Finite Group Databasebeta

← #32997102

Subgroups — #32997102

Order 18688.

452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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#22615285C211yesmaximal, characteristic
2#22608249C211yesmaximal, characteristic
3#22607954C212yesmaximal, complemented
4#22607951C212yesmaximal, complemented
5C73×#1799C211yesmaximal, characteristic
6C2×C4×Dic146C411yescharacteristic, complemented
7C2×C22⋊#10596831—21no—
8#17988523C411yescharacteristic, complemented
9#17988523C2211yescharacteristic
10#17988499C411yescharacteristic, complemented
11#17988499C2211yescharacteristic
12#17988490—21no—
13#17988483—21no—
14#17988460—21no—
15#17988460—21no—
16#17988453C411yescharacteristic, complemented
17#17988313—21no—
18#17988311C2212yes—
19C2×C4×D4×C73C2211yescharacteristic
20C2×#99×C73—21no—
21#380×C73—21no—
22#342×C73C2212yes—
23C22×Dic146C2×C411yescharacteristic
24C22×#10596831—41no—
25C4×Dic146—41no—
26C4×Dic146—41no—
27C2×C4⋊Dic73—21no—
28C2×C4⋊Dic73C2×C411yescharacteristic
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×C22⋊Dic73—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73—21no—
36C2×C4×Dic73—21no—
37C22⋊#10596831—22no—
38C22⋊#10596831—41no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498C2×C411yescharacteristic
43#14556498C2×C411yescharacteristic
44C22×D4×C73D411yescharacteristic
45C23×C4×C73D411yescharacteristic
46C23×C4×C73D411yescharacteristic
47C4×D4×C73—41no—
48C4×D4×C73—41no—
49C2×C4⋊C4×C73—41no—
50C2×C4⋊C4×C73D411yescharacteristic
51C2×C22⋊C4×C73—22no—
52C2×C22⋊C4×C73C2×C411yescharacteristic
53C2×C22⋊C4×C73C2311yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55#99×C73—42no—
56#95×C73—41no—
57C2×Dic146—41no—
58C2×Dic146—42no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C2×#10596831—42no—
64C2×#10596831—82no—
65C4⋊Dic73—42no—
66C4⋊Dic73—41no—
67#11924007—41no—
68#11924007—41no—
69#11924007—81no—
70#11924007—81no—
71C22⋊Dic73—42no—
72C22⋊Dic73—42no—
73C22⋊Dic73—81no—
74C22⋊Dic73—81no—
75C4×Dic73—42no—
76C24×C73C22⋊C411yescharacteristic
77C24×C73C2×D411yescharacteristic
78C2×D4×C73—41no—
79C2×D4×C73—41no—
80C2×D4×C73SD1612yes—
81C2×D4×C73Q1612yes—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—42no—
87C22×C4×C73—81no—
88C22×C4×C73—81no—
89C22×C4×C73C22⋊C411yescharacteristic
90C22×C4×C73C22⋊C411yescharacteristic
91C22×C4×C73C22⋊C411yescharacteristic
92C22×C4×C73C22×C411yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C4⋊C4×C73—41no—
95C4⋊C4×C73—82no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—42no—
99C22⋊C4×C73—42no—
100C42×C73—21no—
101C42×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73—21no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73—41no—
110C23×C73#10312yes—
111C23×C73C2×C22⋊C411yescharacteristic
112C23×C73C2×SD1611yescharacteristic
113C23×C73C2×Q1611yescharacteristic
114D4×C73—42no—
115D4×C73—42no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—41no—
122C2×C4×C73—42no—
123C2×C4×C73—42no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73—41no—
127C2×C4×C73—81no—
128C2×C4×C73—81no—
129C2×C4×C73—82no—
130C2×C4×C73—82no—
131C2×C4×C73—82no—
132C2×C4×C73#9911yescharacteristic
133C2×C4×C73#9911yescharacteristic
134C2×C4×C73#10312yes—
135C2×Dic73—22no—
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—
145C2×Dic73—41no—
146C2×Dic73—41no—
147Dic146—42no—
148Dic146—42no—
149#10596831—82no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—22no—
154C22×C73—21no—
155C22×C73—42no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—81no—
163C22×C73—81no—
164C22×C73C2×#9911yescharacteristic
165C22×C73C2×#10311yescharacteristic
166C22×C73#42111yescharacteristic
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—22no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—162no—
