Finite Group Databasebeta

← #11788820

Subgroups — #11788820

Order 1152.

761 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
1#10595987C211yesmaximal, characteristic, complemented
2#10594856C211yesmaximal, characteristic
3C3×#5005C211yesmaximal, characteristic
4#10591110C211yesmaximal, characteristic
5C2×#63561C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70411—31nomaximal
9#68708—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64096—22no—
15#64086—22no—
16C4×#634—22no—
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20#63962—22no—
21#63866C412yescomplemented
22#63860C412yescomplemented
23#63857—22no—
24C3×#805—22no—
25#63568—22no—
26#63561—22no—
27#5825—31no—
28#5526—31no—
29#5516—31no—
30#5516—31no—
31#5516—61no—
32C3×#421—31no—
33#5236—31no—
34#5139—31no—
35C2×#824—31no—
36C2×#824—31no—
37#5005D311yescharacteristic
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634C2×C412yes—
49C2×#634D412yes—
50C2×C3×#67—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6C2×C411yescharacteristic
58C32×C4⋊C4—21no—
59C32×C22⋊C4—21no—
60C32×C42D412yes—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63#3750—24no—
64C4×C3⋊Dic3—24no—
65C4×C3⋊Dic3D412yes—
66C3×#217—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3C2×C412yes—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77#1912—91noSylow
78C2×C3×#41—31no—
79C2×#235C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#117—21no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89#944—32no—
90#936—32no—
91#935—62no—
92#926—31no—
93#926—31no—
94#926—61no—
95#926C2×D311yescharacteristic
96#924—62no—
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#897—62no—
100#887—62no—
101#887—62no—
102#887—64no—
103#886—62no—
104#877—62no—
105#877—62no—
106#877—64no—
107#875—32no—
108#869—32no—
109C4×Dic6—64no—
110C4×Dic6—62no—
111C4×Dic6—62no—
112C3×#104—62no—
113#837—62no—
114#825—62no—
115#824—62no—
116#824—62no—
117#805—22no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3C22⋊C414yes—
131#634—22no—
132#634—22no—
133#634—22no—
134#634—22no—
135C3×#67—41no—
136C3×#67—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C3×D12—21no—
140C3×D12—21no—
141C3×C4×D3—41no—
142C3×C4×D3—41no—
143C3×Dic6—21no—
144C3×Dic6—21no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8—41no—
147#536—91no—
148#519—91no—
149#421—31no—
150#421—91no—
151C2×#101—91no—
152H(3,ℤ/4)—31no—
153H(3,ℤ/4)—91no—
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C22×C3×C4—21no—
162C22×C3×C4—61no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—21no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—62no—
169#235—21no—
170#235—21no—
171#235—21no—
172#235—21no—
173C2×D12C4×D311yescharacteristic
174C2×C4×D3—21no—
175C2×Dic6—32no—
176C2×Dic6—32no—
177C2×Dic6—32no—
178C2×Dic6—32no—
179C2×Dic6—62no—
180C2×Dic6—62no—
181C2×Dic6—62no—
182C2×Dic6—62no—
183C2×Dic6—62no—
184C2×Dic6—62no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—61no—
189C2×Dic6—61no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C2×Dic6—61no—
193C2×Dic6C4×D311yescharacteristic
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C3×M16—61no—
198C2×C3×C8—61no—
199C2×C3×C8—61no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—61no—
204C3×C22⋊C4—22no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—61no—
208C3×C42—22no—
209C3×C42—32no—
210C3×C42D1212yes—
211C3×C42#6712yes—
212#217—21no—
213#217—64no—
214#217—62no—
215#217—61no—
216#217—61no—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—21no—
219C4⋊Dic3—64no—
220C4⋊Dic3—62no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223Dic3⋊C4—64no—
224Dic3⋊C4—68no—
225Dic3⋊C4—64no—
226Dic3⋊C4—64no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—62no—
230C4×Dic3—68no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3C4×D312yes—
234#208—21no—
235#208—21no—
236#208—21no—
237#208—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C22×C32—41no—
241C22×C32C2×C22⋊C411yescharacteristic
242C22×C32#12011yescharacteristic
243C22×C32#12311yescharacteristic
244C2×C3×D3—42no—
245C2×C3×D3—41no—
246C32×C4—42no—
247C32×C4C4×D411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12111yescharacteristic
251C3⋊Dic3—24no—
252C3⋊Dic3—42no—
253C3×Dic3—42no—
254C3×Dic3—41no—
255C2×#41—31no—
256C22×Q8—91no—
257C2×M16—31no—
258C2×M16—31no—
259C4⋊Q8—92no—
260#124—92no—
261#123—182no—
