Finite Group Databasebeta

← #29575355

Subgroups — #29575355

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839815C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic
3C2×Q8⋊#92418C212yesmaximal, complemented
4#21443660C212yesmaximal, complemented
5C4×C22⋊Q8×C61C211yesmaximal, characteristic
6#16839815—24no—
7C2×C4⋊#92418—21no—
8C2×C4⋊#92418C2212yes—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418—21no—
11C2×C4×#92418C2212yes—
12#16839517—21no—
13Q8⋊#92418—24no—
14C2×C22⋊Q8×C61C411yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C22×C42×C61C2211yescharacteristic
17C61×#391C411yescharacteristic
18C61×#389C411yescharacteristic
19C61×#387—21no—
20C61×#385—21no—
21C61×#380C411yescharacteristic
22C4×C4⋊C4×C61—21no—
23C4×C4⋊C4×C61C2211yescharacteristic
24C4×C22⋊C4×C61—21no—
25C22×#92418—22no—
26C22×#92418—22no—
27C4⋊#92418—24no—
28C4⋊#92418—22no—
29C4⋊#92418—22no—
30C22⋊#92418—24no—
31C22⋊#92418—42no—
32C4×#92418—22no—
33C4×#92418D414yes—
34C22×Q8×C61C2×C411yescharacteristic
35C23×C4×C61C2×C411yescharacteristic
36C23×C4×C61D411yescharacteristic
37C23×C4×C61D411yescharacteristic
38C22⋊Q8×C61—22no—
39C22⋊Q8×C61C814yescomplemented
40C4×Q8×C61—22no—
41C4×Q8×C61—22no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C22⋊C4×C61—21no—
49C2×C22⋊C4×C61—21no—
50C2×C42×C61—22no—
51C2×C42×C61—22no—
52C2×C42×C61—21no—
53C2×C42×C61—21no—
54C2×C42×C61C2×C411yescharacteristic
55C2×C42×C61D411yescharacteristic
56C2×C42×C61D411yescharacteristic
57C2×C42×C61C2311yescharacteristic
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63C24×C61C22⋊C411yescharacteristic
64C2×Q8×C61—21no—
65C2×Q8×C61—22no—
66C2×Q8×C61—22no—
67C2×Q8×C61C2×C812yes—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C2×C812yes—
86C22×C4×C61M1612yes—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C4⋊C4×C61—24no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—22no—
94C4⋊C4×C61—42no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61C2×C812yes—
98C22⋊C4×C61—24no—
99C22⋊C4×C61—42no—
100C42×C61—22no—
101C42×C61—21no—
102C42×C61—22no—
103C42×C61—21no—
104C42×C61—42no—
105C42×C61—41no—
106C42×C61—41no—
107C42×C61C2×D412yes—
108C42×C61#4112yes—
109C2×#92418—24no—
110C2×#92418—42no—
111C2×#92418—42no—
112C2×#92418—42no—
113C2×#92418—42no—
114C2×#92418—42no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61C22⋊C812yes—
122C23×C61C2×C22⋊C411yescharacteristic
123Q8×C61—24no—
124Q8×C61—42no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—24no—
130C2×C4×C61—24no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61C22⋊C812yes—
154C2×C4×C61C4×D412yes—
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12112yes—
157C2×C4×C61#12311yescharacteristic
158C2×C4×C61C22×C811yescharacteristic
159C2×C4×C61C2×M1611yescharacteristic
160C2×C4×C61#13112yes—
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61#13712yes—
163C2×C4×C61#13711yescharacteristic
164#92418—44no—
165#92418—82no—
166#9073—611nomaximal, Sylow
167C22×C61—22no—
168C22×C61—22no—
169C22×C61—22no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61#38611yescharacteristic
175C22×C61C2×C22⋊C811yescharacteristic
176C22×C61#40811yescharacteristic
177C22×C61#41711yescharacteristic
178C22×C61#41911yescharacteristic
179C22×C61#42111yescharacteristic
180C22×C61#42111yescharacteristic
181C4×C61—22no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—42no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61—42no—
188C4×C61—81no—
189C4×C61—81no—
190C4×C61C8×D412yes—
191C4×C61#43512yes—
192C4×C61#46812yes—
193C4×C61#47012yes—
194C2×#431—611no—
195C4×C22⋊Q8D6111yescharacteristic
196#1797—611no—
197C2×Q8⋊C8—612no—
198#1279—612no—
199C2×C61—42no—
200C2×C61#147711yescharacteristic
201C2×C61#147911yescharacteristic
202C2×C61#149511yescharacteristic
203C2×C61#149711yescharacteristic
204C2×C61#186911yescharacteristic
205C2×C61#189411yescharacteristic
206C2×C61#189711yescharacteristic
