Finite Group Databasebeta

← #34003017

Subgroups — #34003017

Order 18688.

740 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626607C211yesmaximal, characteristic
2C2×C4×#11924037C211yesmaximal, characteristic
3#22624819C214yesmaximal, complemented
4C4×#14556547C211yesmaximal, characteristic
5C22×#11924037—21no—
6#17989608C2212yes—
7#17989607—21no—
8#17989604—21no—
9#17989603C412yescomplemented
10#17989590C412yescomplemented
11#17989557—21no—
12C4×#11924037—21no—
13C4×#11924037—21no—
14C4×#11924037—21no—
15C4×#11924037C412yescomplemented
16C4×#11924037C2212yes—
17C2×#14556646C412yescomplemented
18C2×C4×#10596833—21no—
19C2×#14556547—21no—
20C22×C4×Dic73C2211yescharacteristic
21C4×#11924007—21no—
22#17988438C412yes—
23C22⋊C4×Dic73—21no—
24C4×C22⋊Dic73C411yescharacteristic
25#17988432C2212yes—
26C42×Dic73—21no—
27C4×C22⋊C4×C73C411yescharacteristic
28C2×#11924037—28no—
29C2×#11924037—22no—
30C2×#11924037—22no—
31C2×#11924037—22no—
32C22×#10596833—22no—
33#14556658—22no—
34C4⋊#10596833C2×C414yes—
35C22⋊#10596833—22no—
36C22⋊#10596833—22no—
37#14556646—22no—
38#14556646—22no—
39#14556646C2×C414yes—
40C4×#10596833—22no—
41C4×#10596833—22no—
42C4×#10596833—22no—
43C23×Dic73D411yescharacteristic
44C23×Dic73D411yescharacteristic
45#14556547—28no—
46C2×#11924007—22no—
47C2×C22⋊Dic73—21no—
48C2×C4×Dic73—22no—
49C2×C4×Dic73—22no—
50C2×C4×Dic73—21no—
51C2×C4×Dic73C2×C411yescharacteristic
52C2×C4×Dic73C2×C411yescharacteristic
53C2×C4×Dic73C2×C411yescharacteristic
54C2×C4×Dic73C2×C411yescharacteristic
55C2×C4×Dic73C2×C411yescharacteristic
56C2×C4×Dic73D411yescharacteristic
57C2×C4×Dic73D411yescharacteristic
58C2×C4×Dic73D411yescharacteristic
59C2×C4×Dic73D411yescharacteristic
60C2×C4×Dic73Q811yescharacteristic
61C2×C4×Dic73Q811yescharacteristic
62C2×C4×Dic73C2311yescharacteristic
63#14556498—22no—
64#14556498C2×C412yes—
65C23×C4×C73C2×C411yescharacteristic
66C2×C22⋊C4×C73—21no—
67C2×C42×C73—21no—
68#95×C73C2×C412yes—
69#11924037—28no—
70#11924037—28no—
71#11924037—44no—
72C2×#10596833—28no—
73C2×#10596833—24no—
74C2×#10596833—24no—
75C22×Dic73—24no—
76C22×Dic73—24no—
77C22×Dic73—22no—
78C22×Dic73C22⋊C411yescharacteristic
79C22×Dic73C22⋊C411yescharacteristic
80C22×Dic73C22⋊C411yescharacteristic
81C22×Dic73C22⋊C411yescharacteristic
82C22×Dic73C22⋊C411yescharacteristic
83C22×Dic73C22⋊C411yescharacteristic
84C22×Dic73C4⋊C411yescharacteristic
85C22×Dic73C4⋊C411yescharacteristic
86C22×Dic73C4⋊C411yescharacteristic
87C22×Dic73C4⋊C411yescharacteristic
88C22×Dic73C2×D411yescharacteristic
89C22×Dic73C2×D411yescharacteristic
90#11924007—28no—
91C22⋊Dic73—24no—
92C4×Dic73—28no—
93C4×Dic73—42no—
94C4×Dic73—44no—
95C4×Dic73C4211yescharacteristic
96C4×Dic73C4211yescharacteristic
97C4×Dic73C22⋊C411yescharacteristic
98C4×Dic73C22⋊C411yescharacteristic
99C4×Dic73C22⋊C411yescharacteristic
100C4×Dic73C22⋊C411yescharacteristic
101C4×Dic73C4⋊C411yescharacteristic
