Finite Group Databasebeta

← #11786750

Subgroups — #11786750

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2#10592676C211yesmaximal, characteristic, complemented
3#10591131C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591088C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71665—31nomaximal
9#69003—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×C4×#67—22no—
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C3×#893—21no—
19C3×#892—21no—
20C3×D3×C4⋊C4—21no—
21C3×#887—21no—
22#63658—22no—
23#63575—21no—
24#63573—21no—
25#63568C414yescomplemented
26#63566—21no—
27#63563—21no—
28C3×#520—31no—
29#5504D311yescharacteristic
30C2×#837—31no—
31#5232—31no—
32C2×#825—31no—
33#5133—31no—
34#5121—31no—
35#4995—31no—
36#4977—31no—
37#4977—31no—
38#4977—61no—
39C3×#343—31no—
40#4555—31no—
41#4532—31no—
42#4530D311yescharacteristic, complemented
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3C2×C412yescomplemented
62C3×#217—21no—
63C3×(C2×D3)⋊C4—22no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—22no—
67C3×C4×Dic3—22no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yescomplemented
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#1860—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C2×C3×M16—31no—
79C2×C3×M16—31no—
80C3×C4×Q8—61no—
81C3×C4×D4—61no—
82C3×C4×D4—62no—
83C3×#117—31no—
84C3×#117—61no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—61no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C4×#67—22no—
90#926C2×D311yescharacteristic
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—61no—
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#893—21no—
100#892—21no—
101D3×C4⋊C4—21no—
102#887—21no—
103#837—34no—
104#835—61no—
105#832—61no—
106C3⋊#95—64no—
107C3⋊#95—62no—
108C3⋊#95—62no—
109#825—34no—
110#821—61no—
111#818—61no—
112#817—61no—
113#816—61no—
114#808—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—22no—
119C2×C32×C4—42no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—42no—
130C2×C3⋊Dic3—41no—
131C3×#67—22no—
132C3×#67—22no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C3×D12—21no—
137C3×D12C4⋊C412yes—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×C4×D3—82no—
141C3×Dic6—21no—
142C3×Dic6C4⋊C412yes—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145#520—31no—
146#428—91no—
147C2×#104—91no—
148#417—91no—
149#382—91no—
150#343—31no—
151#339—91no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4D1212yes—
164C22×C3×C4#6712yes—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
168C22×Dic3—62no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—62no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174#235—21no—
175#235—21no—
176#235Dic612yes—
177#235C4×D312yes—
178C2×D12#6711yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—22no—
181C2×Dic6#6711yescharacteristic
182C3×M16—32no—
183C3×M16—61no—
184C3×M16—61no—
185C3×M16—61no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—31no—
193C3×C4⋊C4—31no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—62no—
197C3×C22⋊C4—62no—
198C3×C22⋊C4—61no—
199C3×C42—62no—
200C3×C42—61no—
201#217—21no—
202(C2×D3)⋊C4—22no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—121no—
208C4⋊Dic3—121no—
209C4⋊Dic3#6711yescharacteristic
210C4⋊Dic3#6711yescharacteristic
211Dic3⋊C4—22no—
212C4×Dic3—22no—
213C4×Dic3—21no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—62no—
217C4×Dic3—62no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220#208—21no—
221#208—21no—
222#208—21no—
223#208C4×D312yescomplemented
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C22×C32—21no—
227C22×C32—21no—
228C22×C32C4×D411yescharacteristic
229C22×C32#12011yescharacteristic
230C22×C32C22⋊Q811yescharacteristic
231C2×C3×D3—22no—
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C32×C4—42no—
235C32×C4C2×C4⋊C411yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4C22⋊Q811yescharacteristic
238C32×C4#12311yescharacteristic
239C3⋊Dic3—42no—
240C3⋊Dic3—81no—
241C3×Dic3—22no—
242C3×Dic3—41no—
243C3×Dic3—41no—
244C2×#41—31no—
245C2×M16—31no—
246C2×M16—31no—
247C4×Q8—61no—
248C4×D4—61no—
249C4×D4—62no—
250#117—31no—
251#117—61no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4D3211yescharacteristic
255C2×C42—91no—
256#107—181no—
