Finite Group Databasebeta

← #11787327

Subgroups — #11787327

Order 1152.

878 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 99 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×#63980C211yesmaximal, characteristic
2C22×#3724C211yesmaximal, characteristic, complemented
3C2×C22⋊#622C211yesmaximal, characteristic, complemented
4C2×#63739C212yesmaximal, complemented
5#10590075C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C22×C3×#67—21no—
8C23×C3×Dic3—21no—
9C22×#625C2211yescharacteristic
10C22×#622C2212yes—
11#63980—22no—
12#63980C414yescomplemented
13C2×#3724—21no—
14C2×#3724—24no—
15C2×#3724C2211yescharacteristic
16C2×#3724C2212yes—
17C2×(C2×D3)⋊Dic3—21no—
18C22⋊#622—22no—
19#63739—24no—
20C2×#939—61no—
21C22×Dic3⋊C4—61no—
22C24×C32D411yescharacteristic
23C23×C3×D3—21no—
24C22×C3⋊Dic3—22no—
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3C2311yescharacteristic
30C2×C3×#67—24no—
31C2×C3×#67—42no—
32C2×C3×#67—42no—
33C22×C3×Dic3—24no—
34C22×C3×Dic3—22no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—42no—
37C22×C3×Dic3—42no—
38C2×#625—22no—
39C2×#625—22no—
40C2×#625—21no—
41C2×#625C2×C412yescomplemented
42C2×#622—22no—
43C2×#622—22no—
44C2×#622—22no—
45#3724—24no—
46#3724—22no—
47#3724—21no—
48#3724C2×C412yescomplemented
49#3724D414yescomplemented
50(C2×D3)⋊Dic3—24no—
51#1874—91nomaximal, Sylow
52C22×C3×D4—61no—
53C23×C3×C4—61no—
54C22×#67—21no—
55C22×#67—61no—
56C23×Dic3—21no—
57C23×Dic3—61no—
58C23×Dic3—61no—
59C2×#217—61no—
60#939—64no—
61#939—64no—
62C2×(C2×D3)⋊C4—61no—
63C2×Dic3⋊C4—62no—
64C2×Dic3⋊C4—61no—
65C2×Dic3⋊C4—68no—
66C2×Dic3⋊C4—62no—
67C23×C32—21no—
68C23×C32—21no—
69C23×C32—21no—
70C23×C32—21no—
71C23×C32C22⋊C412yes—
72C23×C32D812yes—
73C23×C32SD1612yes—
74C23×C32C2×D411yescharacteristic
75C22×C3×D3—22no—
76C22×C3×D3—41no—
77C22×C3×D3—41no—
78C22×C3×D3—41no—
79C22×C3×D3—41no—
80C22×C3×D3—41no—
81C22×C3×D3—41no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—24no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3C22⋊C412yes—
87C2×C3⋊Dic3C22×C411yescharacteristic
88C2×C3⋊Dic3C2×D412yes—
89C2×C3⋊Dic3C2×D411yescharacteristic
90C2×C3⋊Dic3#4112yes—
91C3×#67—48no—
92C2×C3×Dic3—22no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—48no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—42no—
99#625—24no—
100#625—42no—
101#622—42no—
102C2×#121—91no—
103C22×C4⋊C4—91no—
104C2×#102—92no—
105C2×C22⋊C8—91no—
106#340—92no—
107C24×C3—21no—
108C24×C3—21no—
109C24×C3—61no—
110C23×D3—21no—
111C2×C3×D4—64no—
112C2×C3×D4—122no—
113C2×C3×D4—122no—
114C22×C3×C4—64no—
115C22×C3×C4—62no—
116C22×C3×C4—61no—
117C22×C3×C4—122no—
118C22×C3×C4—122no—
119C2×#67—24no—
120C2×#67—42no—
121C2×#67—42no—
122C2×#67—62no—
123C2×#67—62no—
124C2×#67—122no—
125C2×#67—122no—
126C22×Dic3—24no—
127C22×Dic3—22no—
128C22×Dic3—21no—
129C22×Dic3—42no—
