Finite Group Databasebeta

← #11858878

Subgroups — #11858878

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2#10592825C211yesmaximal, characteristic
3C3×#5118C211yesmaximal, characteristic, complemented
4C3×Dic3×M16C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10591074C211yesmaximal, characteristic
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590648C214yesmaximal, complemented
9#10590647C214yesmaximal, complemented
10#79039—31nomaximal
11#78518—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×#3724C412yes—
20C2×#3722C412yes—
21#63874C414yes—
22#63874C2212yes—
23#63874C2212yes—
24#63647C2214yes—
25C3×#815C2212yescomplemented
26C3×Dic3⋊C8C2214yescomplemented
27C3×C8×Dic3C2212yescomplemented
28Dic3⋊(C3⋊C8)C2214yescomplemented
29#63557C2214yes—
30#63554C2212yescomplemented
31Dic3×C3⋊C8C2212yescomplemented
32C2×#872—31no—
33C2×#872—31no—
34C3×#423—31no—
35C3×C4×M16—31no—
36#5126—31no—
37#5126—31no—
38#5126—31no—
39#5126—31no—
40#5126—61no—
41#5118—31no—
42#5118D311yescharacteristic, complemented
43Dic3×M16—31no—
44Dic3×M16D311yescharacteristic, complemented
45#4924—31no—
46C4×#208—31no—
47#4840—34no—
48#4840—34no—
49#4709—34no—
50#4690—34no—
51C23×C3⋊D3C2×C411yescharacteristic
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2×C411yescharacteristic
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3C2×C412yes—
57C2×C4×C3⋊D3C2312yes—
58C22×C3×Dic3C2×C412yes—
59C22×C3×Dic3C2×C412yes—
60C32×M16—22no—
61C2×C32×C8C2312yes—
62#3748—22no—
63C2×C3⋊(C3⋊C8)C2312yes—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2×C412yes—
66C3×C4×Dic3C2311yescharacteristic
67C3×C4×Dic3C2311yescharacteristic
68C3×C4×Dic3C2312yes—
69C3×#208—22no—
70C3×#208—22no—
71C2×C3×C3⋊C8C2312yes—
72C2×C3×C3⋊C8C2312yes—
73#3724C2×C414yes—
74#3724C2×C414yes—
75#3722C2×C414yes—
76#3722C2×C414yes—
77#2921—91noSylow
78C22×C4×D3—31no—
79C22×C4×D3—31no—
80C22×C4×D3—61no—
81C2×C3×M16—21no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×C42—31no—
87C2×C3×C42—31no—
88C2×(C2×D3)⋊C4—32no—
89C2×(C2×D3)⋊C4—32no—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×C4×Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#872—34no—
100#872—34no—
101#872—32no—
102#872—32no—
103#872—32no—
104#872—32no—
105C3×C4⋊C8—34no—
106C3×#97—32no—
107C3×C4×C8—32no—
108(C2×D3)⋊C8—34no—
109(C2×D3)⋊C8—34no—
110(C2×D3)⋊C8—34no—
111(C2×D3)⋊C8—34no—
112(C2×D3)⋊C8—64no—
113#815—32no—
114#815C2×D312yescomplemented
115Dic3⋊C8—34no—
116Dic3⋊C8C2×D314yescomplemented
117C8×Dic3—32no—
118C8×Dic3C2×D312yescomplemented
119C4⋊(C3⋊C8)—34no—
120#803—32no—
121C4×C3⋊C8—32no—
122C23×C32C22×C411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—42no—
125C22×C3⋊D3C22×C412yes—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4#4112yes—
128C2×C32×C4#4112yes—
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C22×C412yes—
132C4×C3⋊D3—24no—
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—42no—
137C2×C3×Dic3C22×C412yes—
138C2×C3×Dic3C22×C412yes—
139C2×C3×Dic3C22×C414yes—
140C32×C8—22no—
