Finite Group Databasebeta

← #11794309

Subgroups — #11794309

Order 1152.

699 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 699 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C3×#5483C211yesmaximal, characteristic
2C3×#4946C211yesmaximal, characteristic
3#10591693C212yesmaximal
4#10589392C211yesmaximal, characteristic
5#10589186C212yesmaximal
6#71895—31nomaximal
7#69594—31nomaximal
8C23×C3×Dic3C2211yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757C2212yes—
11C2×C3×#217C2212yes—
12C2×C3×#217C2211yescharacteristic
13C3×#924—21no—
14C3×#924—21no—
15C2×C3×Dic3⋊C4—21no—
16C3×#878—22no—
17C3×#878—22no—
18C2×#3724—22no—
19C3×C3⋊#95—21no—
20#63579—22no—
21C3×#543—31no—
22#5483D311yescharacteristic
23C3×#385—31no—
24#5210—32no—
25#4946—32no—
26#4946D311yescharacteristic
27#4527—32no—
28#4526—31no—
29#4526—31no—
30#4526—32no—
31#4526—61no—
32C24×C32C2311yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—22no—
39C22×C3×Dic3—42no—
40C22×C3×Dic3D412yes—
41C22×C3×Dic3D412yes—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C22⋊C4—22no—
45#3757—22no—
46#3757Q814yescomplemented
47C3×#217—22no—
48C3×#217—22no—
49C3×#217—21no—
50C3×#217Q812yescomplemented
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×Dic3⋊C4—22no—
54C3×Dic3⋊C4—22no—
55C3×Dic3⋊C4—42no—
56#3724—44no—
57#2062—91noSylow
58C23×C3×C4—31no—
59C23×Dic3C2×D311yescharacteristic
60C3×C22⋊Q8—62no—
61C3×C22⋊Q8—62no—
62C3×C22⋊Q8—61no—
63C3×C22⋊Q8—61no—
64C2×C3×C4⋊C4—61no—
65C2×C3×C22⋊C4—21no—
66C2×C3×C22⋊C4—31no—
67C2×C3×C22⋊C4—32no—
68C2×C3×C22⋊C4C2×D311yescharacteristic
69C2×C3×C22⋊C4C2×D311yescharacteristic
70C2×#217—32no—
71C2×#217—32no—
72C2×#217—62no—
73C2×#217C2×D312yes—
74C2×#217C2×D311yescharacteristic
75#924—21no—
76#924—21no—
77C2×Dic3⋊C4—21no—
78C2×Dic3⋊C4—62no—
79C2×Dic3⋊C4—62no—
80#878—22no—
81#878—22no—
82C3×#95—61no—
83C3⋊#95—21no—
84C3⋊#95—62no—
85C3⋊#95—62no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32C2×D412yes—
89C23×C32C2×D411yescharacteristic
90C23×C32C2×Q811yescharacteristic
91C23×C32C2×Q812yes—
92C23×C32#4111yescharacteristic
93C2×C32×C4—21no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C3⋊Dic3—24no—
98C2×C3⋊Dic3—42no—
99C2×C3⋊Dic3—42no—
100C2×C3×Dic3—24no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C2×C3×Dic3—22no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—41no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×Dic6—81no—
113C3×Dic6—81no—
114#543—31no—
115#385—31no—
116#385—92no—
117#342—92no—
118#342—91no—
119C24×C3—21no—
120C24×C3C22×D311yescharacteristic
121C24×C3C22×D311yescharacteristic
122C2×C3×Q8—61no—
123C2×C3×Q8—61no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—32no—
127C22×C3×C4—32no—
128C22×C3×C4—62no—
129C22×C3×C4—61no—
130C22×C3×C4—61no—
131C22×C3×C4—122no—
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4#6711yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×Dic3—22no—
137C22×Dic3—21no—
138C22×Dic3—21no—
139C22×Dic3—42no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C22×Dic3—122no—
143C22×Dic3#6712yes—
144C22×Dic3#6712yes—
145C2×Dic6—21no—
146C2×Dic6—21no—
147C3×C4⋊C4—62no—
148C3×C4⋊C4—62no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—122no—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—32no—
155C3×C22⋊C4—42no—
156C3×C22⋊C4—62no—
157C3×C22⋊C4—61no—
158C3×C22⋊C4—62no—
159#217—21no—
160#217—22no—
161#217—22no—
162#217—34no—
163#217—34no—
164#217—64no—
165#217—62no—
166#217—62no—
167#217—122no—
168#217Dic612yescomplemented
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171Dic3⋊C4—22no—
172Dic3⋊C4—22no—
173Dic3⋊C4—42no—
174Dic3⋊C4—124no—
175Dic3⋊C4—124no—
176C22×C32—22no—
177C22×C32—21no—
178C22×C32—22no—
179C22×C32—21no—
180C22×C32—41no—
181C22×C32—42no—
182C22×C32—41no—
183C22×C32#12011yescharacteristic
184C22×C32C22⋊Q812yes—
185C22×C32C22⋊Q811yescharacteristic
186C22×C32C4⋊Q812yes—
187C22×C32C4⋊Q811yescharacteristic
188C32×C4—41no—
189C32×C4—41no—
190C3⋊Dic3—44no—
191C3×Dic3—42no—
192C3×Dic3—42no—
193C3×Dic3—42no—
194C3×Dic3—42no—
195C23×C4—31no—
196C22⋊Q8—62no—
197C22⋊Q8—62no—
198C22⋊Q8—61no—
199C22⋊Q8—61no—
200C2×C4⋊C4—61no—
201C2×C4⋊C4—182no—
202C2×C22⋊C4—31no—
203C2×C22⋊C4—32no—
204C2×C22⋊C4—92no—
205C2×C22⋊C4D3211yescharacteristic
206#95—61no—
207#95—182no—
208C23×C3—21no—
209C23×C3—22no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—22no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—81no—
