Finite Group Databasebeta

← #34003270

Subgroups — #34003270

Order 18688.

562 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#22626607C211yesmaximal, characteristic
2#22626607C211yesmaximal, characteristic
3#22624834C214yesmaximal
4#22612326C211yesmaximal, characteristic
5#17989608—21no—
6#17989608C412yescomplemented
7#17989607—21no—
8#17989607C412yescomplemented
9#17989604—21no—
10#17989604C412yescomplemented
11#17989603—21no—
12#17989603C412yescomplemented
13#17989590—21no—
14#17989590—21no—
15#17989557C2212yes—
16#17989557C2212yes—
17C4×#11924037—21no—
18C4×#11924037—21no—
19C22×C4×Dic73C2211yescharacteristic
20#17988454—21no—
21#17988452—21no—
22#17988448C2212yes—
23#17988447C411yescharacteristic
24C4⋊C4×Dic73—21no—
25C22⋊C4×Dic73C412yes—
26#17988432—21no—
27#380×C73C411yescharacteristic
28C2×#11924037—22no—
29C2×#11924037—22no—
30#14556658—22no—
31#14556658—22no—
32C4⋊#10596833—22no—
33C4⋊#10596833—22no—
34C22⋊#10596833—22no—
35C22⋊#10596833—22no—
36C22⋊#10596833C2×C414yes—
37C22⋊#10596833C2×C414yes—
38#14556646—22no—
39#14556646—22no—
40C4×#10596833—22no—
41C4×#10596833—22no—
42C23×Dic73C2×C411yescharacteristic
43C23×Dic73C2311yescharacteristic
44C2×C4⋊Dic73—21no—
45C2×C22⋊Dic73C2×C412yes—
46C2×C4×Dic73—22no—
47C2×C4×Dic73C2×C411yescharacteristic
48C2×C4×Dic73C2×C411yescharacteristic
49C2×C4×Dic73C2×C411yescharacteristic
50C2×C4×Dic73C2×C411yescharacteristic
51C2×C4×Dic73D411yescharacteristic
52C2×C4×Dic73D411yescharacteristic
53C2×C4×Dic73D411yescharacteristic
54C2×C4×Dic73D411yescharacteristic
55C2×C4×Dic73D411yescharacteristic
56C2×C4×Dic73D411yescharacteristic
57C2×C4×Dic73Q811yescharacteristic
58C2×C4×Dic73Q811yescharacteristic
59#14556498—22no—
60#14556498—22no—
61#14556498—22no—
62#14556498—21no—
63C23×C4×C73C2×C411yescharacteristic
64C2×C4⋊C4×C73—21no—
65C2×C22⋊C4×C73C2×C412yes—
66#95×C73—21no—
67#11924037—42no—
68#11924037—42no—
69#11924037—42no—
70#11924037—42no—
71C2×#10596833—24no—
72C2×#10596833—24no—
73C22×Dic73—22no—
74C22×Dic73—42no—
75C22×Dic73—41no—
76C22×Dic73—41no—
77C22×Dic73C4211yescharacteristic
78C22×Dic73C4211yescharacteristic
79C22×Dic73C22⋊C411yescharacteristic
80C22×Dic73C22⋊C411yescharacteristic
81C22×Dic73C4⋊C411yescharacteristic
82C22×Dic73C4⋊C411yescharacteristic
83C22×Dic73C22×C411yescharacteristic
84C22×Dic73C22×C411yescharacteristic
85C22×Dic73C2×D411yescharacteristic
86C22×Dic73C2×D411yescharacteristic
87C22×Dic73C2×D411yescharacteristic
88C22×Dic73C2×Q811yescharacteristic
89C4⋊Dic73—42no—
90C22⋊Dic73—42no—
91C4×Dic73—44no—
92C4×Dic73C22⋊C411yescharacteristic
93C4×Dic73C22⋊C411yescharacteristic
94C4×Dic73C22⋊C411yescharacteristic
95C4×Dic73C22⋊C411yescharacteristic
96C4×Dic73C22⋊C411yescharacteristic
97C4×Dic73C22⋊C411yescharacteristic
98C4×Dic73C22⋊C411yescharacteristic
99C4×Dic73C22⋊C411yescharacteristic
100C4×Dic73C4⋊C411yescharacteristic
101C4×Dic73C4⋊C411yescharacteristic
102C4×Dic73C4⋊C411yescharacteristic
