Finite Group Databasebeta

← #34026805

Subgroups — #34026805

Order 18688.

868 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626028C212yesmaximal, complemented
2#22625989C214yesmaximal, complemented
3#22625786C212yesmaximal
4#22625786C211yesmaximal, characteristic
5#22625727C212yesmaximal, complemented
6#22625658C212yesmaximal
7C4×#14556648C211yesmaximal, characteristic
8C4×C4⋊C4×D73C211yesmaximal, characteristic
9C2×C4⋊#10596833C2212yes—
10C2×C4⋊#10596833C2214yes—
11C2×#14556648C2211yescharacteristic
12C2×#14556648C2212yes—
13C2×#14556648C2211yescharacteristic
14C2×#14556646C2214yes—
15C2×C4×#10596833C2212yes—
16#17989453C2212yes—
17#17989453C2214yes—
18#17989453C2214yes—
19#17989453C2212yes—
20C2×C4⋊C4×D73C411yescharacteristic
21C2×C4⋊C4×D73C411yescharacteristic
22C2×C42×D73C2211yescharacteristic
23C2×C42×D73C2212yes—
24C4⋊C4×Dic73C2211yescharacteristic
25C4⋊C4×Dic73C2211yescharacteristic
26C4×#11924007C412yes—
27C4×C4⋊Dic73C411yescharacteristic
28#17988438C2212yes—
29#95×D73C412yes—
30C4×C4⋊C4×C73C411yescharacteristic
31C22×#10596833C2312yes—
32C22×#10596833C2314yes—
33C22×#10596833C2312yes—
34C4⋊#10596833—24no—
35C4⋊#10596833—44no—
36#14556648—22no—
37#14556648—24no—
38#14556648Q814yes—
39#14556646—44no—
40C4×#10596833—24no—
41C22×C4×D73C2×C411yescharacteristic
42C22×C4×D73C2×C412yes—
43C22×C4×D73C2×C411yescharacteristic
44C22×C4×D73C2×C412yes—
45C22×C4×D73C2311yescharacteristic
46C2×C4⋊Dic73C2×C411yescharacteristic
47C2×C4⋊Dic73C2×C411yescharacteristic
48C2×#11924007C2×C412yes—
49C2×#11924007C2×C412yes—
50C4⋊C4×D73—24no—
51C4⋊C4×D73—24no—
52C2×C4×Dic73C2×C411yescharacteristic
53C2×C4×Dic73C2×C412yes—
54C2×C4×Dic73C2311yescharacteristic
55C2×C4×Dic73C2312yes—
56C2×C4×Dic73C2312yes—
57C2×C4×Dic73C2311yescharacteristic
58C42×D73—24no—
59C42×D73—44no—
60#14556498C2×C412yes—
61#14556498C2×C412yes—
62#14556498C2×C412yes—
63C2×C4⋊C4×C73C2×C411yescharacteristic
64C2×C4⋊C4×C73C2×C411yescharacteristic
65C2×C42×C73C2×C411yescharacteristic
66C2×C42×C73C2×C412yes—
67#95×C73C2×C412yes—
68C2×#10596833—22no—
69C2×#10596833—22no—
70C2×#10596833—22no—
71C2×#10596833—22no—
72C2×#10596833—24no—
73C2×#10596833—24no—
74C2×#10596833—24no—
75C2×#10596833—22no—
76C2×#10596833C2×Q814yes—
77C23×D73C22×C411yescharacteristic
78C22×Dic73C22×C412yes—
79C22×Dic73C22×C412yes—
80C22×Dic73C22×C411yescharacteristic
81C22×Dic73C22×C411yescharacteristic
82C22×Dic73C2411yescharacteristic
83C2×C4×D73—22no—
84C2×C4×D73—22no—
85C2×C4×D73—22no—
86C2×C4×D73—22no—
87C2×C4×D73—24no—
88C2×C4×D73—22no—
89C2×C4×D73—24no—
90C2×C4×D73—24no—
91C2×C4×D73—22no—
92C2×C4×D73—42no—
93C2×C4×D73—42no—
94C2×C4×D73—41no—
95C2×C4×D73—42no—
96C2×C4×D73M1614yes—
97C2×C4×D73C2×Q812yes—
98C2×C4×D73#4112yes—
99C4⋊Dic73—22no—
100C4⋊Dic73—22no—
101#11924007—24no—
102#11924007—24no—
103C4×Dic73—22no—
104C4×Dic73—22no—
105C4×Dic73—24no—
106C4×Dic73—24no—
107C4×Dic73—42no—
108C4×Dic73#4114yes—
109C22×C4×C73C22×C411yescharacteristic
110C22×C4×C73C22×C412yes—
111C22×C4×C73C22×C411yescharacteristic
