Finite Group Databasebeta

← #32980510

Subgroups — #32980510

Order 18688.

628 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556570C211yesmaximal, characteristic
2C4×C22⋊#10596831C211yesmaximal, characteristic
3C2×#17988317C212yesmaximal, complemented
4#22607770C212yesmaximal, complemented
5C2×#431×C73C211yesmaximal, characteristic
6C2×#14556570C411yescharacteristic
7C2×C4×Dic146C2211yescharacteristic
8C2×C22⋊#10596831—21no—
9C2×C4×#10596831C2212yes—
10#17988493C411yescharacteristic
11#17988485C411yescharacteristic
12#17988471—21no—
13#17988460—21no—
14#17988447C411yescharacteristic
15C4×#11924007—21no—
16C4×C4⋊Dic73C2211yescharacteristic
17C4×C22⋊Dic73—21no—
18#17988342—21no—
19#17988317—24no—
20C22×C42×C73C2211yescharacteristic
21#431×C73—24no—
22C2×C4⋊C8×C73C2212yes—
23C2×C22⋊C8×C73—21no—
24C2×C4×C8×C73—21no—
25C22×Dic146C2×C411yescharacteristic
26C22×#10596831—22no—
27#14556570—22no—
28#14556570C814yescomplemented
29C4×Dic146—22no—
30C4×Dic146—22no—
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×#11924007—21no—
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×C22⋊Dic73—21no—
38C2×C22⋊Dic73—21no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—21no—
41C22⋊#10596831—24no—
42C4×#10596831—22no—
43C4×#10596831—22no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49C23×C4×C73C2×C411yescharacteristic
50C23×C4×C73D411yescharacteristic
51C23×C4×C73D411yescharacteristic
52C22×C8×C73—22no—
53C2×C42×C73—22no—
54C2×C42×C73—22no—
55C2×C42×C73C2×C411yescharacteristic
56C2×C42×C73D411yescharacteristic
57C2×C42×C73D411yescharacteristic
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—22no—
60C4⋊C8×C73D414yes—
61C22⋊C8×C73—24no—
62C4×C8×C73—24no—
63C2×Dic146—22no—
64C2×Dic146—22no—
65C2×Dic146—21no—
66C2×Dic146C2×C812yes—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—21no—
71C2×#10596831—24no—
72C2×#10596831—42no—
73C2×#10596831—42no—
74C4⋊Dic73—21no—
75C4⋊Dic73—22no—
76C4⋊Dic73—22no—
77C4⋊Dic73C2×C812yes—
78#11924007—24no—
79#11924007—42no—
80#11924007—42no—
81C22⋊Dic73—24no—
82C22⋊Dic73—42no—
83C4×Dic73—41no—
84C4×Dic73—41no—
85C4×Dic73—42no—
86C24×C73C22⋊C411yescharacteristic
87C22×C4×C73—22no—
88C22×C4×C73—22no—
89C22×C4×C73—22no—
90C22×C4×C73—21no—
91C22×C4×C73—22no—
92C22×C4×C73—21no—
93C22×C4×C73—22no—
94C22×C4×C73—22no—
95C22×C4×C73—41no—
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C2×C812yes—
100C22×C4×C73M1612yes—
101C22×C4×C73C22×C411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C2×C8×C73—24no—
105C2×C8×C73—42no—
106C2×C8×C73—42no—
107C42×C73—22no—
108C42×C73—21no—
109C42×C73—22no—
110C42×C73—21no—
111C42×C73C2×D412yes—
112C42×C73#4112yes—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73—21no—
119C23×C73C22⋊C812yes—
120C23×C73C2×C22⋊C411yescharacteristic
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—24no—
128C2×C4×C73—24no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—44no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73C22⋊C812yes—
136C2×C4×C73#10412yes—
137C2×C4×C73C4×D412yes—
138C2×C4×C73#12011yescharacteristic
139C2×C4×C73#12112yes—
140C2×C4×C73#12311yescharacteristic
141C2×C4×C73C22×C811yescharacteristic
142C2×C4×C73C2×M1611yescharacteristic
143C2×C4×C73#13112yes—
144C2×C4×C73#13512yes—
145C2×C4×C73#13712yes—
146C2×Dic73—22no—
147C2×Dic73—22no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158Dic146—24no—
159Dic146—42no—
160C8×C73—44no—
161#10596831—44no—
162C22×C73—22no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73#38611yescharacteristic
170C22×C73C2×C22⋊C811yescharacteristic
171C22×C73#40811yescharacteristic
172C22×C73#41611yescharacteristic
173C22×C73#41911yescharacteristic
174C22×C73C2×#10411yescharacteristic
175C22×C73#42111yescharacteristic
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—41no—
180C4×C73C8×D412yes—
181C4×C73#43512yes—
182C4×C73#45212yes—
183C4×C73#48512yes—
184Dic73—42no—
185Dic73—42no—
186Dic73—81no—
187Dic73—81no—
188#8938—731nomaximal, Sylow
189C2×C73—42no—
190C2×C73#147611yescharacteristic
191C2×C73#147911yescharacteristic
192C2×C73#148211yescharacteristic
