Finite Group Databasebeta

← #32996695

Subgroups — #32996695

Order 18688.

616 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#17988523C211yesmaximal, characteristic
2#22608258C211yesmaximal, characteristic
3#22607954C214yesmaximal, complemented
4C73×#1819C211yesmaximal, characteristic
5C22×C4⋊Dic73C411yescharacteristic, complemented
6C22×#11924007—21no—
7C22×C22⋊Dic73—21no—
8#17988551—21no—
9#17988523—21no—
10#17988523—21no—
11#17988523C412yescomplemented
12#17988523C2212yes—
13C2×#14556498C411yescharacteristic, complemented
14#17988311—21no—
15#17988311C2212yes—
16C22×C22⋊C4×C73C2211yescharacteristic
17#379×C73—21no—
18#342×C73—21no—
19#342×C73C2212yes—
20C23×Dic73—21no—
21C23×Dic73—21no—
22C2×#11924012—41no—
23C2×C4⋊Dic73—21no—
24C2×C4⋊Dic73—41no—
25C2×C4⋊Dic73—41no—
26C2×C4⋊Dic73C2×C412yes—
27C2×#11924007—22no—
28C2×#11924007—22no—
29C2×#11924007—44no—
30C2×C22⋊Dic73—22no—
31C2×C22⋊Dic73—22no—
32C2×C22⋊Dic73—44no—
33C22⋊#10596831—22no—
34C22⋊#10596831—41no—
35#14556498—21no—
36#14556498C2×C412yes—
37C25×C73D411yescharacteristic
38C23×C4×C73C2×C411yescharacteristic
39C23×C4×C73D411yescharacteristic
40C2×C22⋊C4×C73—22no—
41C2×C22⋊C4×C73—41no—
42C2×C22⋊C4×C73—41no—
43C2×C22⋊C4×C73—41no—
44C2×C22⋊C4×C73—41no—
45C2×C22⋊C4×C73C2×C411yescharacteristic
46C2×C22⋊C4×C73D411yescharacteristic
47C2×C22⋊C4×C73D411yescharacteristic
48C2×C22⋊C4×C73C2311yescharacteristic
49C22×Dic73—24no—
50C22×Dic73—22no—
51C22×Dic73—22no—
52C22×Dic73—42no—
53C22×Dic73—42no—
54C22×Dic73—42no—
55C22×Dic73—42no—
56C22×Dic73—41no—
57C22×Dic73—41no—
58#11924012—82no—
59C2×#10596831—42no—
60C4⋊Dic73—42no—
61C4⋊Dic73—42no—
62#11924007—44no—
63#11924007—44no—
64C22⋊Dic73—44no—
65C22⋊Dic73—44no—
66C24×C73—22no—
67C24×C73—21no—
68C24×C73—21no—
69C24×C73—41no—
70C24×C73—42no—
71C24×C73—42no—
72C24×C73C22⋊C411yescharacteristic
73C24×C73C22⋊C411yescharacteristic
74C24×C73C2×D411yescharacteristic
75C22×C4×C73—21no—
76C22×C4×C73—21no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—42no—
80C22×C4×C73—42no—
81C22×C4×C73—42no—
82C22×C4×C73C22⋊C411yescharacteristic
83C22×C4×C73C22⋊C411yescharacteristic
84C22×C4×C73C22×C411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22⋊C4×C73—41no—
87C22⋊C4×C73—41no—
88C22⋊C4×C73—41no—
89C22⋊C4×C73—41no—
90C22⋊C4×C73—42no—
91C22⋊C4×C73—42no—
92C22⋊C4×C73—82no—
93C22⋊C4×C73—82no—
94C23×C73—22no—
95C23×C73—22no—
96C23×C73—21no—
97C23×C73—21no—
98C23×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—42no—
104C23×C73—42no—
105C23×C73—41no—
106C23×C73—41no—
107C23×C73—41no—
108C23×C73—41no—
109C23×C73—48no—
110C23×C73—42no—
111C23×C73—42no—
112C23×C73—81no—
113C23×C73—81no—
114C23×C73—84no—
115C23×C73#9911yescharacteristic
116C23×C73#9911yescharacteristic
117C23×C73C2×C22⋊C411yescharacteristic
118C23×C73#13712yes—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—42no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73—41no—
127C2×C4×C73—41no—
128C2×C4×C73—41no—
129C2×C4×C73—41no—
130C2×C4×C73—81no—
131C2×C4×C73—82no—
132C2×C4×C73—82no—
133C2×C4×C73—82no—
134C2×Dic73—24no—
135C2×Dic73—48no—
136C2×Dic73—42no—
137C2×Dic73—42no—
138C2×Dic73—42no—
139C2×Dic73—42no—
140C2×Dic73—42no—
141C2×Dic73—82no—
142C2×Dic73—82no—
143#10596831—82no—
144C22×C73—24no—
145C22×C73—24no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73—21no—
152C22×C73—22no—
153C22×C73—42no—
154C22×C73—42no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—41no—
160C22×C73—81no—
161C22×C73—84no—
162C22×C73—84no—
163C22×C73—81no—
164C22×C73#35212yes—
165C22×C73#35312yes—
166C22×C73C2×#9911yescharacteristic
167C22×C73#41911yescharacteristic
168C22×C73#42111yescharacteristic
169C4×C73—41no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73—162no—
174Dic73—44no—
175Dic73—82no—
176#11809—731nomaximal, Sylow
