Finite Group Databasebeta

← #32996773

Subgroups — #32996773

Order 18688.

414 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615848C211yesmaximal, characteristic
2#22608272C211yesmaximal, characteristic
3#22607951C212yesmaximal, complemented
4#22607930C212yesmaximal, complemented
5C73×#1799C211yesmaximal, characteristic
6C2×#14556570C411yescharacteristic, complemented
7#17988644—21no—
8#17988517C411yescharacteristic, complemented
9#17988515—21no—
10#17988512C2211yescharacteristic
11#17988507C411yescharacteristic, complemented
12#17988501—21no—
13#17988499C2211yescharacteristic
14#17988471—21no—
15#17988460—21no—
16#17988450C411yescharacteristic, complemented
17#17988311—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21#380×C73—21no—
22#342×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24#14556570—41no—
25#14556570—41no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×#11924007—21no—
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×C22⋊Dic73—21no—
31C2×C22⋊Dic73—21no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73—21no—
34C4⋊#10596831—41no—
35C22⋊#10596831—22no—
36#14556502—41no—
37#14556498—21no—
38#14556498—21no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C22×D4×C73D411yescharacteristic
45C23×C4×C73C2×C411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73—41no—
50C2×C4⋊C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73—22no—
52C2×C22⋊C4×C73D411yescharacteristic
53C2×C22⋊C4×C73C2311yescharacteristic
54C2×C42×C73D411yescharacteristic
55#99×C73—42no—
56#95×C73—41no—
57C2×Dic146—41no—
58C2×Dic146—81no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C2×#10596831—42no—
64C4⋊Dic73—41no—
65#11924007—42no—
66#11924007—41no—
67#11924007—41no—
68#11924007—81no—
69C22⋊Dic73—42no—
70C22⋊Dic73—41no—
71C22⋊Dic73—41no—
72C22⋊Dic73—81no—
73C22⋊Dic73—81no—
74C24×C73C22⋊C411yescharacteristic
75C24×C73C2×D411yescharacteristic
76C2×D4×C73—21no—
77C2×D4×C73—21no—
78C2×D4×C73—41no—
79C2×D4×C73—41no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—42no—
85C22×C4×C73—81no—
86C22×C4×C73—81no—
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22⋊C411yescharacteristic
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22×C411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C4⋊C4×C73—41no—
93C4⋊C4×C73—82no—
94C22⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—42no—
97C22⋊C4×C73—42no—
98C42×C73—21no—
99C42×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73C2×C22⋊C411yescharacteristic
110C23×C73AGL(1,ℤ/8)11yescharacteristic
111C23×C73#13711yescharacteristic
112D4×C73—42no—
113D4×C73—42no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—41no—
121C2×C4×C73—42no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73—81no—
128C2×C4×C73—82no—
129C2×C4×C73—82no—
130C2×C4×C73—82no—
131C2×C4×C73#9911yescharacteristic
132C2×C4×C73#9911yescharacteristic
133C2×Dic73—41no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145Dic146—82no—
146#10596831—82no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—41no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—81no—
159C22×C73—81no—
160C22×C73—81no—
161C22×C73C2×#9911yescharacteristic
162C22×C73#41711yescharacteristic
163C22×C73#42111yescharacteristic
164C4×C73—21no—
165C4×C73—21no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—162no—
171Dic73—81no—
172Dic73—81no—
173Dic73—81no—
174Dic73—81no—
175#11826—731nomaximal, Sylow
176C2×C73—21no—
177C2×C73—21no—
178C2×C73—41no—
179C2×C73—41no—
180C2×C73—81no—
181C2×C73#151311yescharacteristic
182C2×C73#212111yescharacteristic
183C2×C73#212911yescharacteristic
184#2638—731no—
185#1799D7311yescharacteristic
186#1466—731no—
187#1351—732no—
188#1344—732no—
189C73#1182611yescharacteristic, complemented, Sylow
190C2×C22⋊Q8—731no—
191C2×C4×D4C2×D7311yescharacteristic
192#432—1461no—
193C2×#99—21no—
194#398—731no—
195#397—731no—
196#397—1461no—
197#395—731no—
198#394—1461no—
199#393—731no—
200#387—1461no—
201#385—1461no—
202#381—731no—
203#380—21no—
204#342C2×D7312yes—
205#323—732no—
206#323—1461no—
207C22×Q8—731no—
208C22×D4C22⋊D7311yescharacteristic
209C23×C4C4×D7311yescharacteristic
210C23×C4C22⋊D7311yescharacteristic
211C22⋊Q8—2921no—
212C22⋊Q8—2921no—
213C4×D4—41no—
214C4×D4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4—1461no—
220C2×C4⋊C4C4×D7311yescharacteristic
221C2×C22⋊C4—22no—
222C2×C22⋊C4—1461no—
223C2×C22⋊C4—1461no—
224C2×C22⋊C4—1461no—
225C2×C22⋊C4—1461no—
226C2×C22⋊C4D29211yescharacteristic
227C2×C22⋊C4C22×D7311yescharacteristic
228C2×C42D29211yescharacteristic
229C4⋊C8—2921no—
230#99—42no—
231C22⋊C8—1462no—
232#97—2921no—
233#95—41no—
234#95—731no—
235#95—731no—
236#95—1461no—
237#95—1461no—
238#95—1461no—
239#95—1461no—
240#95—1461no—
241C24#1192400511yescharacteristic
242C24C2×C22⋊D7311yescharacteristic
243C2×Q8—2921no—
244C2×Q8—5841no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—1461no—
257C22×C4—1461no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4#1192400511yescharacteristic
261C22×C4#1192400511yescharacteristic
262C22×C4#1192400511yescharacteristic
263C22×C4C2×C4×D7311yescharacteristic
264C22×C4C2×D29211yescharacteristic
265C2×C8—2922no—
266C4⋊C4—41no—
267C4⋊C4—82no—
268C4⋊C4—2921no—
269C4⋊C4—2922no—
270C4⋊C4—2921no—
271C4⋊C4—2921no—
272C4⋊C4—5841no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C22⋊C4—2922no—
278C22⋊C4—2921no—
279C22⋊C4—2921no—
280C22⋊C4—5841no—
281C22⋊C4—5841no—
282C42—21no—
283C42—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23C2×#1192400511yescharacteristic
294C23#1455661711yescharacteristic
295C23#1455662211yescharacteristic
296Q8—5842no—
297D4—42no—
298D4—42no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4#1455650511yescharacteristic
329C2×C4#1455650511yescharacteristic
330C8—5842no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22C2×#1455650511yescharacteristic
346C22#1798858611yescharacteristic
347C22#1798860511yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—162no—
355C4—5841no—
356C4—5841no—
357C4—5841no—
358C4—5841no—
359C2—21no—
360C2—21no—
361C2—41no—
362C2—41no—
363C2—81no—
364C2#2260847211yescharacteristic
365C2#2261157511yescharacteristic
366C2#2261160511yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1799C2
socleC22×C73C2×#99
prime radicalC22×D4×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1799D73
hypocenterC73#11826
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #22607951C2semidirect
4. #22607930C2semidirect
6. C2×#14556570C4semidirect
8. #17988517C4semidirect
11. #17988507C4semidirect
16. #17988450C4semidirect
189. C73#11826semidirect

Maximal subgroups

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

subgroupindex
#226158482
#226082722
#226079512
#226079302
C73×#17992
#1182673