Finite Group Databasebeta

← #11788082

Subgroups — #11788082

Order 1152.

1077 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1077 conjugacy classes of subgroups — too many to draw. Only its 172 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
1C2×#64104C211yesmaximal, characteristic
2C22×#3710C211yesmaximal, characteristic, complemented
3#10591325C211yesmaximal, characteristic, complemented
4C2×#63564C212yesmaximal, complemented
5C3×#4529C212yesmaximal, complemented
6#68883—32nomaximal
7C22×C4⋊(C3⋊D3)—21no—
8C22×C4⋊(C3⋊D3)C2211yescharacteristic
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3752—21no—
12#64104—22no—
13#64104C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17C2×#3710—22no—
18C2×#3710—24no—
19#63579—21no—
20#63564—24no—
21C22×D3×C8—32no—
22C2×#895—32no—
23C2×#895—61no—
24C2×#821—32no—
25#4987—32no—
26C2×#809—32no—
27C3×#340—32no—
28#4529D312yescomplemented
29C23×C3⋊D3—21no—
30C23×C3⋊D3D411yescharacteristic
31C22×C32×C4—21no—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4⋊(C3⋊D3)—22no—
35C2×C4⋊(C3⋊D3)—22no—
36C2×C4⋊(C3⋊D3)—24no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)—42no—
39C2×C4⋊(C3⋊D3)—42no—
40C2×C4⋊(C3⋊D3)C2×C412yes—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3C2×C412yes—
44C2×C4×C3⋊D3D412yes—
45C22×C3×Dic3—22no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4C2×C412yes—
48#3752—24no—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8D414yescomplemented
54#3722—42no—
55#3710—28no—
56#1893—91noSylow
57C22×D12—32no—
58C22×D12—61no—
59C22×D12—62no—
60C22×D12—62no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C22×C3×C8—32no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—32no—
66C2×C3×C4⋊C4C2×D312yes—
67C2×(C2×D3)⋊C4—62no—
68C2×(C2×D3)⋊C4—62no—
69C2×(C2×D3)⋊C4—62no—
70C2×C4⋊Dic3C2×D312yes—
71C22×C3⋊C8C2×D312yes—
72C2×D3×C8—64no—
73C2×D3×C8—64no—
74C2×D3×C8—64no—
75#895—38no—
76#895—64no—
77#895—64no—
78#895—64no—
79C3⋊#95—62no—
80#821—64no—
81#809—64no—
82C23×C32C2×D411yescharacteristic
83C22×C3⋊D3—22no—
84C22×C3⋊D3—22no—
85C22×C3⋊D3—22no—
86C22×C3⋊D3—42no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—42no—
90C22×C3⋊D3C22⋊C412yes—
91C22×C3⋊D3D812yes—
92C22×C3⋊D3SD1612yes—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D412yes—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4#4112yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C22⋊C412yes—
102C4⋊(C3⋊D3)—24no—
103C4⋊(C3⋊D3)—48no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—24no—
113C23×C8—91no—
114C2×#121—91no—
115C2×#102—92no—
116#380—91no—
117#340—32no—
118C23×D3—32no—
119C23×D3—61no—
120C23×D3—62no—
121C23×D3—62no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—21no—
125C22×C3×C4—62no—
126C22×C3×C4C22×D312yes—
127C22×Dic3—22no—
128C22×Dic3—32no—
129C22×Dic3—61no—
130C2×D12—34no—
131C2×D12—62no—
132C2×D12—62no—
133C2×D12—62no—
134C2×D12—62no—
135C2×D12—62no—
136C2×D12—68no—
137C2×D12—68no—
138C2×D12—62no—
139C2×D12—62no—
140C2×D12—122no—
141C2×D12—122no—
142C2×D12—124no—
143C2×D12—124no—
144C2×D12—124no—
145C2×D12—124no—
146C2×C4×D3—34no—
147C2×C4×D3—34no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—122no—
155C2×C4×D3—122no—
156C2×C3×C8—34no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—62no—
164C3×C4⋊C4C4×D314yes—
165(C2×D3)⋊C4—68no—
166(C2×D3)⋊C4—68no—
167(C2×D3)⋊C4—124no—
168C4⋊Dic3—22no—
169C4⋊Dic3—22no—
170C2×C3⋊C8—22no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8D1214yescomplemented
173D3×C8—616no—
174C22×C32C2×C22⋊C411yescharacteristic
175C22×C32#12112yes—
176C22×C32C2×D811yescharacteristic
177C22×C32C2×SD1611yescharacteristic
178C22×C32#13512yes—
179C2×C3⋊D3—22no—
180C2×C3⋊D3—22no—
181C2×C3⋊D3—24no—
182C2×C3⋊D3—24no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—82no—
187C2×C3⋊D3—82no—
188C2×C3⋊D3#10214yescomplemented
189C32×C4—42no—
190C32×C4C4×D412yes—
191C32×C4#12011yescharacteristic
192C32×C4#12311yescharacteristic
193C3⋊Dic3—22no—
194C3×Dic3—82no—
195C22×D4—91no—
196C22×D4—181no—
197C23×C4—91no—
198C22×C8—32no—
199C22×C8—184no—
200C22×C8—182no—
201#121—94no—
202#121—182no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4D3211yescharacteristic
205C2×C22⋊C4—181no—
206C2×C22⋊C4—181no—
207#102—184no—
208#95—181no—
209C23×C3—21no—
210C23×C3D3×D412yes—
211C22×D3—34no—
212C22×D3—34no—
213C22×D3—34no—
214C22×D3—62no—
215C22×D3—62no—
216C22×D3—62no—
217C22×D3—62no—
218C22×D3—62no—
219C22×D3—62no—
