Finite Group Databasebeta

← #34008142

Subgroups — #34008142

Order 18688.

572 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#22625785C211yesmaximal, characteristic
2C4×C22⋊#10596833C211yesmaximal, characteristic
3#22624769C212yesmaximal
4#22624769C212yesmaximal
5C2×#17988473C211yesmaximal, characteristic
6C2×C4⋊#10596833—21no—
7C2×C22⋊#10596833C2212yes—
8C2×C22⋊#10596833C2212yes—
9C2×C4×#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12C22×C4⋊Dic73C411yescharacteristic
13C22×C4×Dic73C2211yescharacteristic
14#17988473—21no—
15#17988473—21no—
16#17988473—21no—
17#17988473—21no—
18C2×#14556498C411yescharacteristic
19C2×#14556498C411yescharacteristic
20C2×#14556498C2211yescharacteristic
21C2×#14556498C2211yescharacteristic
22C22×C4⋊C4×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25C4⋊#10596833—42no—
26C22⋊#10596833—22no—
27C22⋊#10596833—24no—
28C22⋊#10596833Q814yes—
29C4×#10596833—42no—
30C23×Dic73C2×C411yescharacteristic
31C23×Dic73C2×C411yescharacteristic
32C23×Dic73C2×C411yescharacteristic
33C23×Dic73C2311yescharacteristic
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73—21no—
36C2×C4⋊Dic73—42no—
37C2×C4×Dic73—42no—
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C23×C4×C73C2×C411yescharacteristic
51C23×C4×C73C2×C411yescharacteristic
52C23×C4×C73C2×C411yescharacteristic
53C2×C4⋊C4×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73—22no—
56C2×C4⋊C4×C73C814yescomplemented
57C2×#10596833—24no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—22no—
68C22×Dic73—22no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73—41no—
72C22×Dic73—41no—
73C22×Dic73—41no—
74C22×Dic73—41no—
75C22×Dic73—41no—
76C22×Dic73C22⋊C411yescharacteristic
77C22×Dic73C22⋊C411yescharacteristic
78C22×Dic73C2×D411yescharacteristic
79C22×Dic73C2×D411yescharacteristic
80C22×Dic73C2×Q812yes—
81C22×Dic73#4112yes—
82C4⋊Dic73—42no—
83C4⋊Dic73—42no—
84C4×Dic73—22no—
85C4×Dic73—22no—
86C4×Dic73—41no—
87C4×Dic73—41no—
88C24×C73C22×C411yescharacteristic
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73—21no—
93C22×C4×C73—41no—
94C22×C4×C73—41no—
95C22×C4×C73—41no—
96C22×C4×C73—41no—
97C22×C4×C73—41no—
98C22×C4×C73—41no—
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C2×C812yes—
102C22×C4×C73C2×C812yes—
103C22×C4×C73C2×C812yes—
104C22×C4×C73M1612yes—
105C4⋊C4×C73—24no—
106C4⋊C4×C73—24no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73C2×C22⋊C411yescharacteristic
112C23×C73C4×Q812yes—
113C23×C73C22×C811yescharacteristic
114C23×C73C2×M1611yescharacteristic
115C23×C73#13112yes—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—22no—
121C2×C4×C73—22no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—42no—
131C2×C4×C73—42no—
132C2×C4×C73C22⋊C812yes—
133C2×C4×C73C22⋊C812yes—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—42no—
144C2×Dic73—42no—
145C2×Dic73—44no—
146C2×Dic73—41no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—82no—
153C2×Dic73—82no—
154C2×Dic73#9912yes—
155C2×Dic73C22⋊Q812yes—
156C2×Dic73#12411yescharacteristic
157C2×Dic73C4⋊Q811yescharacteristic
158#10596833—44no—
159#10596833—82no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—22no—
167C22×C73—22no—
168C22×C73#39111yescharacteristic
169C22×C73C2×C22⋊C811yescharacteristic
170C22×C73#40811yescharacteristic
171C22×C73C2×#9911yescharacteristic
172C22×C73#41011yescharacteristic
173C22×C73#41311yescharacteristic
174C22×C73#41311yescharacteristic
175C22×C73C8×Q812yes—
176C22×C73#44612yes—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—42no—
180C4×C73—42no—
181Dic73—22no—
182Dic73—22no—
183Dic73—21no—
184Dic73—21no—
185Dic73—41no—
186Dic73—81no—
187Dic73—81no—
