Finite Group Databasebeta

← #11778523

Subgroups — #11778523

Order 1152.

489 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 489 conjugacy classes of subgroups — too many to draw. Only its 78 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
1#10594980C211yesmaximal, characteristic
2#10592435C211yesmaximal, characteristic
3#10591353C211yesmaximal, characteristic, complemented
4#10591126C211yesmaximal, characteristic, complemented
5C3×#4469C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic
8#68328—31nomaximal
9#68134—31nomaximal
10#64139C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63966—21no—
15C2×Dic3⋊Dic3—21no—
16#63952—21no—
17#63897—21no—
18#63888—21no—
19#63848—21no—
20#63845—21no—
21C32×C22⋊C8C2211yescharacteristic
22#63648—21no—
23#63645—21no—
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27#63573—21no—
28#63566—21no—
29#5645—31no—
30#5515—31no—
31#5043—31no—
32#4981—31no—
33#4736—31no—
34#4736—31no—
35#4736—61no—
36#4721—31no—
37#4661—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4470—31no—
41#4469D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C2×C32×C8—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—42no—
68#3722—21no—
69#3722—21no—
70#3722—21no—
71Dic32—21no—
72#1609—91noSylow
73C3×C22⋊Q8—31no—
74C2×C3×C4⋊C4—31no—
75#946—61no—
76#930—31no—
77#930—31no—
78#930—61no—
79#929—61no—
80C4×#67—61no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3—61no—
85#924C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4C2×D311yescharacteristic
88#898—61no—
89#898—61no—
90#896—61no—
91#894—61no—
92#894—61no—
93#890—61no—
94#889—61no—
95#886—61no—
96#67⋊C4—61no—
97C3×C22⋊C8—21no—
98C3×C22⋊C8—31no—
99C3×C22⋊C8C2×D311yescharacteristic
100C3×C22⋊C8C2×D311yescharacteristic
101C3×#95—31no—
102#835—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830C2×D311yescharacteristic
107#821—61no—
108#821—61no—
109#821—62no—
110#818—61no—
111#818—61no—
112#818—62no—
113#817—61no—
114#816—61no—
115#808—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C2×C32×C4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121#638—41no—
122#638—41no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—41no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C3×Dic6—41no—
139#624—81no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#539—91no—
143#483—91no—
144#480—91no—
145#398—91no—
146#328—31no—
147#327—91no—
148#324—31no—
149C2×C3×Q8—31no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—121no—
159C22×Dic3—21no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—121no—
163C22×Dic3D1211yescharacteristic
164C22×Dic3D1211yescharacteristic
165C2×D12—31no—
166C2×D12—31no—
167C2×D12—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6D1211yescharacteristic
171C2×C3×C8—22no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—61no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—61no—
180#217—21no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—121no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—62no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—121no—
201C4⋊Dic3—122no—
202C4⋊Dic3D1211yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—21no—
205Dic3⋊C4—21no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—122no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C2×C3⋊C8—21no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32#12011yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C2×C3⋊D3—41no—
220C2×C3⋊D3—41no—
221C2×C3⋊D3—41no—
222C32×C4—21no—
223C32×C4—21no—
224C3⋊Dic3—41no—
225C3⋊Dic3—81no—
226C3×Dic3—42no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—41no—
231#126—181no—
232#125—181no—
233#123—181no—
234#123—181no—
235C22⋊Q8—31no—
236C22⋊Q8—181no—
237#121—91no—
238C4×D4—181no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242#107—181no—
243#106—181no—
244#103—181no—
245#102—181no—
246C22⋊C8—31no—
247C22⋊C8D3211yescharacteristic
248#95—31no—
249#95—181no—
250C23×C3—21no—
251C23×C3C2×D1211yescharacteristic
252C23×C3D3×D411yescharacteristic
253C22×D3—61no—
254C22×D3—61no—
255C22×D3—121no—
256C3×Q8—121no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—42no—
262C2×C3×C4—62no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276#67—121no—
277#67—121no—
278#67—121no—
279#67—121no—
280#67—241no—
281#67—241no—
282C2×Dic3—22no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—41no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—121no—
295C2×Dic3—122no—
296C2×Dic3—121no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—241no—
303C2×Dic3—241no—
304D12—121no—
305D12—121no—
306D12—122no—
307C4×D3—241no—
308C4×D3—241no—
309Dic6—41no—
310C3×C8—42no—
311C3×C8—41no—
312C3×C8—41no—
313C3×C8—121no—
314C3⋊C8—41no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32#44911yescharacteristic
318C2×C32#45611yescharacteristic
319C2×C32#45811yescharacteristic
320C3⋊D3—81no—
321C2×Q8—31no—
322C2×D4—91no—
323C2×D4—181no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—61no—
327C22×C4—181no—
328C22×C4—181no—
329C22×C4C2×D3211yescharacteristic
330C2×C8—21no—
331C2×C8—61no—
332C4⋊C4—31no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—91no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C4⋊C4—181no—
341C4⋊C4—181no—
342C4⋊C4—362no—
343C22⋊C4—61no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C22⋊C4—181no—
348C42—181no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3#88211yescharacteristic
359C22×C3#88211yescharacteristic
360C22×C3#90411yescharacteristic
361C22×C3#90811yescharacteristic
362C22×C3#91411yescharacteristic
363C22×C3#91911yescharacteristic
364C2×D3—121no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—241no—
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—41no—
379C3×C4—122no—
380C3×C4—121no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4—121no—
384Dic3—42no—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3—41no—
389Dic3—121no—
390Dic3—121no—
391Dic3—241no—
392Dic3—242no—
393Dic3—241no—
394Dic3—241no—
395C32#160911yescharacteristic, complemented, Sylow
396C23—181no—
397C23D3×D1211yescharacteristic
398Q8—121no—
399D4—361no—
400D4—361no—
401D4—361no—
402C2×C4—41no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—121no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—181no—
414C2×C4—361no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4—721no—
418C2×C4D3×D1211yescharacteristic
419C2×C4#381111yescharacteristic
420C8—41no—
421C8—121no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3#473411yescharacteristic
432C2×C3#474211yescharacteristic
433C2×C3#474211yescharacteristic
434C2×C3#475211yescharacteristic
435C2×C3#481011yescharacteristic
436C2×C3#482611yescharacteristic
437D3—241no—
438D3—241no—
439D3—481no—
440C22—21no—
441C22—21no—
442C22—361no—
443C22—361no—
444C22—361no—
445C22#6379411yescharacteristic
446C22#6380811yescharacteristic
447C22#6392311yescharacteristic
448C4—21no—
449C4—21no—
450C4—122no—
451C4—121no—
452C4—121no—
453C4—121no—
454C4—121no—
455C4—361no—
456C4—721no—
457C3—21no—
458C3#6813411yescharacteristic, complemented
459C3#6832811yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—721no—
463C2#1059040911yescharacteristic
464C2#1059096711yescharacteristic
465C2#1059102111yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
hypercenterC22⋊C8D32
hypocenterC32#1609
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10591353C2semidirect
4. #10591126C2semidirect
5. C3×#4469C2semidirect
6. C3×#4467C2semidirect
41. #4469D3semidirect
42. #4467D3semidirect
395. C32#1609semidirect
458. C3#68134semidirect
459. C3#68328semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105924352
#105913532
#105911262
C3×#44692
C3×#44672
#105891512
#683283
#681343