Finite Group Databasebeta

← #11788080

Subgroups — #11788080

Order 1152.

1077 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1077 conjugacy classes of subgroups — too many to draw. Only its 172 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
2C22×#3710C211yesmaximal, characteristic, complemented
3C2×C3×#832C212yesmaximal, complemented
4#10591325C211yesmaximal, characteristic, complemented
5#10589164C212yesmaximal, complemented
6#70202—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C22×#638—21no—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×#3757—21no—
11#64147—22no—
12#64147C414yescomplemented
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17C2×#3710—22no—
18C2×#3710—24no—
19C3×#832—24no—
20#63579—21no—
21C2×#938—32no—
22C2×#938—61no—
23C22×D3×C8—32no—
24C2×C3×#102—32no—
25C2×#832D312yescomplemented
26#4987—32no—
27#4551—32no—
28#4529—32no—
29C24×C32—21no—
30C23×C3⋊D3D411yescharacteristic
31C2×C32×D4—22no—
32C2×C32×D4—21no—
33C2×C32×D4—22no—
34C2×C32×D4C2×C412yes—
35C22×C32×C4C2311yescharacteristic
36C2×#638—24no—
37C2×#638—42no—
38C2×#638—42no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3—22no—
43C2×C4×C3⋊D3C2×C412yes—
44C2×C4×C3⋊D3D412yes—
45C22×C3×Dic3—22no—
46#3757—24no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8D414yescomplemented
54#3722—42no—
55#3710—28no—
56#1893—91noSylow
57C22×C3×D4—21no—
58C22×C3×D4C2×D312yes—
59C22×#67—62no—
60C22×#67—62no—
61C22×C4×D3—32no—
62C22×C4×D3—61no—
63C22×C3×C8—32no—
64C2×C3×C4⋊C4—32no—
65C2×#217—62no—
66C2×#217—62no—
67#938—38no—
68#938—64no—
69#938—64no—
70#938—64no—
71C2×(C2×D3)⋊C4—62no—
72C2×C4⋊Dic3—32no—
73C2×C4⋊Dic3—61no—
74C2×C4⋊Dic3C2×D312yes—
75C22×C3⋊C8C2×D312yes—
76C2×D3×C8—64no—
77C2×D3×C8—64no—
78C2×D3×C8—64no—
79C3×#102—64no—
80#832—24no—
81C3⋊#95—62no—
82C23×C32—22no—
83C23×C32—42no—
84C23×C32—41no—
85C23×C32—41no—
86C23×C32—42no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—22no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3C22⋊C412yes—
91C22×C3⋊D3D812yes—
92C22×C3⋊D3SD1612yes—
93C32×D4—24no—
94C32×D4—41no—
95C32×D4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4#4112yes—
100#638—48no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C412yes—
106C4×C3⋊D3—24no—
107C4×C3⋊D3—22no—
108C4×C3⋊D3—22no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—24no—
113C23×C8—91no—
114C2×#121—91no—
115C2×#102—32no—
116#380—91no—
117#340—92no—
118C24×C3—22no—
119C24×C3—22no—
120C23×D3—32no—
121C23×D3—61no—
122C2×C3×D4—22no—
123C2×C3×D4—22no—
124C2×C3×D4—22no—
125C2×C3×D4—22no—
126C2×C3×D4—22no—
127C2×C3×D4—22no—
128C2×C3×D4—22no—
129C2×C3×D4—42no—
130C2×C3×D4—42no—
131C2×C3×D4C4×D314yes—
132C22×C3×C4—21no—
133C22×C3×C4—62no—
134C22×C3×C4C22×D312yes—
135C2×#67—68no—
136C2×#67—68no—
137C2×#67—124no—
138C2×#67—124no—
139C2×#67—124no—
140C2×#67—124no—
141C22×Dic3—22no—
142C22×Dic3—32no—
143C22×Dic3—61no—
144C22×Dic3—62no—
145C22×Dic3—62no—
146C2×C4×D3—34no—
