Finite Group Databasebeta

← #11787226

Subgroups — #11787226

Order 1152.

690 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#10595016C211yesmaximal, characteristic
2C22×#3712C211yesmaximal, characteristic, complemented
3C4×C22⋊#157C211yesmaximal, characteristic, complemented
4C2×#63731C212yesmaximal, complemented
5#10590047C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×#3798C2211yescharacteristic
8C2×C22⋊#157—21no—
9C2×C4×#157C2212yes—
10C3×C4×#67—21no—
11C22×C3×C3⋊C8—21no—
12#63982C411yescharacteristic, complemented
13#63981—21no—
14#63980C411yescharacteristic, complemented
15#63912C411yescharacteristic, complemented
16C4×#626—21no—
17#63874C2211yescharacteristic
18#63865C411yescharacteristic, complemented
19#63853—21no—
20C2×#3712—21no—
21C2×#3712—24no—
22C2×#3712C2212yes—
23#63781—21no—
24#63731—24no—
25C22×ΓL(1,𝔽25)—61no—
26#5547—61no—
27C23×C3⋊D3D411yescharacteristic
28C22×#157—22no—
29C22×C32×C4D411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3D411yescharacteristic
36C2×C4×C3⋊D3C2311yescharacteristic
37C2×C3×#67—21no—
38C2×C3×C4×D3—21no—
39C2×#627C2×C411yescharacteristic
40C2×#626—21no—
41C2×#626—21no—
42C2×#625C2×C411yescharacteristic
43#3798—22no—
44#3798—22no—
45C22⋊#157—24no—
46C4×#157—22no—
47C4×#157—22no—
48C3×#217—21no—
49C3×(C2×D3)⋊C4—21no—
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3—21no—
52C2×C3×C3⋊C8—24no—
53C2×C3×C3⋊C8—22no—
54#3724C2×C411yescharacteristic
55#3724C2×C411yescharacteristic
56Dic3⋊Dic3—21no—
57#3722—21no—
58#3722—21no—
59(C2×D3)⋊Dic3—21no—
60#3712—24no—
61#3712—22no—
62#3712D414yescomplemented
63#1871—91nomaximal, Sylow
64C2×#235—61no—
65C22×C4×D3—61no—
66C22×C4×D3—61no—
67C22×C3×C8—61no—
68C3×C4×D4—61no—
69#939—61no—
70#937—61no—
71C4×#67—21no—
72C4×#67—61no—
73C22×C3⋊C8—21no—
74C2×ΓL(1,𝔽25)—62no—
75C2×ΓL(1,𝔽25)—68no—
76C2×ΓL(1,𝔽25)—62no—
77#896—61no—
78#894—61no—
79#884—61no—
80#883—61no—
81#882—61no—
82#878—61no—
83C4×D12—61no—
84#872—61no—
85C23×C32C22⋊C411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—22no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3C22⋊C411yescharacteristic
90C22×C3⋊D3C2×D411yescharacteristic
91C22×C3×D3—21no—
92C2×#157—24no—
93C2×#157—42no—
94C2×#157—42no—
95C2×C32×C4—21no—
96C2×C32×C4—21no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22×C411yescharacteristic
102C4×C3⋊D3—22no—
103C4×C3⋊D3—21no—
104C4×C3⋊D3—21no—
105C4×C3⋊D3—22no—
106C4×C3⋊D3C2×D412yes—
107C4×C3⋊D3#4112yes—
108C3×#67—42no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C3×C4×D3—41no—
113C3×C4×D3—41no—
114#627—22no—
115#626—42no—
116#626—42no—
117#625—22no—
118C3×C3⋊C8—24no—
119C22×M16—91no—
120#525—91no—
121C2×#104—92no—
122C4×C22⋊C4—91no—
123#339—92no—
124C23×D3—61no—
125C23×D3—61no—
126C2×C3×D4—61no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—61no—
130C2×#67—21no—
131C2×#67—61no—
