Finite Group Databasebeta

← #11801910

Subgroups — #11801910

Order 1152.

1546 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 207 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×#64306C211yesmaximal, characteristic
2C22×C4×#157C211yesmaximal, characteristic, complemented
3#10594969C211yesmaximal, characteristic, complemented
4#10593515C214yesmaximal, complemented
5#10593407C212yesmaximal, complemented
6C4×D32⋊C4C214yesmaximal, complemented
7#10593342C212yesmaximal, complemented
8C23×#157C2212yes—
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C3×#235—21no—
11C2×#3811C2212yes—
12C2×#3805—21no—
13#64306—24no—
14#64306C418yescomplemented
15C2×#3802C2211yescharacteristic
16C2×C4×D32C2212yes—
17C2×#3798—21no—
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C2×C4×#157—24no—
21C2×C4×#157C2212yes—
22C2×C4×#157C2212yes—
23C2×D32⋊C4C2218yes—
24C3×#926—21no—
25#63974C2212yes—
26#63957—21no—
27#63900C2212yes—
28C4×#624C2212yes—
29#63874—21no—
30#63849—21no—
31#63737C2218yes—
32C2×D3×#41—61no—
33D3×#117—61no—
34C23×C3⋊D3C2311yescharacteristic
35C22×D32C2312yes—
36C22×#157—24no—
37C22×#157—28no—
38C22×#157C2314yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4×C3⋊D3C2×C414yes—
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D414yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2311yescharacteristic
47C2×C3×#67—22no—
48C3×#235—28no—
49C2×C3×D12—21no—
50C2×C3×C4×D3—22no—
51C2×C3×Dic6—21no—
52#3811—24no—
53#3811C2×C418yes—
54C2×#627—21no—
55C2×#626—22no—
56C2×#625—21no—
57C2×#624C2314yes—
58C2×#624C2312yes—
59#3805—28no—
60C2×D3×Dic3—22no—
61#3802—22no—
62#3802C2×C414yescomplemented
63C4×D32—24no—
64C4×D32C2×C418yescomplemented
65#3798—28no—
66#3797—22no—
67#3797C2×C414yescomplemented
68#3796—28no—
69C4×#157—24no—
70C4×#157—24no—
71D32⋊C4—216no—
72C3×#217—22no—
73C3×C4⋊Dic3—22no—
74C3×C4×Dic3—22no—
75#3724—22no—
76#3722—22no—
77Dic32—22no—
78#2297—91nomaximal, Sylow
79C2×C3×#41—61no—
80D3×#41—68no—
81D3×#41—68no—
82C2×#239—61no—
83C2×D3×Q8—61no—
84C2×#237—61no—
85C2×#237—62no—
86C2×D3×D4—61no—
87C2×D3×D4—62no—
88C2×#235—21no—
89C2×#235—62no—
90C22×C4×D3—62no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C3×#117—61no—
94#926—21no—
95#892—62no—
96D3×C4⋊C4—62no—
97D3×C22⋊C4—62no—
98#877—62no—
99#872—62no—
100C42×D3—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—24no—
103C22×C3⋊D3C22×C412yes—
104C22×C3⋊D3C2×D411yescharacteristic
105C22×C3⋊D3C2×D412yes—
106C22×C3⋊D3C2411yescharacteristic
107C22×C3×D3—22no—
108C2×D32—22no—
109C2×D32—28no—
110C2×D32C22×C414yes—
111C2×#157—216no—
112C2×#157—24no—
113C2×#157—24no—
114C2×#157#4118yescomplemented
115C2×C32×C4C22⋊C414yescomplemented
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3C22⋊C414yescomplemented
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C4×C3⋊D3C22⋊C414yescomplemented
122C4×C3⋊D3C22⋊C414yescomplemented
123C4×C3⋊D3C22×C412yes—
124C4×C3⋊D3C22×C412yes—
125C4×C3⋊D3C2×D412yes—
126C4×C3⋊D3C2×D412yes—
127C3×#67—28no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—24no—
130C3×D12—24no—
131C3×C4×D3—28no—
132C3×Dic6—24no—
133#627—24no—
134#626—28no—
135#625—24no—