147C2×C4×D3—34no—
148C2×C4×D3—62no—
149C2×C4×D3—62no—
150C2×C4×D3—62no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×C4×D3—122no—
155C2×C4×D3—122no—
156C2×C3×C8—34no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—62no—
161#217—68no—
162#217—68no—
163(C2×D3)⋊C4—124no—
164C4⋊Dic3—22no—
165C4⋊Dic3—22no—
166C4⋊Dic3—34no—
167C4⋊Dic3—62no—
168C4⋊Dic3—62no—
169C4⋊Dic3—62no—
170C2×C3⋊C8—22no—
171C2×C3⋊C8—22no—
172C2×C3⋊C8#6714yescomplemented
173D3×C8—616no—
174C22×C32—42no—
175C22×C32—42no—
176C22×C32—42no—
177C22×C32—82no—
178C22×C32—82no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32#12112yes—
181C22×C32C2×D811yescharacteristic
182C22×C32C2×SD1611yescharacteristic
183C22×C32#13512yes—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—22no—
186C2×C3⋊D3—24no—
187C2×C3⋊D3—24no—
188C2×C3⋊D3#10214yescomplemented
189C32×C4C4×D412yes—
190C32×C4#12011yescharacteristic
191C32×C4#12311yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3—42no—
194C3×Dic3—82no—
195C22×D4—181no—
196C22×D4D3211yescharacteristic
197C23×C4—91no—
198C22×C8—32no—
199C22×C8—184no—
200C22×C8—182no—
201#121—94no—
202#121—182no—
203C2×C4⋊C4—32no—
204C2×C4⋊C4—91no—
205C2×C22⋊C4—181no—
206C2×C22⋊C4—181no—
207#102—64no—
208#95—181no—
209C23×C3—24no—
210C23×C3—24no—
211C23×C3—21no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—44no—
215C23×C3—44no—
216C23×C3—42no—
217C23×C3—42no—
218C23×C3—42no—
219C23×C3—42no—
220C23×C3—42no—
221C23×C3—42no—
222C23×C3D3×D412yes—
223C22×D3—34no—
224C22×D3—34no—
225C22×D3—34no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—62no—
233C22×D3—122no—
234C22×D3—122no—
235C3×D4—24no—
236C3×D4—24no—
237C3×D4—44no—
238C3×D4—42no—
239C3×D4—42no—
240C3×D4—42no—
241C3×D4—42no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—122no—
247C2×C3×C4—122no—
248C2×C3×C4—122no—
249C2×C3×C4C2×C4×D312yes—
250C2×C3×C4#23512yes—
251C2×C3×C4D3×D412yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4#23712yes—
254C2×C3×C4C2×#6712yes—
255#67—1216no—
256#67—1216no—
257C2×Dic3—34no—
258C2×Dic3—42no—
259C2×Dic3—42no—
260C2×Dic3—42no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—62no—
264C2×Dic3—64no—
265C2×Dic3—64no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269C2×Dic3—122no—
270C2×Dic3—122no—
271C4×D3—64no—
272C4×D3—64no—
273C4×D3—64no—
274C4×D3—64no—
275C4×D3—124no—
276C4×D3—122no—
277C4×D3—122no—
278C3×C8—64no—
279C3⋊C8—24no—
280C2×C32—82no—
281C2×C32#38611yescharacteristic
282C2×C32C2×#10211yescharacteristic
283C2×C32#41611yescharacteristic
284C2×C32#46512yes—
285C2×C32#46612yes—
286C3⋊D3—24no—
287C24—21no—
288C24—91no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—184no—
293C2×D4—362no—
294C2×D4—362no—
295C2×D4#62412yes—
296C22×C4—62no—
297C22×C4—91no—
298C22×C4—92no—
299C22×C4—92no—
300C22×C4—182no—
301C22×C4—182no—
302C22×C4—181no—
303C22×C4C2×D3211yescharacteristic
304C2×C8—34no—
305C2×C8—62no—
306C2×C8—62no—
307C2×C8—188no—
