Finite Group Databasebeta

← #11786526

Subgroups — #11786526

Order 1152.

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

normal subgroups only

This group has 598 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×#63957C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3C2×#63743C211yesmaximal, characteristic, complemented
4C2×#63742C211yesmaximal, characteristic, complemented
5#10591720C211yesmaximal, characteristic
6#10590075C211yesmaximal, characteristic, complemented
7#10590075C211yesmaximal, characteristic, complemented
8C23×C3⋊Dic3C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C2×C3×#217—21no—
12C2×C3×#217—21no—
13C2×#3724C2211yescharacteristic
14C2×#3724C2211yescharacteristic
15C2×#3724C2211yescharacteristic
16C2×#3724C2211yescharacteristic
17#63957—22no—
18#63957—22no—
19C2×Dic32—21no—
20C22⋊#622C414yescomplemented
21#63743—22no—
22#63742—22no—
23#63579—21no—
24C2×#877—61no—
25#4942—61no—
26C24×C32D411yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3C2×C412yes—
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3Q812yes—
34C22×C3⋊Dic3C2311yescharacteristic
35C22×C3×Dic3—21no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622—21no—
42C2×#622—21no—
43C2×#622C2×C412yes—
44C2×#622C2×C412yes—
45C3×#217—24no—
46C3×#217—42no—
47#3724—21no—
48#3724—21no—
49#3724—21no—
50#3724—21no—
51#3724—21no—
52#3724—21no—
53#3724D412yes—
54#3724D412yes—
55Dic32—24no—
56#1854—91nomaximal, Sylow
57C23×Dic3—61no—
58C23×Dic3—61no—
59C2×C3×C22⋊C4—61no—
60C2×C3×C22⋊C4—61no—
61C2×#217—21no—
62C2×#217—21no—
63C2×Dic3⋊C4—61no—
64C2×Dic3⋊C4—61no—
65C2×Dic3⋊C4—61no—
66C2×Dic3⋊C4—61no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3—61no—
69#877—64no—
70#877—64no—
71C3⋊#95—61no—
72C3⋊#95—61no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32—21no—
77C23×C32—21no—
78C23×C32—21no—
79C23×C32C4⋊C412yes—
80C23×C32C2×D411yescharacteristic
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—22no—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3C4⋊C412yes—
88C2×C3⋊Dic3C22×C411yescharacteristic
89C2×C3⋊Dic3C2×D411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×Q811yescharacteristic
92C2×C3⋊Dic3#4111yescharacteristic
93C2×C3⋊Dic3#4111yescharacteristic
94C2×C3×Dic3—22no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C2×C3×Dic3—41no—
106#622—22no—
107#622—22no—
108C2×#117—91no—
109C2×#107—91no—
110C2×#106—91no—
111C2×C22⋊C8—91no—
112#380—91no—
113#340—91no—
114#340—91no—
115C24×C3—21no—
116C24×C3—21no—
117C22×C3×C4—61no—
118C22×C3×C4—61no—
119C22×C3×C4—61no—
120C22×C3×C4—61no—
121C22×Dic3—21no—
122C22×Dic3—21no—
123C22×Dic3—21no—
124C22×Dic3—21no—
125C22×Dic3—61no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C22×Dic3—61no—
131C22×Dic3—62no—
132C22×Dic3—62no—
133C22×Dic3—62no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136C22×Dic3—62no—
137C22×Dic3—121no—
138C22×Dic3—121no—
139C22×Dic3—121no—
140C22×Dic3—121no—
141C3×C22⋊C4—64no—
142C3×C22⋊C4—122no—
143#217—24no—
144#217—42no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—121no—
150Dic3⋊C4—121no—
151Dic3⋊C4—121no—
152Dic3⋊C4—121no—
153C4×Dic3—64no—
154C4×Dic3—64no—
155C22×C32—22no—
156C22×C32—22no—
157C22×C32—22no—
158C22×C32—41no—
159C22×C32—41no—
160C22×C32—41no—
161C22×C32—41no—
162C22×C32C2×C4⋊C411yescharacteristic
163C22×C32#12011yescharacteristic
164C22×C32#12311yescharacteristic
165C22×C32#13511yescharacteristic
166C22×C32#13511yescharacteristic
167C22×C32AGL(1,ℤ/8)11yescharacteristic
168C22×C32#13711yescharacteristic
169C3⋊Dic3—22no—
170C3⋊Dic3C4×D411yescharacteristic
171C3⋊Dic3C4×D411yescharacteristic
172C3⋊Dic3C22⋊Q811yescharacteristic
173C3⋊Dic3C22⋊Q811yescharacteristic
174C3×Dic3—42no—
175C3×Dic3—42no—
176C3×Dic3—81no—
177C3×Dic3—81no—
178C23×C4—91no—
179C22×C8—91no—
180C22×C8—91no—
181#117—182no—
182#117—182no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—91no—
187C2×C22⋊C4—61no—
188C2×C22⋊C4—61no—
189C2×C42—181no—
190#107—182no—
