Finite Group Databasebeta

← #11773409

Subgroups — #11773409

Order 1152.

894 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 127 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×#63900C211yesmaximal, characteristic
2C2×#63781C211yesmaximal, characteristic
3C2×#63737C212yesmaximal
4C2×#63737C212yesmaximal
5#10591370C211yesmaximal, characteristic
6C23×#157C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×#624C2212yes—
9C22×#624C2211yescharacteristic
10C22×#624C2211yescharacteristic
11C2×C3×C4⋊Dic3—21no—
12C2×#3724—21no—
13#63900—24no—
14#63781C414yescomplemented
15#63737—24no—
16#63737—24no—
17C3×C3⋊#95—21no—
18#63579—21no—
19C2×D3×C4⋊C4—61no—
20D3×#95—61no—
21C23×C3⋊D3C2311yescharacteristic
22C22×#157—22no—
23C22×#157—22no—
24C22×#157—22no—
25C22×#157—22no—
26C22×#157—22no—
27C22×#157—22no—
28C22×#157C2×C414yes—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3D411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3Q812yes—
35C22×C3×Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×#624—22no—
39C2×#624—22no—
40C2×#624—22no—
41C2×#624—22no—
42C2×#624—22no—
43C2×#624—22no—
44C2×#624—22no—
45C2×#624—22no—
46C2×#624—22no—
47C2×#624—21no—
48C2×#624—21no—
49C2×#624D414yes—
50C2×#624D412yes—
51C2×#624Q812yes—
52C3×C4⋊Dic3—24no—
53#3724—24no—
54#1442—91nomaximal, Sylow
55C22×C4×D3—61no—
56C22×C4×D3—61no—
57C22×C4×D3—61no—
58C22×C4×D3—62no—
59C22×C4×D3—61no—
60C2×C3×C4⋊C4—61no—
61C2×C4⋊Dic3—21no—
62C2×Dic3⋊C4—62no—
63D3×C4⋊C4—68no—
64C3×#95—61no—
65C3⋊#95—21no—
66C3⋊#95—61no—
67C3⋊#95—61no—
68C23×C32C2×D411yescharacteristic
69C22×C3⋊D3C22×C411yescharacteristic
70C22×C3⋊D3C2×D411yescharacteristic
71C22×C3⋊D3C2×D412yes—
72C22×C3⋊D3C2×Q811yescharacteristic
73C22×C3⋊D3C2×Q811yescharacteristic
74C22×C3⋊D3#4112yes—
75C22×C3⋊D3#4112yes—
76C22×C3⋊D3#4112yes—
77C22×C3⋊D3#4111yescharacteristic
78C22×C3⋊D3#4111yescharacteristic
79C2×#157—24no—
80C2×#157—24no—
81C2×#157—24no—
82C2×#157—42no—
83C2×#157—42no—
84C2×#157—42no—
85C2×#157—42no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4C4⋊C412yes—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3C4⋊C412yes—
92C4×C3⋊D3—24no—
93C4×C3⋊D3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—42no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—42no—
102C2×C3×Dic3—41no—
103#624—24no—
104#624—24no—
105#624—24no—
106#624—24no—
107#624—42no—
108#624—42no—
109#624—42no—
110#624—42no—
111C22×C4⋊C4—91no—
112C2×#95—91no—
113C2×#95—91no—
114C2×#95—92no—
115C2×#95—92no—
116C23×D3—61no—
117C23×D3—61no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—61no—
121C22×C3×C4—61no—
122C22×C3×C4—62no—
123C22×Dic3—21no—
124C22×Dic3—21no—
125C22×Dic3—22no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—64no—
131C2×C4×D3—62no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C4×D3—62no—
135C2×C4×D3—64no—
136C2×C4×D3—64no—