112C22×C4×C73C22×C412yes—
113C22×C4×C73C22×C411yescharacteristic
114C4⋊C4×C73—22no—
115C4⋊C4×C73M1614yes—
116C42×C73—22no—
117C42×C73—42no—
118C23×C73C23×C411yescharacteristic
119C22×D73—21no—
120C22×D73—21no—
121C22×D73—21no—
122C22×D73—21no—
123C22×D73C4×Q812yes—
124C22×D73C2×M1612yes—
125C22×D73#13112yes—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—21no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—22no—
136C2×C4×C73#11712yes—
137C2×C4×C73C4×Q812yes—
138C2×C4×C73C2×M1612yes—
139C2×C4×C73C2×M1614yes—
140C2×C4×C73C2×M1612yes—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—22no—
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—22no—
149C2×Dic73—22no—
150C2×Dic73—22no—
151C2×Dic73#11712yes—
152C2×Dic73C2×M1612yes—
153C2×Dic73C22×Q811yescharacteristic
154C2×Dic73C2×#4111yescharacteristic
155C2×Dic73C2×#4112yes—
156C2×Dic73H(5,𝔽2)12yes—
157C4×D73—28no—
158C4×D73—24no—
159C4×D73—24no—
160C4×D73—44no—
161C4×D73—48no—
162C4×D73—48no—
163#10596833—24no—
164#10596833—42no—
165#10596833—44no—
166C22×C73C2×#11711yescharacteristic
167C22×C73C2×C4×Q811yescharacteristic
168C22×C73#51811yescharacteristic
169C22×C73C22×M1611yescharacteristic
170C22×C73C22×M1611yescharacteristic
171C22×C73C2×#13111yescharacteristic
172C22×C73#56811yescharacteristic
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—22no—
177C2×D73—22no—
178C2×D73—22no—
179C2×D73#44614yes—
180C4×C73—22no—
181C4×C73—24no—
182C4×C73—41no—
183C4×C73—42no—
184C4×C73#43214yes—
185Dic73—22no—
186Dic73—22no—
187Dic73—42no—
188Dic73—42no—
189Dic73#55312yes—
190Dic73#55412yes—
191#22629—731nomaximal, Sylow
192C2×C73#234511yescharacteristic
193C2×C73C2×#43211yescharacteristic
194C2×C73#292411yescharacteristic
195C2×C73C2×#44611yescharacteristic
196C2×C73Q8×M1611yescharacteristic
197C2×C73#297411yescharacteristic
198C2×C73#297511yescharacteristic
199D73—24no—
200C2×C4×C4⋊C4—731no—
201#1939—732no—
202#1917—734no—
203#1797—731no—
204#1797—732no—
205#1770—732no—
206#1749—732no—
207C4×C22⋊C8—731no—
208C73#2262911yescharacteristic, complemented, Sylow
209C22×C4⋊C4—731no—
210C22×C4⋊C4—731no—
211C22×C42—732no—
212C22×C42—731no—
213C2×C4⋊C8—734no—
214C2×C4⋊C8—732no—
215C2×C22⋊C8—731no—
216C2×C22⋊C8—731no—
217C2×C22⋊C8—732no—
218C2×#97—734no—
219C2×C4×C8—732no—
220C4×C4⋊C4—731no—
221C4×C4⋊C4—731no—
222C4×C4⋊C4—731no—
223C4×C4⋊C4—732no—
224C4×C4⋊C4—732no—
225C4×C4⋊C4#6440811yescharacteristic
226C2×#95—732no—
227#336—732no—
228#336—734no—
229#336—732no—
230#336—734no—
231C23×C4—732no—
232C23×C4—732no—
233C23×C4—731no—
234C23×C4—731no—
235C23×C4—731no—
236C22×C8—732no—
237C22×C8—732no—
238C22×C8—734no—
239C2×C4⋊C4—732no—
240C2×C4⋊C4—732no—
241C2×C4⋊C4—731no—
242C2×C4⋊C4—731no—
243C2×C4⋊C4—1464no—
244C2×C4⋊C4—1464no—
245C2×C4⋊C4C2×#6440811yescharacteristic
246C2×C4⋊C4C2×#6440811yescharacteristic
247C2×C42—2924no—
248C2×C42—732no—
249C2×C42—731no—
250C2×C42—731no—
251C2×C42—732no—
252C2×C42—732no—
253C2×C42—731no—
254C2×C42—1464no—
255C2×C42C2×#6440811yescharacteristic
