Finite Group Databasebeta

← #11773449

Subgroups — #11773449

Order 1152.

982 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 982 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#3773C212yesmaximal
2C2×#63900C211yesmaximal, characteristic
3C2×#63781C211yesmaximal, characteristic
4C2×#63737C212yesmaximal
5#10591370C211yesmaximal, characteristic
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2212yes—
9C22×#624C2211yescharacteristic
10C22×#624C2211yescharacteristic
11C2×#3773—24no—
12C2×#3773—24no—
13C2×#3773—24no—
14C2×C3×C4⋊Dic3—21no—
15C2×#3724—21no—
16#63900—24no—
17#63781C414yescomplemented
18#63737—24no—
19C3×C3⋊#95—21no—
20#63579—21no—
21C2×D3×C4⋊C4—61no—
22D3×#95—61no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157C2×C414yes—
29C22×#157D414yes—
30C22×#157Q814yes—
31C22×C32×C4D411yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3Q812yes—
37C22×C3×Dic3—22no—
38C22×C3×Dic3—21no—
39C22×C3×Dic3—21no—
40C2×#624—22no—
41C2×#624—22no—
42C2×#624—22no—
43C2×#624—22no—
44C2×#624—22no—
45C2×#624—22no—
46C2×#624—22no—
47C2×#624—22no—
48C2×#624—22no—
49C2×#624—21no—
50C2×#624—21no—
51C2×#624D414yes—
52C2×#624D412yes—
53C2×#624Q812yes—
54#3773—216no—
55C3×C4⋊Dic3—24no—
56#3724—24no—
57#1444—91nomaximal, Sylow
58C22×C4×D3—61no—
59C22×C4×D3—61no—
60C22×C4×D3—61no—
61C22×C4×D3—62no—
62C22×C4×D3—61no—
63C2×C3×C4⋊C4—61no—
64C2×C4⋊Dic3—21no—
65C2×Dic3⋊C4—62no—
66D3×C4⋊C4—68no—
67C3×#95—61no—
68C3⋊#95—21no—
69C3⋊#95—61no—
70C3⋊#95—61no—
71C23×C32C2×D411yescharacteristic
72C22×C3⋊D3C22×C411yescharacteristic
73C22×C3⋊D3C2×D412yes—
74C22×C3⋊D3C2×D411yescharacteristic
75C22×C3⋊D3C2×D412yes—
76C22×C3⋊D3C2×Q812yes—
77C22×C3⋊D3C2×Q811yescharacteristic
78C22×C3⋊D3C2×Q811yescharacteristic
79C22×C3⋊D3#4112yes—
80C22×C3⋊D3#4111yescharacteristic
81C22×C3⋊D3#4111yescharacteristic
82C2×#157—24no—
83C2×#157—24no—
84C2×#157—24no—
85C2×#157—24no—
86C2×#157—24no—
87C2×#157—24no—
88C2×#157C4⋊C418yescomplemented
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4C4⋊C412yescomplemented
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3C4⋊C412yescomplemented
95C4×C3⋊D3—24no—
96C4×C3⋊D3—24no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C2×C3×Dic3—42no—
105C2×C3×Dic3—41no—
106#624—24no—
107#624—24no—
108#624—24no—
109#624—24no—
110#624—42no—
111#624—42no—
112#624—42no—
113#624—42no—
114C22×C4⋊C4—91no—
115C22×C4⋊C4—92no—
116C2×#95—91no—
117C2×#95—91no—
118C2×#95—92no—
119C23×D3—61no—
120C23×D3—61no—
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—61no—
124C22×C3×C4—61no—
125C22×C3×C4—62no—
126C22×Dic3—21no—
127C22×Dic3—21no—
128C22×Dic3—22no—
129C22×Dic3—61no—
130C22×Dic3—61no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—64no—
134C2×C4×D3—62no—
135C2×C4×D3—62no—
136C2×C4×D3—62no—
137C2×C4×D3—62no—
138C2×C4×D3—64no—
139C2×C4×D3—64no—
140C2×C4×D3—64no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C4×D3—122no—
144C2×C4×D3—122no—