177C2×C73—21no—
178C2×C73—21no—
179C2×C73—22no—
180C2×C73—22no—
181C2×C73—42no—
182C2×C73—81no—
183C2×C73#151111yescharacteristic
184C2×C73C2×#35211yescharacteristic
185C2×C73C2×#35311yescharacteristic
186C2×#399—731no—
187#1819D7311yescharacteristic
188#1462—731no—
189#1352—734no—
190C73#1180911yescharacteristic, complemented, Sylow
191C22×C4⋊C4—731no—
192C22×C4⋊C4—1461no—
193C22×C22⋊C4—1461no—
194C22×C22⋊C4C2×D7311yescharacteristic
195#407—1461no—
196#399—732no—
197#399—732no—
198#399—1461no—
199#399—1461no—
200#379—21no—
201C2×#95—731no—
202#342—21no—
203#342C2×D7312yes—
204#323—732no—
205#323—1461no—
206C25C22⋊D7311yescharacteristic
207C23×C4—1461no—
208C23×C4—1461no—
209C23×C4C4×D7311yescharacteristic
210C23×C4D29211yescharacteristic
211C2×M16—2921no—
212C2×C4⋊C4—2921no—
213C2×C4⋊C4—2921no—
214C2×C4⋊C4—2924no—
215C2×C4⋊C4—732no—
216C2×C4⋊C4—1461no—
217C2×C4⋊C4—1462no—
218C2×C4⋊C4—1462no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—41no—
221C2×C22⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—41no—
224C2×C22⋊C4—2924no—
225C2×C22⋊C4—1462no—
226C2×C22⋊C4—1462no—
227C2×C22⋊C4C4×D7311yescharacteristic
228C2×C22⋊C4D29211yescharacteristic
229C2×C22⋊C4C22⋊D7311yescharacteristic
230C2×C22⋊C4C22×D7311yescharacteristic
231C22⋊C8—2921no—
232C22⋊C8—1462no—
233#95—732no—
234#95—1461no—
235C24—22no—
236C24—21no—
237C24—21no—
238C24—41no—
239C24—42no—
240C24—42no—
241C24#1192400511yescharacteristic
242C24#1192400511yescharacteristic
243C24C2×C22⋊D7311yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—2922no—
252C22×C4—2922no—
253C22×C4—2922no—
254C22×C4—2922no—
255C22×C4—2921no—
256C22×C4—2921no—
257C22×C4—1462no—
258C22×C4—1464no—
259C22×C4—1462no—
260C22×C4#1192400511yescharacteristic
261C22×C4#1192400511yescharacteristic
262C22×C4C2×C4×D7311yescharacteristic
263C22×C4C2×D29211yescharacteristic
264M16—5842no—
265C2×C8—2922no—
266C4⋊C4—2922no—
267C4⋊C4—2922no—
268C4⋊C4—2924no—
269C4⋊C4—2924no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—82no—
277C22⋊C4—82no—
278C22⋊C4—2924no—
279C22⋊C4—2924no—
280C23—22no—
281C23—22no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—42no—
290C23—42no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—48no—
296C23—42no—
297C23—42no—
298C23—81no—
299C23—81no—
300C23—84no—
301C23#1455650511yescharacteristic
302C23#1455650511yescharacteristic
303C23C2×#1192400511yescharacteristic
304C23#1455662112yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4—2928no—
321C2×C4—2922no—
322C2×C4—2922no—
323C2×C4—2922no—
324C2×C4—2922no—
325C2×C4—2922no—
326C2×C4—5842no—
327C2×C4—5842no—
328C2×C4—1464no—
329C8—5842no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—84no—
348C22—84no—
349C22—81no—
350C22#1798837612yes—
351C22#1798837912yes—
352C22C2×#1455650511yescharacteristic
353C22#1798859511yescharacteristic
354C22#1798860511yescharacteristic
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—162no—
360C4—2924no—
361C4—5842no—
362C2—21no—
363C2—21no—
364C2—22no—
365C2—22no—
366C2—42no—
367C2—81no—
368C2#2260846311yescharacteristic
369C2C2×#1798837611yescharacteristic
370C2C2×#1798837911yescharacteristic
subgroupG/H
centerC22C2×#14556505
commutatorC22×C4×C73C22×C4
FrattiniC2×C22⋊C4C22×D73
FittingC73×#1819C2
socleC22×C73C2×#99
prime radicalC25×C73D4
cosocleC2×C22⋊C4×C73C23
hypercenter#1819D73
hypocenterC73#11809
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #1819

Complements

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

NH ≅ G/Ntype
3. #22607954C2semidirect
5. C22×C4⋊Dic73C4semidirect
11. #17988523C4semidirect
13. C2×#14556498C4semidirect
190. C73#11809semidirect

Maximal subgroups

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

subgroupindex
C2×#179885232
#226082582
#226079542
C73×#18192
#1180973