Finite Group Databasebeta

← #11788317

Subgroups — #11788317

Order 1152.

993 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 993 conjugacy classes of subgroups — too many to draw. Only its 134 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×#64147C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic, complemented
3C2×C3×#833C212yesmaximal, complemented
4#10591074C211yesmaximal, characteristic, complemented
5#10589168C212yesmaximal, complemented
6#70081—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638C412yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×#3757C412yes—
11#64147—21no—
12#64147—21no—
13#64147—21no—
14#64147—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×#208C2212yes—
17C2×C3×#208C2212yes—
18C2×#3712—21no—
19#63818—24no—
20C2×#3710—21no—
21C3×#833—24no—
22#63557—21no—
23#63557—21no—
24C2×#938—32no—
25C2×#938—61no—
26C2×D3×M16—32no—
27C2×C3×#100—32no—
28C2×#833D312yescomplemented
29#5126—32no—
30#4554—32no—
31#4554—32no—
32C24×C32C2×C412yes—
33C23×C3⋊D3C2×C411yescharacteristic
34C2×C32×D4—21no—
35C2×C32×D4—21no—
36C2×C32×D4—22no—
37C2×C32×D4—22no—
38C22×C32×C4C2311yescharacteristic
39C2×#638—22no—
40C2×#638—22no—
41C2×#638—44no—
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C412yes—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C4×C3⋊D3D411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50#3757—22no—
51#3757—22no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C3×#208—22no—
55C3×#208—22no—
56C3×#208—22no—
57C3×#208D414yescomplemented
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60#3712—24no—
61#3710—24no—
62#1900—91noSylow
63C22×C3×D4—21no—
64C22×C3×D4C2×D312yes—
65C22×#67—34no—
66C22×#67—62no—
67C22×C4×D3—32no—
68C22×C4×D3—61no—
69C2×C3×M16—32no—
70C2×C3×M16—32no—
71C2×#217—34no—
72C2×#217—62no—
73#938—62no—
74#938—62no—
75#938—62no—
76#938—62no—
77#938—62no—
78#938—62no—
79#938—62no—
80#938—62no—
81C2×C4⋊Dic3—32no—
82C2×C4⋊Dic3—61no—
83C2×#208C2×D312yes—
84C2×#208C2×D312yes—
85D3×M16—64no—
86D3×M16—64no—
87C2×ΓL(1,𝔽25)—62no—
88C2×D3×C8—62no—
89C3×#100—64no—
90#833—24no—
91(C2×D3)⋊C8—62no—
92(C2×D3)⋊C8—62no—
93C23×C32—22no—
94C23×C32—24no—
95C23×C32—42no—
96C23×C32—42no—
97C23×C32C22×C411yescharacteristic
98C22×C3⋊D3—22no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3C22⋊C411yescharacteristic
102C22×C3⋊D3C22⋊C411yescharacteristic
103C32×D4—41no—
104C32×D4—42no—
105C32×D4—41no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D412yes—
109C2×C32×C4#4112yes—
110#638—44no—
111#638—44no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22⋊C411yescharacteristic
117C4×C3⋊D3—21no—
118C4×C3⋊D3—21no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3—21no—
122C4×C3⋊D3—21no—
123C3×C3⋊C8—24no—
124C3×C3⋊C8—42no—
125C22×M16—91no—
126C2×#121—91no—
127C2×#100—32no—
128#407—91no—
129#343—92no—
130C24×C3—22no—
131C24×C3C4×D314yes—
132C23×D3—32no—
133C23×D3—61no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—42no—
143C2×C3×D4—42no—
144C22×C3×C4—21no—
145C22×C3×C4C22×D312yes—
146C2×#67—64no—
147C2×#67—64no—
148C2×#67—64no—
149C2×#67—64no—
150C2×#67—128no—
151C2×#67—128no—
152C22×Dic3—32no—
153C22×Dic3—34no—
154C22×Dic3—62no—
155C22×Dic3—61no—
156C2×C4×D3—32no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—32no—
160C2×C4×D3—61no—
161C2×C4×D3—61no—
162C2×C4×D3—61no—
163C2×C4×D3—61no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—122no—
169C2×C4×D3—122no—
170C3×M16—34no—
171C3×M16—62no—
172C3×M16—62no—
173C3×M16—62no—
174C2×C3×C8—62no—
175C2×C3×C8—62no—
176#217—64no—
177#217—64no—
178#217—64no—
179#217—64no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184#208—22no—
185#208—22no—
186#208—22no—
187#208#6714yescomplemented
188C2×C3⋊C8—22no—
189C2×C3⋊C8—22no—
190ΓL(1,𝔽25)—68no—
191D3×C8—68no—
192C22×C32—21no—
193C22×C32—21no—
194C22×C32—42no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32—84no—
198C22×C32C2×C22⋊C411yescharacteristic
199C22×C32C4×D412yes—
200C2×C3⋊D3—21no—
201C2×C3⋊D3—21no—
202C2×C3⋊D3—21no—
203C2×C3⋊D3—21no—
204C2×C3⋊D3—21no—
205C2×C3⋊D3—44no—
206C2×C3⋊D3#10012yescomplemented
207C32×C4#12011yescharacteristic
208C32×C4#12112yes—
209C32×C4#12311yescharacteristic
210C3⋊Dic3—21no—
211C3⋊Dic3—21no—
212C3⋊Dic3—42no—
213C22×D4—92no—
214C22×D4D3211yescharacteristic
215C23×C4—91no—
216C2×M16—32no—
217C2×M16—32no—
218C2×M16—181no—
