Finite Group Databasebeta

← #11790550

Subgroups — #11790550

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4C2×#63647C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×#63641C211yesmaximal, characteristic, complemented
7C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#69916—34nomaximal
9C23×C32×C4C2211yescharacteristic
10C22×#638C411yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×#3757C411yescharacteristic
15C4×#638—22no—
16C4×#638—22no—
17C2×#3752C411yescharacteristic
18C2×#3750C411yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C32×C22⋊C8—22no—
23#63657—22no—
24#63647—22no—
25#63647—22no—
26#63641—22no—
27C8×C3⋊Dic3—22no—
28C2×C4×#67—34no—
29C2×C3×C22⋊C8D314yescomplemented
30C2×#830—34no—
31C2×(C2×D3)⋊C8—34no—
32C2×(C2×D3)⋊C8—34no—
33C2×Dic3⋊C8—34no—
34C2×C8×Dic3—34no—
35C24×C32C2×C411yescharacteristic
36C23×C3⋊D3C2×C411yescharacteristic
37C22×C32×C4—21no—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C2×#638—22no—
46C2×#638—22no—
47C2×#638C814yescomplemented
48C22×C3⋊Dic3C2×C411yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
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×C4×C3⋊D3—21no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C2×C32×C8D412yescomplemented
63#3757—22no—
64#3752—22no—
65#3750—22no—
66C4×C3⋊Dic3D412yes—
67C4×C3⋊Dic3D412yes—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)D412yescomplemented
74#1954—91noSylow
75C23×C3×C4C2×D314yes—
76C22×#67—34no—
77C22×C4×D3—34no—
78C22×C3×C8C2×D314yes—
79C22×C3×C8C2×D314yes—
80C2×#217—34no—
81C4×#67—68no—
82C4×#67—68no—
83C2×(C2×D3)⋊C4—34no—
84C2×Dic3⋊C4—34no—
85C2×C4×Dic3—34no—
86C22×C3⋊C8—34no—
87C22×C3⋊C8—34no—
88C3×C22⋊C8—28no—
89#830—68no—
90(C2×D3)⋊C8—68no—
91(C2×D3)⋊C8—68no—
92Dic3⋊C8—68no—
93C8×Dic3—68no—
94C23×C32—21no—
95C23×C32—21no—
96C23×C32—21no—
97C23×C32—21no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32C2×C812yes—
101C23×C32C22×C411yescharacteristic
102C22×C3⋊D3—21no—
103C22×C3⋊D3—21no—
104C22×C3⋊D3—21no—
105C22×C3⋊D3—21no—
106C22×C3⋊D3—21no—
107C22×C3⋊D3—21no—
108C22×C3⋊D3C2×C812yes—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122#638—28no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3C22⋊C412yes—
129C2×C3⋊Dic3C22⋊C412yes—
130C2×C3⋊Dic3C2×C812yes—
131C2×C3⋊Dic3M1612yes—
132C4×C3⋊D3—41no—
133C4×C3⋊D3—41no—
134C4×C3⋊D3—41no—
135C4×C3⋊D3—41no—
136C32×C8—22no—
137C32×C8—41no—
138C3⋊(C3⋊C8)—22no—
139C3⋊(C3⋊C8)—41no—
140C2×C4×D4—91no—
141C2×C4⋊C8—91no—
142C2×C22⋊C8—91no—
143C2×C22⋊C8—91no—
144C2×C22⋊C8—91no—
145C2×C22⋊C8C3⋊D311yescharacteristic, complemented
146C2×C4×C8—91no—
147C24×C3C4×D314yes—
148C23×D3—34no—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4—24no—
152C22×C3×C4—24no—
153C22×C3×C4—24no—
154C22×C3×C4—24no—
155C22×C3×C4C4×D314yes—
156C22×C3×C4C22×D314yes—
157C2×#67—316no—
158C2×#67—68no—
159C2×#67—68no—
160C22×Dic3—34no—
161C22×Dic3—34no—
162C22×Dic3—34no—
163C2×C4×D3—64no—
164C2×C4×D3—64no—
165C2×C4×D3—64no—
166C2×C4×D3—64no—
167C2×C4×D3—64no—
168C2×C4×D3—64no—
169C2×C3×C8—24no—
170C2×C3×C8—24no—
171C2×C3×C8—24no—