132C2×#67—61no—
133C2×#67—61no—
134C22×Dic3—61no—
135C22×Dic3—61no—
136#235—122no—
137#235—122no—
138C2×D12—61no—
139C2×D12—61no—
140C2×C4×D3—21no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—61no—
144C2×C4×D3—61no—
145C2×C4×D3—61no—
146C2×C4×D3—61no—
147C2×C4×D3—61no—
148C2×C4×D3—61no—
149C2×C4×D3—64no—
150C2×C4×D3—64no—
151C2×C4×D3—122no—
152C2×C4×D3—122no—
153C2×Dic6—61no—
154C2×C3×C8—64no—
155C2×C3×C8—62no—
156C3×C4⋊C4—61no—
157C3×C22⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C42—61no—
160#217—21no—
161#217—61no—
162(C2×D3)⋊C4—21no—
163(C2×D3)⋊C4—61no—
164(C2×D3)⋊C4—61no—
165(C2×D3)⋊C4—61no—
166(C2×D3)⋊C4—61no—
167(C2×D3)⋊C4—61no—
168C4⋊Dic3—61no—
169Dic3⋊C4—21no—
170Dic3⋊C4—61no—
171Dic3⋊C4—61no—
172Dic3⋊C4—61no—
173C4×Dic3—21no—
174C2×C3⋊C8—24no—
175C2×C3⋊C8—22no—
176ΓL(1,𝔽25)—64no—
177ΓL(1,𝔽25)—64no—
178ΓL(1,𝔽25)—68no—
179C22×C32—21no—
180C22×C32—21no—
181C22×C32#10412yescomplemented
182C22×C32C2×C22⋊C411yescharacteristic
183C2×C3⋊D3—21no—
184C2×C3⋊D3—21no—
185C2×C3⋊D3—21no—
186C2×C3⋊D3—21no—
187C2×C3⋊D3—21no—
188C2×C3⋊D3—44no—
189C2×C3⋊D3#12112yes—
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193#157—44no—
194C32×C4—21no—
195C32×C4#12011yescharacteristic
196C32×C4#12311yescharacteristic
197C3⋊Dic3—21no—
198C3⋊Dic3C4×D412yes—
199C3×Dic3—41no—
200C3×Dic3—41no—
201C3×Dic3—41no—
202C2×#41—91no—
203C23×C4—91no—
204C2×M16—92no—
205C2×M16—184no—
206C2×M16—181no—
207C22×C8—61no—
208#123—181no—
209C22⋊Q8—91no—
210C22⋊Q8—91no—
211#121—91no—
212#121—91no—
213#120—181no—
214C4×D4—61no—
215C4×D4—181no—
216#117—91no—
217C2×C22⋊C4—181no—
218C2×C42—92no—
219#104—184no—
220#95—181no—
221C23×C3—21no—
222C23×C3—21no—
223C23×C3—61no—
224C22×D3—21no—
225C22×D3—61no—
226C22×D3—61no—
227C22×D3—61no—
228C22×D3—61no—
229C22×D3—64no—
230C22×D3—122no—
231C22×D3—122no—
232C22×D3—122no—
233C22×D3—122no—
234C22×D3—122no—
235C3×D4—122no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—41no—
243C2×C3×C4—41no—
244C2×C3×C4—61no—
245C2×C3×C4—61no—
246C2×C3×C4—61no—
247C2×C3×C4—121no—
248C2×C3×C4—121no—
249#67—42no—
250#67—122no—
251#67—122no—
252#67—122no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—61no—
260C2×Dic3—64no—
261C2×Dic3—122no—
262D12—122no—
263D12—122no—
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—62no—
267C4×D3—62no—
268C4×D3—62no—
269C4×D3—62no—
270C4×D3—62no—
271C4×D3—64no—
272C4×D3—64no—
273C4×D3—62no—
274C4×D3—122no—
275C4×D3—121no—
276C4×D3—121no—
277C4×D3—122no—
278Dic6—122no—
279C3×C8—64no—
280C3⋊C8—24no—
281C2×C32—22no—
282C2×C32#38611yescharacteristic
283C2×C32C2×#10411yescharacteristic
284C2×C32#42111yescharacteristic
285C3⋊D3—22no—
286C3⋊D3—41no—
287C3×D3—81no—
288C24—91no—
289#41—182no—
290#41—182no—
291C2×Q8—91no—
292C2×D4—61no—
293C2×D4—91no—
294C2×D4—181no—
295C2×D4—181no—
296C22×C4—61no—
297C22×C4—91no—