137C2×C4×D3—64no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—122no—
141C2×C4×D3—122no—
142C2×C4×D3—122no—
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—
150C3×C4⋊C4—64no—
151C4⋊Dic3—24no—
152Dic3⋊C4—68no—
153C22×C32C2×C4⋊C411yescharacteristic
154C22×C32#12011yescharacteristic
155C22×C32#12111yescharacteristic
156C22×C32C22⋊Q811yescharacteristic
157C22×C32#12311yescharacteristic
158C22×C32#12411yescharacteristic
159C22×C32#12411yescharacteristic
160C2×C3⋊D3#11712yes—
161C2×C3⋊D3C4×D412yes—
162C2×C3⋊D3C4×D411yescharacteristic
163C2×C3⋊D3C4×Q811yescharacteristic
164C2×C3⋊D3#12112yes—
165C2×C3⋊D3C22⋊Q812yes—
166C2×C3⋊D3C22⋊Q812yes—
167C2×C3⋊D3#12312yes—
168C2×C3⋊D3#12312yes—
169C2×C3⋊D3#12412yes—
170C2×C3⋊D3#12512yes—
171C2×C3⋊D3#12512yes—
172C2×C3⋊D3#12511yescharacteristic
173C2×C3⋊D3#12612yes—
174C2×C3⋊D3#12612yes—
175C2×C3⋊D3C4⋊Q811yescharacteristic
176#157—44no—
177C32×C4—22no—
178C3⋊Dic3—22no—
179C3×Dic3—42no—
180C3×Dic3—44no—
181C3×Dic3—42no—
182C23×C4—92no—
183C23×C4—91no—
184C23×C4—91no—
185C23×C4—91no—
186C23×C4—92no—
187C2×C4⋊C4—61no—
188C2×C4⋊C4—184no—
189C2×C4⋊C4—181no—
190#95—61no—
191#95—94no—
192#95—181no—
193#95—184no—
194#95—184no—
195C23×C3—21no—
196C23×C3—21no—
197C22×D3—61no—
198C22×D3—61no—
199C22×D3—62no—
200C22×D3—61no—
201C22×D3—61no—
202C22×D3—62no—
203C22×D3—61no—
204C22×D3—61no—
205C22×D3—61no—
206C22×D3—61no—
207C22×D3—61no—
208C22×D3—61no—
209C22×D3—62no—
210C22×D3—62no—
211C22×D3—62no—
212C22×D3—61no—
213C22×D3—62no—
214C22×D3—61no—
215C22×D3—62no—
216C22×D3—62no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—22no—
220C2×C3×C4—22no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—64no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230C2×C3×C4—121no—
231C2×C3×C4—121no—
232C2×Dic3—24no—
233C2×Dic3—22no—
234C2×Dic3—22no—
235C2×Dic3—41no—
236C2×Dic3—41no—
237C2×Dic3—42no—
238C2×Dic3—42no—
239C2×Dic3—41no—
240C2×Dic3—41no—
241C2×Dic3—62no—
242C2×Dic3—62no—
243C2×Dic3—62no—
244C2×Dic3—62no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C4×D3—68no—
248C4×D3—68no—
249C4×D3—124no—
250C4×D3—124no—
251C4×D3—124no—
252C4×D3—124no—
253C4×D3—124no—
254C4×D3—124no—
255C4×D3—124no—
256C4×D3—124no—
257C4×D3—124no—
258C4×D3—124no—
259C2×C32#38211yescharacteristic
260C2×C32#38511yescharacteristic
261C2×C32#38911yescharacteristic
262C2×C32#39311yescharacteristic
263C2×C32#39411yescharacteristic
264C2×C32#39711yescharacteristic
265C2×C32#40011yescharacteristic
266C3⋊D3#38712yes—
267C3⋊D3#38812yes—
268C3⋊D3#39812yes—
269C3⋊D3#40012yes—
270C24—91no—
271C22×C4—61no—
272C22×C4—61no—
273C22×C4—62no—
274C22×C4—92no—
275C22×C4—94no—
276C22×C4—92no—
277C22×C4—91no—
278C22×C4—92no—
279C22×C4—92no—
280C22×C4—94no—
281C22×C4—182no—
282C22×C4—182no—
283C22×C4—182no—
284C22×C4—181no—
285C22×C4—181no—
286C22×C4—182no—
287C22×C4—182no—
288C22×C4—182no—
289C22×C4—182no—
290C22×C4—182no—
291C22×C4—182no—