219C2×M16—184no—
220C22×C8—181no—
221#121—181no—
222#121—181no—
223#121—181no—
224#121—181no—
225C2×C4⋊C4—91no—
226C2×C22⋊C4—92no—
227#100—64no—
228C22⋊C8—181no—
229C22⋊C8—181no—
230C23×C3—24no—
231C23×C3—24no—
232C23×C3—24no—
233C23×C3—24no—
234C23×C3—21no—
235C23×C3—44no—
236C23×C3—44no—
237C23×C3—44no—
238C23×C3—44no—
239C23×C3—44no—
240C23×C3C2×C4×D312yes—
241C22×D3—32no—
242C22×D3—32no—
243C22×D3—61no—
244C22×D3—61no—
245C22×D3—64no—
246C22×D3—64no—
247C22×D3—62no—
248C22×D3—62no—
249C22×D3—122no—
250C22×D3—122no—
251C22×D3—122no—
252C3×D4—44no—
253C3×D4—42no—
254C3×D4—42no—
255C3×D4—42no—
256C3×D4—42no—
257C3×D4—42no—
258C3×D4—42no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4#23512yes—
264C2×C3×C4D3×D412yes—
265C2×C3×C4D3×D412yes—
266C2×C3×C4D3×D412yes—
267C2×C3×C4#23712yes—
268C2×C3×C4C2×#6712yes—
269#67—128no—
270#67—128no—
271#67—128no—
272#67—128no—
273C2×Dic3—32no—
274C2×Dic3—32no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—64no—
280C2×Dic3—64no—
281C2×Dic3—122no—
282C2×Dic3—124no—
283C2×Dic3—124no—
284C4×D3—62no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—62no—
290C4×D3—62no—
291C4×D3—62no—
292C4×D3—122no—
293C4×D3—122no—
294C4×D3—121no—
295C4×D3—121no—
296C4×D3—121no—
297C4×D3—121no—
298C3×C8—64no—
299C3×C8—122no—
300C3⋊C8—24no—
301C3⋊C8—42no—
302C2×C32—22no—
303C2×C32—82no—
304C2×C32#38611yescharacteristic
305C2×C32C2×#10011yescharacteristic
306C2×C32#41311yescharacteristic
307C3⋊D3—22no—
308C3⋊D3—41no—
309C24—91no—
310C24#62412yes—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—182no—
316C2×D4—182no—
317C2×D4—364no—
318C22×C4—91no—
319C22×C4—91no—
320C22×C4—91no—
321C22×C4—91no—
322C22×C4—91no—
323C22×C4—92no—
324C22×C4—182no—
325C22×C4—182no—
326C22×C4C2×D3211yescharacteristic
327M16—34no—
328M16—62no—
329M16—62no—
330M16—62no—
331M16—184no—
332C2×C8—62no—
333C2×C8—62no—
334C2×C8—184no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—182no—
338C22⋊C4—182no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3—44no—
350C22×C3—44no—
351C22×C3—84no—
352C22×C3—84no—
353C22×C3—88no—
354C22×C3D3×C22⋊C412yes—
355C22×C3#67⋊C412yes—
356C22×C3C4×#6712yes—
357C2×D3—34no—
358C2×D3—62no—
359C2×D3—62no—
360C2×D3—62no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—124no—
370C2×D3—124no—
371C2×D3—128no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4#88312yes—
376C3×C4#88412yes—
377C3×C4#93712yes—
378C3×C4#93812yes—
379Dic3—62no—
380Dic3—62no—
381Dic3—121no—
382Dic3—121no—
383Dic3—124no—
384Dic3—124no—
385C32#190011yescharacteristic, complemented, Sylow
386C23—22no—
387C23—24no—
388C23—42no—
389C23—42no—
390C23—91no—
391C23—91no—
392C23—182no—
393C23—182no—
394C23—361no—
395C23C2×#62411yescharacteristic
396D4—42no—
397D4—41no—
398D4—41no—
399D4—364no—
400D4—364no—
401C2×C4—91no—
402C2×C4—91no—
403C2×C4—182no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—181no—
407C2×C4—181no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—182no—
411C2×C4—362no—
412C2×C4#380412yes—
413C2×C4D3×#6712yes—
414C2×C4#381111yescharacteristic
415C2×C4#381111yescharacteristic
416C8—64no—
417C8—122no—
418C2×C3—24no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—84no—
425C2×C3—84no—
426C2×C3D3×#10012yes—
427C2×C3#474512yes—
428C2×C3#495612yes—
429D3—64no—
430D3—122no—
431D3—122no—
432D3—122no—
433C22—21no—
434C22—21no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—84no—
439C22—92no—
440C22—181no—
441C22—181no—
442C22—181no—
443C22—181no—
444C22—181no—
445C22—364no—
446C22#6395212yes—
447C22#6397411yescharacteristic
448C4—181no—
449C4—181no—
450C4—362no—
451C4#6395812yes—
452C4#6397511yescharacteristic
453C4#6398311yescharacteristic
454C3—21no—
455C3#7008112yescomplemented
456C2—22no—
457C2—82no—
458C2—182no—
459C2—361no—
460C2#1059150311yescharacteristic
461C2#1059150411yescharacteristic
462C2#1059172211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64147C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1900
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C2×C3×#833C2semidirect
4. #10591074C2semidirect
5. #10589168C2semidirect
28. C2×#833D3semidirect
57. C3×#208D4semidirect
187. #208#67semidirect
206. C2×C3⋊D3#100semidirect
385. C32#1900semidirect
455. C3#70081semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C2×#638182
C2×C3×#8332
#105910742
#105891682
#700813