Finite Group Databasebeta

← #11778142

Subgroups — #11778142

Order 1152.

635 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 635 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595971C211yesmaximal, characteristic, complemented
2C3×#4991C211yesmaximal, characteristic
3#10591172C212yesmaximal
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589154C212yesmaximal, complemented
6#69704—31nomaximal
7#68138—31nomaximal
8C22×C3×D12C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10#64135—21no—
11#64133—21no—
12#64133C2212yes—
13#64099—22no—
14#64097—22no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×#3716—22no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20#63563—22no—
21#5500—31no—
22#5500—31no—
23#5500—61no—
24C3×#394—31no—
25#5218—32no—
26#4991D311yescharacteristic
27#4731—32no—
28C3×#324—31no—
29#4528D311yescharacteristic, complemented
30#4467—32no—
31#4452—32no—
32C23×C3×D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×#634—21no—
37C2×#634D412yes—
38C22×C3×Dic3—21no—
39C2×C3×D12—22no—
40C2×C3×D12—42no—
41C32×C4⋊C4—22no—
42#3757—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)D412yes—
47#3750—22no—
48#3750—22no—
49C4×C3⋊Dic3—22no—
50C3×(C2×D3)⋊C4—42no—
51C3×(C2×D3)⋊C4—42no—
52C2×C3×C3⋊C8—22no—
53#3716—44no—
54#1599—91noSylow
55C22×C3×D4—31no—
56C22×D12C2×D311yescharacteristic
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60C2×C3×C22⋊C4—61no—
61C2×C3×C22⋊C4—61no—
62C2×#214—62no—
63C2×(C2×D3)⋊C4—21no—
64C2×(C2×D3)⋊C4—21no—
65#926—62no—
66#926—61no—
67#926—61no—
68#924—32no—
69#924—32no—
70#924—62no—
71#924—62no—
72#924—61no—
73#924—61no—
74C2×#204—62no—
75#890—62no—
76#890—62no—
77#890—64no—
78#888—62no—
79#888—62no—
80#888—64no—
81C3×C22⋊C8—32no—
82C3×#95—31no—
83#832—62no—
84C3⋊#95C2×D311yescharacteristic
85#830C2×D312yes—
86#821—62no—
87C23×C32C2×D411yescharacteristic
88C22×C3×D3—22no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C22×C3×D3—41no—
92C22×C3×D3—41no—
93C22×C3×D3—41no—
94C22×C3×D3—41no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4SD1612yescomplemented
101C2×C32×C4C2×D412yes—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—22no—
104#634—42no—
105#634—81no—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C3×D12—24no—
110C3×D12—42no—
111C3×C3⋊C8—42no—
112#544—91no—
113#450—92no—
114#394—31no—
115#328—92no—
116#324—31no—
117C24×C3—61no—
118C23×D3—21no—
119C2×C3×D4—62no—
120C2×C3×D4—122no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—61no—
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4D1211yescharacteristic
127C22×C3×C4#6711yescharacteristic
128C22×C3×C4#6711yescharacteristic
129C22×C3×C4C22×D311yescharacteristic
130C22×C3×C4C22×D311yescharacteristic
131C22×Dic3—21no—
132C2×D12—22no—
133C2×D12—42no—
134C2×Dic6—32no—
135C2×Dic6—32no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×C3×C8—62no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C22⋊C4—122no—
145C3×C22⋊C4—122no—
146#217—64no—
147#217—62no—
148#217—62no—
149#214—124no—
150(C2×D3)⋊C4—42no—
151(C2×D3)⋊C4—42no—
152C4⋊Dic3—32no—
153C4⋊Dic3—32no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—62no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—62no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164Dic3⋊C4—64no—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167Dic3⋊C4—64no—
168Dic3⋊C4—62no—
169Dic3⋊C4—62no—
170C4×Dic3—64no—
171C4×Dic3—62no—
172C4×Dic3—62no—
173C2×C3⋊C8—22no—
174#204—124no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32#12011yescharacteristic
178C22×C32C2×SD1611yescharacteristic
179C22×C32#13711yescharacteristic
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C2×C3×D3—81no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—41no—
190C3⋊Dic3—42no—
191C3⋊Dic3—42no—
192C3×Dic3—81no—
193C22×D4—31no—
194C2×SD16—182no—
195C4⋊Q8—182no—
196#125—182no—
197C22⋊Q8—92no—
198C22⋊Q8—181no—
199#117—181no—
200C2×C4⋊C4D3211yescharacteristic
