#1279—732no—
205#1279—732no—
206C73#870811yescharacteristic, complemented, Sylow
207C2×#117—731no—
208C2×#117#6440811yescharacteristic
209C22×C42—731no—
210C2×C4⋊C8—732no—
211C2×C22⋊C8—1461no—
212C2×C22⋊C8—1461no—
213C2×C4×C8—732no—
214C4×C4⋊C4—731no—
215C4×C4⋊C4—731no—
216C4×C4⋊C4—731no—
217C4×C4⋊C4—731no—
218C4×C22⋊C4—1461no—
219C4×C22⋊C4—1461no—
220#376—1461no—
221C43—1461no—
222#336—1461no—
223#336—1461no—
224C23×C4—731no—
225C23×C4—731no—
226C23×C4C2×#6440811yescharacteristic
227C22×C8—1462no—
228C22×C8—1462no—
229#117—22no—
230#117—1462no—
231#117—1462no—
232#117#1059683314yescomplemented
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4C2×#6440811yescharacteristic
236C2×C4⋊C4C2×#6440811yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—1461no—
239C2×C42—21no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42—731no—
244C2×C42—1461no—
245C2×C42—1461no—
246C2×C42—1461no—
247C2×C42—1461no—
248C2×C42—1462no—
249C2×C42—1462no—
250C2×C42—1461no—
251C4⋊C8—1462no—
252C4⋊C8—1462no—
253C22⋊C8—2922no—
254C22⋊C8—1464no—
255C4×C8—1462no—
256C4×C8—1462no—
257#95—1461no—
258#95—1461no—
259#95—1461no—
260#95—1461no—
261C24C22⋊#6440811yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—2921no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—1461no—
274C22×C4—1462no—
275C22×C4—1462no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4—1461no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4C22⋊#6440811yescharacteristic
282C22×C4C2×#1059683312yes—
283C22×C4#1192403712yes—
284C22×C4C22×#6440811yescharacteristic
285C2×C8—2922no—
286C2×C8—2922no—
287C2×C8—2922no—
288C2×C8—2922no—
289C2×C8—2922no—
290C2×C8—1464no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—732no—
294C4⋊C4—732no—
295C4⋊C4—1461no—
296C4⋊C4—1461no—
297C4⋊C4C2×#1059683312yes—
298C4⋊C4C2×#1059683312yes—
299C22⋊C4—24no—
300C22⋊C4—1464no—
301C42—24no—
302C42—2922no—
303C42—2921no—
304C42—2921no—
305C42—2922no—
306C42—2922no—
307C42—732no—
308C42—732no—
309C42—1462no—
310C42—1462no—
311C42—1464no—
312C42—1461no—
313C42—1461no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C22⋊#1059683312yes—
321C23C2×C22⋊#6440811yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—2922no—
339C2×C4—2922no—
340C2×C4—2924no—
341C2×C4—732no—
342C2×C4—732no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—732no—
346C2×C4—732no—
347C2×C4—1461no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4C22⋊#1059683312yes—
357C2×C4#1455667011yescharacteristic
358C2×C4#1455667011yescharacteristic
359C2×C4C22×#1059683311yescharacteristic
360C2×C4C2×#1192403711yescharacteristic
361C2×C4D73⋊M1611yescharacteristic
362C2×C4D73⋊M1611yescharacteristic
363C8—2924no—
364C8—5842no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22#1798953011yescharacteristic
373C22C2×C22⋊#1059683311yescharacteristic
374C22#1798955911yescharacteristic
375C22#1798957711yescharacteristic
376C22#1798957811yescharacteristic
377C22D73⋊#10411yescharacteristic
378C22#1798958411yescharacteristic
379C4—22no—
380C4—42no—
381C4—42no—
382C4—2921no—
383C4—2922no—
384C4—2922no—
385C4—732no—
386C4—732no—
387C4—1462no—
388C4—1462no—
389C4#1798960311yescharacteristic
390C4#1798960311yescharacteristic
391C4#1798960711yescharacteristic
392C4#1798960711yescharacteristic
393C2—42no—
394C2#2262522211yescharacteristic
395C2#2262522611yescharacteristic
396C2#2262526411yescharacteristic
397C2#2262526811yescharacteristic
398C2#2262582111yescharacteristic
399C2#2262583611yescharacteristic
400C2#2262583911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×#117×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×#117#64408
hypocenterC73#8708
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #22624767C2semidirect
4. #22624767C2semidirect
55. #117×C73C8semidirect
206. C73#8708semidirect
232. #117#10596833semidirect

Maximal subgroups

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

subgroupindex
#226257852
C4×C22⋊#105968332
#226247672
#117×Dic732
#870873