Finite Group Databasebeta

← #11791445

Subgroups — #11791445

Order 1152.

1284 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×#63641C211yesmaximal, characteristic, complemented
6C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic, complemented
8#70161—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—21no—
11C22×#638—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15#64149—22no—
16#64149C414yescomplemented
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3—21no—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#102—22no—
22#63659—22no—
23#63658—21no—
24#63648—22no—
25#63641—22no—
26#63636—22no—
27C2×#940—34no—
28C2×C3×#102D314yescomplemented
29C2×#832—34no—
30C2×#821—34no—
31C2×Dic3⋊C8—34no—
32Dic3×C4⋊C4—34no—
33C2×#809—34no—
34C24×C32—21no—
35C23×C3⋊D3—21no—
36C2×C32×D4—21no—
37C2×C32×D4—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4C2×C412yes—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—24no—
45C2×#638—24no—
46C2×#638—42no—
47C2×#638—42no—
48C2×#638—42no—
49C2×#638—42no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2×C412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4D412yescomplemented
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yescomplemented
66C4×C3⋊Dic3—42no—
67C4×C3⋊Dic3C2×C412yes—
68C4×C3⋊Dic3D412yes—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72#1982—91noSylow
73C22×C3×D4C2×D314yes—
74C22×#67—64no—
75C22×#67—64no—
76C22×D12—34no—
77C22×C3×C8C2×D314yes—
78C2×C3×C4⋊C4C2×D314yes—
79#940—316no—
80#940—68no—
81C2×C4⋊Dic3—34no—
82C2×C4×Dic3—34no—
83C2×C4×Dic3—64no—
84C22×C3⋊C8—34no—
85C3×#102—28no—
86#832—68no—
87C3⋊#95—64no—
88#821—68no—
89Dic3⋊C8—68no—
90#809—68no—
91C23×C32—22no—
92C23×C32—41no—
93C23×C32—41no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C2×D411yescharacteristic
99C22×C3⋊D3—22no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3—41no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C32×D4—22no—
107C32×D4—22no—
108C32×D4—41no—
109C32×D4—41no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119#638—48no—
120#638—48no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3C22⋊C412yes—
127C2×C3⋊Dic3C22⋊C412yes—
128C2×C3⋊Dic3D812yes—
129C2×C3⋊Dic3SD1612yes—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C32×C8—41no—
135C3⋊(C3⋊C8)—41no—
136C2×#127—91no—
137C2×C4⋊C8—91no—
138C2×#102—91no—
139C2×#102—91no—
140C2×#102—91no—
141C2×#102C3⋊D311yescharacteristic, complemented
142C4×C4⋊C4—91no—
143C24×C3—24no—
144C23×D3—64no—
145C2×C3×D4—24no—
146C2×C3×D4—24no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4—24no—
150C2×C3×D4C4×D318yes—
151C22×C3×C4—24no—
152C22×C3×C4C22×D314yes—
153C2×#67—616no—
154C2×#67—616no—
155C2×#67—128no—
156C2×#67—128no—
157C2×#67—128no—
158C2×#67—128no—
159C22×Dic3—34no—
160C22×Dic3—34no—
161C22×Dic3—64no—
162C2×D12—38no—
163C2×D12—64no—
164C2×D12—64no—
165C2×D12—64no—
166C2×D12—64no—
167C2×D12—64no—
168C2×C3×C8—24no—
169C2×C3×C8—24no—
