Finite Group Databasebeta

← #34004907

Subgroups — #34004907

Order 18688.

496 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22625864C211yesmaximal, characteristic
2#22625847C211yesmaximal, characteristic
3C2×#17989446C212yesmaximal
4#22624809C212yesmaximal
5#22612502C211yesmaximal, characteristic
6C2×#14556658—21no—
7C2×#14556658C2212yes—
8C2×#14556658C2212yes—
9C2×C4⋊#10596833—21no—
10#17989453—21no—
11#17989453—21no—
12#17989446—24no—
13C2×#14556590C2211yescharacteristic
14C2×#14556556—21no—
15#17988491—21no—
16#17988485C411yescharacteristic
17#17988482—21no—
18#17988456C2211yescharacteristic
19C4⋊C4×Dic73C411yescharacteristic
20C4⋊C4×Dic73C411yescharacteristic
21#17988438—21no—
22C42×Dic73C2211yescharacteristic
23#389×C73C411yescharacteristic
24C22×#10596833—22no—
25C22×#10596833—22no—
26#14556658—22no—
27#14556658—22no—
28#14556658—22no—
29#14556658—22no—
30#14556658—42no—
31C4⋊#10596833—42no—
32C22×Dic146—21no—
33#14556590—21no—
34#14556590—21no—
35#14556590D412yes—
36#14556590Q812yes—
37#14556556—44no—
38C2×C4⋊Dic73C2×C411yescharacteristic
39C2×C4⋊Dic73C2×C411yescharacteristic
40C2×#11924007—21no—
41C2×#11924007—21no—
42C2×#11924007—21no—
43C2×#11924007—21no—
44C2×C4×Dic73—21no—
45C2×C4×Dic73—21no—
46C2×C4×Dic73C2×C411yescharacteristic
47C2×C4×Dic73D411yescharacteristic
48C2×C4×Dic73D411yescharacteristic
49C2×C4×Dic73D411yescharacteristic
50C2×C4×Dic73D411yescharacteristic
51C2×C4×Dic73C2311yescharacteristic
52#14556498—21no—
53#14556498—21no—
54#14556498—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73C2×C411yescharacteristic
57C2×C4⋊C4×C73C2×C411yescharacteristic
58C2×C42×C73C2×C411yescharacteristic
59#95×C73—21no—
60C2×#10596833—42no—
61C2×#10596833—42no—
62C2×#10596833—42no—
63C2×#10596833—42no—
64C2×#10596833—42no—
65C2×#10596833—42no—
66C2×Dic146—22no—
67C2×Dic146—22no—
68C2×Dic146—42no—
69C2×Dic146—42no—
70C22×Dic73—21no—
71C22×Dic73—21no—
72C22×Dic73C22⋊C411yescharacteristic
73C22×Dic73C22⋊C411yescharacteristic
74C22×Dic73C2×D411yescharacteristic
75C22×Dic73C2×D411yescharacteristic
76C4⋊Dic73—21no—
77C4⋊Dic73—41no—
78C4⋊Dic73C4⋊C412yes—
79#11924007—22no—
80#11924007—22no—
81#11924007—42no—
82#11924007—41no—
83#11924007—42no—
84#11924007—41no—
85C4×Dic73—22no—
86C4×Dic73—22no—
87C4×Dic73—22no—
88C4×Dic73—21no—
89C4×Dic73—21no—
90C4×Dic73—42no—
91C4×Dic73—42no—
92C4×Dic73SD1612yes—
93C4×Dic73Q1612yes—
94C4×Dic73C2×D411yescharacteristic
95C4×Dic73C2×Q811yescharacteristic
96C4×Dic73#4111yescharacteristic
97C4×Dic73#4111yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C22⋊C411yescharacteristic
102C22×C4×C73C22×C411yescharacteristic
103C4⋊C4×C73—21no—
104C4⋊C4×C73—41no—
105C4⋊C4×C73—42no—
106C4⋊C4×C73C4⋊C412yes—
107C42×C73—41no—
108C23×C73C2×C22⋊C411yescharacteristic
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—22no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—41no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73#10312yes—
123C2×C4×C73C2×C4⋊C411yescharacteristic
124C2×C4×C73#11711yescharacteristic
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—22no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73#10112yes—
136C2×Dic73#10312yes—
137C2×Dic73#12111yescharacteristic
138C2×Dic73#12111yescharacteristic
139C2×Dic73C22⋊Q811yescharacteristic
140C2×Dic73C22⋊Q811yescharacteristic
141C2×Dic73C2×SD1611yescharacteristic
142C2×Dic73C2×Q1611yescharacteristic
143C2×Dic73#13512yes—
144C2×Dic73AGL(1,ℤ/8)11yescharacteristic
145C2×Dic73AGL(1,ℤ/8)12yes—
146C2×Dic73#13711yescharacteristic
147Dic146—44no—
148Dic146—44no—
149#10596833—82no—
150#10596833—82no—
151C22×C73#38011yescharacteristic
152C22×C73C2×#10111yescharacteristic
153C22×C73#41311yescharacteristic
154C22×C73C2×#10311yescharacteristic
155C22×C73#41611yescharacteristic
156C22×C73#41711yescharacteristic
157C22×C73#41811yescharacteristic
158C4×C73—22no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—42no—
162C4×C73—41no—
163C4×C73—81no—
164Dic73—22no—
165Dic73—22no—
166Dic73—42no—
167Dic73—81no—
168Dic73#46011yescharacteristic
