Finite Group Databasebeta

← #32981429

Subgroups — #32981429

Order 18688.

456 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619014C211yesmaximal, characteristic
2C2×#17988695C211yesmaximal, characteristic
3#22608327C211yesmaximal, characteristic
4#22608325C211yesmaximal, characteristic
5#22608254C211yesmaximal, characteristic
6#22607762C211yesmaximal, characteristic
7C73×#1281C211yesmaximal, characteristic
8C22×Dic292C411yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10C2×C4×Dic146C2211yescharacteristic
11#17988717—22no—
12#17988714—22no—
13#17988695—22no—
14#17988695—22no—
15#17988641—22no—
16#17988640C2211yescharacteristic
17#17988640C2211yescharacteristic
18C2×#14556523C411yescharacteristic
19C2×#14556516C411yescharacteristic
20C2×#14556516C411yescharacteristic
21#17988319—22no—
22#17988317—22no—
23#17988312—22no—
24#431×C73C2211yescharacteristic
25#431×C73C2211yescharacteristic
26C2×#97×C73C2211yescharacteristic
27C22×Dic146C2×C411yescharacteristic
28C22×Dic146C2×C411yescharacteristic
29C2×Dic292—22no—
30C2×Dic292—22no—
31C2×Dic292—22no—
32C4×Dic146—21no—
33C4×Dic146—21no—
34C4×Dic146—21no—
35C4×Dic146—21no—
36C4×Dic146—21no—
37C4×Dic146—21no—
38C4×Dic146D412yes—
39C4×Dic146D412yes—
40C2×C4⋊Dic73C2×C411yescharacteristic
41C2×C4⋊Dic73C2×C411yescharacteristic
42C2×#11924007—21no—
43C2×#11924007—21no—
44C2×C4×Dic73—21no—
45C2×C4×Dic73—21no—
46#14556523—22no—
47C4⋊#10596831—21no—
48C4⋊#10596831—21no—
49#14556520—24no—
50#14556516—22no—
51#14556516—22no—
52C22⋊#10596831—21no—
53C22⋊#10596831—21no—
54#14556501—24no—
55C4×#10596831—21no—
56C4×#10596831D412yes—
57C22×C8×C73C2×C411yescharacteristic
58C22×C8×C73C2×C411yescharacteristic
59C2×C42×C73C2311yescharacteristic
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C22⋊C8×C73—21no—
63C22⋊C8×C73D412yes—
64#97×C73—21no—
65#97×C73—21no—
66C4×C8×C73—21no—
67C4×C8×C73—21no—
68C2×Dic146—21no—
69C2×Dic146—21no—
70C2×Dic146—21no—
71C2×Dic146—21no—
72C2×Dic146—21no—
73C2×Dic146—21no—
74C2×Dic146—21no—
75C2×Dic146—21no—
76C2×Dic146—21no—
77C2×Dic146—21no—
78C2×Dic146C22⋊C412yes—
79C2×Dic146M1612yes—
80C22×Dic73—21no—
81C22×Dic73—21no—
82C22×Dic73—21no—
83C22×Dic73—21no—
84Dic292—28no—
85C2×#10596831—22no—
86C2×#10596831—41no—
87C4⋊Dic73—21no—
88C4⋊Dic73—21no—
89C4⋊Dic73—21no—
90C4⋊Dic73C22⋊C412yes—
91#11924007—22no—
92#11924007—22no—
93#11924007—41no—
94#11924007—41no—
95C4×Dic73—22no—
96C4×Dic73—22no—
97C4×Dic73—41no—
98C4×Dic73—41no—
99C22×C4×C73C22×C411yescharacteristic
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73#4111yescharacteristic
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—21no—
105C2×C8×C73—22no—
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73—41no—
109C2×C8×C73M1612yes—
110C42×C73C2×D411yescharacteristic
111C42×C73C2×D411yescharacteristic
112C42×C73C2×D411yescharacteristic
113C42×C73#4111yescharacteristic
114C23×C73C4×D411yescharacteristic
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73C2×C22⋊C411yescharacteristic
118C2×C4×C73C4×D411yescharacteristic
119C2×C4×C73#12011yescharacteristic
120C2×C4×C73#12111yescharacteristic
121C2×C4×C73#12111yescharacteristic
122C2×C4×C73#12311yescharacteristic
123C2×C4×C73C2×M1611yescharacteristic
124C2×C4×C73C2×M1611yescharacteristic
125C2×C4×C73#13111yescharacteristic
126C2×C4×C73#13111yescharacteristic
127C2×Dic73—22no—
128C2×Dic73—22no—
129C2×Dic73—22no—
130C2×Dic73—41no—
131C2×Dic73—41no—
132C2×Dic73—41no—
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—81no—
136C2×Dic73—81no—
137Dic146—22no—
138Dic146—22no—
139Dic146—22no—
140Dic146—22no—
141Dic146—41no—
142Dic146—41no—
143Dic146—41no—
144Dic146—41no—
145C8×C73—22no—
146C8×C73—42no—
147C8×C73—41no—
148C8×C73—81no—
149#10596831—42no—
150#10596831—81no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73#38611yescharacteristic
154C22×C73#43511yescharacteristic
155C22×C73#43611yescharacteristic
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73#40711yescharacteristic
161C4×C73#40811yescharacteristic
162C4×C73#43511yescharacteristic
163C4×C73#43611yescharacteristic
164Dic73—42no—
165Dic73—42no—