130C22×Dic3—42no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C22×Dic3—61no—
134C22×Dic3—62no—
135C22×Dic3—62no—
136C22×Dic3—61no—
137C22×Dic3—62no—
138C22×Dic3—62no—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C22×Dic3—122no—
142C22×Dic3—122no—
143#217—64no—
144(C2×D3)⋊C4—64no—
145Dic3⋊C4—62no—
146Dic3⋊C4—64no—
147Dic3⋊C4—64no—
148Dic3⋊C4—68no—
149Dic3⋊C4—62no—
150C22×C32—22no—
151C22×C32—22no—
152C22×C32—22no—
153C22×C32—22no—
154C22×C32—22no—
155C22×C32—22no—
156C22×C32#10214yescomplemented
157C22×C32C2×C22⋊C411yescharacteristic
158C22×C32#12011yescharacteristic
159C22×C32#12311yescharacteristic
160C22×C32C2×D811yescharacteristic
161C22×C32C2×SD1611yescharacteristic
162C22×C32AGL(1,ℤ/8)11yescharacteristic
163C22×C32#13711yescharacteristic
164C2×C3×D3—42no—
165C2×C3×D3—42no—
166C2×C3×D3—42no—
167C2×C3×D3—81no—
168C2×C3×D3—81no—
169C2×C3×D3—81no—
170C2×C3×D3—81no—
171C3⋊Dic3—22no—
172C3⋊Dic3C4×D412yes—
173C3⋊Dic3#12112yes—
174C3×Dic3—42no—
175C3×Dic3—44no—
176C22×D4—61no—
177C22×D4—91no—
178C23×C4—61no—
179C23×C4—91no—
180C22×C8—92no—
181#121—94no—
182#121—182no—
183C2×C4⋊C4—92no—
184C2×C4⋊C4—91no—
185C2×C4⋊C4—184no—
186C2×C4⋊C4—181no—
187C2×C22⋊C4—181no—
188#102—184no—
189C22⋊C8—182no—
190C23×C3—22no—
191C23×C3—22no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—22no—
197C23×C3—22no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—22no—
201C23×C3—22no—
202C23×C3—41no—
203C23×C3—41no—
204C23×C3—41no—
205C23×C3—41no—
206C23×C3—62no—
207C23×C3—121no—
208C23×C3—121no—
209C23×C3—121no—
210C23×C3—121no—
211C23×C3—121no—
212C23×C3—121no—
213C22×D3—22no—
214C22×D3—41no—
215C22×D3—41no—
216C22×D3—41no—
217C22×D3—41no—
218C22×D3—41no—
219C22×D3—41no—
220C3×D4—128no—
221C2×C3×C4—64no—
222C2×C3×C4—62no—
223C2×C3×C4—128no—
224C2×C3×C4—122no—
225C2×C3×C4—122no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228#67—48no—
229#67—124no—
230#67—124no—
231C2×Dic3—24no—
232C2×Dic3—22no—
233C2×Dic3—48no—
234C2×Dic3—42no—
235C2×Dic3—42no—
236C2×Dic3—41no—
237C2×Dic3—41no—
238C2×Dic3—62no—
239C2×Dic3—61no—
240C2×Dic3—61no—
241C2×Dic3—62no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—62no—
245C2×Dic3—62no—
246C2×Dic3—62no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—68no—
250C2×Dic3—68no—
251C2×Dic3—62no—
252C2×Dic3—124no—
253C2×Dic3—124no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256C2×C32—24no—
257C2×C32#38611yescharacteristic
258C2×C32C2×#10211yescharacteristic
259C2×C32#41711yescharacteristic
260C2×C32#44711yescharacteristic
261C2×C32#44811yescharacteristic
262C2×C32#48011yescharacteristic
263C2×C32#48111yescharacteristic
264C3×D3—82no—
265C24—61no—
266C24GO+(4,𝔽2)11yescharacteristic
267C2×D4—64no—
268C2×D4—92no—
269C2×D4—122no—
270C2×D4—122no—
271C2×D4—182no—
272C2×D4—182no—
273C2×D4—181no—
274C22×C4—64no—
275C22×C4—61no—
276C22×C4—62no—
277C22×C4—91no—