257#106—181no—
258#104—94no—
259#103—181no—
260#102—181no—
261#95—182no—
262C23×C3—21no—
263C23×C3—61no—
264C23×C3C2×D1211yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—21no—
267C3×Q8—32no—
268C3×Q8—61no—
269C3×D4—32no—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—61no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—44no—
285C2×C3×C4—61no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—242no—
291C2×C3×C4C2×Dic611yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—22no—
304#67—22no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—124no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—121no—
322C2×Dic3—121no—
323D12—21no—
324D12Dic3⋊C412yes—
325C4×D3—22no—
326C4×D3—22no—
327C4×D3—82no—
328Dic6—21no—
329Dic6Dic3⋊C412yes—
330C3×C8—62no—
331C3×C8—121no—
332C3⋊C8—22no—
333C3⋊C8—41no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38511yescharacteristic
337C2×C32#45411yescharacteristic
338C2×C32#45511yescharacteristic
339C3×D3—42no—
340#41—32no—
341#41—32no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C22×C4—62no—
348C22×C4—61no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4#62612yes—
352C22×C4C2×D3211yescharacteristic
353M16—32no—
354M16—61no—
355M16—61no—
356M16—61no—
357C2×C8—61no—
358C2×C8—61no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—31no—
362C4⋊C4—31no—
363C4⋊C4—62no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C22⋊C4—62no—
367C22⋊C4—61no—
368C42—62no—
369C42—61no—
370C42—92no—
371C42—181no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3C4×D1211yescharacteristic
385C22×C3#88211yescharacteristic
386C22×C3#89711yescharacteristic
387C22×C3#92411yescharacteristic
388C22×C3C4×#6711yescharacteristic
389C22×C3#95311yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—62no—
400C3×C4—82no—
401C3×C4—121no—
402C3×C4—121no—
403C3×C4#67⋊C411yescharacteristic
404C3×C4#88311yescharacteristic
405C3×C4D3×C4⋊C411yescharacteristic
406C3×C4#89611yescharacteristic
407C3×C4C2×Dic3⋊C411yescharacteristic
408C3×C4#92411yescharacteristic
409C3×C4C4×#6711yescharacteristic
410C3×C4#92911yescharacteristic
411Dic3—22no—
412Dic3—41no—
413Dic3—41no—
414Dic3—124no—
415Dic3—122no—
416Dic3—122no—
417Dic3—242no—
418Dic3—241no—
419Dic3—241no—
420C32#186011yescharacteristic, complemented, Sylow
421C23—61no—
422C23C2×#62611yescharacteristic
423Q8—32no—
424Q8—61no—
425D4—32no—
426D4—62no—
427D4—62no—
428D4—61no—
429C2×C4—22no—
430C2×C4—42no—
431C2×C4—61no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—182no—
437C2×C4—242no—
438C2×C4—361no—
439C2×C4—361no—
440C2×C4—362no—
441C2×C4—361no—
442C2×C4D3×Dic611yescharacteristic
443C2×C4#379511yescharacteristic
444C2×C4#379811yescharacteristic
445C2×C4C4×D3211yescharacteristic
446C2×C4D3×#6711yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C8—62no—
449C8—121no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—122no—
460C2×C3#466811yescharacteristic
461C2×C3#474611yescharacteristic
462C2×C3#475311yescharacteristic
463C2×C3#521011yescharacteristic
464C2×C3#524211yescharacteristic
465C2×C3#524511yescharacteristic
466D3—42no—
467C22—21no—
468C22—21no—
469C22—62no—
470C22—121no—
471C22—121no—
472C22#6385711yescharacteristic
473C22C4×#62611yescharacteristic
474C22#6397711yescharacteristic
475C4—42no—
476C4—62no—
477C4—121no—
478C4—121no—
479C4—362no—
480C4—721no—
481C4#6385111yescharacteristic
482C4D3×Dic3⋊C411yescharacteristic
483C4#6387911yescharacteristic
484C4#6390511yescharacteristic
485C3—21no—
486C3#6900311yescharacteristic, complemented
487C3#7166511yescharacteristic, complemented
488C2—21no—
489C2—21no—
490C2—122no—
491C2#1059127811yescharacteristic
492C2#1059151311yescharacteristic
493C2#1059164611yescharacteristic
subgroupG/H
centerC22#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1860
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592676C2semidirect
3. #10591131C2semidirect
6. C3×#4530C2semidirect
7. #10589160C2semidirect
25. #63568C4semidirect
42. #4530D3semidirect
61. C4×C3⋊Dic3C2×C4semidirect
72. C3×#208C2×C4semidirect
223. #208C4×D3semidirect
420. C32#1860semidirect
486. C3#69003semidirect
487. C3#71665semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105926762
#105911312
C2×#635682
#105910882
C3×#45302
#105891602
#716653
#690033