308C4⋊C4—62no—
309C4⋊C4—62no—
310C4⋊C4—92no—
311C4⋊C4—181no—
312C22⋊C4—184no—
313C22⋊C4—362no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—44no—
320C22×C3—44no—
321C22×C3—44no—
322C22×C3—44no—
323C22×C3—44no—
324C22×C3—44no—
325C22×C3—84no—
326C22×C3—84no—
327C22×C3—82no—
328C22×C3—82no—
329C22×C3—82no—
330C22×C3—82no—
331C22×C3D3×C22⋊C412yes—
332C22×C3#88412yes—
333C22×C3D3×D812yes—
334C22×C3#91212yes—
335C22×C3D3×SD1612yes—
336C22×C3#91612yes—
337C22×C3#93812yes—
338C2×D3—38no—
339C2×D3—64no—
340C2×D3—64no—
341C2×D3—64no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—122no—
347C2×D3—122no—
348C2×D3—124no—
349C2×D3—124no—
350C3×C4—22no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—242no—
354C3×C4#67⋊C412yes—
355C3×C4#88312yes—
356C3×C4C4×#6712yes—
357C3×C4#93712yes—
358Dic3—64no—
359Dic3—82no—
360Dic3—122no—
361Dic3—124no—
362Dic3—124no—
363C32#189311yescharacteristic, complemented, Sylow
364C23—22no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23—42no—
369C23—92no—
370C23—92no—
371C23—92no—
372C23—182no—
373C23—182no—
374C23#381111yescharacteristic
375D4—24no—
376D4—41no—
377D4—41no—
378D4—368no—
379C2×C4—92no—
380C2×C4—122no—
381C2×C4—122no—
382C2×C4—122no—
383C2×C4—182no—
384C2×C4—184no—
385C2×C4—182no—
386C2×C4—182no—
387C2×C4—182no—
388C2×C4—361no—
389C2×C4—361no—
390C2×C4#380412yes—
391C2×C4C2×#62411yescharacteristic
392C2×C4D3×#6712yes—
393C2×C4#381111yescharacteristic
394C8—64no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—22no—
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—84no—
401C2×C3—84no—
402C2×C3D3×#10212yes—
403C2×C3#477212yes—
404C2×C3#477512yes—
405C2×C3#477812yes—
406C2×C3#495612yes—
407C2×C3#515712yes—
408C2×C3#517112yes—
409D3—68no—
410D3—124no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—82no—
415C22—82no—
416C22—94no—
417C22—182no—
418C22—184no—
419C22—184no—
420C22—182no—
421C22#6392611yescharacteristic
422C22#6393011yescharacteristic
423C22#6393612yes—
424C22#6395812yes—
425C22#6397411yescharacteristic
426C4—182no—
427C4—242no—
428C4—362no—
429C4#6395212yes—
430C4#6397511yescharacteristic
431C4#6398311yescharacteristic
432C3—21no—
433C3#7020212yescomplemented
434C2—82no—
435C2—184no—
436C2#1059141611yescharacteristic
437C2#1059142411yescharacteristic
438C2#1059145512yes—
439C2#1059146512yes—
440C2#1059172211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×#64147C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1893
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×#3710C2semidirect
3. C2×C3×#832C2semidirect
4. #10591325C2semidirect
5. #10589164C2semidirect
12. #64147C4semidirect
25. C2×#832D3semidirect
53. C2×C3×C3⋊C8D4semidirect
172. C2×C3⋊C8#67semidirect
188. C2×C3⋊D3#102semidirect
363. C32#1893semidirect
433. C3#70202semidirect

Maximal subgroups

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

subgroupindex
C2×#641472
C22×#37102
C2×C3×#8322
#105913252
#105891642
#702023