103C4×Dic73C4⋊C411yescharacteristic
104C4×Dic73C4⋊C411yescharacteristic
105C4×Dic73C4⋊C411yescharacteristic
106C4×Dic73C4⋊C411yescharacteristic
107C4×Dic73C4⋊C411yescharacteristic
108C24×C73C22×C411yescharacteristic
109C22×C4×C73—22no—
110C22×C4×C73—42no—
111C22×C4×C73C4211yescharacteristic
112C22×C4×C73C4211yescharacteristic
113C22×C4×C73C22⋊C411yescharacteristic
114C22×C4×C73C22⋊C411yescharacteristic
115C22×C4×C73C4⋊C411yescharacteristic
116C22×C4×C73C4⋊C411yescharacteristic
117C4⋊C4×C73—42no—
118C22⋊C4×C73—42no—
119C23×C73—21no—
120C23×C73—21no—
121C23×C73—41no—
122C23×C73—41no—
123C23×C73C2×C4211yescharacteristic
124C23×C73C2×C22⋊C411yescharacteristic
125C23×C73C2×C4⋊C411yescharacteristic
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—42no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73#9511yescharacteristic
136C2×C4×C73#9511yescharacteristic
137C2×C4×C73#9511yescharacteristic
138C2×C4×C73#9511yescharacteristic
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—22no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—42no—
154C2×Dic73—42no—
155C2×Dic73—42no—
156C2×Dic73#9511yescharacteristic
157C2×Dic73#9511yescharacteristic
158C2×Dic73#9511yescharacteristic
159C2×Dic73#9511yescharacteristic
160C2×Dic73C2×C22⋊C411yescharacteristic
161C2×Dic73C2×C22⋊C411yescharacteristic
162C2×Dic73C2×C4⋊C411yescharacteristic
163C2×Dic73C2×C4⋊C411yescharacteristic
164#10596833—44no—
165#10596833—44no—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—42no—
175C22×C73—42no—
176C22×C73C2×#9511yescharacteristic
177C22×C73#41011yescharacteristic
178C22×C73#41011yescharacteristic
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—82no—
183C4×C73#34412yes—
184Dic73—21no—
185Dic73—21no—
186Dic73—21no—
187Dic73—21no—
188Dic73—21no—
189Dic73—21no—
190Dic73—21no—
191Dic73—82no—
192Dic73#34412yes—
193#8113—731nomaximal, Sylow
194C2×C73—21no—
195C2×C73—21no—
196C2×C73—41no—
197C2×C73—41no—
198C2×C73#174011yescharacteristic
199C2×C73C2×#34411yescharacteristic
200C2×C73C2×#34411yescharacteristic
201#2920—731no—
202#2920—731no—
203#2283—731no—
204#1306—734no—
205C73#811311yescharacteristic, complemented, Sylow
206C22×C42—731no—
207#432—732no—
208#432—732no—
209#432—1461no—
210#432—1461no—
211#431—732no—
212#431—732no—
213#431—1461no—
214#431—1461no—
215#423—1461no—
216#423—1461no—
217#407—732no—
218#407—732no—
219C4×M16—1461no—
220C4×M16—1461no—
221#383—1461no—
222#382—1461no—
223#381—732no—
224#380—731no—
225#380#6440811yescharacteristic
226C4×C4⋊C4—1461no—
227C4×C22⋊C4—732no—
228#376—1461no—
229C23×C4—731no—
230C23×C4—731no—
231C23×C4C2×#6440811yescharacteristic
232C2×M16—1462no—
233C2×M16—1462no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—1461no—
236C2×C22⋊C4—732no—
237C2×C22⋊C4C2×#6440812yes—
238C2×C42—731no—
239C2×C42—731no—
240C2×C42—731no—
241C2×C42—731no—
242C2×C42—731no—
243C2×C42—731no—
244C2×C42—731no—
245C2×C42—731no—
246C2×C42—731no—