166Dic73—42no—
167Dic73—81no—
168#9092—731nomaximal, Sylow
169C2×C73—21no—
170C2×C73—21no—
171C2×C73#187011yescharacteristic
172C2×C73#190211yescharacteristic
173C2×C73#190511yescharacteristic
174#2983—731no—
175C2×#441—731no—
176#1479—731no—
177#1479—731no—
178#1461—731no—
179#1281D7311yescharacteristic
180#1275—731no—
181C73#909211yescharacteristic, complemented, Sylow
182C22×Q16—731no—
183C2×C4×Q8—731no—
184C2×C4×Q8—731no—
185#446—1462no—
186#446—1462no—
187#441—1462no—
188#441—1462no—
189#432—1462no—
190#431—731no—
191#431—731no—
192#431C2×D7311yescharacteristic
193#431C2×D7311yescharacteristic
194C2×#106—731no—
195C2×#103—731no—
196C2×#103—731no—
197C2×#97C2×D7311yescharacteristic
198Q8⋊C8—1462no—
199Q8⋊C8—1462no—
200#324—1462no—
201C22×Q8—731no—
202C22×Q8—731no—
203C2×Q16—1462no—
204C2×Q16—1462no—
205C2×Q16—1462no—
206C22×C8C4×D7311yescharacteristic
207C22×C8C4×D7311yescharacteristic
208C4×Q8—732no—
209C4×Q8—732no—
210C4×Q8—1461no—
211C4×Q8—1461no—
212C4×Q8—1461no—
213C4×Q8—1461no—
214C4×Q8—1461no—
215C4×Q8—1461no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—731no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C42—1461no—
221C2×C42—1461no—
222C2×C42C22×D7311yescharacteristic
223#106—1462no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—1464no—
227C4⋊C8—1461no—
228C4⋊C8—1461no—
229#103—1462no—
230#103—1462no—
231C22⋊C8—21no—
232C22⋊C8—1461no—
233C22⋊C8—1461no—
234C22⋊C8D29212yes—
235#97—21no—
236#97—21no—
237#97—1464no—
238C4×C8—21no—
239C4×C8—21no—
240C4×C8—732no—
241C4×C8—1461no—
242C2×Q8—732no—
243C2×Q8—732no—
244C2×Q8—1461no—
245C2×Q8—1461no—
246C2×Q8—1461no—
247C2×Q8—1461no—
248C2×Q8—1461no—
249C2×Q8—1461no—
250C2×Q8—1461no—
251C2×Q8—1461no—
252C2×Q8—1461no—
253C2×Q8—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4C2×C4×D7311yescharacteristic
259C22×C4C2×D29211yescharacteristic
260C22×C4#1192402811yescharacteristic
261Q16—1468no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—41no—
269C2×C8—2921no—
270C2×C8—1462no—
271C2×C8#1192401112yes—
272C4⋊C4—2921no—
273C4⋊C4—2921no—
274C4⋊C4—732no—
275C4⋊C4—1461no—
276C4⋊C4—1461no—
277C4⋊C4—1461no—
278C4⋊C4—1462no—
279C4⋊C4—1462no—
280C42—2921no—
281C42—2921no—
282C42—1462no—
283C42—1462no—
284C42D4×D7311yescharacteristic
285C42D4×D7311yescharacteristic
286C42D4×D7311yescharacteristic
287C42#1192402911yescharacteristic
288C23C4×D29211yescharacteristic
289Q8—2921no—
290Q8—2921no—
291Q8—2921no—
292Q8—2921no—
293Q8—1462no—
294Q8—1462no—
295Q8—1462no—
296Q8—1462no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—2921no—
300C2×C4—2921no—
301C2×C4—2921no—
302C2×C4—2921no—
303C2×C4—2921no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—1462no—
307C2×C4—1462no—
308C2×C4—1462no—
309C2×C4C22⋊C4×D7311yescharacteristic
310C2×C4#1455655311yescharacteristic
311C2×C4#1455656111yescharacteristic
312C2×C4#1455656411yescharacteristic
313C2×C4#1455656611yescharacteristic
314C2×C4#1455657611yescharacteristic
315C2×C4M16×D7311yescharacteristic
316C2×C4C2×#1192401111yescharacteristic
317C2×C4#1455659711yescharacteristic
318C2×C4#1455659911yescharacteristic
319C8—22no—
320C8—42no—
321C8—41no—
322C8—81no—
323C8—2922no—
324C8—5841no—
325C22—21no—
326C22—21no—
327C22#1798846511yescharacteristic
328C22#1798866011yescharacteristic
329C22#1798866611yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—2922no—
335C4—2922no—
336C4—2922no—
337C4—5841no—
338C4#1798854911yescharacteristic
339C4#1798855211yescharacteristic
340C4#1798865711yescharacteristic
341C4#1798866411yescharacteristic
342C2—21no—
343C2—21no—
344C2#2261022711yescharacteristic
345C2#2261040311yescharacteristic
346C2#2261042411yescharacteristic
subgroupG/H
centerC22#17988465
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1281C2
socleC22×C73#386
prime radicalC23×C73C4×D4
cosocleC2×C42×C73C23
hypercenter#1281D73
hypocenterC73#9092
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
181. C73#9092semidirect

Maximal subgroups

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

subgroupindex
#226190142
C2×#179886952
#226083272
#226083252
#226082542
#226077622
C73×#12812
#909273