Finite Group Databasebeta

← #11795396

Subgroups — #11795396

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#821C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic
4#10591230C211yesmaximal, characteristic, complemented
5C2×#63574C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589416C211yesmaximal, characteristic, complemented
8#70640—31nomaximal
9#70181—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—22no—
18C3×#821—22no—
19C3×#818—22no—
20#63579—22no—
21#63574—22no—
22#63562—22no—
23C2×C3×#107—31no—
24C2×C3×#102—31no—
25#5221—31no—
26C2×#832—31no—
27C2×#821D311yescharacteristic
28C2×#818D311yescharacteristic, complemented
29#4988—31no—
30#4977—31no—
31#4977—31no—
32C2×#809—31no—
33C2×#808—31no—
34C2×#808—31no—
35#4550—31no—
36#4550—31no—
37#4550—61no—
38C23×C3×D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3D412yes—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C4×C3⋊Dic3—21no—
54C4×C3⋊Dic3—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)D412yes—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64(C2×D3)⋊Dic3—44no—
65#2092—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C22×C3×C8—21no—
69C22×C3×C8C2×D311yescharacteristic
70C22×C3×C8C2×D311yescharacteristic
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—31no—
74C2×#217—62no—
75C2×(C2×D3)⋊C4—62no—
76C2×C4⋊Dic3C2×D311yescharacteristic
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×C4×Dic3—31no—
80C2×C4×Dic3—31no—
81C2×C4×Dic3—61no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—31no—
84C22×C3⋊C8—61no—
85C3×#107—62no—
86C3×#102—62no—
87#832—62no—
88C3⋊#95—62no—
89C3⋊#95—62no—
90#821—22no—
91#818—22no—
92#809—62no—
93#808—62no—
94#808—62no—
95C23×C32C2×D411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—41no—
98C22×C3×D3—41no—
99C22×C3×D3—42no—
100C22×C3×D3—42no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×Q811yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3×Dic3—41no—
111C2×C3×Dic3—41no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C3×D12—22no—
117C3×D12—22no—
118C3×D12—41no—
119C3×D12—41no—
120C32×C8—22no—
121C3⋊(C3⋊C8)—22no—
122C2×#107—31no—
123C2×#106—91no—
124C2×#102—31no—
125C2×#102—91no—
126#390—91no—
127#382—91no—
128#336—91no—
129C24×C3—61no—
130C23×D3—21no—
131C2×C3×D4—32no—
132C2×C3×D4—61no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C22×C3×C4—21no—
138C22×C3×C4—61no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3—21no—
144C22×Dic3—21no—
145C22×Dic3—21no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C22×Dic3—62no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12Dic612yes—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—21no—
159C2×C3×C8—22no—
160C2×C3×C8—41no—
161C2×C3×C8—41no—
162C2×C3×C8#6712yes—
163C2×C3×C8#6712yes—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170#217—124no—
171(C2×D3)⋊C4—124no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4×Dic3—61no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—61no—
182C4×Dic3—121no—
183C4×Dic3—121no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—32no—
186C2×C3⋊C8—62no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—121no—
192C2×C3⋊C8—121no—
193C22×C32C22⋊Q811yescharacteristic
194C22×C32#12311yescharacteristic
195C22×C32#12711yescharacteristic
196C22×C32#13512yes—
197C22×C32AGL(1,ℤ/8)12yes—
198C2×C3×D3—42no—
199C2×C3×D3—44no—
200C2×C3×D3—82no—
201C2×C3×D3—81no—
202C2×C3×D3—81no—
203C32×C4C22⋊Q811yescharacteristic
204C32×C4C22⋊Q811yescharacteristic
205C32×C4#12311yescharacteristic
206C32×C4#12311yescharacteristic
207C3⋊Dic3—42no—
208C3×Dic3—81no—
209C3×Dic3—81no—
210C3×Dic3—81no—
211C22×D4—31no—
212C22×C8—91no—
213C22×C8D3211yescharacteristic
214C2×C4⋊C4—31no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—31no—
217C2×C22⋊C4—182no—
218C2×C42—91no—
219#107—62no—
220#106—182no—
221#102—62no—
222#102—182no—
223#95—182no—
224C23×C3—21no—
225C23×C3—62no—
226C23×C3—121no—
227C23×C3—122no—
228C23×C3—122no—
229C23×C3—121no—
230C23×C3D3×D411yescharacteristic
231C23×C3D3×D411yescharacteristic
232C22×D3—22no—
233C22×D3—41no—
234C22×D3—42no—
235C22×D3—42no—
236C22×D3—41no—
237C3×D4—62no—