298C22×C4—91no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—182no—
303C22×C4—182no—
304C22×C4—182no—
305C22×C4GO+(4,𝔽2)11yescharacteristic
306M16—94no—
307M16—182no—
308M16—184no—
309C2×C8—64no—
310C2×C8—62no—
311C4⋊C4—61no—
312C4⋊C4—91no—
313C4⋊C4—91no—
314C4⋊C4—181no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—184no—
321C42—61no—
322C42—182no—
323C42—182no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3—121no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—62no—
339C2×D3—62no—
340C2×D3—62no—
341C2×D3—62no—
342C2×D3—121no—
343C2×D3—121no—
344C2×D3—121no—
345C2×D3—121no—
346C2×D3—121no—
347C2×D3—121no—
348C2×D3—121no—
349C2×D3—121no—
350C2×D3—128no—
351C2×D3—128no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—41no—
358C3×C4—121no—
359C3×C4—121no—
360C3×C4—121no—
361Dic3—41no—
362Dic3—41no—
363Dic3—41no—
364Dic3—62no—
365Dic3—62no—
366Dic3—62no—
367Dic3—121no—
368C32#187111yescharacteristic, complemented, Sylow
369C23—61no—
370C23—91no—
371C23—91no—
372C23—182no—
373C23—182no—
374C23—361no—
375C23D32⋊C411yescharacteristic
376Q8—182no—
377D4—122no—
378D4—182no—
379D4—362no—
380D4—362no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—61no—
384C2×C4—61no—
385C2×C4—61no—
386C2×C4—91no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—91no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—181no—
396C2×C4—181no—
397C2×C4—184no—
398C2×C4—362no—
399C2×C4—362no—
400C2×C4D32⋊C411yescharacteristic
401C2×C4C2×GO+(4,𝔽2)11yescharacteristic
402C8—64no—
403C2×C3—24no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—42no—
411C2×C3—241no—
412D3—81no—
413D3—122no—
414D3—122no—
415D3—122no—
416D3—122no—
417C22—21no—
418C22—21no—
419C22—92no—
420C22—121no—
421C22—121no—
422C22—121no—
423C22—181no—
424C22—181no—
425C22—181no—
426C22—181no—
427C22—181no—
428C22—364no—
429C22#6373112yescomplemented
430C22C2×D32⋊C411yescharacteristic
431C4—21no—
432C4—92no—
433C4—121no—
434C4—121no—
435C4—121no—
436C4—181no—
437C4—364no—
438C4#6423311yescharacteristic
439C4#6424111yescharacteristic
440C3—21no—
441C3—21no—
442C2—22no—
443C2—182no—
444C2—241no—
445C2—361no—
446C2C2×#6373111yescharacteristic
447C2#1059332411yescharacteristic
448C2#1059351411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radical#10595016C2
cosocleC2×C4×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1871
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3712C2semidirect
3. C4×C22⋊#157C2semidirect
4. C2×#63731C2semidirect
5. #10590047C2semidirect
12. #63982C4semidirect
14. #63980C4semidirect
15. #63912C4semidirect
18. #63865C4semidirect
62. #3712D4semidirect
181. C22×C32#104semidirect
368. C32#1871semidirect
429. C22#63731semidirect

Maximal subgroups

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

subgroupindex
#105950162
C22×#37122
C4×C22⋊#1572
C2×#637312
#105900472
#18719