201C2×C22⋊C4—61no—
202C2×C22⋊C4—61no—
203#102—182no—
204C22⋊C8—32no—
205#95—31no—
206C23×C3—21no—
207C23×C3—62no—
208C23×C3—121no—
209C23×C3—121no—
210C23×C3—121no—
211C23×C3—121no—
212C23×C3—121no—
213C23×C3—121no—
214C23×C3C2×D1211yescharacteristic
215C23×C3C2×#6711yescharacteristic
216C22×D3—22no—
217C22×D3—41no—
218C22×D3—41no—
219C22×D3—41no—
220C22×D3—41no—
221C22×D3—41no—
222C22×D3—41no—
223C3×D4—64no—
224C3×D4—122no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—81no—
241C2×C3×C4—81no—
242C2×C3×C4—121no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4#20412yescomplemented
246C2×C3×C4#21412yescomplemented
247C2×C3×C4D3×D412yes—
248C2×C3×C4D3×D412yes—
249C2×Dic3—41no—
250C2×Dic3—41no—
251C2×Dic3—41no—
252C2×Dic3—64no—
253C2×Dic3—64no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—62no—
257C2×Dic3—62no—
258D12—24no—
259D12—42no—
260Dic6—122no—
261Dic6—122no—
262Dic6—242no—
263Dic6—242no—
264Dic6—241no—
265Dic6—241no—
266C3×C8—122no—
267C3⋊C8—42no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32#44811yescharacteristic
271C2×C32#45411yescharacteristic
272C2×C32B(4,𝔽2)11yescharacteristic
273C3×D3—82no—
274C24—61no—
275C2×Q8—92no—
276C2×Q8—181no—
277C2×D4—62no—
278C2×D4—122no—
279C22×C4—61no—
280C22×C4#62611yescharacteristic
281C22×C4#62611yescharacteristic
282C22×C4C2×D3211yescharacteristic
283SD16—364no—
284C2×C8—62no—
285C4⋊C4—22no—
286C4⋊C4—92no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C22⋊C4—122no—
293C22⋊C4—122no—
294C22⋊C4—182no—
295C42—182no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3—241no—
312C22×C3#88211yescharacteristic
313C22×C3C2×#20411yescharacteristic
314C22×C3#90911yescharacteristic
315C22×C3C2×#21411yescharacteristic
316C22×C3#93711yescharacteristic
317C22×C3#95111yescharacteristic
318C2×D3—42no—
319C2×D3—42no—
320C2×D3—42no—
321C2×D3—81no—
322C2×D3—81no—
323C2×D3—81no—
324C2×D3—81no—
325C3×C4—24no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—42no—
331C3×C4—42no—
332C3×C4—41no—
333C3×C4—41no—
334C3×C4—241no—
335Dic3—81no—
336Dic3—124no—
337Dic3—124no—
338Dic3—122no—
339Dic3—122no—
340Dic3—122no—
341Dic3—122no—
342C32#159911yescharacteristic, complemented, Sylow
343C23—62no—
344C23—121no—
345C23—121no—
346C23—121no—
347C23—121no—
348C23—121no—
349C23—121no—
350C23C2×#62611yescharacteristic
351Q8—362no—
352Q8—721no—
353D4—64no—
354D4—122no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—121no—
361C2×C4—121no—
362C2×C4—121no—
363C2×C4—182no—
364C2×C4—182no—
365C2×C4#371612yescomplemented
366C2×C4#381112yes—
367C8—122no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—41no—
376C2×C3—41no—
377C2×C3—242no—
378C2×C3#473811yescharacteristic
379C2×C3#474111yescharacteristic
380C2×C3#475311yescharacteristic
381C2×C3#503211yescharacteristic
382C2×C3#504011yescharacteristic
383C2×C3#506211yescharacteristic
384D3—82no—
385C22—21no—
386C22—21no—
387C22—122no—
388C22—122no—
389C22—122no—
390C22—241no—
391C22—241no—
392C22—241no—
393C22—241no—
394C22C2×#371611yescharacteristic
395C22#6383111yescharacteristic
396C22#6398111yescharacteristic
397C4—22no—
398C4—22no—
399C4—41no—
400C4—241no—
401C4—362no—
402C4—362no—
403C3—21no—
404C3#6813811yescharacteristic, complemented
405C3#6970411yescharacteristic, complemented
406C2—21no—
407C2—21no—
408C2—242no—
409C2#1059118111yescharacteristic
410C2#1059153211yescharacteristic
411C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1599
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595971C2semidirect
4. C3×#4528C2semidirect
5. #10589154C2semidirect
29. #4528D3semidirect
100. C2×C32×C4SD16semidirect
245. C2×C3×C4#204semidirect
246. C2×C3×C4#214semidirect
342. C32#1599semidirect
365. C2×C4#3716semidirect
404. C3#68138semidirect
405. C3#69704semidirect

Maximal subgroups

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

subgroupindex
#105959712
C3×#49912
#105911722
C3×#45282
#105891542
#697043
#681383