Finite Group Databasebeta

← #11792004

Subgroups — #11792004

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3C2×#64106C211yesmaximal, characteristic
4C2×C32×#103C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic
6C2×#63643C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70273—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14#64155—22no—
15#64155—22no—
16C2×#3756—22no—
17C2×#3756—22no—
18C2×#3756—22no—
19C2×#3752—21no—
20C2×#3752—21no—
21C2×C4⋊(C3⋊Dic3)—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750—21no—
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#64106—22no—
26#64106—22no—
27C32×#103—22no—
28#63647—22no—
29#63643—22no—
30C2×#946—34no—
31C22×#216—34no—
32C2×#897—34no—
33C2×C3×#103D314yescomplemented
34C2×(C2×D3)⋊C8—34no—
35C2×#816—34no—
36#4529—34no—
37C23×C3⋊D3D411yescharacteristic
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8D412yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3D411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634D412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67#3756—28no—
68#3752—24no—
69#3752—24no—
70C4⋊(C3⋊Dic3)—24no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)D412yes—
73#3750—24no—
74C2×C3⋊(C3⋊C8)—21no—
75C2×C3⋊(C3⋊C8)—21no—
76C2×C3⋊(C3⋊C8)D412yes—
77#2001—91noSylow
78C22×C3×Q8C2×D314yes—
79C22×C4×D3—34no—
80C22×Dic6—34no—
81C22×C3×C8C2×D314yes—
82C2×C3×C4⋊C4C2×D314yes—
83#946—68no—
84#946—68no—
85C2×#216—68no—
86C2×#216—68no—
87C2×#216—68no—
88C2×(C2×D3)⋊C4—64no—
89C2×(C2×D3)⋊C4—64no—
90C2×C4⋊Dic3—34no—
91C2×C4⋊Dic3—64no—
92C2×Dic3⋊C4—64no—
93C22×C3⋊C8—34no—
94#897—68no—
95#897—68no—
96C3×#103—28no—
97(C2×D3)⋊C8—68no—
98#816—68no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—21no—
101C22×C3⋊D3—21no—
102C22×C3⋊D3—21no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3—21no—
105C22×C3⋊D3—21no—
106C22×C3⋊D3Q1612yescomplemented
107C32×Q8—22no—
108C32×Q8—22no—
109C32×Q8—41no—
110C32×Q8—41no—
111C2×C32×C4—22no—
112C2×C32×C4—22no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C4×C3⋊D3—41no—
133C4×C3⋊D3—41no—
134C4×C3⋊D3—41no—
135C4×C3⋊D3—41no—
136#634—22no—
137#634—22no—
138#634—41no—
139#634—41no—
140C32×C8—41no—
141C3⋊(C3⋊C8)—22no—
142C22×Q16—91no—
143C2×C22⋊Q8—91no—
144C2×C22⋊Q8—91no—
145C2×#103—91no—
146C2×#103C3⋊D311yescharacteristic, complemented
147C2×C22⋊C8—91no—
148#340—91no—
149C23×D3—34no—
150C2×C3×Q8—24no—
151C2×C3×Q8—24no—
152C2×C3×Q8—24no—
153C2×C3×Q8—24no—
154C2×C3×Q8—24no—
155C2×C3×Q8D1218yes—
156C22×C3×C4—24no—
157C22×C3×C4—24no—
158C22×C3×C4C22×D314yes—
159C22×Dic3—34no—
160C22×Dic3—64no—
161C22×Dic3—64no—
162C2×C4×D3—64no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×Dic6—38no—
169C2×Dic6—64no—
170C2×Dic6—64no—
171C2×Dic6—64no—
172C2×Dic6—64no—
173C2×Dic6—64no—
174C2×C3×C8—24no—
175C2×C3×C8—24no—
176C2×C3×C8—24no—
177C3×C4⋊C4—24no—
178C3×C4⋊C4#6718yes—
179#216—632no—
180(C2×D3)⋊C4—616no—
181(C2×D3)⋊C4—616no—
182C4⋊Dic3—38no—
183C4⋊Dic3—616no—
184C4⋊Dic3—64no—
185Dic3⋊C4—616no—
186C2×C3⋊C8—38no—
187C2×C3⋊C8—64no—
188C2×C3⋊C8—64no—
189C22×C32#12011yescharacteristic
190C22×C32#12011yescharacteristic
191C22×C32#12111yescharacteristic
192C22×C32C2×Q1611yescharacteristic
193C22×C32#13511yescharacteristic
194C22×C32#13711yescharacteristic
195C22×C32#13711yescharacteristic
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
198C2×C3⋊D3—22no—
199C2×C3⋊D3—41no—
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—41no—
203C32×C4—42no—
204C32×C4—42no—
205C32×C4#12011yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12111yescharacteristic
208C32×C4#12711yescharacteristic
209C3⋊Dic3—42no—
210C3⋊Dic3—41no—
211C3⋊Dic3—42no—
212C22×Q8—91no—
213C22×Q8C2×C3⋊D311yescharacteristic
214C23×C4—91no—
215C2×Q16—182no—
216C2×Q16—182no—
217C2×Q16—182no—
218C22×C8—91no—
219C22×C8C2×C3⋊D311yescharacteristic
220C22⋊Q8—182no—
221C22⋊Q8—182no—
222C22⋊Q8—182no—
223C22⋊Q8—182no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—181no—
226C2×C4⋊C4—181no—
227C2×C4⋊C4C2×C3⋊D311yescharacteristic
228C2×C22⋊C4—181no—
229C2×C22⋊C4—181no—
230#103—22no—
231#103—182no—
232C22⋊C8—182no—
233C23×C3D3×D414yes—
234C22×D3—38no—
235C22×D3—64no—