172C2×C3×C8—24no—
173C2×C3×C8—24no—
174C2×C3×C8#6718yescomplemented
175#217—68no—
176(C2×D3)⋊C4—68no—
177Dic3⋊C4—68no—
178C4×Dic3—38no—
179C4×Dic3—38no—
180C2×C3⋊C8—38no—
181C2×C3⋊C8—64no—
182C2×C3⋊C8—64no—
183C2×C3⋊C8—64no—
184C2×C3⋊C8—64no—
185C2×C3⋊C8—64no—
186C22×C32—22no—
187C22×C32—22no—
188C22×C32—22no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32C2×C22⋊C411yescharacteristic
194C22×C32C4×D411yescharacteristic
195C22×C32C4×D411yescharacteristic
196C22×C32C22×C811yescharacteristic
197C22×C32C2×M1611yescharacteristic
198C22×C32#13111yescharacteristic
199C22×C32#13111yescharacteristic
200C2×C3⋊D3—22no—
201C2×C3⋊D3—22no—
202C2×C3⋊D3—22no—
203C2×C3⋊D3—41no—
204C2×C3⋊D3—41no—
205C2×C3⋊D3—41no—
206C2×C3⋊D3—41no—
207C32×C4—41no—
208C32×C4#12111yescharacteristic
209C32×C4#12111yescharacteristic
210C32×C4#12411yescharacteristic
211C32×C4#12711yescharacteristic
212C3⋊Dic3—22no—
213C3⋊Dic3—41no—
214C3⋊Dic3C22⋊C814yescomplemented
215C22×D4—91no—
216C23×C4—91no—
217C23×C4C2×C3⋊D311yescharacteristic
218C22×C8—91no—
219C22×C8—91no—
220C22×C8C2×C3⋊D311yescharacteristic
221C22×C8C2×C3⋊D311yescharacteristic
222C4×D4—182no—
223C4×D4—182no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—91no—
226C2×C22⋊C4—91no—
227C2×C42—91no—
228C4⋊C8—182no—
229C22⋊C8—22no—
230C22⋊C8—182no—
231C22⋊C8—182no—
232C22⋊C8—182no—
233C4×C8—182no—
234C23×C3—24no—
235C23×C3—24no—
236C23×C3—24no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3D3×C818yes—
241C23×C3C2×C4×D314yes—
242C22×D3—38no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—64no—
246C22×D3—64no—
247C22×D3—64no—
248C22×D3—64no—
249C2×C3×C4—24no—
250C2×C3×C4—24no—
251C2×C3×C4—24no—
252C2×C3×C4—44no—
253C2×C3×C4—44no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4#23514yes—
257C2×C3×C4D3×D414yes—
258C2×C3×C4D3×D414yes—
259C2×C3×C4D3×D414yes—
260C2×C3×C4#23714yes—
261C2×C3×C4C2×#6714yes—
262#67—632no—
263C2×Dic3—38no—
264C2×Dic3—38no—
265C2×Dic3—38no—
266C2×Dic3—38no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—64no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C4×D3—124no—
273C4×D3—124no—
274C4×D3—124no—
275C4×D3—124no—
276C3×C8—28no—
277C3×C8—44no—
278C3⋊C8—68no—
279C3⋊C8—124no—
280C2×C32—42no—
281C2×C32#39011yescharacteristic
282C2×C32C2×C22⋊C811yescharacteristic
283C2×C32#40811yescharacteristic
284C2×C32C8×D411yescharacteristic
285C2×C32C8×D411yescharacteristic
286C2×C32#43611yescharacteristic
287C2×C32#43611yescharacteristic
288C3⋊D3—42no—
289C24—91no—
290C24C4×C3⋊D311yescharacteristic
291C2×D4—94no—
292C2×D4—182no—
293C2×D4—182no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—181no—
304C22×C4—181no—
305C22×C4—181no—
306C22×C4—181no—
307C22×C4—181no—
308C22×C4—181no—
309C22×C4C4×C3⋊D311yescharacteristic
310C22×C4C22×C3⋊D311yescharacteristic
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—92no—
317C2×C8—181no—
318C2×C8—181no—
319C2×C8—181no—
320C2×C8—181no—
321C2×C8—181no—
322C2×C8#63812yescomplemented
323C4⋊C4—182no—
324C22⋊C4—182no—
325C22⋊C4—182no—
326C42—92no—
327C42—92no—
328C22×C3—28no—
