Finite Group Databasebeta

← #11787908

Subgroups — #11787908

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595987C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic
4#10591086C211yesmaximal, characteristic
5C2×#63561C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70325—31nomaximal
9#68766—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64096—22no—
15#64086—22no—
16C4×#634—22no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—22no—
21#63860—22no—
22#63860C414yescomplemented
23C3×#809—22no—
24#63563—22no—
25#63561—22no—
26C2×#936—31no—
27#5516—31no—
28#5516—31no—
29#5516—61no—
30C2×#875—31no—
31C3×#418—31no—
32#5215—31no—
33C2×#824—31no—
34C2×#824—31no—
35#5131—31no—
36#5001D311yescharacteristic
37C3×#339—31no—
38#4555—31no—
39#4532D311yescharacteristic, complemented
40#4523—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634C2×C412yes—
49C2×#634D412yes—
50C22×C3×Dic3—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12C2×C412yes—
57C32×C4⋊C4D412yes—
58C32×C22⋊C4—21no—
59C32×C42—21no—
60#3757—21no—
61C4⋊(C3⋊Dic3)D412yes—
62#3750—24no—
63C4×C3⋊Dic3—24no—
64C4×C3⋊Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C412yes—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—28no—
74#1888—91noSylow
75C22×C3×D4—31no—
76C22×D12C2×D311yescharacteristic
77C22×Dic6—31no—
78C22×Dic6—31no—
79C22×Dic6—61no—
80C2×C3×M16—31no—
81C2×C3×M16—31no—
82C3×#117—21no—
83C3×#117C2×D311yescharacteristic
84C3×#117C2×D311yescharacteristic
85C2×C3×C42—31no—
86C2×#217—62no—
87#936—34no—
88#936—62no—
89C2×(C2×D3)⋊C4—62no—
90#926—31no—
91#926—31no—
92#926—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96#887—64no—
97#887—62no—
98#887—62no—
99#877—62no—
100#877—62no—
101#877—64no—
102#875—34no—
103#875—62no—
104C4×Dic6—62no—
105C4×Dic6—62no—
106C4×Dic6—64no—
107C3×#102—62no—
108#832—62no—
109#824—62no—
110#824—62no—
111#821—62no—
112#809—22no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—22no—
115C22×C3×D3—44no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C2×C32×C4—22no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3C22⋊C414yes—
129#634—22no—
130#634—22no—
131#634—22no—
132#634—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—42no—
135C3×D12—22no—
136C3×D12—22no—
137C3×D12—41no—
138C3×D12—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141C2×#124—91no—
142#519—91no—
143#418—31no—
144#418—91no—
145C2×#101—91no—
146#339—31no—
147#339—91no—
148C24×C3—61no—
149C23×D3—21no—
150C2×C3×D4—32no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C2×C3×D4—61no—
156C22×C3×C4—21no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—62no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12C4×D312yes—
170C2×Dic6—32no—
171C2×Dic6—32no—
172C2×Dic6—32no—
173C2×Dic6—32no—
174C2×Dic6—62no—
175C2×Dic6—62no—
176C2×Dic6—62no—
177C2×Dic6—62no—
178C2×Dic6—62no—
179C2×Dic6—62no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C3×M16—61no—
189C3×M16—61no—
190C3×M16—61no—
191C3×M16—61no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4D1212yes—
196C3×C4⋊C4#6712yes—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—21no—
199C3×C22⋊C4—21no—
200C3×C42—22no—
201C3×C42—21no—
202C3×C42—21no—
203C3×C42—32no—
204C3×C42—61no—
205#217—68no—
206#217—62no—
207#217—61no—
208#217—61no—
209(C2×D3)⋊C4—68no—
210C4⋊Dic3—32no—
211C4⋊Dic3—32no—
212C4⋊Dic3—62no—
213Dic3⋊C4—68no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216C4×Dic3—21no—
217C4×Dic3—68no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C4×Dic3—62no—
221C4×Dic3—61no—
222C4×Dic3—61no—
223C4×Dic3C4×D312yes—
224#208—21no—
225#208—21no—
226#208—21no—
227#208—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C22×C32—22no—
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32#12311yescharacteristic
234C2×C3×D3—44no—
235C2×C3×D3—42no—
236C2×C3×D3—82no—
237C2×C3×D3—82no—
238C32×C4—42no—
239C32×C4C4×D411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12111yescharacteristic
243C3⋊Dic3—24no—
244C3⋊Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—91no—
247C22×D4—31no—
248C2×M16—31no—
249C2×M16—31no—
250#124—94no—
251#124—182no—
252C4×Q8—182no—
253C4×Q8—182no—
254#117—91no—
255#117—182no—
256#117D3211yescharacteristic