102C4×Dic73C4⋊C411yescharacteristic
103C4×Dic73C4⋊C411yescharacteristic
104C4×Dic73C4⋊C411yescharacteristic
105C4×Dic73C4⋊C411yescharacteristic
106C4×Dic73C4⋊C411yescharacteristic
107C4×Dic73C22×C411yescharacteristic
108C4×Dic73C22×C411yescharacteristic
109C4×Dic73C2×D411yescharacteristic
110C4×Dic73C2×Q811yescharacteristic
111C24×C73C22⋊C411yescharacteristic
112C22×C4×C73—22no—
113C22×C4×C73—42no—
114C22×C4×C73C4211yescharacteristic
115C22×C4×C73C4211yescharacteristic
116C22×C4×C73C22⋊C411yescharacteristic
117C22×C4×C73C4⋊C411yescharacteristic
118C22×C4×C73C4⋊C411yescharacteristic
119C22×C4×C73C22×C411yescharacteristic
120C22⋊C4×C73—24no—
121C42×C73—42no—
122C23×C73—22no—
123C23×C73—22no—
124C23×C73—41no—
125C23×C73#9511yescharacteristic
126C23×C73#9511yescharacteristic
127C23×C73C2×C22⋊C411yescharacteristic
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—24no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—42no—
136C2×C4×C73—42no—
137C2×C4×C73#9511yescharacteristic
138C2×C4×C73#9511yescharacteristic
139C2×C4×C73C2×C4211yescharacteristic
140C2×C4×C73C2×C4⋊C411yescharacteristic
141C2×Dic73—22no—
142C2×Dic73—22no—
143C2×Dic73—22no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73—24no—
152C2×Dic73—42no—
153C2×Dic73—42no—
154C2×Dic73#9511yescharacteristic
155C2×Dic73#9511yescharacteristic
156C2×Dic73#9511yescharacteristic
157C2×Dic73#9511yescharacteristic
158C2×Dic73#10414yes—
159C2×Dic73#10414yes—
160C2×Dic73C2×C22⋊C411yescharacteristic
161C2×Dic73C2×C22⋊C411yescharacteristic
162C2×Dic73C2×C4⋊C411yescharacteristic
163C2×Dic73C2×C4⋊C411yescharacteristic
164#10596833—28no—
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—44no—
174C22×C73#33912yes—
175C22×C73C2×#9511yescharacteristic
176C22×C73C2×#10412yes—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—44no—
181C4×C73#34412yes—
182Dic73—21no—
183Dic73—21no—
184Dic73—21no—
185Dic73—21no—
186Dic73—44no—
187Dic73#33912yes—
188Dic73#33912yes—
189Dic73#33912yes—
190Dic73C2×#10412yes—
191#8068—731nomaximal, Sylow
192C2×C73—22no—
193C2×C73—22no—
194C2×C73—41no—
195C2×C73C2×#33911yescharacteristic
196C2×C73C2×#33911yescharacteristic
197C2×C73C2×#34411yescharacteristic
198#2920—731no—
199C2×C4×M16—731no—
200C4×#117—731no—
201#1300—734no—
202C73#806811yescharacteristic, complemented, Sylow
203C22×M16—1461no—
204C2×#117—1461no—
205C22×C42—731no—
206#432—732no—
207#432—1461no—
208#431—732no—
209#431—1461no—
210#423—732no—
211#407—1461no—
212C4×M16—732no—
213C4×M16—732no—
214C4×M16—1461no—
215C4×M16—1461no—
216C4×M16—1461no—
217C2×#97—732no—
218C2×C4×C8—1461no—
219C4×C4⋊C4—732no—
220C4×C4⋊C4—1461no—
221C4×C22⋊C4—731no—
222C4×C22⋊C4—1461no—
223C4×C22⋊C4#6440811yescharacteristic
224#376—732no—
225C43—1461no—
226C23×C4—731no—
227C23×C4—731no—
228C23×C4C2×#6440811yescharacteristic
229C2×M16—1462no—
230C2×M16—1462no—
231C2×M16—1462no—
232C2×M16—1468no—
233C22×C8—1462no—
234#117—1468no—