329C22×C3—28no—
330C22×C3—28no—
331C22×C3—44no—
332C22×C3—44no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3D3×C22⋊C414yes—
336C22×C3#67⋊C414yes—
337C22×C3C2×D3×C814yes—
338C22×C3#90114yes—
339C22×C3D3×M1614yes—
340C22×C3#90714yes—
341C22×C3C4×#6714yes—
342C2×D3—68no—
343C2×D3—68no—
344C2×D3—68no—
345C2×D3—124no—
346C2×D3—124no—
347C2×D3—124no—
348C2×D3—124no—
349C3×C4—44no—
350C3×C4#88414yes—
351C3×C4#88514yes—
352C3×C4#93914yes—
353C3×C4#94014yes—
354Dic3—316no—
355Dic3—68no—
356Dic3—124no—
357C32#195411yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—92no—
365C23—181no—
366C23—181no—
367C23—181no—
368C23—181no—
369C23—181no—
370C23—181no—
371C23C8×C3⋊D312yes—
372C23C2×C4×C3⋊D311yescharacteristic
373D4—188no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—92no—
382C2×C4—92no—
383C2×C4—92no—
384C2×C4—92no—
385C2×C4—181no—
386C2×C4—181no—
387C2×C4—181no—
388C2×C4—181no—
389C2×C4—181no—
390C2×C4—361no—
391C2×C4—361no—
392C2×C4—361no—
393C2×C4—361no—
394C2×C4#382811yescharacteristic
395C2×C4D4×C3⋊D311yescharacteristic
396C2×C4D4×C3⋊D311yescharacteristic
397C2×C4D4×C3⋊D311yescharacteristic
398C2×C4#383011yescharacteristic
399C2×C4C2×#63811yescharacteristic
400C8—22no—
401C8—41no—
402C8—182no—
403C8—361no—
404C2×C3—48no—
405C2×C3D3×C22⋊C814yes—
406C2×C3#67⋊C814yes—
407C2×C3#472714yes—
408C2×C3#472914yes—
409C2×C3#495714yes—
410C2×C3C8×#6714yes—
411C2×C3#512814yes—
412D3—128no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—182no—
421C22—182no—
422C22—182no—
423C22—361no—
424C22—361no—
425C22—361no—
426C22—361no—
427C22C22⋊C4×C3⋊D311yescharacteristic
428C22#6409011yescharacteristic
429C22C2×C8×C3⋊D311yescharacteristic
430C22#6411011yescharacteristic
431C22M16×C3⋊D311yescharacteristic
432C22#6411611yescharacteristic
433C22C4×#63811yescharacteristic
434C4—41no—
435C4—94no—
436C4—182no—
437C4—361no—
438C4#6409311yescharacteristic
439C4#6409411yescharacteristic
440C4#6414811yescharacteristic
441C4#6414911yescharacteristic
442C3#6991614yescomplemented
443C2—42no—
444C2—362no—
445C2C3⋊D3×C22⋊C811yescharacteristic
446C2#1059242411yescharacteristic
447C2#1059242611yescharacteristic
448C2#1059242811yescharacteristic
449C2#1059265611yescharacteristic
450C2C8×#63811yescharacteristic
451C2#1059282711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutatorC22×C32C22×C8
FittingC2×C32×C22⋊C8C2
socleC23×C32C22×C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C8C3⋊D3
hypocenterC32#1954
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C22⋊C8C2semidirect
3. C2×#63657C2semidirect
4. C2×#63647C2semidirect
5. C2×#63647C2semidirect
6. C2×#63641C2semidirect
7. C2×C8×C3⋊Dic3C2semidirect
29. C2×C3×C22⋊C8D3semidirect
47. C2×#638C8semidirect
62. C2×C32×C8D4semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
145. C2×C22⋊C8C3⋊D3semidirect
174. C2×C3×C8#67semidirect
214. C3⋊Dic3C22⋊C8semidirect
322. C2×C8#638semidirect
357. C32#1954semidirect
442. C3#69916semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C32×C22⋊C82
C2×#636572
C2×#636472
C2×#636412
C2×C8×C3⋊Dic32
#699163