145C2×C4×D3—122no—
146C2×C4×D3—122no—
147C2×C4×D3—122no—
148C2×C4×D3—122no—
149C2×C4×D3—122no—
150C2×C4×D3—122no—
151C2×C4×D3—122no—
152C2×C4×D3—122no—
153C3×C4⋊C4—64no—
154C4⋊Dic3—24no—
155Dic3⋊C4—68no—
156C22×C32C2×C4⋊C411yescharacteristic
157C22×C32#12011yescharacteristic
158C22×C32#12111yescharacteristic
159C22×C32C22⋊Q811yescharacteristic
160C22×C32#12311yescharacteristic
161C22×C32#12711yescharacteristic
162C22×C32C4⋊Q811yescharacteristic
163C2×C3⋊D3C2×C4⋊C412yes—
164C2×C3⋊D3C4×D411yescharacteristic
165C2×C3⋊D3C4×D412yes—
166C2×C3⋊D3C4×Q811yescharacteristic
167C2×C3⋊D3#12012yes—
168C2×C3⋊D3#12112yes—
169C2×C3⋊D3C22⋊Q812yes—
170C2×C3⋊D3C22⋊Q812yes—
171C2×C3⋊D3C22⋊Q812yes—
172C2×C3⋊D3C22⋊Q812yes—
173C2×C3⋊D3#12312yes—
174C2×C3⋊D3#12512yes—
175C2×C3⋊D3#12511yescharacteristic
176C2×C3⋊D3C4⋊Q812yes—
177C2×C3⋊D3C4⋊Q811yescharacteristic
178C2×C3⋊D3C4⋊Q812yes—
179#157—28no—
180C32×C4—22no—
181C3⋊Dic3—22no—
182C3×Dic3—42no—
183C3×Dic3—44no—
184C3×Dic3—42no—
185C23×C4—91no—
186C23×C4—92no—
187C23×C4—91no—
188C23×C4—92no—
189C23×C4—91no—
190C2×C4⋊C4—61no—
191C2×C4⋊C4—184no—
192C2×C4⋊C4—181no—
193C2×C4⋊C4—184no—
194C2×C4⋊C4—184no—
195C2×C4⋊C4—184no—
196#95—61no—
197#95—94no—
198#95—181no—
199#95—184no—
200C23×C3—21no—
201C23×C3—21no—
202C22×D3—61no—
203C22×D3—61no—
204C22×D3—62no—
205C22×D3—61no—
206C22×D3—61no—
207C22×D3—62no—
208C22×D3—62no—
209C22×D3—62no—
210C22×D3—61no—
211C22×D3—61no—
212C22×D3—61no—
213C22×D3—61no—
214C22×D3—62no—
215C22×D3—62no—
216C22×D3—61no—
217C22×D3—61no—
218C22×D3—62no—
219C22×D3—61no—
220C22×D3—62no—
221C22×D3—61no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—64no—
229C2×C3×C4—62no—
230C2×C3×C4—62no—
231C2×C3×C4—122no—
232C2×C3×C4—121no—
233C2×C3×C4—121no—
234C2×C3×C4—122no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×Dic3—24no—
238C2×Dic3—22no—
239C2×Dic3—22no—
240C2×Dic3—42no—
241C2×Dic3—41no—
242C2×Dic3—41no—
243C2×Dic3—42no—
244C2×Dic3—41no—
245C2×Dic3—41no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252C4×D3—68no—
253C4×D3—68no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—124no—
257C4×D3—124no—
258C4×D3—124no—
259C4×D3—124no—
260C4×D3—124no—
261C4×D3—124no—
262C4×D3—124no—
263C4×D3—124no—
264C2×C32#38411yescharacteristic
265C2×C32#38511yescharacteristic
266C2×C32#38911yescharacteristic
267C2×C32#39211yescharacteristic
268C2×C32#39511yescharacteristic
269C2×C32#39811yescharacteristic
270C2×C32#39911yescharacteristic
271C3⋊D3#38512yes—
272C3⋊D3#38912yes—
273C3⋊D3#39512yes—
274C3⋊D3#39812yes—
275C24—91no—
276C22×C4—61no—
277C22×C4—61no—
278C22×C4—62no—
279C22×C4—92no—
280C22×C4—94no—
281C22×C4—92no—
282C22×C4—94no—
283C22×C4—94no—
284C22×C4—94no—
285C22×C4—91no—
286C22×C4—92no—
287C22×C4—92no—
288C22×C4—182no—
289C22×C4—182no—
290C22×C4—182no—
291C22×C4—181no—
292C22×C4—181no—
293C22×C4—182no—
294C22×C4—182no—
295C22×C4—182no—
296C22×C4—182no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4—182no—