220C22×D3—62no—
221C22×D3—64no—
222C22×D3—64no—
223C22×D3—122no—
224C22×D3—122no—
225C22×D3—124no—
226C22×D3—122no—
227C22×D3—122no—
228C22×D3—124no—
229C22×D3—122no—
230C22×D3—122no—
231C22×D3—122no—
232C22×D3—122no—
233C22×D3—122no—
234C22×D3—122no—
235C2×C3×C4—24no—
236C2×C3×C4—24no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—42no—
242C2×C3×C4—42no—
243C2×C3×C4—42no—
244C2×C3×C4—42no—
245C2×C3×C4—122no—
246C2×C3×C4—122no—
247C2×C3×C4—122no—
248C2×C3×C4C2×C4×D312yes—
249C2×C3×C4C2×D1212yes—
250C2×C3×C4#23512yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4#23912yes—
254C2×Dic3—34no—
255C2×Dic3—42no—
256C2×Dic3—42no—
257C2×Dic3—42no—
258C2×Dic3—62no—
259C2×Dic3—62no—
260C2×Dic3—62no—
261C2×Dic3—122no—
262D12—64no—
263D12—64no—
264D12—124no—
265D12—122no—
266D12—122no—
267D12—1216no—
268D12—1216no—
269D12—122no—
270D12—122no—
271C4×D3—64no—
272C4×D3—64no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—124no—
276C4×D3—122no—
277C4×D3—122no—
278C3×C8—64no—
279C3⋊C8—24no—
280C2×C32#38611yescharacteristic
281C2×C32C2×#10211yescharacteristic
282C2×C32#41611yescharacteristic
283C2×C32#46512yes—
284C2×C32#46612yes—
285C3⋊D3—24no—
286C3⋊D3—82no—
287C24—91no—
288C24—181no—
289C2×D4—92no—
290C2×D4—184no—
291C2×D4—182no—
292C2×D4—182no—
293C2×D4—181no—
294C2×D4—362no—
295C2×D4—362no—
296C22×C4—21no—
297C22×C4—62no—
298C22×C4—91no—
299C22×C4—92no—
300C22×C4—92no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4C2×D3211yescharacteristic
304C2×C8—34no—
305C2×C8—62no—
306C2×C8—62no—
307C2×C8—188no—
308C4⋊C4—21no—
309C4⋊C4—62no—
310C4⋊C4—62no—
311C4⋊C4#62412yes—
312C22⋊C4—184no—
313C22⋊C4—362no—
314C22×C3—22no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3D3×C22⋊C412yes—
320C22×C3#88412yes—
321C22×C3#89512yes—
322C22×C3D3×D812yes—
323C22×C3D3×SD1612yes—
324C22×C3#91612yes—
325C22×C3#91912yes—
326C2×D3—38no—
327C2×D3—64no—
328C2×D3—64no—
329C2×D3—64no—
330C2×D3—64no—
331C2×D3—64no—
332C2×D3—64no—
333C2×D3—64no—
334C2×D3—122no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—122no—
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—124no—
342C2×D3—124no—
343C2×D3—124no—
344C2×D3—244no—
345C2×D3—244no—
346C2×D3—242no—
347C2×D3—242no—
348C2×D3—242no—
349C2×D3—242no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—44no—
354C3×C4—44no—
355C3×C4—242no—
356C3×C4C4×D1212yes—
357C3×C4#88212yes—
358C3×C4#89312yes—
359C3×C4#89412yes—
360Dic3—64no—
361Dic3—82no—
362Dic3—122no—
363C32#189311yescharacteristic, complemented, Sylow
364C23—92no—
365C23—92no—
366C23—92no—
367C23—182no—
368C23—182no—
369C23—182no—
370C23—362no—
371C23—361no—
372C23—361no—
373C23—362no—
374C23#381111yescharacteristic
375D4—184no—
376D4—368no—
377D4—361no—
378D4—361no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—92no—
383C2×C4—122no—
384C2×C4—122no—
385C2×C4—122no—
386C2×C4—182no—
387C2×C4—184no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4#379912yes—
391C2×C4D3×D1212yes—
392C2×C4C2×#62411yescharacteristic
393C2×C4#381111yescharacteristic
394C8—64no—
395C2×C3—22no—
396C2×C3—22no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3#466512yes—
401C2×C3D3×#10212yes—
402C2×C3#477512yes—
403C2×C3#480412yes—
404C2×C3#480712yes—
405C2×C3#486412yes—
406C2×C3#488312yes—
407D3—68no—
408D3—124no—
409D3—244no—
410D3—244no—
411C22—94no—
412C22—184no—
413C22—184no—
414C22—182no—
415C22—182no—
416C22—362no—
417C22—362no—
418C22—362no—
419C22—722no—
420C22—722no—
421C22#6391012yes—
422C22#6392611yescharacteristic
423C22#6393011yescharacteristic
424C22#6395012yes—
425C22#6397411yescharacteristic
426C4—42no—
427C4—182no—
428C4—242no—
429C4#6389412yes—
430C4#6389711yescharacteristic
431C4#6392311yescharacteristic
432C3—21no—
433C3#6888312yescomplemented
434C2—184no—
435C2—722no—
436C2#1059050912yes—
437C2#1059052312yes—
438C2#1059138011yescharacteristic
439C2#1059141611yescharacteristic
440C2#1059156011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#64104C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1893
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3710C2semidirect
3. #10591325C2semidirect
4. C2×#63564C2semidirect
5. C3×#4529C2semidirect
13. #64104C4semidirect
28. #4529D3semidirect
53. C2×C3×C3⋊C8D4semidirect
172. C2×C3⋊C8D12semidirect
188. C2×C3⋊D3#102semidirect
363. C32#1893semidirect
433. C3#68883semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C22×#37102
#105913252
C2×#635642
C3×#45292
#688833