247C2×C42—731no—
248C2×C42—731no—
249C2×C42—731no—
250C2×C42—1462no—
251C4⋊C8—1462no—
252C4⋊C8—1462no—
253C4⋊C8—1462no—
254C4⋊C8—1462no—
255C22⋊C8—734no—
256C22⋊C8—734no—
257C22⋊C8—1462no—
258C22⋊C8—1462no—
259#97—1462no—
260#97—1462no—
261C4×C8—1462no—
262C4×C8—1462no—
263#95—21no—
264#95—1462no—
265#95—1462no—
266#95—1462no—
267#95—1461no—
268C24C22×#6440811yescharacteristic
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—2922no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—731no—
284C22×C4—731no—
285C22×C4—731no—
286C22×C4—1462no—
287C22×C4C4×#6440811yescharacteristic
288C22×C4C4×#6440811yescharacteristic
289C22×C4C22⋊#6440811yescharacteristic
290C22×C4C22⋊#6440811yescharacteristic
291C22×C4C4⋊#6440811yescharacteristic
292C22×C4C4⋊#6440811yescharacteristic
293M16—2922no—
294M16—2922no—
295M16—2922no—
296M16—2922no—
297C2×C8—1464no—
298C2×C8—1464no—
299C4⋊C4—42no—
300C4⋊C4—2922no—
301C22⋊C4—42no—
302C22⋊C4—2922no—
303C42—2924no—
304C42—731no—
305C42—731no—
306C42—731no—
307C42—731no—
308C42—731no—
309C42—731no—
310C42—731no—
311C42—731no—
312C42—731no—
313C42—731no—
314C42—731no—
315C42—731no—
316C42—731no—
317C42—731no—
318C42—731no—
319C42—731no—
320C23—21no—
321C23—21no—
322C23—41no—
323C23—41no—
324C23C2×C4×#6440811yescharacteristic
325C23C2×C22⋊#6440811yescharacteristic
326C23C2×C4⋊#6440811yescharacteristic
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—2921no—
346C2×C4—731no—
347C2×C4—731no—
348C2×C4—731no—
349C2×C4—731no—
350C2×C4—731no—
351C2×C4—731no—
352C2×C4—731no—
353C2×C4—731no—
354C2×C4—1462no—
355C2×C4—1462no—
356C2×C4—1462no—
357C2×C4—1461no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4—1461no—
361C2×C4(C2×#64408)⋊C411yescharacteristic
362C2×C4(C2×#64408)⋊C411yescharacteristic
363C2×C4(C2×#64408)⋊C411yescharacteristic
364C2×C4(C2×#64408)⋊C411yescharacteristic
365C8—2924no—
366C8—2924no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—42no—
376C22—42no—
377C22C2×(C2×#64408)⋊C411yescharacteristic
378C22#1798956711yescharacteristic
379C22#1798956811yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—82no—
384C4—5842no—
385C4—732no—
386C4—1461no—
387C4—1461no—
388C4—1461no—
389C4—1461no—
390C4—1461no—
391C4—1461no—
392C4—1461no—
393C4#1798946812yes—
394C2—21no—
395C2—21no—
396C2—41no—
397C2—41no—
398C2#2262563111yescharacteristic
399C2C2×#1798946811yescharacteristic
400C2#2262563911yescharacteristic
subgroupG/H
centerC22C2×(C2×#64408)⋊C4
commutatorC23×C73C2×C42
FrattiniC24C22×#64408
Fitting#380×C73C4
socleC22×C73C2×#95
prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenter#380#64408
hypocenterC73#8113
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
6. #17989608C4semidirect
8. #17989607C4semidirect
10. #17989604C4semidirect
12. #17989603C4semidirect
205. C73#8113semidirect

Maximal subgroups

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

subgroupindex
#226266072
#226248342
#226123262
#811373