235C2×C4⋊C4—1462no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—1461no—
238C2×C42—21no—
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—731no—
251C2×C42—1462no—
252C2×C42—1461no—
253C2×C42—1462no—
254C4⋊C8—734no—
255C4⋊C8—1462no—
256C22⋊C8—1462no—
257C22⋊C8—1462no—
258#97—734no—
259#97—1462no—
260#97—1462no—
261C4×C8—1462no—
262C4×C8—1462no—
263C4×C8—1462no—
264#95—732no—
265#95—1462no—
266#95C2×#6440812yes—
267C24C22⋊#6440811yescharacteristic
268C22×C4—22no—
269C22×C4—42no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
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—1462no—
283C22×C4—1464no—
284C22×C4—1464no—
285C22×C4C4×#6440811yescharacteristic
286C22×C4C4×#6440811yescharacteristic
287C22×C4C22⋊#6440811yescharacteristic
288C22×C4C4⋊#6440811yescharacteristic
289C22×C4C4⋊#6440811yescharacteristic
290C22×C4C22×#6440811yescharacteristic
291M16—2924no—
292M16—1468no—
293M16—1468no—
294C2×C8—1464no—
295C2×C8—1464no—
296C2×C8—1468no—
297C4⋊C4—1468no—
298C22⋊C4—24no—
299C22⋊C4—1464no—
300C42—42no—
301C42—2922no—
302C42—2924no—
303C42—731no—
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—1468no—
320C23—22no—
321C23—22no—
322C23—41no—
323C23(C2×#64408)⋊C411yescharacteristic
324C23(C2×#64408)⋊C411yescharacteristic
325C23C2×C22⋊#6440811yescharacteristic
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—2922no—
336C2×C4—2922no—
337C2×C4—734no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—731no—
342C2×C4—734no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—1464no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4—1462no—
356C2×C4—1462no—
357C2×C4—1462no—
358C2×C4(C2×#64408)⋊C411yescharacteristic
359C2×C4(C2×#64408)⋊C411yescharacteristic
360C2×C4C2×C4×#6440811yescharacteristic
361C2×C4C2×C4⋊#6440811yescharacteristic
362C8—2924no—
363C8—1468no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—44no—
372C22#1798945812yes—
373C22C2×(C2×#64408)⋊C411yescharacteristic
374C22D73⋊#10412yes—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—44no—
379C4—2924no—
380C4—732no—
381C4—732no—
382C4—732no—
383C4—732no—
384C4—1461no—
385C4—1461no—
386C4—1461no—
387C4—1461no—
388C4#1798946812yes—
389C2—22no—
390C2—22no—
391C2—41no—
392C2#2262560711yescharacteristic
393C2C2×#1798945811yescharacteristic
394C2C2×#1798946811yescharacteristic
subgroupG/H
centerC2×C4(C2×#64408)⋊C4
commutatorC2×C4×C73C2×C42
FrattiniC22×C4C22×#64408
FittingC4×C22⋊C4×C73C4
socleC22×C73C2×#95
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC4×C22⋊C4#64408
hypocenterC73#8068
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #22624819C2semidirect
9. #17989603C4semidirect
10. #17989590C4semidirect
15. C4×#11924037C4semidirect
17. C2×#14556646C4semidirect
202. C73#8068semidirect

Maximal subgroups

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

subgroupindex
#226266072
C2×C4×#119240372
#226248192
C4×#145565472
#806873