170C2×C3×C8—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4#6718yescomplemented
173C4⋊Dic3—38no—
174C4⋊Dic3—64no—
175C4×Dic3—38no—
176C4×Dic3—38no—
177C4×Dic3—128no—
178C2×C3⋊C8—64no—
179C2×C3⋊C8—64no—
180C2×C3⋊C8—64no—
181C22×C32—42no—
182C22×C32—42no—
183C22×C32—42no—
184C22×C32—81no—
185C22×C32—81no—
186C22×C32—81no—
187C22×C32—81no—
188C22×C32C2×C22⋊C411yescharacteristic
189C22×C32#12111yescharacteristic
190C22×C32#12111yescharacteristic
191C22×C32C2×D811yescharacteristic
192C22×C32C2×SD1611yescharacteristic
193C22×C32AGL(1,ℤ/8)11yescharacteristic
194C22×C32AGL(1,ℤ/8)11yescharacteristic
195C2×C3⋊D3—42no—
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—81no—
199C2×C3⋊D3—81no—
200C2×C3⋊D3—81no—
201C2×C3⋊D3—81no—
202C32×C4—42no—
203C32×C4C4×D411yescharacteristic
204C32×C4C4×D411yescharacteristic
205C32×C4#12411yescharacteristic
206C32×C4#12711yescharacteristic
207C3⋊Dic3—22no—
208C3⋊Dic3—42no—
209C3⋊Dic3#10214yescomplemented
210C22×D4—91no—
211C22×D4—181no—
212C22×D4—181no—
213C22×D4C2×C3⋊D311yescharacteristic
214C22×C8—91no—
215C22×C8C2×C3⋊D311yescharacteristic
216#127—94no—
217#127—182no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4C2×C3⋊D311yescharacteristic
220C2×C42—91no—
221C2×C42—181no—
222C4⋊C8—182no—
223#102—22no—
224#102—182no—
225#102—182no—
226#102—182no—
227#95—181no—
228C23×C3—28no—
229C23×C3—44no—
230C23×C3—44no—
231C23×C3—44no—
232C23×C3—44no—
233C23×C3—44no—
234C23×C3—44no—
235C23×C3D3×D414yes—
236C22×D3—68no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—124no—
240C22×D3—124no—
241C22×D3—124no—
242C22×D3—124no—
243C3×D4—28no—
244C3×D4—28no—
245C3×D4—44no—
246C3×D4—44no—
247C2×C3×C4—28no—
248C2×C3×C4—44no—
249C2×C3×C4—44no—
250C2×C3×C4C2×C4×D314yes—
251C2×C3×C4#23514yes—
252C2×C3×C4D3×D414yes—
253C2×C3×C4D3×D414yes—
254C2×C3×C4#23714yes—
255C2×C3×C4C2×#6714yes—
256#67—1232no—
257#67—1232no—
258C2×Dic3—38no—
259C2×Dic3—38no—
260C2×Dic3—38no—
261C2×Dic3—38no—
262C2×Dic3—64no—
263C2×Dic3—64no—
264C2×Dic3—68no—
265C2×Dic3—124no—
266C2×Dic3—124no—
267D12—68no—
268D12—68no—
269D12—124no—
270D12—124no—
271C3×C8—44no—
272C3⋊C8—124no—
273C2×C32—82no—
274C2×C32#39011yescharacteristic
275C2×C32C2×#10211yescharacteristic
276C2×C32#41811yescharacteristic
277C2×C32#45911yescharacteristic
278C2×C32#45911yescharacteristic
279C2×C32#46011yescharacteristic
280C2×C32#46011yescharacteristic
281C3⋊D3—82no—
282C24—21no—
283C24—181no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—92no—
290C2×D4—184no—
291C2×D4—184no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—362no—
298C2×D4—362no—
299C2×D4—362no—
300C2×D4—362no—
301C2×D4C4×C3⋊D312yes—
302C22×C4—21no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—181no—
306C22×C4C22×C3⋊D311yescharacteristic
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—92no—
315C4⋊C4—181no—
316C4⋊C4#63812yescomplemented
317C42—92no—
318C42—92no—
319C42—362no—
320C22×C3—48no—
321C22×C3—48no—
322C22×C3—48no—
323C22×C3—84no—