257C2×C22⋊C4—182no—
258C2×C42—31no—
259#102—62no—
260#102—182no—
261#101—182no—
262C23×C3—21no—
263C23×C3—62no—
264C23×C3—124no—
265C23×C3—121no—
266C23×C3—121no—
267C23×C3D3×D411yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—44no—
271C22×D3—41no—
272C22×D3—41no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—121no—
276C3×D4—121no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—62no—
287C2×C3×C4—122no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—34no—
302C2×Dic3—34no—
303C2×Dic3—42no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—64no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314D12—22no—
315D12—22no—
316D12—41no—
317D12—41no—
318Dic6—64no—
319Dic6—64no—
320Dic6—64no—
321Dic6—64no—
322Dic6—62no—
323Dic6—62no—
324Dic6—62no—
325Dic6—62no—
326Dic6—62no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330C3×C8—121no—
331C3×C8—121no—
332C3⋊C8—41no—
333C3⋊C8—41no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38611yescharacteristic
337C2×C32#45412yes—
338C3×D3—82no—
339C24—61no—
340C2×Q8—92no—
341C2×Q8—92no—
342C2×Q8—181no—
343C2×Q8—181no—
344C2×Q8—181no—
345C2×Q8—181no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—92no—
354C22×C4C2×D3211yescharacteristic
355M16—61no—
356M16—61no—
357M16—61no—
358M16—61no—
359C2×C8—61no—
360C2×C8—61no—
361C4⋊C4—92no—
362C4⋊C4—184no—
363C4⋊C4#62612yes—
364C22⋊C4—21no—
365C22⋊C4—188no—
366C22⋊C4—181no—
367C42—21no—
368C42—32no—
369C42—61no—
370C42—184no—
371C42—181no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—42no—
378C22×C3—124no—
379C22×C3—122no—
380C22×C3—242no—
381C22×C3—242no—
382C22×C3D3×C22⋊C411yescharacteristic
383C22×C3D3×C22⋊C411yescharacteristic
384C22×C3#88211yescharacteristic
385C22×C3#88311yescharacteristic
386C22×C3#89411yescharacteristic
387C22×C3#93711yescharacteristic
388C2×D3—44no—
389C2×D3—42no—
390C2×D3—82no—
391C2×D3—82no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—44no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—122no—
400C3×C4C4×D1211yescharacteristic
401C3×C4#67⋊C411yescharacteristic
402C3×C4#88411yescharacteristic
403C3×C4#88411yescharacteristic
404C3×C4#89311yescharacteristic
405C3×C4#89511yescharacteristic
406C3×C4C4×#6711yescharacteristic
407C3×C4#93811yescharacteristic
408Dic3—42no—
409Dic3—68no—
410Dic3—64no—
411Dic3—64no—
412Dic3—124no—
413Dic3—122no—
414Dic3—122no—
415C32#188811yescharacteristic, complemented, Sylow
416C23—62no—
417C23—124no—
418C23—121no—
419C23—121no—
420C23#381111yescharacteristic
421Q8—182no—
422Q8—182no—
423Q8—182no—
424Q8—182no—
425D4—62no—
426D4—62no—
427D4—121no—
428D4—121no—
429C2×C4—22no—
430C2×C4—62no—
431C2×C4—94no—
432C2×C4—122no—
433C2×C4—182no—
434C2×C4—182no—
435C2×C4—182no—
436C2×C4#379611yescharacteristic
437C2×C4#379811yescharacteristic
438C2×C4C4×D3211yescharacteristic
439C2×C4#380211yescharacteristic
440C2×C4C2×#62611yescharacteristic
441C2×C4#381111yescharacteristic
442C8—121no—
443C8—121no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—22no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—242no—
453C2×C3#466511yescharacteristic
454C2×C3#482712yes—
455C2×C3#495611yescharacteristic
456C2×C3#520112yes—
457D3—82no—
458C22—22no—
459C22—124no—
460C22—122no—
461C22—242no—
462C22—242no—
463C22#6385311yescharacteristic
464C22#6392111yescharacteristic
465C22#6398111yescharacteristic
466C4—42no—
467C4—122no—
468C4—184no—
469C4—362no—
470C4#6388111yescharacteristic
471C4C4×#62611yescharacteristic
472C4#6391211yescharacteristic
473C4#6391611yescharacteristic
474C3—21no—
475C3#6876611yescharacteristic, complemented
476C3#7032511yescharacteristic, complemented
477C2—21no—
478C2—21no—
479C2—242no—
480C2#1059138711yescharacteristic
481C2#1059168612yes—
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1888
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595987C2semidirect
5. C2×#63561C2semidirect
6. C3×#4532C2semidirect
7. #10589162C2semidirect
22. #63860C4semidirect
39. #4532D3semidirect
415. C32#1888semidirect
475. C3#68766semidirect
476. C3#70325semidirect

Maximal subgroups

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

subgroupindex
#105959872
C2×#638602
C3×#50012
#105910862
C2×#635612
C3×#45322
#105891622
#703253
#687663