136#624—22no—
137#624—28no—
138#624C22×C414yes—
139D3×Dic3—28no—
140C22×#41—91no—
141C2×#117—91no—
142C22×C42—91no—
143#391—92no—
144#390—92no—
145#386—94no—
146C4×C22⋊C4—94no—
147C23×D3—62no—
148C23×D3—61no—
149C23×D3—61no—
150C3×#41—68no—
151C2×C3×Q8—61no—
152C2×C3×D4—61no—
153C2×C3×D4—62no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—62no—
157C2×#67—22no—
158C2×#67—62no—
159C2×#67—62no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—62no—
163#239—68no—
164D3×Q8—64no—
165D3×Q8—64no—
166#237—68no—
167#237—616no—
168D3×D4—64no—
169D3×D4—68no—
170D3×D4—64no—
171D3×D4—68no—
172#235—28no—
173#235—616no—
174C2×D12—21no—
175C2×D12—62no—
176C2×C4×D3—22no—
177C2×C4×D3—68no—
178C2×C4×D3—62no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—64no—
192C2×C4×D3—68no—
193C2×C4×D3—62no—
194C2×Dic6—21no—
195C2×Dic6—62no—
196C3×C4⋊C4—62no—
197C3×C22⋊C4—62no—
198C3×C42—62no—
199#217—22no—
200(C2×D3)⋊C4—64no—
201C4⋊Dic3—22no—
202Dic3⋊C4—64no—
203C4×Dic3—22no—
204C4×Dic3—64no—
205C22×C32—22no—
206C22×C32C2×C22⋊C412yes—
207C22×C32C22×D411yescharacteristic
208C2×C3⋊D3—22no—
209C2×C3⋊D3—24no—
210C2×C3⋊D3—24no—
211C2×C3⋊D3C2×C22⋊C412yes—
212C2×C3⋊D3C23×C411yescharacteristic
213C2×C3⋊D3C22×D411yescharacteristic
214C2×C3⋊D3C2×#4114yes—
215C2×C3×D3—24no—
216C2×C3×D3—44no—
217D32—28no—
218D32—44no—
219#157—28no—
220C32×C4C2×C22⋊C412yes—
221C32×C4C2×C22⋊C412yes—
222C3⋊Dic3C2×C22⋊C412yes—
223C3⋊Dic3C2×C22⋊C412yes—
224C3×Dic3—24no—
225C3×Dic3—44no—
226C2×#41—61no—
227C2×#41—98no—
228C2×#41—181no—
229C2×#41—181no—
230C2×#41—181no—
231C2×#41—184no—
232C22×Q8—91no—
233C22×D4—92no—
234C22×D4—91no—
235C23×C4—92no—
236C23×C4—91no—
237C23×C4—92no—
238#117—61no—
239#117—181no—
240#117—181no—
241#117—181no—
242C2×C4⋊C4—92no—
243C2×C22⋊C4—92no—
244C2×C22⋊C4—98no—
245C2×C42—92no—
246C2×C42—92no—
247C2×C42—92no—
248C2×C42—184no—
249#95—98no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—62no—
253C22×D3—22no—
254C22×D3—64no—
255C22×D3—61no—
256C22×D3—61no—
257C22×D3—62no—
258C22×D3—62no—
259C22×D3—61no—
260C22×D3—61no—
261C22×D3—62no—
262C22×D3—62no—
263C22×D3—64no—
264C22×D3—128no—
265C22×D3—124no—
266C22×D3—124no—
267C3×Q8—64no—
268C3×D4—64no—
269C3×D4—68no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—24no—
275C2×C3×C4—24no—
276C2×C3×C4—68no—
277C2×C3×C4—62no—
278C2×C3×C4—64no—
279#67—28no—
280#67—68no—
281#67—68no—
282C2×Dic3—22no—
283C2×Dic3—24no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—61no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—68no—
291D12—24no—
292D12—68no—
293C4×D3—28no—
294C4×D3—64no—
295C4×D3—64no—
296C4×D3—64no—
297C4×D3—64no—
298C4×D3—64no—
299C4×D3—62no—
300C4×D3—62no—
301C4×D3—62no—
302C4×D3—62no—
303C4×D3—62no—
304C4×D3—62no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—64no—
308C4×D3—68no—
309C4×D3—128no—
310Dic6—24no—
311Dic6—68no—
312C2×C32—22no—
313C2×C32C22×C22⋊C411yescharacteristic
314C2×C32#53212yes—
315C3⋊D3—22no—
316C3⋊D3C4×#4112yes—
317C3⋊D3#52512yes—
318C3×D3—44no—
319C24—92no—
320C24—91no—
321#41—68no—
322#41—188no—
323#41—188no—
324#41—188no—
325C2×Q8—61no—
326C2×Q8—94no—
327C2×Q8—181no—