191#106—182no—
192C22⋊C8—94no—
193#95—181no—
194C23×C3—22no—
195C23×C3—22no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—41no—
203C23×C3—41no—
204C23×C3—41no—
205C23×C3—41no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—41no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—121no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217C2×C3×C4—121no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220C2×C3×C4—121no—
221C2×C3×C4—121no—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—41no—
225C2×Dic3—41no—
226C2×Dic3—41no—
227C2×Dic3—41no—
228C2×Dic3—41no—
229C2×Dic3—41no—
230C2×Dic3—41no—
231C2×Dic3—41no—
232C2×Dic3—41no—
233C2×Dic3—41no—
234C2×Dic3—62no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—61no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—64no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—64no—
253C2×Dic3—62no—
254C2×Dic3—122no—
255C2×Dic3—122no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—121no—
259C2×Dic3—121no—
260C2×C32—42no—
261C2×C32#38511yescharacteristic
262C2×C32#42711yescharacteristic
263C2×C32#42811yescharacteristic
264C2×C32#44911yescharacteristic
265C2×C32#45211yescharacteristic
266C2×C32#48211yescharacteristic
267C2×C32#48511yescharacteristic
268C24GO+(4,𝔽2)11yescharacteristic
269C22×C4—61no—
270C22×C4—61no—
271C22×C4—61no—
272C22×C4—61no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—92no—
276C22×C4—92no—
277C22×C4—181no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4—181no—
281C2×C8—92no—
282C2×C8—92no—
283C2×C8—181no—
284C2×C8—181no—
285C2×C8—181no—
286C2×C8—181no—
287C4⋊C4—92no—
288C4⋊C4—92no—
289C4⋊C4—181no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C22⋊C4—64no—
296C22⋊C4—122no—
297C42—184no—
298C22×C3—24no—
299C22×C3—24no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—42no—
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—42no—
326C3×C4—122no—
327C3×C4—122no—
328C3×C4—241no—
329C3×C4—241no—
330Dic3—42no—
331Dic3—42no—
332Dic3—61no—
333Dic3—61no—
334Dic3—61no—
335Dic3—61no—
336Dic3—61no—
337Dic3—61no—
338Dic3—61no—
339Dic3—61no—
340Dic3—64no—
341Dic3—81no—
342Dic3—81no—
343Dic3—122no—
344C32#185411yescharacteristic, complemented, Sylow
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23#377312yes—
352C23C2×GO+(4,𝔽2)11yescharacteristic
353C2×C4—62no—
354C2×C4—62no—
355C2×C4—91no—
356C2×C4—91no—
357C2×C4—91no—
358C2×C4—91no—
359C2×C4—91no—
360C2×C4—91no—
361C2×C4—92no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4—121no—
365C2×C4—121no—
366C2×C4—121no—
367C2×C4—121no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—121no—
371C2×C4—121no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4—182no—
375C2×C4—182no—
376C2×C4—181no—
377C2×C4—181no—
378C8—182no—
379C8—182no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—44no—
395C2×C3—44no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22#6423311yescharacteristic
404C22C2×#377311yescharacteristic
405C22#6423611yescharacteristic
406C22#6423711yescharacteristic
407C22#6423711yescharacteristic
408C22#6423911yescharacteristic
409C22#6424111yescharacteristic
410C4—91no—
411C4—91no—
412C4—91no—
413C4—91no—
414C4—122no—
415C4—122no—
416C4—182no—
417C4—241no—
418C4—241no—
419C3—21no—
420C3—21no—
421C2—42no—
422C2#1059348511yescharacteristic
423C2#1059349411yescharacteristic
424C2#1059350111yescharacteristic
425C2#1059350711yescharacteristic
426C2#1059351111yescharacteristic
427C2#1059352111yescharacteristic
428C2#1059352411yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
Fitting, prime radicalC24×C32D4
socleC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1854
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
3. C2×#63743C2semidirect
4. C2×#63742C2semidirect
6. #10590075C2semidirect
7. #10590075C2semidirect
20. C22⋊#622C4semidirect
344. C32#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#639572
C2×C22⋊#6222
C2×#637432
C2×#637422
#105917202
#105900752
#18549