262C22⋊Q8—182no—
263C4×Q8—182no—
264C4×Q8—182no—
265#117—31no—
266#117—91no—
267#117—182no—
268#117D3211yescharacteristic
269#104—62no—
270#104—182no—
271#101—182no—
272C23×C3—21no—
273C23×C3—61no—
274C23×C3D3×D411yescharacteristic
275C23×C3D3×D411yescharacteristic
276C22×D3—21no—
277C3×Q8—61no—
278C3×Q8—61no—
279C3×D4—61no—
280C3×D4—61no—
281C3×D4—121no—
282C3×D4—121no—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—61no—
293C2×C3×C4—62no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308#67—41no—
309#67—41no—
310C2×Dic3—22no—
311C2×Dic3—21no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—64no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—64no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324D12—21no—
325D12—21no—
326C4×D3—41no—
327C4×D3—41no—
328Dic6—21no—
329Dic6—21no—
330Dic6—64no—
331Dic6—64no—
332Dic6—64no—
333Dic6—64no—
334Dic6—62no—
335Dic6—62no—
336Dic6—62no—
337Dic6—62no—
338Dic6—62no—
339Dic6—62no—
340Dic6—62no—
341Dic6—62no—
342C3×C8—121no—
343C3×C8—121no—
344C3⋊C8—41no—
345C3⋊C8—41no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32#38611yescharacteristic
350C3×D3—81no—
351#41—61no—
352#41—61no—
353#41—61no—
354#41—61no—
355C2×Q8—31no—
356C2×Q8—92no—
357C2×Q8—92no—
358C2×Q8—181no—
359C2×Q8—181no—
360C2×Q8—181no—
361C2×Q8—181no—
362C2×D4—31no—
363C2×D4—61no—
364C22×C4—61no—
365C22×C4—92no—
366C22×C4C2×D3211yescharacteristic
367M16—61no—
368M16—61no—
369M16—61no—
370M16—61no—
371C2×C8—61no—
372C2×C8—61no—
373C4⋊C4—21no—
374C4⋊C4—61no—
375C4⋊C4—184no—
376C4⋊C4—184no—
377C4⋊C4—181no—
378C22⋊C4—21no—
379C22⋊C4—61no—
380C22⋊C4—184no—
381C22⋊C4—181no—
382C42—32no—
383C42—92no—
384C42—184no—
385C42#62612yes—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—42no—
392C22×C3—122no—
393C22×C3—121no—
394C22×C3D3×C22⋊C411yescharacteristic
395C22×C3D3×C22⋊C411yescharacteristic
396C22×C3#88211yescharacteristic
397C22×C3#88311yescharacteristic
398C22×C3#89411yescharacteristic
399C22×C3#93711yescharacteristic
400C2×D3—42no—
401C2×D3—41no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—44no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—122no—
410C3×C4—121no—
411C3×C4C4×D1211yescharacteristic
412C3×C4#67⋊C411yescharacteristic
413C3×C4#88411yescharacteristic
414C3×C4#88411yescharacteristic
415C3×C4#89311yescharacteristic
416C3×C4#89511yescharacteristic
417C3×C4C4×#6711yescharacteristic
418C3×C4#93811yescharacteristic
419Dic3—42no—
420Dic3—41no—
421Dic3—68no—
422Dic3—64no—
423Dic3—64no—
424Dic3—124no—
425Dic3—122no—
426Dic3—122no—
427C32#191211yescharacteristic, complemented, Sylow
428C23—61no—
429C23#381111yescharacteristic
430Q8—61no—
431Q8—61no—
432Q8—182no—
433Q8—182no—
434Q8—182no—
435Q8—182no—
436D4—61no—
437D4—61no—
438D4—121no—
439D4—121no—
440C2×C4—22no—
441C2×C4—62no—
442C2×C4—61no—
443C2×C4—94no—
444C2×C4—121no—
445C2×C4—121no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4#379611yescharacteristic
450C2×C4#379811yescharacteristic
451C2×C4C4×D3211yescharacteristic
452C2×C4#380211yescharacteristic
453C2×C4C2×#62611yescharacteristic
454C2×C4#381111yescharacteristic
455C8—121no—
456C8—121no—
457C2×C3—22no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—241no—
468C2×C3#466511yescharacteristic
469C2×C3#495611yescharacteristic
470D3—81no—
471C22—41no—
472C22—122no—
473C22—121no—
474C22#6385311yescharacteristic
475C22#6392111yescharacteristic
476C22#6398111yescharacteristic
477C4—42no—
478C4—122no—
479C4—121no—
480C4—184no—
481C4—362no—
482C4#6388111yescharacteristic
483C4C4×#62611yescharacteristic
484C4#6391211yescharacteristic
485C4#6391611yescharacteristic
486C3—21no—
487C3#6870811yescharacteristic, complemented
488C3#7041111yescharacteristic, complemented
489C2—21no—
490C2—21no—
491C2—21no—
492C2—241no—
493C2#1059138711yescharacteristic
subgroupG/H
centerC2#10591387
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1912
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595987C2semidirect
5. C2×#63561C2semidirect
6. C3×#4531C2semidirect
7. #10589158C2semidirect
21. #63866C4semidirect
22. #63860C4semidirect
41. #4531D3semidirect
427. C32#1912semidirect
487. C3#68708semidirect
488. C3#70411semidirect

Maximal subgroups

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

subgroupindex
#105959872
#105948562
C3×#50052
#105911102
C2×#635612
C3×#45312
#105891582
#704113
#687083