Finite Group Databasebeta

← #34001386

Subgroups — #34001386

Order 18688.

522 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 110 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#22625823C211yesmaximal, characteristic
2C4×#14556648C211yesmaximal, characteristic
3#22624751C212yesmaximal, complemented
4#22624750C212yesmaximal, complemented
5C4×#14556567C211yesmaximal, characteristic
6C2×#14556648—21no—
7C2×#14556648—21no—
8C2×C4×#10596833—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×#14556567C411yescharacteristic
13C2×C42×D73C2211yescharacteristic
14#17988494C2211yescharacteristic
15#17988483C2211yescharacteristic
16#17988468—21no—
17#17988458—21no—
18#17988444C411yescharacteristic
19C4×#11924007—21no—
20C4×C4⋊Dic73C411yescharacteristic
21C4×#11924005—21no—
22C2×C4×Q8×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556648—24no—
26#14556648—42no—
27C4×#10596833—42no—
28C22×C4×D73C2×C411yescharacteristic
29C22×C4×D73D411yescharacteristic
30C22×C4×D73D411yescharacteristic
31#14556567—22no—
32#14556567C814yescomplemented
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924005—21no—
38C2×#11924005—21no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73D411yescharacteristic
41C2×C4×Dic73D411yescharacteristic
42C2×C4×Dic73C2311yescharacteristic
43C42×D73—42no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C22×Q8×C73C2×C411yescharacteristic
50C4×Q8×C73—42no—
51C2×C4⋊C4×C73—21no—
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C42×C73—21no—
54C2×C42×C73C2×C411yescharacteristic
55C2×#10596833—24no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C23×D73C22⋊C411yescharacteristic
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C2×D411yescharacteristic
66C22×Dic73C2×D411yescharacteristic
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—22no—
70C2×C4×D73—22no—
71C2×C4×D73—41no—
72C2×C4×D73—41no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73C2×C812yes—
76C2×C4×D73M1612yes—
77C4⋊Dic73—21no—
78C4⋊Dic73—41no—
79C4⋊Dic73C2×C812yes—
80#11924007—24no—
81#11924007—42no—
82#11924005—24no—
83#11924005—42no—
84C4×Dic73—22no—
85C4×Dic73—41no—
86C4×Dic73—41no—
87C4×Dic73—42no—
88C2×Q8×C73—21no—
89C2×Q8×C73—41no—
90C2×Q8×C73—41no—
91C2×Q8×C73C2×C812yes—
92C22×C4×C73—21no—
93C22×C4×C73—21no—
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22×C411yescharacteristic
97C4⋊C4×C73—41no—
98C4⋊C4×C73—42no—
99C42×C73—22no—
100C42×C73—42no—
101C23×C73C2×C22⋊C411yescharacteristic
102C22×D73—21no—
103C22×D73—21no—
104C22×D73—21no—
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73C22⋊C812yes—
109Q8×C73—42no—
110Q8×C73—42no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—22no—
118C2×C4×C73—41no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73#9912yes—
124C2×C4×C73#10412yes—
125C2×C4×C73C22×C811yescharacteristic
126C2×C4×C73C2×M1611yescharacteristic
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—22no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73C22⋊C812yes—
140C2×Dic73#13512yes—
141C2×Dic73#13712yes—
142C4×D73—42no—
143C4×D73—42no—
144C4×D73—44no—
145C4×D73—44no—
146#10596833—44no—
147#10596833—82no—
148C22×C73C2×C22⋊C811yescharacteristic
149C22×C73C2×#9911yescharacteristic
150C22×C73#41311yescharacteristic
151C22×C73#41611yescharacteristic
152C22×C73#41911yescharacteristic
153C22×C73C2×#10411yescharacteristic
154C22×C73#42111yescharacteristic
155C2×D73—22no—
156C2×D73—22no—
157C2×D73—22no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—22no—
165C4×C73—22no—
166C4×C73—42no—
167C4×C73—81no—
168Dic73—22no—
169Dic73—22no—
170Dic73—22no—
171Dic73—42no—
172Dic73—81no—
173#7583—731nomaximal, Sylow
174C2×C73#145911yescharacteristic
175C2×C73#147611yescharacteristic
176C2×C73#147911yescharacteristic
177C2×C73#150811yescharacteristic
178C2×C73#151611yescharacteristic