193C2×C73#148511yescharacteristic
194C2×C73#186911yescharacteristic
195C2×C73#187111yescharacteristic
196C2×C73#187311yescharacteristic
197C2×#431D7311yescharacteristic
198C4×C22⋊Q8—731no—
199C4×C22⋊C8—731no—
200C2×Q8⋊C8—732no—
201#1279—732no—
202C73#893811yescharacteristic, complemented, Sylow
203C2×C22⋊Q8—731no—
204C2×C4×Q8—731no—
205C22×C42C2×D7311yescharacteristic
206#431—24no—
207C2×C4⋊C8C2×D7312yes—
208C2×C22⋊C8—21no—
209C2×C22⋊C8—1461no—
210C2×C4×C8—21no—
211C2×C4×C8—732no—
212#391—731no—
213#389—731no—
214#387—1461no—
215#385—1461no—
216#380—731no—
217C4×C4⋊C4—731no—
218C4×C4⋊C4—1461no—
219C4×C22⋊C4—1461no—
220#336—1461no—
221Q8⋊C8—1464no—
222C22×Q8—731no—
223C23×C4C4×D7311yescharacteristic
224C23×C4D29211yescharacteristic
225C23×C4C22⋊D7311yescharacteristic
226C22×C8—22no—
227C22×C8—1462no—
228C22⋊Q8—734no—
229C22⋊Q8—1462no—
230C4×Q8—1462no—
231C4×Q8—1462no—
232C2×C4⋊C4—731no—
233C2×C4⋊C4—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4—1461no—
237C2×C4⋊C4—1461no—
238C2×C22⋊C4—1461no—
239C2×C22⋊C4—1461no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—1461no—
243C2×C42—1461no—
244C2×C42C4×D7311yescharacteristic
245C2×C42D29211yescharacteristic
246C2×C42C22⋊D7311yescharacteristic
247C2×C42C22×D7311yescharacteristic
248C4⋊C8—22no—
249C4⋊C8C22⋊D7314yes—
250C22⋊C8—24no—
251C22⋊C8—1464no—
252C4×C8—24no—
253C4×C8—1462no—
254C4×C8—1462no—
255#95—1461no—
256#95—1461no—
257#95—1461no—
258#95—1461no—
259#95—1461no—
260C24#1192400511yescharacteristic
261C2×Q8—732no—
262C2×Q8—1462no—
263C2×Q8—1462no—
264C2×Q8—1461no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4#1192400511yescharacteristic
279C22×C4#1192400511yescharacteristic
280C22×C4#1192400511yescharacteristic
281C22×C4C8×D7312yes—
282C22×C4#1192401112yes—
283C22×C4C2×C4×D7311yescharacteristic
284C22×C4C2×C22⋊D7311yescharacteristic
285C22×C4C2×D29211yescharacteristic
286C2×C8—24no—
287C2×C8—42no—
288C2×C8—42no—
289C2×C8—2922no—
290C2×C8—2922no—
291C2×C8—1464no—
292C4⋊C4—2922no—
293C4⋊C4—2922no—
294C4⋊C4—732no—
295C4⋊C4—1462no—
296C4⋊C4—1462no—
297C4⋊C4—1464no—
298C4⋊C4—1461no—
299C22⋊C4—2922no—
300C22⋊C4—1464no—
301C42—22no—
302C42—21no—
303C42—22no—
304C42—21no—
305C42—2921no—
306C42—2921no—
307C42—2922no—
308C42C2×C22⋊D7312yes—
309C42#1192402812yes—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23#1455650312yes—
317C23C2×#1192400511yescharacteristic
318Q8—2922no—
319Q8—1464no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2921no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—1462no—
345C2×C4—1462no—
346C2×C4#1455650312yes—
347C2×C4#1455651712yes—
348C2×C4C4×C22⋊D7312yes—
349C2×C4#1455656011yescharacteristic
350C2×C4#1455656512yes—
351C2×C4#1455657411yescharacteristic
352C2×C4C2×C8×D7311yescharacteristic
353C2×C4C2×#1192401111yescharacteristic
354C2×C4#1455659712yes—
355C2×C4#1455661112yes—
356C2×C4#1455662112yes—
357C8—44no—
358C8—2924no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22#1798846611yescharacteristic
367C22C2×#1455650311yescharacteristic
368C22#1798855311yescharacteristic
369C22#1798858111yescharacteristic
370C22#1798859511yescharacteristic
371C22C2×#1455651711yescharacteristic
372C22#1798860311yescharacteristic
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—2922no—
378C4—2922no—
379C4—5841no—
380C4—5841no—
381C4C8×C22⋊D7312yes—
382C4#1798865812yes—
383C4#1798874912yes—
384C4#1798892812yes—
385C2—42no—
386C2#2260831111yescharacteristic
387C2#2260832511yescharacteristic
388C2#2260833711yescharacteristic
389C2#2260835111yescharacteristic
390C2#2261022311yescharacteristic
391C2#2261023311yescharacteristic
392C2#2261024311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC2×#431×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C42×C73C23
hypercenterC2×#431D73
hypocenterC73#8938
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. C2×#17988317C2semidirect
4. #22607770C2semidirect
28. #14556570C8semidirect
202. C73#8938semidirect

Maximal subgroups

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

subgroupindex
C4×#145565702
C4×C22⋊#105968312
C2×#179883172
#226077702
C2×#431×C732
#893873