141C3⋊(C3⋊C8)—22no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—22no—
144C2×#117—91no—
145#433—94no—
146#433—94no—
147#423—31no—
148#423—91no—
149#407—91no—
150#407—91no—
151C4×M16—31no—
152C4×M16—91no—
153C23×D3—31no—
154C23×D3—31no—
155C23×D3—61no—
156C22×C3×C4—21no—
157C22×C3×C4—32no—
158C22×C3×C4—32no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3C4×D312yes—
165C22×Dic3C4×D312yes—
166C2×C4×D3—32no—
167C2×C4×D3—32no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—62no—
174C2×C4×D3—62no—
175C2×C4×D3—62no—
176C2×C4×D3—122no—
177C2×C4×D3—122no—
178C3×M16—22no—
179C3×M16—22no—
180C3×M16—42no—
181C3×M16—62no—
182C3×M16—62no—
183C2×C3×C8—22no—
184C2×C3×C8—32no—
185C2×C3×C8—32no—
186C2×C3×C8C22×D312yes—
187C2×C3×C8C22×D312yes—
188C3×C42—32no—
189C3×C42—32no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—32no—
193(C2×D3)⋊C4—34no—
194(C2×D3)⋊C4—34no—
195(C2×D3)⋊C4—34no—
196(C2×D3)⋊C4—34no—
197Dic3⋊C4—34no—
198Dic3⋊C4—34no—
199Dic3⋊C4—34no—
200Dic3⋊C4—34no—
201C4×Dic3C4×D312yes—
202C4×Dic3C4×D312yes—
203C4×Dic3C22×D311yescharacteristic
204C4×Dic3C22×D311yescharacteristic
205C4×Dic3C22×D312yes—
206#208—22no—
207#208—22no—
208#208—62no—
209#208—62no—
210#208—122no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—62no—
214C2×C3⋊C8C22×D312yes—
215C2×C3⋊C8C22×D312yes—
216C22×C32—22no—
217C22×C32#11712yes—
218C22×C32C23×C411yescharacteristic
219C2×C3⋊D3—22no—
220C2×C3⋊D3—22no—
221C2×C3⋊D3—22no—
222C2×C3⋊D3—44no—
223C32×C4#11712yes—
224C32×C4C2×#4111yescharacteristic
225C32×C4C2×#4111yescharacteristic
226C3⋊Dic3—22no—
227C3×Dic3—22no—
228C3×Dic3—22no—
229C3×Dic3—24no—
230C23×C4—91no—
231C2×M16—31no—
232C2×M16—31no—
233C2×M16—91no—
234C2×M16D3211yescharacteristic
235#117—94no—
236#117—92no—
237#117—92no—
238C2×C4⋊C4—92no—
239C2×C22⋊C4—92no—
240C2×C42—31no—
241C2×C42—31no—
242C4⋊C8—34no—
243C4⋊C8—94no—
244C22⋊C8—94no—
245C22⋊C8—94no—
246#97—32no—
247#97—92no—
248C4×C8—32no—
249C4×C8—92no—
250C23×C3—21no—
251C23×C3C2×C4×D311yescharacteristic
252C23×C3C2×C4×D311yescharacteristic
253C22×D3—32no—
254C22×D3—32no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C22×D3—122no—
259C22×D3—122no—
260C22×D3—122no—
261C22×D3—124no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—22no—
266C2×C3×C4—34no—
267C2×C3×C4—32no—
268C2×C3×C4—32no—
269C2×C3×C4—122no—
270C2×C3×C4—122no—
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4#23512yes—
274C2×C3×C4#23512yes—
275C2×C3×C4#23712yes—
276C2×C3×C4#23912yes—
277C2×C3×C4C23×D311yescharacteristic
278C2×C3×C4C23×D311yescharacteristic
279C2×Dic3—32no—
280C2×Dic3—32no—
281C2×Dic3—42no—
282C2×Dic3—42no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—62no—
286C2×Dic3—122no—
287C2×Dic3C2×C4×D312yes—
288C2×Dic3C2×C4×D312yes—
289C2×Dic3C2×C4×D314yes—
290C4×D3—64no—
291C4×D3—64no—
292C4×D3—62no—
293C4×D3—62no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—122no—
297C4×D3—122no—
298C4×D3—124no—
299C3×C8—22no—
300C3×C8—22no—
301C3×C8—42no—
302C3×C8—62no—
303C3×C8—62no—
304C3⋊C8—22no—
305C3⋊C8—22no—
306C3⋊C8—62no—
307C3⋊C8—62no—