328C2×Q8—182no—
329C2×D4—62no—
330C2×D4—61no—
331C2×D4—98no—
332C2×D4—94no—
333C2×D4—182no—
334C2×D4—182no—
335C2×D4—181no—
336C2×D4—184no—
337C22×C4—62no—
338C22×C4—92no—
339C22×C4—98no—
340C22×C4—94no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—94no—
347C22×C4—94no—
348C22×C4—94no—
349C22×C4—184no—
350C22×C4—182no—
351C22×C4—188no—
352C22×C4—184no—
353C22×C4GO+(4,𝔽2)11yescharacteristic
354C4⋊C4—62no—
355C4⋊C4—182no—
356C22⋊C4—62no—
357C22⋊C4—182no—
358C22⋊C4—1816no—
359C42—62no—
360C42—182no—
361C42—184no—
362C42—184no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—64no—
370C22×C3—124no—
371C2×D3—24no—
372C2×D3—44no—
373C2×D3—61no—
374C2×D3—61no—
375C2×D3—61no—
376C2×D3—61no—
377C2×D3—64no—
378C2×D3—64no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—128no—
382C2×D3—124no—
383C2×D3—124no—
384C2×D3—124no—
385C2×D3—124no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—128no—
389C3×C4—22no—
390C3×C4—22no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—64no—
394C3×C4—124no—
395Dic3—24no—
396Dic3—44no—
397Dic3—62no—
398Dic3—62no—
399Dic3—62no—
400Dic3—62no—
401C32#229711yescharacteristic, complemented, Sylow
402C23—62no—
403C23—94no—
404C23—91no—
405C23—91no—
406C23—92no—
407C23—92no—
408C23—184no—
409C23—182no—
410C23—188no—
411C23C2×GO+(4,𝔽2)11yescharacteristic
412Q8—64no—
413Q8—184no—
414D4—68no—
415D4—64no—
416D4—188no—
417D4—184no—
418C2×C4—62no—
419C2×C4—68no—
420C2×C4—64no—
421C2×C4—94no—
422C2×C4—91no—
423C2×C4—91no—
424C2×C4—94no—
425C2×C4—92no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—92no—
429C2×C4—94no—
430C2×C4—94no—
431C2×C4—98no—
432C2×C4—182no—
433C2×C4—188no—
434C2×C4—188no—
435C2×C4—184no—
436C2×C4—184no—
437C2×C4—1816no—
438C2×C4D32⋊C414yescomplemented
439C2×C4C2×GO+(4,𝔽2)11yescharacteristic
440C2×C4C2×GO+(4,𝔽2)11yescharacteristic
441C2×C3—22no—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—42no—
446C2×C3—42no—
447C2×C3—124no—
448D3—44no—
449D3—62no—
450D3—62no—
451D3—62no—
452D3—62no—
453D3—122no—
454D3—122no—
455C22—22no—
456C22—64no—
457C22—94no—
458C22—91no—
459C22—91no—
460C22—92no—
461C22—124no—
462C22—184no—
463C22—184no—
464C22—188no—
465C22—182no—
466C22—364no—
467C22C2×D32⋊C412yes—
468C22C22×GO+(4,𝔽2)11yescharacteristic
469C4—64no—
470C4—92no—
471C4—92no—
472C4—124no—
473C4—188no—
474C4C2×D32⋊C412yes—
475C4C2×D32⋊C412yes—
476C3—21no—
477C3—21no—
478C2—22no—
479C2—92no—
480C2—92no—
481C2—124no—
482C2—182no—
483C2#1059651112yes—
484C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2297
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×#157C2semidirect
3. #10594969C2semidirect
4. #10593515C2semidirect
5. #10593407C2semidirect
6. C4×D32⋊C4C2semidirect
7. #10593342C2semidirect
14. #64306C4semidirect
62. #3802C2×C4semidirect
64. C4×D32C2×C4semidirect
67. #3797C2×C4semidirect
114. C2×#157#41semidirect
115. C2×C32×C4C22⋊C4semidirect
118. C2×C3⋊Dic3C22⋊C4semidirect
121. C4×C3⋊D3C22⋊C4semidirect
122. C4×C3⋊D3C22⋊C4semidirect
401. C32#2297semidirect
438. C2×C4D32⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C22×C4×#1572
#105949692
#105935152
#105934072
C4×D32⋊C42
#105933422
#22979