238C3×D4—62no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4—122no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4C2×Dic611yescharacteristic
254C2×C3×C4#23511yescharacteristic
255C2×C3×C4#23511yescharacteristic
256C2×C3×C4#23511yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4#23711yescharacteristic
260C2×C3×C4#23711yescharacteristic
261C2×C3×C4D3×Q811yescharacteristic
262C2×C3×C4#23911yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—42no—
268C2×Dic3—41no—
269C2×Dic3—41no—
270C2×Dic3—41no—
271C2×Dic3—64no—
272C2×Dic3—62no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280D12—22no—
281D12—22no—
282D12—41no—
283D12—41no—
284C3×C8—22no—
285C3×C8—22no—
286C3×C8—42no—
287C3⋊C8—62no—
288C3⋊C8—62no—
289C3⋊C8—122no—
290C2×C32#39911yescharacteristic
291C2×C32#47812yes—
292C2×C32#48212yes—
293C2×C32#49511yescharacteristic
294C2×C32#49611yescharacteristic
295C3×D3—82no—
296C24—61no—
297C2×D4—32no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C22×C4—61no—
304C22×C4—61no—
305C22×C4—61no—
306C22×C4—92no—
307C22×C4C2×D3211yescharacteristic
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8#62512yes—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C22⋊C4—364no—
321C42—181no—
322C42—181no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—124no—
329C22×C3—122no—
330C22×C3—242no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3#87811yescharacteristic
334C22×C3#88311yescharacteristic
335C22×C3#89411yescharacteristic
336C22×C3#89611yescharacteristic
337C22×C3#91112yes—
338C22×C3#91212yes—
339C22×C3#91412yes—
340C22×C3#91912yes—
341C22×C3#94011yescharacteristic
342C22×C3#94011yescharacteristic
343C2×D3—42no—
344C2×D3—44no—
345C2×D3—81no—
346C2×D3—81no—
347C2×D3—82no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—241no—
353C3×C4—241no—
354C3×C4—241no—
355C3×C4#87811yescharacteristic
356C3×C4#88311yescharacteristic
357C3×C4#89411yescharacteristic
358C3×C4#89611yescharacteristic
359C3×C4#92411yescharacteristic
360C3×C4#92911yescharacteristic
361C3×C4#93511yescharacteristic
362C3×C4#94611yescharacteristic
363Dic3—81no—
364Dic3—81no—
365Dic3—81no—
366Dic3—124no—
367Dic3—122no—
368Dic3—122no—
369C32#209211yescharacteristic, complemented, Sylow
370C23—62no—
371C23—122no—
372C23—122no—
373C23—121no—
374C23—121no—
375C23#380211yescharacteristic
376D4—62no—
377D4—62no—
378D4—121no—
379D4—121no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—121no—
384C2×C4—121no—
385C2×C4—121no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—182no—
389C2×C4D3×Dic611yescharacteristic
390C2×C4#379911yescharacteristic
391C2×C4#380211yescharacteristic
392C2×C4#380411yescharacteristic
393C2×C4#380411yescharacteristic
394C2×C4C2×#62511yescharacteristic
395C8—22no—
396C8—182no—
397C2×C3—22no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—22no—
402C2×C3—242no—
403C2×C3#476612yes—
404C2×C3#478412yes—
405C2×C3#488512yes—
406C2×C3#489112yes—
407C2×C3#494911yescharacteristic
408C2×C3#499311yescharacteristic
409C2×C3#515411yescharacteristic
410C2×C3#515511yescharacteristic
411C2×C3#517611yescharacteristic
412C2×C3#519111yescharacteristic
413D3—82no—
414C22—124no—
415C22—122no—
416C22—241no—
417C22—241no—
418C22—242no—
419C22#6379812yes—
420C22#6381012yes—
421C22#6385411yescharacteristic
422C22#6389911yescharacteristic
423C22#6391411yescharacteristic
424C4—241no—
425C4—241no—
426C4—241no—
427C4—362no—
428C4#6385411yescharacteristic
429C4#6385611yescharacteristic
430C4#6389911yescharacteristic
431C4#6396111yescharacteristic
432C3—21no—
433C3#7018111yescharacteristic, complemented
434C3#7064011yescharacteristic, complemented
435C2—242no—
436C2#1059065112yes—
437C2#1059078012yes—
438C2#1059086911yescharacteristic
439C2#1059088711yescharacteristic
440C2#1059132411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
4. #10591230C2semidirect
5. C2×#63574C2semidirect
7. #10589416C2semidirect
28. C2×#818D3semidirect
369. C32#2092semidirect
433. C3#70181semidirect
434. C3#70640semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8212
C2×C3×#8182
#105913232
#105912302
C2×#635742
C2×#635622
#105894162
#706403
#701813