Finite Group Databasebeta

← #11787002

Subgroups — #11787002

Order 1152.

532 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#63838C211yesmaximal, characteristic
2C2×#63742C211yesmaximal, characteristic
3C2×#63740C211yesmaximal, characteristic
4C2×#63740C211yesmaximal, characteristic
5#10591328C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic
7#10590075C211yesmaximal, characteristic
8C22×#627C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×Dic3⋊C4—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16C2×Dic3⋊Dic3—21no—
17C2×Dic32—21no—
18#63838—22no—
19#63838—22no—
20#63742—22no—
21#63740—22no—
22#63740C414yescomplemented
23C3×C3⋊#95—21no—
24C2×#887—61no—
25#4647—61no—
26C22×C32×C4D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C22×C3×Dic3—21no—
30C22×C3×Dic3—21no—
31C22×C3×Dic3—21no—
32C22×C3×Dic3—21no—
33C2×#627—21no—
34C2×#627—21no—
35C2×#627—21no—
36C2×#627C2×C412yes—
37C2×#627D412yes—
38C2×#627Q812yes—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622—21no—
42C2×#622—21no—
43C2×#622—21no—
44C2×#622C2×C412yes—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C3×Dic3⋊C4—24no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51#3724—21no—
52#3724C2×C412yes—
53#3724D412yes—
54Dic3⋊Dic3—42no—
55Dic32—24no—
56#1865—91nomaximal, Sylow
57C22×Dic6—61no—
58C2×C3×C4⋊C4—61no—
59C2×C4⋊Dic3—61no—
60C2×Dic3⋊C4—21no—
61C2×Dic3⋊C4—61no—
62C2×Dic3⋊C4—61no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—61no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69#887—64no—
70#887—64no—
71C3×#95—61no—
72C3⋊#95—21no—
73C23×C32C2×D411yescharacteristic
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3SD1612yes—
80C2×C3⋊Dic3C22×C411yescharacteristic
81C2×C3⋊Dic3C2×D411yescharacteristic
82C2×C3⋊Dic3C2×D411yescharacteristic
83C2×C3⋊Dic3C2×Q811yescharacteristic
84C2×C3⋊Dic3#4111yescharacteristic
85C2×C3⋊Dic3#4111yescharacteristic
86C2×C3×Dic3—22no—
87C2×C3×Dic3—22no—
88C2×C3×Dic3—22no—
89C2×C3×Dic3—22no—
90C2×C3×Dic3—22no—
91C2×C3×Dic3—41no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98#627—22no—
99#627—22no—
100#627—22no—
101#627C4⋊C414yescomplemented
102#622—22no—
103#622—41no—
104C2×C4×Q8—91no—
105C2×#106—91no—
106C2×#103—91no—
107C2×#103—91no—
108#389—91no—
109#340—91no—
110#336—91no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—61no—
114C22×C3×C4—61no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×Dic3—21no—
118C22×Dic3—21no—
119C22×Dic3—21no—
120C22×Dic3—21no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C2×Dic6—62no—
126C2×Dic6—62no—
127C2×Dic6—62no—
128C2×Dic6—62no—
129C2×Dic6—62no—
130C2×Dic6—62no—
131C3×C4⋊C4—64no—
132C4⋊Dic3—122no—
133Dic3⋊C4—24no—
134Dic3⋊C4—62no—
135Dic3⋊C4—62no—
136Dic3⋊C4—62no—
137Dic3⋊C4—62no—
138Dic3⋊C4—121no—
139Dic3⋊C4—121no—
140Dic3⋊C4—122no—
141C4×Dic3—64no—
142C4×Dic3—64no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—121no—
146C4×Dic3—121no—
147C22×C32C4×D411yescharacteristic
148C22×C32#12011yescharacteristic
149C22×C32C22⋊Q811yescharacteristic
150C22×C32C2×SD1611yescharacteristic
151C22×C32#13511yescharacteristic
152C22×C32#13711yescharacteristic
153C22×C32#13711yescharacteristic
154C32×C4—41no—
155C3⋊Dic3—22no—
156C3⋊Dic3C2×C4⋊C411yescharacteristic
157C3⋊Dic3C4×D411yescharacteristic
158C3⋊Dic3C22⋊Q811yescharacteristic
159C3⋊Dic3#12311yescharacteristic
160C3×Dic3—24no—
161C3×Dic3—42no—
162C3×Dic3—42no—
163C3×Dic3—81no—
164C22×Q8—91no—
165C22×C8—91no—
166C22×C8—91no—
167C4×Q8—182no—