300C22×C4—182no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4GO+(4,𝔽2)11yescharacteristic
306C4⋊C4—64no—
307C4⋊C4—184no—
308C4⋊C4—1816no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—62no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—61no—
336C2×D3—61no—
337C2×D3—61no—
338C2×D3—61no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—62no—
343C2×D3—62no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—61no—
348C2×D3—61no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—61no—
352C2×D3—61no—
353C2×D3—62no—
354C2×D3—62no—
355C3×C4—24no—
356C3×C4—42no—
357C3×C4—122no—
358C3×C4—124no—
359C3×C4—122no—
360Dic3—42no—
361Dic3—44no—
362Dic3—42no—
363Dic3—64no—
364Dic3—122no—
365C32#144411yescharacteristic, complemented, Sylow
366C23—91no—
367C23—91no—
368C23—92no—
369C23—91no—
370C23—91no—
371C23—92no—
372C23—92no—
373C23—91no—
374C23—91no—
375C23—92no—
376C23C2×GO+(4,𝔽2)11yescharacteristic
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—62no—
380C2×C4—62no—
381C2×C4—64no—
382C2×C4—98no—
383C2×C4—92no—
384C2×C4—122no—
385C2×C4—121no—
386C2×C4—121no—
387C2×C4—122no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4—184no—
393C2×C4—184no—
394C2×C4—184no—
395C2×C4—184no—
396C2×C4—184no—
397C2×C4—184no—
398C2×C4—184no—
399C2×C4—184no—
400C2×C4—184no—
401C2×C4—184no—
402C2×C4—181no—
403C2×C4—181no—
404C2×C4—362no—
405C2×C4—362no—
406C2×C4—362no—
407C2×C4—362no—
408C2×C4#377312yescomplemented
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423D3—62no—
424D3—62no—
425D3—62no—
426D3—62no—
427D3—62no—
428D3—62no—
429D3—62no—
430D3—62no—
431C22—92no—
432C22—92no—
433C22—92no—
434C22—92no—
435C22—92no—
436C22—92no—
437C22—91no—
438C22—91no—
439C22—91no—
440C22—91no—
441C22—92no—
442C22—92no—
443C22—92no—
444C22—92no—
445C22—92no—
446C22—92no—
447C22D32⋊Q811yescharacteristic
448C22#6422211yescharacteristic
449C22#6423011yescharacteristic
450C22#6423111yescharacteristic
451C22#6423311yescharacteristic
452C22C2×#377311yescharacteristic
453C22#6424111yescharacteristic
454C4—22no—
455C4—122no—
456C4—122no—
457C4—124no—
458C4—188no—
459C4—182no—
460C3—21no—
461C3—21no—
462C2—92no—
463C2—92no—
464C2—92no—
465C2—92no—
466C2#1059333911yescharacteristic
467C2#1059340811yescharacteristic
468C2#1059341111yescharacteristic
469C2#1059341211yescharacteristic
470C2#1059341311yescharacteristic
471C2#1059345511yescharacteristic
472C2#1059348511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC22×C3⋊D3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1444
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
17. #63781C4semidirect
88. C2×#157C4⋊C4semidirect
91. C2×C32×C4C4⋊C4semidirect
94. C2×C3⋊Dic3C4⋊C4semidirect
365. C32#1444semidirect
408. C2×C4#3773semidirect

Maximal subgroups

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

subgroupindex
C22×#37732
C2×#639002
C2×#637812
C2×#637372
#105913702
#14449