Finite Group Databasebeta

← #34003203

Subgroups — #34003203

Order 18688.

994 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 156 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#22626375C212yesmaximal
2#22624830C214yesmaximal
3#22612310C211yesmaximal, characteristic
4C2×#14556670—22no—
5#17989530—22no—
6#17989529—22no—
7#17989529C414yescomplemented
8#17989528C2214yes—
9C4×C22⋊#64408—22no—
10C4×C22⋊#64408C414yescomplemented
11C23×C4×D73C2211yescharacteristic
12C2×#14556550C411yescharacteristic, complemented
13#17988448C412yescomplemented
14#17988444—22no—
15#17988442C2212yes—
16C4×#11924005—22no—
17C2×#117×C73C411yescharacteristic, complemented
18#14556670—44no—
19#14556670—44no—
20C2×C4⋊#64408—24no—
21C2×C22⋊#64408—24no—
22C2×C22⋊#64408—24no—
23C2×C22⋊#64408C2×C418yes—
24C2×C4×#64408—24no—
25(C2×#64408)⋊C4—24no—
26(C2×#64408)⋊C4—24no—
27C24×D73C2311yescharacteristic
28C23×Dic73C2×C411yescharacteristic
29C22×C4×D73—42no—
30C22×C4×D73—42no—
31C22×C4×D73C2×C412yes—
32C22×C4×D73C2×C412yes—
33C22×C4×D73D412yes—
34C22×C4×D73D412yes—
35C22×C4×D73D411yescharacteristic
36C22×C4×D73D411yescharacteristic
37C22×C4×D73Q811yescharacteristic
38C22×C4×D73Q811yescharacteristic
39#14556550—42no—
40C2×C4⋊Dic73—21no—
41C2×C22⋊Dic73C2×C412yes—
42C2×#11924005—24no—
43C2×C4×Dic73—21no—
44#14556498—24no—
45C23×C4×C73C2×C411yescharacteristic
46#117×C73—42no—
47C2×C4⋊C4×C73—21no—
48C2×C22⋊C4×C73C2×C412yes—
49C2×C42×C73—21no—
50C22×#64408—28no—
51C4⋊#64408—48no—
52C22⋊#64408—48no—
53C22⋊#64408—44no—
54C22⋊#64408—44no—
55C22⋊#64408—48no—
56C4×#64408—48no—
57C23×D73—44no—
58C23×D73—41no—
59C23×D73—41no—
60C23×D73C22×C412yes—
61C23×D73C2×D411yescharacteristic
62C23×D73C2×D412yes—
63C23×D73C2×Q811yescharacteristic
64C22×Dic73—22no—
65C22×Dic73—41no—
66C22×Dic73—41no—
67C22×Dic73C4212yes—
68C22×Dic73C22⋊C412yes—
69C22×Dic73C4⋊C411yescharacteristic
70C22×Dic73C4⋊C411yescharacteristic
71C2×C4×D73—24no—
72C2×C4×D73—24no—
73C2×C4×D73—44no—
74C2×C4×D73—44no—
75C2×C4×D73—42no—
76C2×C4×D73—42no—
77C2×C4×D73—42no—
78C2×C4×D73—42no—
79C2×C4×D73—42no—
80C2×C4×D73—42no—
81C2×C4×D73C22⋊C412yes—
82C2×C4×D73C22⋊C412yes—
83C2×C4×D73C22⋊C412yes—
84C2×C4×D73C22⋊C412yes—
85C2×C4×D73C4⋊C412yes—
86C2×C4×D73C4⋊C412yes—
87C2×C4×D73C4⋊C412yes—
88C2×C4×D73C4⋊C412yes—
89C4⋊Dic73—42no—
90C22⋊Dic73—42no—
91#11924005—48no—
92C4×Dic73—42no—
93C24×C73C22×C411yescharacteristic
94C22×C4×C73—22no—
95C22×C4×C73—22no—
96C22×C4×C73—22no—
97C22×C4×C73C4211yescharacteristic
98C22×C4×C73C4211yescharacteristic
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C4⋊C411yescharacteristic
102C22×C4×C73C4⋊C411yescharacteristic
103C4⋊C4×C73—42no—
104C22⋊C4×C73—42no—
105C42×C73—42no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—42no—
109C23×C73C2×C4211yescharacteristic
110C23×C73C2×C22⋊C411yescharacteristic
111C23×C73C2×C4⋊C411yescharacteristic
112C22×D73—22no—
113C22×D73—22no—
114C22×D73—24no—
115C22×D73—24no—