188#9880—731nomaximal, Sylow
189C2×C73—22no—
190C2×C73—22no—
191C2×C73#145811yescharacteristic
192C2×C73#145911yescharacteristic
193C2×C73#146811yescharacteristic
194C2×C73#147311yescharacteristic
195C2×C73#198411yescharacteristic
196C2×C73#199611yescharacteristic
197C2×C73#199811yescharacteristic
198C2×#387—731no—
199#1797—731no—
200C4×C22⋊C8—731no—
201#1280—732no—
202#1280—732no—
203C73#988011yescharacteristic, complemented, Sylow
204C22×C4⋊C4—731no—
205C22×C4⋊C4#6440811yescharacteristic
206C22×C42—731no—
207C2×C4⋊C8—1461no—
208C2×C22⋊C8—732no—
209C2×C22⋊C8—732no—
210C2×C4×C8—1461no—
211#387—1461no—
212#387—1461no—
213#387—1461no—
214#387—1461no—
215C2×#95—731no—
216C2×#95—731no—
217C2×#95—731no—
218C2×#95—731no—
219#336—1461no—
220#336—1461no—
221C23×C4—731no—
222C23×C4—731no—
223C23×C4—731no—
224C23×C4—731no—
225C23×C4C2×#6440811yescharacteristic
226C23×C4C2×#6440811yescharacteristic
227C23×C4C2×#6440811yescharacteristic
228C22×C8—1462no—
229C22×C8—1462no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—2922no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4#1059683314yescomplemented
237C2×C42—2922no—
238C2×C42—731no—
239C2×C42—731no—
240C2×C42—731no—
241C2×C42—731no—
242C4⋊C8—2922no—
243C22⋊C8—734no—
244C22⋊C8—1464no—
245C22⋊C8—1462no—
246C4×C8—2922no—
247#95—1461no—
248#95—1461no—
249#95—1461no—
250#95—1461no—
251#95—1461no—
252#95—1461no—
253#95—1461no—
254#95—1461no—
255C24C22×#6440811yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—2921no—
273C22×C4—732no—
274C22×C4—732no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4—1462no—
284C22×C4—1462no—
285C22×C4C22⋊#6440811yescharacteristic
286C22×C4C22⋊#6440811yescharacteristic
287C22×C4C2×#1059683312yes—
288C22×C4C2×#1059683312yes—
289C22×C4C2×#1059683312yes—
290C22×C4#1192403712yes—
291C2×C8—2922no—
292C2×C8—2922no—
293C2×C8—2922no—
294C2×C8—2922no—
295C2×C8—2922no—
296C2×C8—1464no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—2922no—
300C4⋊C4—2922no—
301C42—2921no—
302C42—2921no—
303C42—1462no—
304C42—1462no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23C2×C22⋊#6440811yescharacteristic
310C23Q8×#6440812yes—
311C23C22×#1059683311yescharacteristic
312C23C2×#1192403711yescharacteristic
313C23#1455667912yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—2924no—
331C2×C4—2921no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—5842no—
340C2×C4—5842no—
341C2×C4—731no—
342C2×C4—732no—
343C2×C4—731no—
344C2×C4—732no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1461no—
354C2×C4C22⋊#1059683312yes—
355C2×C4C22⋊#1059683312yes—
356C8—2924no—
357C8—5842no—
358C22—22no—
359C22—22no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22(C2×#64408)⋊Q811yescharacteristic
367C22C2×C22⋊#1059683311yescharacteristic
368C22#1798956211yescharacteristic
369C22D73⋊#9911yescharacteristic
370C22#1798956611yescharacteristic
371C22#1798957311yescharacteristic
372C22#1798957411yescharacteristic
373C22Q8×#1059683312yes—
374C22#1798963812yes—
375C4—22no—
376C4—22no—
377C4—42no—
378C4—42no—
379C4—2921no—
380C4—5841no—
381C4—5841no—
382C4—1462no—
383C4—1461no—
384C4—1461no—
385C4—1462no—
386C2—22no—
387C2—22no—
388C2#2262516211yescharacteristic
389C2#2262516711yescharacteristic
390C2#2262519911yescharacteristic
391C2#2262521411yescharacteristic
392C2#2262610011yescharacteristic
393C2#2262612211yescharacteristic
394C2#2262612511yescharacteristic
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#9880
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
56. C2×C4⋊C4×C73C8semidirect
203. C73#9880semidirect
236. C2×C4⋊C4#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
#226247692
C2×#179884732
#988073