Finite Group Databasebeta

← #34004792

Subgroups — #34004792

Order 18688.

682 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#22625787C212yesmaximal
2C2×#17989432C212yesmaximal
3#22624769C212yesmaximal
4C2×C4⋊C4×Dic73C211yesmaximal, characteristic
5C2×#14556658—22no—
6C2×C22⋊#10596833C2214yes—
7#17989453—22no—
8#17989432—24no—
9C22×C4⋊Dic73C2211yescharacteristic
10C22×C4×Dic73C411yescharacteristic
11C22×C4×Dic73C411yescharacteristic
12C22×C4×Dic73C2211yescharacteristic
13C4⋊C4×Dic73—22no—
14C4⋊C4×Dic73—22no—
15C2×#14556498C411yescharacteristic
16C2×#14556498C2211yescharacteristic
17C22×C4⋊C4×C73C411yescharacteristic
18C22×#10596833—24no—
19#14556658—44no—
20C22⋊#10596833—24no—
21C22⋊#10596833—24no—
22C23×Dic73C2×C411yescharacteristic
23C23×Dic73C2×C411yescharacteristic
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2311yescharacteristic
26C2×C4⋊Dic73—22no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73D412yes—
29C2×C4⋊Dic73Q812yes—
30C2×C4×Dic73—21no—
31C2×C4×Dic73—21no—
32C2×C4×Dic73—22no—
33C2×C4×Dic73—21no—
34C2×C4×Dic73—21no—
35C2×C4×Dic73—42no—
36C2×C4×Dic73—42no—
37C2×C4×Dic73C814yescomplemented
38C2×C4×Dic73D412yes—
39C2×C4×Dic73D412yes—
40#14556498—22no—
41#14556498—22no—
42C23×C4×C73C2×C411yescharacteristic
43C23×C4×C73C2×C411yescharacteristic
44C23×C4×C73C2×C411yescharacteristic
45C2×C4⋊C4×C73—22no—
46C2×C4⋊C4×C73—22no—
47C2×C4⋊C4×C73—22no—
48C2×#10596833—44no—
49C2×#10596833—44no—
50C2×#10596833—44no—
51C22×Dic73—22no—
52C22×Dic73—22no—
53C22×Dic73—21no—
54C22×Dic73—21no—
55C22×Dic73—21no—
56C22×Dic73—21no—
57C22×Dic73—41no—
58C22×Dic73—41no—
59C22×Dic73—41no—
60C22×Dic73—41no—
61C22×Dic73—41no—
62C22×Dic73—41no—
63C22×Dic73C22⋊C411yescharacteristic
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C4⋊C412yes—
66C22×Dic73C2×C812yes—
67C22×Dic73C2×C812yes—
68C22×Dic73M1612yes—
69C22×Dic73C2×D412yes—
70C22×Dic73C2×D411yescharacteristic
71C22×Dic73C2×Q811yescharacteristic
72C22×Dic73#4112yes—
73C4⋊Dic73—24no—
74C4⋊Dic73—24no—
75C4×Dic73—24no—
76C4×Dic73—24no—
77C4×Dic73—24no—
78C4×Dic73—42no—
79C4×Dic73—42no—
80C4×Dic73—42no—
81C24×C73C22×C411yescharacteristic
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73—41no—
93C22×C4×C73—41no—
94C22×C4×C73C22⋊C412yes—
95C22×C4×C73C4⋊C412yes—
96C22×C4×C73C2×C812yes—
97C22×C4×C73M1612yes—
98C22×C4×C73M1612yes—
99C4⋊C4×C73—28no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73C2×C22⋊C411yescharacteristic
105C23×C73C2×C4⋊C411yescharacteristic
106C23×C73#11711yescharacteristic
107C23×C73C22×C811yescharacteristic
108C23×C73C2×M1611yescharacteristic
109C23×C73C2×M1611yescharacteristic
110C23×C73C2×M1611yescharacteristic
111C2×C4×C73—22no—
112C2×C4×C73—22no—
113C2×C4×C73—22no—
114C2×C4×C73—22no—
115C2×C4×C73—22no—
116C2×C4×C73—22no—
117C2×C4×C73—22no—
118C2×C4×C73—22no—
119C2×C4×C73—22no—
120C2×C4×C73—22no—
121C2×C4×C73—42no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—42no—
127C2×C4×C73C4⋊C814yescomplemented
128C2×Dic73—22no—
129C2×Dic73—21no—
130C2×Dic73—22no—
131C2×Dic73—21no—
132C2×Dic73—24no—
133C2×Dic73—24no—
134C2×Dic73—22no—
135C2×Dic73—22no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—42no—
139C2×Dic73—42no—
140C2×Dic73—42no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—42no—
146C2×Dic73—42no—
147C2×Dic73C22⋊C812yes—
148C2×Dic73C22⋊C812yes—
149C2×Dic73#9912yes—
150C2×Dic73#10112yes—
151C2×Dic73#12112yes—
152C2×Dic73C22⋊Q812yes—
153#10596833—84no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73#38011yescharacteristic
167C22×C73C2×C22⋊C811yescharacteristic
168C22×C73#40711yescharacteristic
169C22×C73C2×#9911yescharacteristic
170C22×C73#41011yescharacteristic
171C22×C73C2×#10111yescharacteristic
172C22×C73#41311yescharacteristic
173C22×C73C2×C4⋊C811yescharacteristic
174C22×C73#42311yescharacteristic
175C22×C73#43111yescharacteristic
176C22×C73#43211yescharacteristic
177C4×C73—24no—
178C4×C73—42no—
179C4×C73—42no—
180Dic73—22no—
181Dic73—22no—
182Dic73—22no—
183Dic73—42no—
184Dic73—42no—
185Dic73#32414yescomplemented
186#8558—731nomaximal, Sylow
187C2×C73—21no—
188C2×C73—21no—
189C2×C73—21no—
190C2×C73—21no—