168C4×Q8—182no—
169C2×C4⋊C4—61no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—181no—
174C2×C42—91no—
175C2×C42—181no—
176#106—182no—
177#103—94no—
178#103—182no—
179#95—61no—
180C23×C3—21no—
181C23×C3—21no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—41no—
187C2×C3×C4—41no—
188C2×C3×C4—62no—
189C2×C3×C4—62no—
190C2×C3×C4—62no—
191C2×C3×C4—62no—
192C2×C3×C4—62no—
193C2×C3×C4—121no—
194C2×C3×C4—121no—
195C2×C3×C4—121no—
196C2×C3×C4—121no—
197C2×C3×C4—121no—
198C2×C3×C4—121no—
199C2×C3×C4—121no—
200C2×Dic3—22no—
201C2×Dic3—22no—
202C2×Dic3—22no—
203C2×Dic3—22no—
204C2×Dic3—22no—
205C2×Dic3—41no—
206C2×Dic3—41no—
207C2×Dic3—41no—
208C2×Dic3—41no—
209C2×Dic3—41no—
210C2×Dic3—41no—
211C2×Dic3—41no—
212C2×Dic3—62no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—61no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—121no—
229C2×Dic3—121no—
230Dic6—64no—
231Dic6—64no—
232Dic6—64no—
233Dic6—64no—
234C2×C32#38511yescharacteristic
235C2×C32C4×SD1611yescharacteristic
236C2×C32#44111yescharacteristic
237C2×C32#44811yescharacteristic
238C2×C32#45211yescharacteristic
239C2×C32#47511yescharacteristic
240C2×C32#47911yescharacteristic
241C2×Q8—92no—
242C2×Q8—92no—
243C2×Q8—92no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×Q8—181no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4—61no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4GO+(4,𝔽2)11yescharacteristic
254C2×C8—92no—
255C2×C8—181no—
256C2×C8—181no—
257C2×C8—181no—
258C2×C8—181no—
259C2×C8—181no—
260C4⋊C4—64no—
261C4⋊C4—92no—
262C4⋊C4—92no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—362no—
268C42—181no—
269C42—181no—
270C42—184no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C3×C4—42no—
286C3×C4—42no—
287C3×C4—64no—
288C3×C4—122no—
289C3×C4—122no—
290C3×C4—241no—
291Dic3—24no—
292Dic3—42no—
293Dic3—42no—
294Dic3—61no—
295Dic3—61no—
296Dic3—61no—
297Dic3—61no—
298Dic3—61no—
299Dic3—61no—
300Dic3—61no—
301Dic3—61no—
302Dic3—64no—
303Dic3—81no—
304Dic3—122no—
305C32#186511yescharacteristic, complemented, Sylow
306C23C2×GO+(4,𝔽2)11yescharacteristic
307Q8—94no—
308Q8—182no—
309Q8—182no—
310Q8—182no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—62no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—62no—
319C2×C4—91no—
320C2×C4—91no—
321C2×C4—91no—
322C2×C4—91no—
323C2×C4—91no—
324C2×C4—91no—
325C2×C4—92no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4—121no—
331C2×C4—121no—
332C2×C4—121no—
333C2×C4—181no—
334C2×C4—181no—
335C8—182no—
336C8—361no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C22D32⋊Q811yescharacteristic
352C22#6422611yescharacteristic
353C22#6422711yescharacteristic
354C22C4×GO+(4,𝔽2)11yescharacteristic
355C22#6423711yescharacteristic
356C22#6423911yescharacteristic
357C22#6424111yescharacteristic
358C4—41no—
359C4—64no—
360C4—91no—
361C4—91no—
362C4—91no—
363C4—91no—
364C4—122no—
365C4—122no—
366C4—182no—
367C4—241no—
368C3—21no—
369C3—21no—
370C2#1059336911yescharacteristic
371C2#1059337311yescharacteristic
372C2#1059338511yescharacteristic
373C2#1059339811yescharacteristic
374C2#1059343311yescharacteristic
375C2#1059343611yescharacteristic
376C2#1059352411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1865
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
22. #63740C4semidirect
101. #627C4⋊C4semidirect
305. C32#1865semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
C2×#637422
C2×#637402
#105913282
#105902072
#105900752
#18659