116C22×D73—24no—
117C22×D73—42no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73—42no—
121C22×D73—42no—
122C22×D73—42no—
123C22×D73—48no—
124C22×D73—48no—
125C22×D73C2×C22⋊C412yes—
126C22×D73C2×C4⋊C412yes—
127C2×#64408—48no—
128C2×#64408—48no—
129C2×#64408—48no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—22no—
133C2×C4×C73—22no—
134C2×C4×C73—22no—
135C2×C4×C73—22no—
136C2×C4×C73—44no—
137C2×C4×C73—42no—
138C2×C4×C73#9511yescharacteristic
139C2×C4×C73#9511yescharacteristic
140C2×C4×C73#9511yescharacteristic
141C2×C4×C73#9511yescharacteristic
142C2×C4×C73#9912yes—
143C2×C4×C73#9912yes—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—42no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—44no—
150C2×Dic73—42no—
151C2×Dic73#9512yes—
152C2×Dic73#9512yes—
153C4×D73—24no—
154C4×D73—24no—
155C4×D73—24no—
156C4×D73—24no—
157C4×D73—42no—
158C4×D73—42no—
159C4×D73—42no—
160C4×D73—42no—
161C22×C73—22no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—22no—
165C22×C73—22no—
166C22×C73—42no—
167C22×C73—42no—
168C22×C73C2×#9511yescharacteristic
169C22×C73C2×#9911yescharacteristic
170C22×C73C2×#9911yescharacteristic
171C2×D73—22no—
172C2×D73—22no—
173C2×D73—22no—
174C2×D73—22no—
175C2×D73—22no—
176C2×D73—44no—
177C2×D73—44no—
178C2×D73—44no—
179C2×D73—48no—
180C2×D73—44no—
181C2×D73#41014yes—
182#64408—88no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—82no—
186C4×C73#34212yes—
187C4×C73#34212yes—
188Dic73—22no—
189Dic73—22no—
190Dic73—82no—
191#8100—731nomaximal, Sylow
192C2×C73—21no—
193C2×C73—21no—
194C2×C73—41no—
195C2×C73—41no—
196C2×C73C2×#34211yescharacteristic
197C2×C73#174012yes—
198D73—24no—
199D73—42no—
200#2280—731no—
201#2280—732no—
202#1304—734no—
203C73#810011yescharacteristic, complemented, Sylow
204C24×C4—731no—
205C2×#117—731no—
206C2×#117—1462no—
207C2×#117#6440811yescharacteristic, complemented
208#381—732no—
209#381—1462no—
210#380—734no—
211#380—1462no—
212#380—1462no—
213#379—734no—
214#379—732no—
215C4×C22⋊C4—734no—
216C4×C22⋊C4—1462no—
217C4×C22⋊C4—1462no—
218C25—731no—
219C23×C4—2922no—
220C23×C4—2922no—
221C23×C4—731no—
222C23×C4—732no—
223C23×C4—732no—
224C23×C4—732no—
225C23×C4—731no—
226C23×C4—731no—
227C23×C4—731no—
228C23×C4—731no—
229C23×C4—732no—
230C23×C4C2×#6440811yescharacteristic
231#117—42no—
232#117—2924no—
233#117—2924no—
234#117—2922no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1464no—
237C2×C4⋊C4—1461no—
238C2×C22⋊C4—738no—
239C2×C22⋊C4—732no—
240C2×C22⋊C4—1464no—
241C2×C22⋊C4—1464no—
242C2×C22⋊C4—1464no—
243C2×C22⋊C4C2×#6440812yes—
244C2×C42—21no—
245C2×C42—1464no—
246C2×C42—1461no—
247#95—1464no—
248#95—1464no—
249#95—1464no—
250C24—2921no—
251C24—2921no—
252C24—2924no—
253C24—731no—
254C24—732no—
255C24—732no—
256C24—731no—
257C24C22×#6440811yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—2922no—
262C22×C4—2922no—
263C22×C4—2924no—
264C22×C4—2924no—
265C22×C4—2922no—
266C22×C4—2922no—