256C2×C42C2×#6440812yes—
257C4⋊C8—2924no—
258C4⋊C8—1464no—
259C22⋊C8—734no—
260C22⋊C8—1462no—
261C22⋊C8—1464no—
262#97—2924no—
263C4×C8—1464no—
264#95—732no—
265#95—732no—
266#95—732no—
267#95C2×#6440812yes—
268C24—731no—
269C22×C4—2922no—
270C22×C4—2922no—
271C22×C4—2922no—
272C22×C4—2921no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—732no—
277C22×C4—732no—
278C22×C4—734no—
279C22×C4—732no—
280C22×C4—732no—
281C22×C4—1462no—
282C22×C4—1464no—
283C22×C4—1464no—
284C22×C4—1462no—
285C22×C4—1462no—
286C22×C4—1462no—
287C22×C4—1464no—
288C22×C4—1462no—
289C22×C4—1462no—
290C22×C4C22×#6440811yescharacteristic
291C22×C4C22×#6440812yes—
292C22×C4C22×#6440811yescharacteristic
293C22×C4C22×#6440812yes—
294C22×C4C22×#6440811yescharacteristic
295C2×C8—734no—
296C2×C8—1462no—
297C2×C8—1464no—
298C2×C8—1462no—
299C2×C8—1464no—
300C2×C8—1462no—
301C2×C8—1464no—
302C2×C8—1462no—
303C2×C8—1462no—
304C4⋊C4—22no—
305C4⋊C4—1464no—
306C4⋊C4—1462no—
307C4⋊C4—1464no—
308C4⋊C4—1462no—
309C4⋊C4#1192403814yes—
310C42—22no—
311C42—42no—
312C42—2922no—
313C42—734no—
314C42—1464no—
315C42—1464no—
316C42—1462no—
317C42—1462no—
318C23—732no—
319C23—732no—
320C23—732no—
321C23—1461no—
322C23—1461no—
323C23—1461no—
324C23—1461no—
325C23C23×#6440811yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—2928no—
337C2×C4—2928no—
338C2×C4—2924no—
339C2×C4—732no—
340C2×C4—731no—
341C2×C4—731no—
342C2×C4—732no—
343C2×C4—732no—
344C2×C4—732no—
345C2×C4—1464no—
346C2×C4—1464no—
347C2×C4—1462no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1468no—
358C2×C4#1455667012yes—
359C2×C4Q8×#6440812yes—
360C2×C4D73⋊M1612yes—
361C2×C4C2×#1192403814yes—
362C2×C4C2×#1192403812yes—
363C8—2922no—
364C8—2924no—
365C8—1464no—
366C22—734no—
367C22—1462no—
368C22—1462no—
369C22—1462no—
370C22—1462no—
371C22—1462no—
372C22—1462no—
373C22C2×#1455667011yescharacteristic
374C22C2×Q8×#6440811yescharacteristic
375C22#1798965411yescharacteristic
376C22C2×D73⋊M1611yescharacteristic
377C22C22×#1192403811yescharacteristic
378C22D73⋊#13111yescharacteristic
379C22#1798966611yescharacteristic
380C4—22no—
381C4—24no—
382C4—41no—
383C4—42no—
384C4—2922no—
385C4—2922no—
386C4—732no—
387C4—732no—
388C4—1462no—
389C4—1462no—
390C4#1798960914yes—
391C2—1464no—
392C2#2262644011yescharacteristic
393C2C2×#1798960911yescharacteristic
394C2#2262662511yescharacteristic
395C2D73⋊#44611yescharacteristic
396C2Q8×#1192403811yescharacteristic
397C2#2262679111yescharacteristic
398C2#2262679411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutator, socleC23×C73C23×C4
FittingC4×C4⋊C4×C73C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenterC4×C4⋊C4#64408
hypocenterC73#22629
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #22626028C2semidirect
2. #22625989C2semidirect
5. #22625727C2semidirect
208. C73#22629semidirect

Maximal subgroups

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

subgroupindex
#226260282
#226259892
#226257862
#226257272
#226256582
C4×#145566482
C4×C4⋊C4×D732
#2262973