324C22×C3—84no—
325C22×C3—84no—
326C22×C3—84no—
327C22×C3D3×C22⋊C414yes—
328C22×C3#88414yes—
329C22×C3D3×D814yes—
330C22×C3#91114yes—
331C22×C3D3×SD1614yes—
332C22×C3#91414yes—
333C22×C3#93914yes—
334C2×D3—128no—
335C2×D3—128no—
336C2×D3—128no—
337C2×D3—244no—
338C2×D3—244no—
339C2×D3—244no—
340C2×D3—244no—
341C3×C4—48no—
342C3×C4#67⋊C414yes—
343C3×C4#88514yes—
344C3×C4C4×#6714yes—
345C3×C4#94014yes—
346Dic3—316no—
347Dic3—68no—
348Dic3—128no—
349C32#198211yescharacteristic, complemented, Sylow
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—182no—
358C23—361no—
359C23—361no—
360C23—361no—
361C23—361no—
362C23—361no—
363C23—361no—
364C23D4×C3⋊D311yescharacteristic
365D4—22no—
366D4—22no—
367D4—41no—
368D4—41no—
369D4—182no—
370D4—182no—
371D4—368no—
372D4—368no—
373D4—361no—
374D4—361no—
375C2×C4—22no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—92no—
379C2×C4—92no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—361no—
386C2×C4—361no—
387C2×C4C2×C4×C3⋊D311yescharacteristic
388C2×C4#382811yescharacteristic
389C2×C4D4×C3⋊D311yescharacteristic
390C2×C4D4×C3⋊D311yescharacteristic
391C2×C4#383011yescharacteristic
392C2×C4C2×#63811yescharacteristic
393C8—41no—
394C8—361no—
395C2×C3—88no—
396C2×C3#476214yes—
397C2×C3D3×#10214yes—
398C2×C3#477014yes—
399C2×C3#478614yes—
400C2×C3#495714yes—
401C2×C3#515014yes—
402C2×C3#516314yes—
403D3—248no—
404C22—42no—
405C22—42no—
406C22—42no—
407C22—81no—
408C22—81no—
409C22—81no—
410C22—81no—
411C22—362no—
412C22—362no—
413C22—362no—
414C22—721no—
415C22—721no—
416C22—721no—
417C22—721no—
418C22C22⋊C4×C3⋊D311yescharacteristic
419C22#6409311yescharacteristic
420C22D8×C3⋊D311yescharacteristic
421C22#6412011yescharacteristic
422C22SD16×C3⋊D311yescharacteristic
423C22#6412311yescharacteristic
424C22#6414811yescharacteristic
425C4—42no—
426C4—94no—
427C4—182no—
428C4—362no—
429C4#6409011yescharacteristic
430C4#6409411yescharacteristic
431C4C4×#63811yescharacteristic
432C4#6414911yescharacteristic
433C3#7016114yescomplemented
434C2—82no—
435C2—722no—
436C2#1059246111yescharacteristic
437C2C3⋊D3×#10211yescharacteristic
438C2#1059246911yescharacteristic
439C2#1059248511yescharacteristic
440C2#1059265611yescharacteristic
441C2#1059284911yescharacteristic
442C2#1059286211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64149C2
cosocleC22×C32×C4C23
hypercenterC2×#102C3⋊D3
hypocenterC32#1982
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C2×#63659C2semidirect
4. C2×#63648C2semidirect
5. C2×#63641C2semidirect
6. C4⋊C4×C3⋊Dic3C2semidirect
7. C2×#63636C2semidirect
16. #64149C4semidirect
28. C2×C3×#102D3semidirect
63. C32×C4⋊C4D4semidirect
65. C4⋊(C3⋊Dic3)D4semidirect
141. C2×#102C3⋊D3semidirect
172. C3×C4⋊C4#67semidirect
209. C3⋊Dic3#102semidirect
316. C4⋊C4#638semidirect
349. C32#1982semidirect
433. C3#70161semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C32×#1022
C2×#636592
C2×#636482
C2×#636412
C4⋊C4×C3⋊Dic32
C2×#636362
#701613