267C22×C4—2922no—
268C22×C4—2922no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—732no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—732no—
275C22×C4—732no—
276C22×C4—732no—
277C22×C4—732no—
278C22×C4—732no—
279C22×C4—732no—
280C22×C4—732no—
281C22×C4—732no—
282C22×C4—732no—
283C22×C4—1468no—
284C22×C4—1462no—
285C22×C4—1464no—
286C22×C4—1464no—
287C22×C4C4×#6440811yescharacteristic
288C22×C4C4×#6440811yescharacteristic
289C22×C4C22⋊#6440811yescharacteristic
290C22×C4C22⋊#6440811yescharacteristic
291C22×C4C4⋊#6440811yescharacteristic
292C22×C4C4⋊#6440811yescharacteristic
293C4⋊C4—42no—
294C4⋊C4—2922no—
295C4⋊C4—2928no—
296C22⋊C4—42no—
297C22⋊C4—2928no—
298C22⋊C4—2928no—
299C22⋊C4—2924no—
300C22⋊C4—2924no—
301C22⋊C4—2922no—
302C22⋊C4—2928no—
303C42—42no—
304C42—2928no—
305C42—2922no—
306C23—21no—
307C23—21no—
308C23—42no—
309C23—2922no—
310C23—2921no—
311C23—2921no—
312C23—2922no—
313C23—2922no—
314C23—2922no—
315C23—2928no—
316C23—2928no—
317C23—732no—
318C23—732no—
319C23—1464no—
320C23—1464no—
321C23—1464no—
322C23—1462no—
323C23—1462no—
324C23C2×C4×#6440811yescharacteristic
325C23C2×C22⋊#6440811yescharacteristic
326C23C2×C4⋊#6440811yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—2922no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2924no—
340C2×C4—2928no—
341C2×C4—2928no—
342C2×C4—2928no—
343C2×C4—2922no—
344C2×C4—2922no—
345C2×C4—2921no—
346C2×C4—2921no—
347C2×C4—732no—
348C2×C4—732no—
349C2×C4—1462no—
350C2×C4—1462no—
351C2×C4—1464no—
352C2×C4—1464no—
353C2×C4—1464no—
354C2×C4—1464no—
355C2×C4(C2×#64408)⋊C411yescharacteristic
356C2×C4(C2×#64408)⋊C411yescharacteristic
357C2×C4(C2×#64408)⋊C411yescharacteristic
358C2×C4(C2×#64408)⋊C411yescharacteristic
359C2×C4#1455664912yes—
360C2×C4#1455665012yes—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—2924no—
369C22—2924no—
370C22—2924no—
371C22—2928no—
372C22—2924no—
373C22—734no—
374C22—1462no—
375C22—1462no—
376C22—1462no—
377C22—1462no—
378C22—1462no—
379C22C2×(C2×#64408)⋊C411yescharacteristic
380C22C2×#1455664911yescharacteristic
381C22C2×#1455665011yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—5842no—
386C4—5848no—
387C4—1462no—
388C4—1462no—
389C4#1798946512yes—
390C4#1798946512yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—2922no—
396C2—1464no—
397C2C2×#1798946511yescharacteristic
398C2#2262562912yes—
subgroupG/H
centerC2×C4(C2×#64408)⋊C4
commutatorC23×C73C2×C42
FrattiniC24C22×#64408
FittingC2×#117×C73C4
socleC22×C73C2×#95
prime radical, cosocleC24×D73C23
hypercenterC2×#117#64408
hypocenterC73#8100
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
7. #17989529C4semidirect
10. C4×C22⋊#64408C4semidirect
12. C2×#14556550C4semidirect
13. #17988448C4semidirect
17. C2×#117×C73C4semidirect
203. C73#8100semidirect
207. C2×#117#64408semidirect

Maximal subgroups

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

subgroupindex
#226263752
#226248302
#226123102
#810073