218C23×C3—81no—
219C23×C3C2×Dic611yescharacteristic
220C23×C3#23511yescharacteristic
221C23×C3D3×D412yes—
222C23×C3D3×Q811yescharacteristic
223C23×C3D3×Q812yes—
224C23×C3D3×Q812yes—
225C23×C3#23911yescharacteristic
226C23×C3C2×#6711yescharacteristic
227C23×C3C2×#6711yescharacteristic
228C23×C3C2×#6712yes—
229C3×Q8—241no—
230C3×Q8—241no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—64no—
242C2×C3×C4—62no—
243C2×C3×C4—62no—
244C2×C3×C4—62no—
245C2×C3×C4—62no—
246C2×C3×C4—81no—
247C2×C3×C4—81no—
248C2×C3×C4—121no—
249C2×C3×C4—121no—
250C2×C3×C4—122no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—122no—
254C2×C3×C4—122no—
255C2×Dic3—22no—
256C2×Dic3—24no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—22no—
260C2×Dic3—41no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—42no—
264C2×Dic3—41no—
265C2×Dic3—42no—
266C2×Dic3—42no—
267C2×Dic3—64no—
268C2×Dic3—64no—
269C2×Dic3—124no—
270C2×Dic3—122no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273C2×Dic3—122no—
274C2×Dic3—242no—
275C2×Dic3—242no—
276Dic6—81no—
277Dic6—81no—
278C2×C32—21no—
279C2×C32—22no—
280C2×C32—22no—
281C2×C32—21no—
282C2×C32#39511yescharacteristic
283C2×C32B(4,𝔽2)11yescharacteristic
284C2×C32#45811yescharacteristic
285C24C2×D3211yescharacteristic
286C2×Q8—61no—
287C2×Q8—61no—
288C22×C4—32no—
289C22×C4—32no—
290C22×C4—61no—
291C22×C4—61no—
292C22×C4—62no—
293C22×C4—122no—
294C22×C4—182no—
295C22×C4#62511yescharacteristic
296C22×C4#62511yescharacteristic
297C4⋊C4—62no—
298C4⋊C4—62no—
299C4⋊C4—61no—
300C4⋊C4—61no—
301C4⋊C4—122no—
302C4⋊C4—364no—
303C22⋊C4—22no—
304C22⋊C4—32no—
305C22⋊C4—61no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—94no—
309C22⋊C4—182no—
310C22×C3—22no—
311C22×C3—21no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—42no—
331C22×C3—42no—
332C22×C3—41no—
333C22×C3—81no—
334C22×C3—82no—
335C22×C3—81no—
336C22×C3#88812yes—
337C22×C3#89612yes—
338C22×C3#92411yescharacteristic
339C22×C3#93711yescharacteristic
340C22×C3#94412yes—
341C22×C3#94411yescharacteristic
342C22×C3#94411yescharacteristic
343C22×C3#94611yescharacteristic
344C22×C3#94612yes—
345C22×C3#95311yescharacteristic
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—81no—
351C3×C4—81no—
352C3×C4—122no—
353C3×C4—122no—
354C3×C4—122no—
355C3×C4—122no—
356Dic3—42no—
357Dic3—42no—
358Dic3—42no—
359Dic3—42no—
360Dic3—124no—
361Dic3—124no—
362Dic3—244no—
363C32#206211yescharacteristic, complemented, Sylow
364C23—41no—
365C23—41no—
366C23D3×Dic611yescharacteristic
367C23#379712yes—
368C23#379911yescharacteristic
369C23C2×#62511yescharacteristic
370C23D3×#6712yes—
371Q8—241no—
372Q8—241no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—62no—
378C2×C4—64no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—62no—
382C2×C4—121no—
383C2×C4—121no—
384C2×C4—122no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—122no—
388C2×C4—122no—
389C2×C4—184no—
390C2×C4—362no—
391C2×C4—362no—
392C2×C3—22no—
393C2×C3—21no—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—22no—
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—42no—
404C2×C3—41no—
405C2×C3—42no—
406C2×C3—41no—
407C2×C3#497911yescharacteristic
408C2×C3#503211yescharacteristic
409C2×C3#505311yescharacteristic
410C2×C3#523011yescharacteristic
411C2×C3#524311yescharacteristic
412C2×C3#524411yescharacteristic
413C22—21no—
414C22—22no—
415C22—21no—
416C22—22no—
417C22—41no—
418C22—42no—
419C22—41no—
420C22#6383912yes—
421C22#6385611yescharacteristic
422C22#6387311yescharacteristic
423C22#6388812yes—
424C22#6397611yescharacteristic
425C4—41no—
426C4—41no—
427C4—122no—
428C4—122no—
429C4—122no—
430C4—122no—
431C4—364no—
432C3—21no—
433C3#6959411yescharacteristic, complemented
434C3#7189511yescharacteristic, complemented
435C2—21no—
436C2—22no—
437C2—22no—
438C2—21no—
439C2#1059134411yescharacteristic
440C2#1059153011yescharacteristic
441C2#1059153311yescharacteristic
subgroupG/H
centerC22#63976
commutator, prime radical, cosocleC24×C32C23
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
hypercenterC2×C22⋊C4D32
hypocenterC32#2062
LCSG ▷ C24×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
46. #3757Q8semidirect
50. C3×#217Q8semidirect
168. #217Dic6semidirect
363. C32#2062semidirect
433. C3#69594semidirect
434. C3#71895semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C3×#49462
#105916932
#105893922
#105891862
#718953
#695943