179C2×C73#152911yescharacteristic
180C2×C73#155411yescharacteristic
181D73—42no—
182C4×C22⋊Q8—731no—
183#1817—731no—
184C4×C22⋊C8—731no—
185#1272—732no—
186#1271—732no—
187C73#758311yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—731no—
189C2×C4×Q8#6440811yescharacteristic
190C22×C42—731no—
191C2×C22⋊C8—1461no—
192C2×C22⋊C8—1461no—
193C2×C4×C8—1461no—
194#391—731no—
195#389—731no—
196#387—1461no—
197#385—1461no—
198#380—731no—
199C4×C4⋊C4—731no—
200C4×C4⋊C4—1461no—
201C4×C22⋊C4—1461no—
202#336—732no—
203#336—732no—
204#336—1461no—
205C22×Q8C2×#6440811yescharacteristic
206C23×C4—731no—
207C23×C4—731no—
208C23×C4—731no—
209C22×C8—1462no—
210C22×C8—1462no—
211C22⋊Q8—734no—
212C22⋊Q8—1462no—
213C4×Q8—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217C2×C4⋊C4—1461no—
218C2×C4⋊C4—1461no—
219C2×C4⋊C4C2×#6440811yescharacteristic
220C2×C22⋊C4—1461no—
221C2×C22⋊C4—1461no—
222C2×C42—21no—
223C2×C42—2922no—
224C2×C42—731no—
225C2×C42—731no—
226C2×C42—731no—
227C2×C42—1461no—
228C2×C42C2×#6440811yescharacteristic
229C22⋊C8—2922no—
230C22⋊C8—1464no—
231C4×C8—2922no—
232#95—1461no—
233#95—1461no—
234#95—1461no—
235#95—1461no—
236#95—1461no—
237C24—731no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8#1192403612yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—2921no—
245C22×C4—2921no—
246C22×C4—2921no—
247C22×C4—2921no—
248C22×C4—732no—
249C22×C4—732no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—1462no—
254C22×C4—1462no—
255C22×C4—1461no—
256C22×C4—1461no—
257C22×C4—1462no—
258C22×C4—1462no—
259C22×C4C22⋊#6440811yescharacteristic
260C22×C4C22⋊#6440811yescharacteristic
261C22×C4C22×#6440811yescharacteristic
262C2×C8—2922no—
263C2×C8—2922no—
264C2×C8—2922no—
265C2×C8—2922no—
266C2×C8—2922no—
267C2×C8—1464no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—2921no—
271C4⋊C4—2922no—
272C4⋊C4—732no—
273C4⋊C4—1464no—
274C4⋊C4—1461no—
275C22⋊C4—2922no—
276C22⋊C4—1464no—
277C42—22no—
278C42—42no—
279C42—2921no—
280C42—2921no—
281C42—2922no—
282C42—1462no—
283C23—732no—
284C23—1461no—
285C23—1461no—
286C23—1461no—
287C23—1461no—
288C23—1461no—
289C23—1461no—
290C23C2×C22⋊#6440811yescharacteristic
291Q8—42no—
292Q8—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—2924no—
306C2×C4—2924no—
307C2×C4—2922no—
308C2×C4—2922no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—2921no—
314C2×C4—732no—
315C2×C4—732no—
316C2×C4—732no—
317C2×C4—1462no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4#1455664912yes—
325C2×C4#1455665612yes—
326C2×C4C2×#1192403611yescharacteristic
327C2×C4D73⋊M1611yescharacteristic
328C8—2924no—
329C8—5842no—
330C22—2921no—
331C22—2921no—
332C22—2921no—
333C22—2921no—
334C22—1462no—
335C22—1462no—
336C22—1462no—
337C22#1798955511yescharacteristic
338C22C2×#1455664911yescharacteristic
339C22#1798957311yescharacteristic
340C22#1798957711yescharacteristic
341C22#1798958011yescharacteristic
342C22C2×#1455665611yescharacteristic
343C22#1798958411yescharacteristic
344C4—22no—
345C4—22no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—2922no—
351C4—5841no—
352C4—1462no—
353C4—1462no—
354C4—1462no—
355C2—2922no—
356C2#2262516611yescharacteristic
357C2#2262522511yescharacteristic
358C2#2262523411yescharacteristic
359C2#2262533111yescharacteristic
360C2#2262535711yescharacteristic
361C2#2262539811yescharacteristic
362C2#2262545611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×Q8×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×C4×Q8#64408
hypocenterC73#7583
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #22624751C2semidirect
4. #22624750C2semidirect
32. #14556567C8semidirect
187. C73#7583semidirect

Maximal subgroups

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

subgroupindex
#226258232
C4×#145566482
#226247512
#226247502
C4×#145565672
#758373