278C22×C4—91no—
279C22×C4—92no—
280C22×C4—92no—
281C22×C4—122no—
282C22×C4—122no—
283C22×C4—182no—
284C22×C4—182no—
285C2×C8—182no—
286C2×C8—182no—
287C2×C8—182no—
288C4⋊C4—94no—
289C4⋊C4—92no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4—184no—
293C22⋊C4—184no—
294C22×C3—24no—
295C22×C3—24no—
296C22×C3—24no—
297C22×C3—24no—
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—24no—
315C22×C3—24no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—122no—
323C22×C3—122no—
324C22×C3—122no—
325C22×C3—241no—
326C22×C3—241no—
327C22×C3—241no—
328C22×C3—241no—
329C2×D3—42no—
330C2×D3—42no—
331C2×D3—42no—
332C2×D3—81no—
333C2×D3—81no—
334C2×D3—81no—
335C2×D3—81no—
336C3×C4—124no—
337C3×C4—122no—
338Dic3—44no—
339Dic3—42no—
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—64no—
345Dic3—122no—
346C32#187411yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—62no—
352C23—121no—
353C23—121no—
354C23—121no—
355C23—121no—
356C23—121no—
357C23—121no—
358C23D32⋊C412yes—
359C23#377412yes—
360C23#377512yes—
361C23C2×GO+(4,𝔽2)11yescharacteristic
362D4—128no—
363D4—184no—
364D4—362no—
365C2×C4—62no—
366C2×C4—64no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—92no—
372C2×C4—128no—
373C2×C4—122no—
374C2×C4—121no—
375C2×C4—122no—
376C2×C4—121no—
377C2×C4—184no—
378C2×C4—184no—
379C2×C4—181no—
380C2×C4—181no—
381C8—362no—
382C2×C3—28no—
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—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—44no—
398C2×C3—242no—
399D3—82no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—122no—
407C22—122no—
408C22—122no—
409C22—241no—
410C22—241no—
411C22—241no—
412C22—241no—
413C22#6373914yescomplemented
414C22C2×D32⋊C411yescharacteristic
415C22#6423311yescharacteristic
416C22C2×#377411yescharacteristic
417C22#6423611yescharacteristic
418C22C2×#377511yescharacteristic
419C22#6423911yescharacteristic
420C22#6424111yescharacteristic
421C4—92no—
422C4—92no—
423C4—122no—
424C4—124no—
425C4—182no—
426C3—21no—
427C3—21no—
428C2—24no—
429C2—242no—
430C2C2×#6373911yescharacteristic
431C2#1059349211yescharacteristic
432C2#1059349611yescharacteristic
433C2#1059349711yescharacteristic
434C2#1059351411yescharacteristic
435C2#1059351911yescharacteristic
436C2#1059352511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC24×C32D4
socleC23×C32C2×D4
prime radicalC2×#63980C2
cosocleC22×C3⋊Dic3C23
hypercenterC24GO+(4,𝔽2)
hypocenterC32#1874
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#3724C2semidirect
3. C2×C22⋊#622C2semidirect
4. C2×#63739C2semidirect
5. #10590075C2semidirect
12. #63980C4semidirect
41. C2×#625C2×C4semidirect
48. #3724C2×C4semidirect
49. #3724D4semidirect
156. C22×C32#102semidirect
346. C32#1874semidirect
413. C22#63739semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
C22×#37242
C2×C22⋊#6222
C2×#637392
#105900752
#18749