Finite Group Databasebeta

← #11778110

Subgroups — #11778110

Order 1152.

767 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 767 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595981C211yesmaximal, characteristic, complemented
2C3×#4991C211yesmaximal, characteristic, complemented
3#10591162C212yesmaximal, complemented
4C3×#4528C211yesmaximal, characteristic, complemented
5#10589151C212yesmaximal, complemented
6#69703—31nomaximal
7#68131—31nomaximal
8C2×#3828—21no—
9C22×C3×D12C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—21no—
12#64139C2212yes—
13#64106—22no—
14#64104—22no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×#3714—22no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20#63563—22no—
21#5510—31no—
22#5510—31no—
23#5510—61no—
24C3×#394—31no—
25#5217—32no—
26#4991D311yescharacteristic, complemented
27#4732—32no—
28C3×#324—31no—
29#4528D311yescharacteristic, complemented
30#4470—32no—
31#4451—32no—
32C23×C3×D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×#638—22no—
37#3828—42no—
38#3828—42no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)D412yes—
42C2×C4×C3⋊D3—22no—
43C2×#634—21no—
44C22×C3×Dic3—21no—
45C2×C3×D12—22no—
46C2×C3×D12—42no—
47C32×C4⋊C4—22no—
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D412yes—
52C3×(C2×D3)⋊C4—42no—
53C3×(C2×D3)⋊C4—42no—
54C2×C3×C3⋊C8—22no—
55#3714—44no—
56#1598—91noSylow
57C22×C3×D4—31no—
58C2×#235—62no—
59C2×#235—61no—
60C2×#235—61no—
61C22×D12C2×D311yescharacteristic
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×C3×C22⋊C4—61no—
66C2×C3×C22⋊C4—61no—
67C2×#213—62no—
68#930—32no—
69#930—32no—
70#930—62no—
71#930—62no—
72#930—61no—
73#930—61no—
74C2×(C2×D3)⋊C4—21no—
75C2×(C2×D3)⋊C4—21no—
76C2×D24—62no—
77#897—62no—
78#897—62no—
79#897—64no—
80#895—62no—
81#895—62no—
82#895—64no—
83C3×C22⋊C8—32no—
84C3×#95—31no—
85#832—62no—
86C3⋊#95C2×D311yescharacteristic
87#830C2×D312yes—
88#821—62no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—22no—
91C22×C3×D3—22no—
92C22×C3×D3—41no—
93C22×C3×D3—41no—
94C22×C3×D3—41no—
95C22×C3×D3—41no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4D812yescomplemented
104C2×C32×C4C2×D412yes—
105#638—42no—
106#638—42no—
107C2×C3⋊Dic3—22no—
108C4⋊(C3⋊D3)—42no—
109C4⋊(C3⋊D3)—42no—
110C4⋊(C3⋊D3)—81no—
111C4×C3⋊D3—44no—
112#634—42no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C3×D12—24no—
117C3×D12—42no—
118C3×C3⋊C8—42no—
119#537—91no—
120#447—92no—
121#394—31no—
122#327—92no—
123#324—31no—
124C24×C3—61no—
125C23×D3—21no—
126C2×C3×D4—62no—
127C2×C3×D4—122no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C22×C3×C4D1211yescharacteristic
133C22×C3×C4D1211yescharacteristic
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C2×#67—64no—
139C2×#67—62no—
140C2×#67—62no—
141C22×Dic3—21no—
142#235—124no—
143#235—122no—
144#235—122no—
145#235—124no—
146#235—122no—
147#235—122no—
148C2×D12—22no—
149C2×D12—32no—
150C2×D12—32no—
151C2×D12—42no—
152C2×D12—62no—
153C2×D12—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—62no—
157C2×D12—61no—
158C2×D12—61no—
159C2×C4×D3—64no—
160C2×C4×D3—62no—
161C2×C4×D3—62no—
162C2×Dic6—62no—
163C2×Dic6—61no—
164C2×Dic6—61no—
165C2×C3×C8—62no—
166C3×C4⋊C4—24no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—22no—
169C3×C22⋊C4—122no—
170C3×C22⋊C4—122no—
171#213—124no—
172(C2×D3)⋊C4—42no—
173(C2×D3)⋊C4—42no—
174(C2×D3)⋊C4—64no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—64no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180C4⋊Dic3—32no—
181C4⋊Dic3—32no—
182C4⋊Dic3—62no—
183C4⋊Dic3—62no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C2×C3⋊C8—22no—
187D24—124no—
188C22×C32—21no—
189C22×C32—21no—
190C22×C32#12011yescharacteristic
191C22×C32C2×D811yescharacteristic
192C22×C32AGL(1,ℤ/8)11yescharacteristic
193C2×C3⋊D3—42no—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3—42no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C2×C3×D3—81no—
202C2×C3×D3—81no—
203C32×C4—22no—
204C32×C4—22no—
205C32×C4—41no—
206C3⋊Dic3—42no—
207C3×Dic3—81no—
208C2×#41—181no—
209C22×D4—31no—
210C2×D8—182no—
211C22⋊Q8—182no—
212#121—92no—
213#121—182no—
214#121—181no—
215C2×C4⋊C4D3211yescharacteristic
216C2×C22⋊C4—61no—
217C2×C22⋊C4—61no—
218#102—182no—
219C22⋊C8—32no—
220#95—31no—
221C23×C3—21no—
222C23×C3—62no—
223C23×C3—121no—
224C23×C3—121no—
225C23×C3—121no—
226C23×C3—121no—
227C23×C3—121no—
228C23×C3—121no—