292C22×C4—182no—
293C22×C4—182no—
294C22×C4—182no—
295C22×C4—182no—
296C22×C4—182no—
297C22×C4—182no—
298C22×C4—182no—
299C22×C4—182no—
300C22×C4GO+(4,𝔽2)11yescharacteristic
301C4⋊C4—64no—
302C4⋊C4—184no—
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—21no—
315C22×C3—21no—
316C22×C3—21no—
317C2×D3—62no—
318C2×D3—62no—
319C2×D3—62no—
320C2×D3—62no—
321C2×D3—62no—
322C2×D3—62no—
323C2×D3—62no—
324C2×D3—62no—
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—62no—
329C2×D3—61no—
330C2×D3—61no—
331C2×D3—61no—
332C2×D3—61no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—62no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—61no—
343C2×D3—61no—
344C2×D3—62no—
345C2×D3—62no—
346C2×D3—62no—
347C2×D3—61no—
348C2×D3—61no—
349C3×C4—24no—
350C3×C4—42no—
351C3×C4—124no—
352C3×C4—122no—
353C3×C4—122no—
354Dic3—44no—
355Dic3—42no—
356Dic3—42no—
357Dic3—64no—
358Dic3—122no—
359C32#144211yescharacteristic, complemented, Sylow
360C23—91no—
361C23—91no—
362C23—92no—
363C23—92no—
364C23—91no—
365C23—91no—
366C23—92no—
367C23—91no—
368C23—91no—
369C23—92no—
370C23C2×GO+(4,𝔽2)11yescharacteristic
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—62no—
374C2×C4—62no—
375C2×C4—64no—
376C2×C4—92no—
377C2×C4—122no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—122no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—184no—
384C2×C4—184no—
385C2×C4—184no—
386C2×C4—184no—
387C2×C4—184no—
388C2×C4—184no—
389C2×C4—181no—
390C2×C4—181no—
391C2×C4—184no—
392C2×C4—184no—
393C2×C4—184no—
394C2×C4—362no—
395C2×C4—362no—
396C2×C4—362no—
397C2×C4—362no—
398C2×C4—362no—
399C2×C4—362no—
400C2×C4—362no—
401C2×C4—362no—
402C2×C4#377312yes—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417D3—62no—
418D3—62no—
419D3—62no—
420D3—62no—
421D3—62no—
422D3—62no—
423D3—62no—
424D3—62no—
425C22—92no—
426C22—92no—
427C22—92no—
428C22—92no—
429C22—92no—
430C22—92no—
431C22—92no—
432C22—92no—
433C22—92no—
434C22—92no—
435C22—91no—
436C22—91no—
437C22—91no—
438C22—91no—
439C22—92no—
440C22—92no—
441C22D32⋊Q811yescharacteristic
442C22#6422111yescharacteristic
443C22#6422111yescharacteristic
444C22#6423011yescharacteristic
445C22#6423311yescharacteristic
446C22C2×#377311yescharacteristic
447C22#6424111yescharacteristic
448C4—22no—
449C4—124no—
450C4—122no—
451C4—122no—
452C4—182no—
453C4—364no—
454C3—21no—
455C3—21no—
456C2—92no—
457C2—92no—
458C2—92no—
459C2—92no—
460C2#1059334311yescharacteristic
461C2#1059334411yescharacteristic
462C2#1059340111yescharacteristic
463C2#1059340211yescharacteristic
464C2#1059340411yescharacteristic
465C2#1059341211yescharacteristic
466C2#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#1442
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
14. #63781C4semidirect
359. C32#1442semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#637812
C2×#637372
#105913702
#14429