191C2×C73C2×#32411yescharacteristic
192C2×C73#145811yescharacteristic
193C2×C73#146511yescharacteristic
194C2×C73#146711yescharacteristic
195C2×C73#179711yescharacteristic
196C2×C73#179911yescharacteristic
197C2×C73#180111yescharacteristic
198C2×C4×C4⋊C4—731no—
199#1797—732no—
200C2×#324—732no—
201#1280—732no—
202C73#855811yescharacteristic, complemented, Sylow
203C22×C4⋊C4—731no—
204C22×C4⋊C4#6440811yescharacteristic
205C22×C42—731no—
206C22×C42—731no—
207C22×C42—731no—
208C2×C4⋊C8—1462no—
209C2×C22⋊C8—734no—
210C4×C4⋊C4—1462no—
211C4×C4⋊C4—1462no—
212C2×#95—731no—
213C2×#95—731no—
214#336—1462no—
215#324—1464no—
216C23×C4—731no—
217C23×C4—731no—
218C23×C4—731no—
219C23×C4—731no—
220C23×C4C2×#6440811yescharacteristic
221C23×C4C2×#6440811yescharacteristic
222C23×C4C2×#6440811yescharacteristic
223C22×C8—1464no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—732no—
228C2×C4⋊C4—732no—
229C2×C4⋊C4—1462no—
230C2×C4⋊C4—1462no—
231C2×C42—2922no—
232C2×C42—2922no—
233C2×C42—732no—
234C2×C42—732no—
235C2×C42—734no—
236C2×C42—1461no—
237C2×C42—1461no—
238C2×C42—1461no—
239C2×C42—1461no—
240C2×C42—1462no—
241C4⋊C8—2924no—
242C22⋊C8—1464no—
243C22⋊C8—1464no—
244#95—1462no—
245#95—1462no—
246C24C22×#6440811yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—2921no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4—2921no—
263C22×C4—2921no—
264C22×C4—2921no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—732no—
268C22×C4—732no—
269C22×C4—732no—
270C22×C4—731no—
271C22×C4—732no—
272C22×C4—732no—
273C22×C4—731no—
274C22×C4—732no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4—1461no—
279C22×C4—1462no—
280C22×C4—1462no—
281C22×C4C22⋊#6440812yes—
282C22×C4C4⋊#6440812yes—
283C22×C4#1192403612yes—
284C22×C4#1192403712yes—
285C22×C4#1192403712yes—
286C2×C8—2924no—
287C2×C8—2924no—
288C2×C8—2924no—
289C4⋊C4—28no—
290C4⋊C4—1464no—
291C4⋊C4—1464no—
292C42—2922no—
293C42—2922no—
294C42—2922no—
295C42—1464no—
296C42—1464no—
297C42—1464no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23C2×C22⋊#6440811yescharacteristic
303C23C2×C4⋊#6440811yescharacteristic
304C23#1455667011yescharacteristic
305C23C2×#1192403611yescharacteristic
306C23C2×#1192403711yescharacteristic
307C23C2×#1192403711yescharacteristic
308C23D73⋊M1611yescharacteristic
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—2922no—
326C2×C4—2922no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—2921no—
334C2×C4—2922no—
335C2×C4—2921no—
336C2×C4—732no—
337C2×C4—732no—
338C2×C4—732no—
339C2×C4—732no—
340C2×C4—732no—
341C2×C4—732no—
342C2×C4—1462no—
343C2×C4—1462no—
344C2×C4—1464no—
345C2×C4—1464no—
346C2×C4—1461no—
347C2×C4—1462no—
348C2×C4—1462no—
349C2×C4—1461no—
350C2×C4#1455665814yescomplemented
351C8—5844no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22#1798952911yescharacteristic
365C22#1798955511yescharacteristic
366C22#1798955711yescharacteristic
367C22D73⋊#9911yescharacteristic
368C22#1798956811yescharacteristic
369C22D73⋊#10111yescharacteristic
370C22#1798957411yescharacteristic
371C22C2×#1455665811yescharacteristic
372C22#1798959011yescharacteristic
373C22#1798960411yescharacteristic
374C22#1798960711yescharacteristic
375C4—24no—
376C4—42no—
377C4—42no—
378C4—2922no—
379C4—2922no—
380C4—734no—
381C4—1462no—
382C4—1462no—
383C4—1462no—
384C2—21no—
385C2—21no—
386C2—21no—
387C2—21no—
388C2#2262516011yescharacteristic
389C2#2262516511yescharacteristic
390C2#2262518711yescharacteristic
391C2#2262519411yescharacteristic
392C2#2262578711yescharacteristic
393C2#2262579411yescharacteristic
394C2#2262579811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC23×C73C22×C8
FrattiniC24C22×#64408
FittingC22×C4⋊C4×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC23×Dic73C23
hypercenterC22×C4⋊C4#64408
hypocenterC73#8558
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
37. C2×C4×Dic73C8semidirect
127. C2×C4×C73C4⋊C8semidirect
185. Dic73#324semidirect
202. C73#8558semidirect
350. C2×C4#14556658semidirect

Maximal subgroups

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

subgroupindex
#226257872
C2×#179894322
#226247692
C2×C4⋊C4×Dic732
#855873