229C23×C3C2×D1211yescharacteristic
230C23×C3C2×#6711yescharacteristic
231C22×D3—22no—
232C22×D3—41no—
233C22×D3—41no—
234C22×D3—41no—
235C22×D3—41no—
236C22×D3—41no—
237C22×D3—41no—
238C22×D3—64no—
239C22×D3—62no—
240C22×D3—62no—
241C3×D4—64no—
242C3×D4—122no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—22no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—81no—
259C2×C3×C4—81no—
260C2×C3×C4—121no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4D2412yescomplemented
264C2×C3×C4#21312yescomplemented
265C2×C3×C4D3×D412yes—
266C2×C3×C4D3×D412yes—
267#67—124no—
268#67—124no—
269#67—122no—
270#67—122no—
271#67—122no—
272#67—122no—
273C2×Dic3—41no—
274C2×Dic3—41no—
275C2×Dic3—41no—
276C2×Dic3—64no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279D12—24no—
280D12—42no—
281D12—122no—
282D12—122no—
283D12—124no—
284D12—122no—
285D12—122no—
286D12—242no—
287D12—242no—
288D12—241no—
289D12—241no—
290C4×D3—128no—
291C4×D3—124no—
292C4×D3—124no—
293Dic6—124no—
294Dic6—122no—
295Dic6—122no—
296C3×C8—122no—
297C3⋊C8—42no—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32#44711yescharacteristic
301C2×C32#45411yescharacteristic
302C2×C32B(4,𝔽2)11yescharacteristic
303C3⋊D3—82no—
304C3×D3—82no—
305C24—61no—
306#41—362no—
307#41—362no—
308C2×Q8—181no—
309C2×D4—62no—
310C2×D4—92no—
311C2×D4—122no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—182no—
315C22×C4—61no—
316C22×C4—182no—
317C22×C4#62611yescharacteristic
318C22×C4#62611yescharacteristic
319C22×C4C2×D3211yescharacteristic
320D8—364no—
321C2×C8—62no—
322C4⋊C4—22no—
323C4⋊C4—92no—
324C4⋊C4—181no—
325C22⋊C4—122no—
326C22⋊C4—122no—
327C22⋊C4—182no—
328C22⋊C4—182no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—21no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—122no—
339C22×C3—122no—
340C22×C3—122no—
341C22×C3—241no—
342C22×C3—241no—
343C22×C3—241no—
344C22×C3—241no—
345C22×C3#88211yescharacteristic
346C22×C3C2×D2411yescharacteristic
347C22×C3#90811yescharacteristic
348C22×C3C2×#21311yescharacteristic
349C22×C3#93711yescharacteristic
350C22×C3#94911yescharacteristic
351C2×D3—42no—
352C2×D3—42no—
353C2×D3—42no—
354C2×D3—81no—
355C2×D3—81no—
356C2×D3—81no—
357C2×D3—81no—
358C2×D3—124no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C3×C4—24no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—42no—
373C3×C4—42no—
374C3×C4—41no—
375C3×C4—41no—
376C3×C4—241no—
377Dic3—81no—
378Dic3—124no—
379Dic3—122no—
380Dic3—122no—
381C32#159811yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—121no—
386C23—121no—
387C23—121no—
388C23—121no—
389C23—182no—
390C23C2×#62611yescharacteristic
391Q8—362no—
392D4—64no—
393D4—122no—
394D4—362no—
395D4—362no—
396D4—362no—
397D4—362no—
398D4—721no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—182no—
408C2×C4—364no—
409C2×C4#371412yescomplemented
410C2×C4#381112yes—
411C8—122no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—41no—
420C2×C3—41no—
421C2×C3—242no—
422C2×C3#473211yescharacteristic
423C2×C3#474111yescharacteristic
424C2×C3#475311yescharacteristic
425C2×C3#503211yescharacteristic
426C2×C3#503611yescharacteristic
427C2×C3#506211yescharacteristic
428D3—82no—
429D3—244no—
430D3—242no—
431D3—242no—
432C22—21no—
433C22—21no—
434C22—122no—
435C22—122no—
436C22—122no—
437C22—241no—
438C22—241no—
439C22—241no—
440C22—241no—
441C22—362no—
442C22—362no—
443C22—362no—
444C22C2×#371411yescharacteristic
445C22#6382511yescharacteristic
446C22#6398111yescharacteristic
447C4—22no—
448C4—22no—
449C4—41no—
450C4—241no—
451C4—362no—
452C3—21no—
453C3#6813111yescharacteristic, complemented
454C3#6970311yescharacteristic, complemented
455C2—21no—
456C2—21no—
457C2—242no—
458C2—722no—
459C2#1059116811yescharacteristic
460C2#1059153211yescharacteristic
461C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
hypercenterC2×C4⋊C4D32
hypocenterC32#1598
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595981C2semidirect
2. C3×#4991C2semidirect
3. #10591162C2semidirect
4. C3×#4528C2semidirect
5. #10589151C2semidirect
26. #4991D3semidirect
29. #4528D3semidirect
103. C2×C32×C4D8semidirect
263. C2×C3×C4D24semidirect
264. C2×C3×C4#213semidirect
381. C32#1598semidirect
409. C2×C4#3714semidirect
453. C3#68131semidirect
454. C3#69703semidirect

Maximal subgroups

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

subgroupindex
#105959812
C3×#49912
#105911622
C3×#45282
#105891512
#697033
#681313