308C3⋊C8—122no—
309C2×C32—22no—
310C2×C32C2×#11711yescharacteristic
311C2×C32#56812yes—
312C3⋊D3—42no—
313C24—91no—
314C22×C4—32no—
315C22×C4—32no—
316C22×C4—91no—
317C22×C4—92no—
318C22×C4—92no—
319C22×C4—182no—
320C22×C4—182no—
321C22×C4C2×D3211yescharacteristic
322M16—22no—
323M16—62no—
324M16—62no—
325M16—182no—
326C2×C8—32no—
327C2×C8—32no—
328C2×C8—92no—
329C2×C8C2×D3212yes—
330C4⋊C4—94no—
331C4⋊C4—94no—
332C22⋊C4—94no—
333C22⋊C4—94no—
334C42—31no—
335C42—31no—
336C42—32no—
337C42—32no—
338C42—32no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—42no—
344C22×C3#87212yes—
345C22×C3#89212yes—
346C22×C3C22×C4×D311yescharacteristic
347C22×C3C22×C4×D311yescharacteristic
348C2×D3—64no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—124no—
358C2×D3—124no—
359C2×D3—128no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—22no—
363C3×C4—64no—
364C3×C4—62no—
365C3×C4—62no—
366C3×C4#87212yes—
367C3×C4#89212yes—
368C3×C4C2×#23511yescharacteristic
369C3×C4C2×#23511yescharacteristic
370C3×C4C2×#23711yescharacteristic
371C3×C4C2×#23911yescharacteristic
372Dic3—22no—
373Dic3—22no—
374Dic3—24no—
375Dic3—62no—
376Dic3—62no—
377Dic3—122no—
378C32#292111yescharacteristic, complemented, Sylow
379C23—92no—
380C23—182no—
381C23—362no—
382C23C4×D3211yescharacteristic
383C2×C4—32no—
384C2×C4—32no—
385C2×C4—34no—
386C2×C4—92no—
387C2×C4—122no—
388C2×C4—122no—
389C2×C4—182no—
390C2×C4—182no—
391C2×C4—182no—
392C2×C4—184no—
393C2×C4#379912yes—
394C2×C4C4×D3211yescharacteristic
395C2×C4#380412yes—
396C2×C4C22×D3211yescharacteristic
397C8—22no—
398C8—62no—
399C8—62no—
400C8—182no—
401C2×C3—22no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—42no—
406C2×C3C2×#87211yescharacteristic
407C2×C3C2×#89211yescharacteristic
408C2×C3#574512yes—
409C2×C3#574512yes—
410D3—124no—
411D3—122no—
412D3—122no—
413C22—22no—
414C22—182no—
415C22—182no—
416C22—182no—
417C22—364no—
418C22#6383612yes—
419C22C2×C4×D3211yescharacteristic
420C4—62no—
421C4—62no—
422C4—64no—
423C4—182no—
424C4#6383612yes—
425C4C2×#379911yescharacteristic
426C4C2×#380411yescharacteristic
427C3—21no—
428C3#7851811yescharacteristic, complemented
429C3#7903911yescharacteristic, complemented
430C2—22no—
431C2—362no—
432C2#1059472212yes—
433C2C2×#6383611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2921
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5118C2semidirect
4. C3×Dic3×M16C2semidirect
5. #10591115C2semidirect
7. Dic3×#208C2semidirect
8. #10590648C2semidirect
9. #10590647C2semidirect
25. C3×#815C22semidirect
26. C3×Dic3⋊C8C22semidirect
27. C3×C8×Dic3C22semidirect
28. Dic3⋊(C3⋊C8)C22semidirect
30. #63554C22semidirect
31. Dic3×C3⋊C8C22semidirect
42. #5118D3semidirect
44. Dic3×M16D3semidirect
114. #815C2×D3semidirect
116. Dic3⋊C8C2×D3semidirect
118. C8×Dic3C2×D3semidirect
378. C32#2921semidirect
428. C3#78518semidirect
429. C3#79039semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
#105928252
C3×#51182
C3×Dic3×M162
#105911152
#105910742
Dic3×#2082
#105906482
#105906472
#790393
#785183