169Dic73#46211yescharacteristic
170Dic73#46312yes—
171Dic73#47511yescharacteristic
172Dic73#47711yescharacteristic
173Dic73#47812yes—
174#8591—731nomaximal, Sylow
175C2×C73#154211yescharacteristic
176C2×C73#154911yescharacteristic
177C2×C73#155211yescharacteristic
178C2×C73#155711yescharacteristic
179C2×C73#180111yescharacteristic
180C2×C73#180311yescharacteristic
181C2×C73#180411yescharacteristic
182C4×C4⋊Q8—731no—
183#1842—731no—
184#1831—731no—
185C2×#332—732no—
186#1296—732no—
187C73#859111yescharacteristic, complemented, Sylow
188C2×C4⋊Q8—731no—
189C2×C4×Q8—1461no—
190C2×C4⋊C8—732no—
191C2×C4⋊C8—732no—
192C2×C4⋊C8—1461no—
193C2×C4⋊C8—1461no—
194#391—1461no—
195#389—731no—
196#389—1461no—
197#389#6440811yescharacteristic
198#384—731no—
199C4×C4⋊C4—731no—
200C4×C4⋊C4—731no—
201C4×C4⋊C4—1461no—
202C43—731no—
203#336—1461no—
204#336—1461no—
205#332—1464no—
206C22×Q8—1461no—
207C22×C8—1462no—
208C22×C8—1462no—
209C4⋊Q8—732no—
210C4⋊Q8—732no—
211C4⋊Q8—1461no—
212C4⋊Q8—1461no—
213C4×Q8—2924no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4—1461no—
221C2×C4⋊C4C2×#6440811yescharacteristic
222C2×C4⋊C4C2×#6440811yescharacteristic
223C2×C42—731no—
224C2×C42—731no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—731no—
228C2×C42—731no—
229C2×C42—1461no—
230C2×C42—1461no—
231C2×C42C2×#6440811yescharacteristic
232C4⋊C8—2922no—
233C4⋊C8—2922no—
234C4⋊C8—1462no—
235C4⋊C8—1462no—
236C4⋊C8—1462no—
237C4⋊C8—1462no—
238#95—21no—
239#95—1461no—
240#95—1461no—
241#95—1461no—
242C2×Q8—2922no—
243C2×Q8—2922no—
244C2×Q8—1462no—
245C2×Q8—1462no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—731no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—1461no—
253C22×C4—1461no—
254C22×C4C22⋊#6440811yescharacteristic
255C22×C4C22⋊#6440811yescharacteristic
256C22×C4C22×#6440811yescharacteristic
257C2×C8—2922no—
258C2×C8—2922no—
259C2×C8—2922no—
260C2×C8—2922no—
261C2×C8—2922no—
262C2×C8—2922no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—2921no—
267C4⋊C4—2922no—
268C4⋊C4—2921no—
269C4⋊C4—2921no—
270C4⋊C4—2922no—
271C4⋊C4—732no—
272C4⋊C4—1462no—
273C4⋊C4—1462no—
274C4⋊C4—1461no—
275C4⋊C4C4⋊#6440812yes—
276C42—41no—
277C42—2922no—
278C42—2922no—
279C42—732no—
280C42—732no—
281C42—731no—
282C42—731no—
283C42—731no—
284C42—731no—
285C42—1461no—
286C42—1462no—
287C42—1462no—
288C42—1461no—
289C42—1462no—
290C23C2×C22⋊#6440811yescharacteristic
291Q8—2924no—
292Q8—2924no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—2921no—
307C2×C4—2921no—
308C2×C4—2921no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—731no—
312C2×C4—731no—
313C2×C4—731no—
314C2×C4—731no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—732no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—732no—
321C2×C4—732no—
322C2×C4—732no—
323C2×C4—1462no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4#1455665412yes—
329C2×C4C2×C4⋊#6440811yescharacteristic
330C2×C4#1455667011yescharacteristic
331C8—5842no—
332C8—5842no—
333C22#1798952911yescharacteristic
334C22D73⋊#10111yescharacteristic
335C22#1798957411yescharacteristic
336C22C2×#1455665411yescharacteristic
337C22#1798957711yescharacteristic
338C22#1798957811yescharacteristic
339C22#1798957911yescharacteristic
340C4—21no—
341C4—21no—
342C4—22no—
343C4—42no—
344C4—41no—
345C4—81no—
346C4—2922no—
347C4—5841no—
348C4—731no—
349C4—731no—
350C4—731no—
351C4—731no—
352C4—732no—
353C4—732no—
354C4—1462no—
355C4—1462no—
356C2#2262543311yescharacteristic
357C2#2262544711yescharacteristic
358C2#2262545311yescharacteristic
359C2#2262546311yescharacteristic
360C2#2262579811yescharacteristic
361C2#2262580011yescharacteristic
362C2#2262580111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#389×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#389#64408
hypocenterC73#8591
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
187. C73#8591semidirect

Maximal subgroups

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

subgroupindex
#226258642
#226258472
C2×#179894462
#226248092
#226125022
#859173