236C22×D3—64no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3—64no—
240C22×D3—64no—
241C3×Q8—28no—
242C3×Q8—28no—
243C3×Q8—44no—
244C3×Q8—44no—
245C2×C3×C4—28no—
246C2×C3×C4—28no—
247C2×C3×C4—44no—
248C2×C3×C4—44no—
249C2×C3×C4—44no—
250C2×C3×C4—44no—
251C2×C3×C4C2×D1214yes—
252C2×C3×C4#23514yes—
253C2×C3×C4D3×D414yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4D3×D414yes—
256C2×C3×C4C2×#6714yes—
257C2×Dic3—64no—
258C2×Dic3—68no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—68no—
262C2×Dic3—124no—
263C2×Dic3—124no—
264C2×Dic3—124no—
265C2×Dic3—124no—
266C4×D3—124no—
267C4×D3—124no—
268C4×D3—124no—
269C4×D3—124no—
270Dic6—68no—
271Dic6—68no—
272Dic6—124no—
273Dic6—124no—
274C3×C8—44no—
275C3⋊C8—68no—
276C2×C32#39211yescharacteristic
277C2×C32#45111yescharacteristic
278C2×C32#45111yescharacteristic
279C2×C32#45211yescharacteristic
280C2×C32#45211yescharacteristic
281C2×C32#46711yescharacteristic
282C2×C32#47011yescharacteristic
283C3⋊D3—42no—
284C24—91no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—92no—
291C2×Q8—181no—
292C2×Q8—181no—
293C2×Q8—181no—
294C2×Q8—181no—
295C2×Q8—181no—
296C2×Q8C4⋊(C3⋊D3)12yes—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—91no—
300C22×C4—181no—
301C22×C4—181no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—181no—
307C22×C4—181no—
308C22×C4C22×C3⋊D311yescharacteristic
309Q16—188no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—92no—
314C2×C8—181no—
315C2×C8—181no—
316C4⋊C4—21no—
317C4⋊C4—92no—
318C4⋊C4—184no—
319C4⋊C4—184no—
320C4⋊C4—181no—
321C4⋊C4#63812yes—
322C22⋊C4—184no—
323C22⋊C4—184no—
324C22×C3#88214yes—
325C22×C3#88414yes—
326C22×C3#91514yes—
327C22×C3#91614yes—
328C22×C3D3×Q1614yes—
329C22×C3#91814yes—
330C22×C3#93714yes—
331C2×D3—68no—
332C2×D3—68no—
333C2×D3—68no—
334C2×D3—124no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—124no—
338C3×C4—48no—
339C3×C4—48no—
340C3×C4#88214yes—
341C3×C4#88414yes—
342C3×C4#93014yes—
343C3×C4#94014yes—
344Dic3—128no—
345Dic3—124no—
346Dic3—128no—
347C32#200111yescharacteristic, complemented, Sylow
348C23—92no—
349C23—181no—
350C23—181no—
351C23—181no—
352C23—181no—
353C23—181no—
354C23—181no—
355C23D4×C3⋊D311yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—182no—
361Q8—182no—
362Q8—361no—
363Q8—361no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—182no—
371C2×C4—181no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4—361no—
376C2×C4—361no—
377C2×C4—361no—
378C2×C4—361no—
379C2×C4—361no—
380C2×C4—361no—
381C2×C4—361no—
382C2×C4—361no—
383C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
384C2×C4#382811yescharacteristic
385C2×C4D4×C3⋊D311yescharacteristic
386C2×C4D4×C3⋊D311yescharacteristic
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4C2×#63811yescharacteristic
389C8—41no—
390C8—182no—
391C2×C3#480814yes—
392C2×C3#480914yes—
393C2×C3#481314yes—
394C2×C3#481614yes—
395C2×C3#496014yes—
396C2×C3#517314yes—
397C2×C3#518614yes—
398D3—128no—
399C22—182no—
400C22—182no—
401C22—182no—
402C22—361no—
403C22—361no—
404C22—361no—
405C22—361no—
406C22#6409111yescharacteristic
407C22#6409311yescharacteristic
408C22#6412411yescharacteristic
409C22#6412511yescharacteristic
410C22Q16×C3⋊D311yescharacteristic
411C22#6412711yescharacteristic
412C22#6414611yescharacteristic
413C4—42no—
414C4—42no—
415C4—361no—
416C4—362no—
417C4—362no—
418C4#6409111yescharacteristic
419C4#6409311yescharacteristic
420C4#6413911yescharacteristic
421C4#6414911yescharacteristic
422C3#7027314yescomplemented
423C2—362no—
424C2#1059250711yescharacteristic
425C2#1059250811yescharacteristic
426C2#1059251211yescharacteristic
427C2#1059251511yescharacteristic
428C2#1059265911yescharacteristic
429C2#1059287211yescharacteristic
430C2#1059288511yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC2×#103C3⋊D3
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C22×#3756C2semidirect
4. C2×C32×#103C2semidirect
6. C2×#63643C2semidirect
7. #10589395C2semidirect
33. C2×C3×#103D3semidirect
106. C22×C3⋊D3Q16semidirect
146. C2×#103C3⋊D3semidirect
347. C32#2001semidirect
422. C3#70273semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C22×#37562
C2×#641062
C2×C32×#1032
C2×#636472
C2×#636432
#105893952
#702733