207C2×C22⋊Q8Dic6111yescharacteristic
208C2×C4×Q8C2×D6111yescharacteristic
209C22×C42C2×D6111yescharacteristic
210#431—1224no—
211C2×C4⋊C8—612no—
212C2×C4⋊C8—1221no—
213C2×C22⋊C8—1221no—
214C2×C22⋊C8—1221no—
215C2×C4×C8—612no—
216#391Dic6111yescharacteristic
217#389Dic6111yescharacteristic
218#387—21no—
219#385—21no—
220#380Dic6111yescharacteristic
221C4×C4⋊C4—21no—
222C4×C4⋊C4C2×D6111yescharacteristic
223C4×C22⋊C4—21no—
224#336—1221no—
225Q8⋊C8—1224no—
226C61#907311yescharacteristic, complemented, Sylow
227C22×Q8C2×Dic6111yescharacteristic
228C23×C4C2×Dic6111yescharacteristic
229C23×C4C22⋊D6111yescharacteristic
230C23×C4C22⋊D6111yescharacteristic
231C22×C8—1222no—
232C22×C8—1222no—
233C22⋊Q8—22no—
234C22⋊Q8#9241814yescomplemented
235C4×Q8—22no—
236C4×Q8—22no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×Dic6111yescharacteristic
241C2×C4⋊C4C2×Dic6111yescharacteristic
242C2×C4⋊C4C2×Dic6111yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C2×Dic6111yescharacteristic
250C2×C42C22⋊D6111yescharacteristic
251C2×C42C22⋊D6111yescharacteristic
252C2×C42C22×D6111yescharacteristic
253C4⋊C8—1224no—
254C4⋊C8—1222no—
255C4⋊C8—1222no—
256C22⋊C8—1224no—
257C22⋊C8—2442no—
258C4×C8—614no—
259C4×C8—1222no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265C24C22⋊Dic6111yescharacteristic
266C2×Q8—21no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8C2×#9241812yes—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×#9241812yes—
285C22×C4#1175819412yes—
286C22×C4C22⋊Dic6111yescharacteristic
287C22×C4C22⋊Dic6111yescharacteristic
288C22×C4C22⋊Dic6111yescharacteristic
289C22×C4C22×Dic6111yescharacteristic
290C22×C4C2×C22⋊D6111yescharacteristic
291C22×C4C2×C22⋊D6111yescharacteristic
292C2×C8—1224no—
293C2×C8—2442no—
294C2×C8—2442no—
295C2×C8—2442no—
296C2×C8—2442no—
297C2×C8—2442no—
298C4⋊C4—24no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—42no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4C2×#9241812yes—
306C22⋊C4—24no—
307C22⋊C4—42no—
308C42—22no—
309C42—21no—
310C42—22no—
311C42—21no—
312C42—42no—
313C42—41no—
314C42—41no—
315C42D4×D6112yes—
316C42#1175822412yes—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C22⋊#9241812yes—
324C23C2×C22⋊Dic6111yescharacteristic
325Q8—24no—
326Q8—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4C22⋊#9241812yes—
356C2×C4D4×Dic6112yes—
357C2×C4#1451974511yescharacteristic
358C2×C4#1451974912yes—
359C2×C4#1451975811yescharacteristic
360C2×C4C22×#9241811yescharacteristic
361C2×C4C2×#1175819411yescharacteristic
362C2×C4#1451978412yes—
363C2×C4#1451980211yescharacteristic
364C2×C4#1451980711yescharacteristic
365C2×C4#1451980812yes—
366C8—4882no—
367C8—2444no—
368C22—22no—
369C22—22no—
370C22—22no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22#1683964211yescharacteristic
376C22C2×C22⋊#9241811yescharacteristic
377C22#1683972911yescharacteristic
378C22#1683976311yescharacteristic
379C22#1683977111yescharacteristic
380C22#1683977911yescharacteristic
381C22#1683977911yescharacteristic
382C4—21no—
383C4—21no—
384C4—22no—
385C4—41no—
386C4—42no—
387C4—41no—
388C4—42no—
389C4—81no—
390C4—81no—
391C4D4×#9241812yes—
392C4#1683983412yes—
393C4#1684001012yes—
394C4#1684001812yes—
395C2—42no—
396C2#2144420611yescharacteristic
397C2#2144421411yescharacteristic
398C2#2144428411yescharacteristic
399C2#2144429211yescharacteristic
400C2#2144611211yescharacteristic
401C2#2144625311yescharacteristic
402C2#2144626811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC4×C22⋊Q8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenterC4×C22⋊Q8D61
hypocenterC61#9073
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×Q8⋊#92418C2semidirect
4. #21443660C2semidirect
39. C22⋊Q8×C61C8semidirect
226. C61#9073semidirect
234. C22⋊Q8#92418semidirect

Maximal subgroups

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

subgroupindex
C2×#168398152
#214457992
C2×Q8⋊#924182
#214436602
C4×C22⋊Q8×C612
#907361