174Dic73—42no—
175Dic73—81no—
176Dic73—81no—
177Dic73—81no—
178#11897—731nomaximal, Sylow
179C2×C73—21no—
180C2×C73—21no—
181C2×C73—41no—
182C2×C73—42no—
183C2×C73—41no—
184C2×C73#152011yescharacteristic
185C2×C73#212011yescharacteristic
186C2×C73#212711yescharacteristic
187#2580—731no—
188#1799D7311yescharacteristic
189#1459—731no—
190#1352—732no—
191#1351—732no—
192C73#1189711yescharacteristic, complemented, Sylow
193C2×C4×Q8—731no—
194C2×C4×D4C2×D7311yescharacteristic
195C2×#99—21no—
196C2×C22⋊C8—1461no—
197#399—731no—
198#399—731no—
199#393—731no—
200#393—731no—
201#390—1461no—
202#389—1461no—
203#385—1461no—
204#385—1461no—
205#382—731no—
206#380—21no—
207#342C2×D7312yes—
208#324—1461no—
209#323—732no—
210C22×Q8—731no—
211C22×D4C22⋊D7311yescharacteristic
212C23×C4D29211yescharacteristic
213C23×C4C22⋊D7311yescharacteristic
214C22×C8—2921no—
215C4×Q8—2921no—
216C4×Q8—2921no—
217C4×D4—41no—
218C4×D4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—731no—
221C2×C4⋊C4—1461no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4D29211yescharacteristic
226C2×C22⋊C4—22no—
227C2×C22⋊C4—1461no—
228C2×C22⋊C4—1461no—
229C2×C22⋊C4—1461no—
230C2×C22⋊C4—1461no—
231C2×C22⋊C4C4×D7311yescharacteristic
232C2×C22⋊C4C22×D7311yescharacteristic
233C2×C42—1461no—
234C2×C42C4×D7311yescharacteristic
235#99—42no—
236C22⋊C8—2921no—
237C22⋊C8—1462no—
238#95—41no—
239#95—731no—
240#95—731no—
241#95—1461no—
242#95—1461no—
243#95—1461no—
244C24#1192400511yescharacteristic
245C24C2×C22⋊D7311yescharacteristic
246C2×Q8—2921no—
247C2×Q8—2922no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4#1192401612yes—
251C2×D4#1192401812yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4#1192400511yescharacteristic
264C22×C4#1192400511yescharacteristic
265C22×C4#1192400511yescharacteristic
266C22×C4C2×C4×D7311yescharacteristic
267C22×C4C2×D29211yescharacteristic
268C2×C8—2922no—
269C2×C8—5842no—
270C4⋊C4—41no—
271C4⋊C4—82no—
272C4⋊C4—2921no—
273C4⋊C4—2922no—
274C4⋊C4—2921no—
275C4⋊C4—2921no—
276C4⋊C4—5841no—
277C4⋊C4—5841no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—2922no—
283C22⋊C4—2922no—
284C22⋊C4—5841no—
285C22⋊C4—5841no—
286C42—21no—
287C42—21no—
288C42—2922no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1455651412yes—
298C23C2×#1192400511yescharacteristic
299C23C2×#1192401611yescharacteristic
300C23C2×#1192401811yescharacteristic
301Q8—2922no—
302Q8—2922no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—82no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2921no—
325C2×C4—2921no—
326C2×C4—2921no—
327C2×C4—2921no—
328C2×C4—2921no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2921no—
332C2×C4—1462no—
333C2×C4#1455650511yescharacteristic
334C2×C4#1455650511yescharacteristic
335C2×C4#1455651412yes—
336C8—5842no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—42no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—81no—
350C22—81no—
351C22C2×#1455650511yescharacteristic
352C22C2×#1455651411yescharacteristic
353C22#1798860511yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—162no—
361C4—2922no—
362C4—5841no—
363C4—5841no—
364C4—5841no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—42no—
369C2—41no—
370C2#2260850211yescharacteristic
371C2#2261157011yescharacteristic
372C2#2261159811yescharacteristic
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#11897
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. #22607954C2semidirect
4. #22607951C2semidirect
6. C2×C4×Dic146C4semidirect
8. #17988523C4semidirect
10. #17988499C4semidirect
16. #17988453C4semidirect
192. C73#11897semidirect

Maximal subgroups

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

subgroupindex
#226152852
#226082492
#226079542
#226079512
C73×#17992
#1189773