Finite Group Databasebeta

← C2×#10593308 #11857409

Subgroups — C2×#10593308 #11857409

Order 1152.

1406 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1406 conjugacy classes of subgroups — too many to draw. Only its 199 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
2C2×#64283C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4#10593308C218yesmaximal, direct product factor
5C2×D32⋊C8C214yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C3×#235—21no—
8C2×#3811C412yes—
9C2×#3805—21no—
10#64306—22no—
11#64306—22no—
12#64306C414yes—
13#64306C2214yes—
14C2×#3802C411yescharacteristic
15C2×C4×D32C2212yes—
16C2×#3798—21no—
17C2×#3797C411yescharacteristic
18C2×#3796—21no—
19C2×#3792—21no—
20#64283—22no—
21#64283C2214yescomplemented
22C2×#3788—21no—
23C2×#3787C2212yes—
24C22×C3×C3⋊C8—21no—
25C2×#3710—22no—
26C2×#3710—21no—
27C2×#3710C2212yes—
28C2×#3710C2214yescomplemented
29D32⋊C8C22116yescomplemented
30C2×D3×#41—61no—
31C22×D3×C8—61no—
32C23×C3⋊D3C2×C411yescharacteristic
33C22×D32C2×C412yes—
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D412yes—
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×C4×C3⋊D3C2312yes—
44C2×C3×#67—22no—
45C3×#235—24no—
46C3×#235—24no—
47C2×C3×D12—21no—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6—21no—
50#3811—24no—
51#3811C2×C418yes—
52C2×#627—21no—
53C2×#626—22no—
54C2×#625—21no—
55C2×#624C2×C412yes—
56#3805—24no—
57#3805—24no—
58C2×D3×Dic3—22no—
59#3802—22no—
60#3802C2×C414yes—
61C4×D32—22no—
62C4×D32—22no—
63C4×D32C2×C414yes—
64C4×D32C2314yes—
65#3798—24no—
66#3798—24no—
67#3797—22no—
68#3797C2×C414yes—
69#3796—24no—
70#3796—24no—
71#3792—24no—
72C2×#622—22no—
73#3788—24no—
74#3787—22no—
75#3787C2314yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8—24no—
78#3710—22no—
79#3710—24no—
80#3710C2314yes—
81C2×#408—91nomaximal, Sylow
82C2×C3×#41—61no—
83D3×#41—64no—
84D3×#41—64no—
85D3×#41—64no—
86D3×#41—64no—
87C2×#239—61no—
88C2×D3×Q8—61no—
89C2×#237—61no—
90C2×#237—62no—
91C2×D3×D4—61no—
92C2×D3×D4—62no—
93C2×#235—21no—
94C2×#235—62no—
95C22×C4×D3—62no—
96C22×C4×D3—61no—
97C22×C4×D3—61no—
98C22×C3×C8—61no—
99C22×C3⋊C8—21no—
100C2×D3×C8—62no—
101C2×D3×C8—64no—
102C2×D3×C8—64no—
103C2×D3×C8—62no—
104C23×C32C22⋊C411yescharacteristic
105C22×C3⋊D3—24no—
106C22×C3⋊D3C22⋊C411yescharacteristic
107C22×C3⋊D3C22⋊C412yes—
108C22×C3⋊D3C22×C412yes—
109C22×C3⋊D3C22×C411yescharacteristic
110C22×C3×D3—22no—
111C2×D32—22no—
112C2×D32—28no—
113C2×D32C22×C414yes—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C412yes—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D412yes—
118C2×C3⋊Dic3C22⋊C412yes—
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D412yes—
122C4×C3⋊D3C22⋊C412yes—
123C4×C3⋊D3C22⋊C412yes—
124C4×C3⋊D3C22⋊C412yes—
125C4×C3⋊D3C22×C412yes—
126C4×C3⋊D3C22×C411yescharacteristic
127C4×C3⋊D3C2×D412yes—
128C4×C3⋊D3C2×D411yescharacteristic
129C4×C3⋊D3C2×D411yescharacteristic
130C4×C3⋊D3C2×D412yes—
131C4×C3⋊D3C2411yescharacteristic
132C3×#67—28no—
133C2×C3×Dic3—22no—
134C3×D12—24no—
135C3×C4×D3—24no—
136C3×C4×D3—24no—
137C3×Dic6—24no—
138#627—24no—
139#626—28no—
140#625—24no—
141#624—22no—
142#624C22×C414yes—
143D3×Dic3—24no—
144D3×Dic3—24no—
145#622—24no—
146C3×C3⋊C8—24no—
147C22×#41—91no—
148C22×M16—91no—
149C23×C8—91no—
150#408—98no—
151C2×C22⋊C8—94no—
152C23×D3—62no—
153C23×D3—61no—
154C23×D3—61no—
155C3×#41—64no—
156C3×#41—64no—
157C2×C3×Q8—61no—
158C2×C3×D4—61no—
159C2×C3×D4—62no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—62no—
163C2×#67—22no—
164C2×#67—62no—
165C2×#67—62no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—62no—
169#239—64no—
170#239—64no—
171D3×Q8—64no—
172D3×Q8—64no—
173#237—64no—
174#237—64no—
175#237—68no—
176#237—68no—
177D3×D4—64no—
178D3×D4—68no—
179D3×D4—64no—
180D3×D4—68no—
181#235—24no—
182#235—24no—
183#235—68no—
184#235—68no—
185C2×D12—21no—
186C2×D12—62no—
187C2×C4×D3—22no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—61no—
193C2×C4×D3—62no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—61no—
204C2×C4×D3—62no—
205C2×C4×D3—61no—
206C2×C4×D3—62no—
207C2×C4×D3—64no—
208C2×C4×D3—64no—
209C2×C4×D3—62no—
210C2×Dic6—21no—
211C2×Dic6—62no—
212C2×C3×C8—64no—
213C2×C3×C8—62no—
214C2×C3⋊C8—24no—
215C2×C3⋊C8—22no—
216D3×C8—64no—
217D3×C8—64no—
218D3×C8—68no—
219C22×C32—22no—
220C22×C32C2×C22⋊C412yes—
221C22×C32C2×C22⋊C411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—24no—
224C2×C3⋊D3—24no—
225C2×C3⋊D3C2×C22⋊C412yes—
226C2×C3⋊D3C2×C22⋊C411yescharacteristic
227C2×C3⋊D3#13114yes—
228C2×C3⋊D3C23×C411yescharacteristic
229C2×C3×D3—24no—
230C2×C3×D3—44no—
231D32—28no—
232D32—44no—
233C32×C4C2×C22⋊C412yes—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4C22×D411yescharacteristic
236C3⋊Dic3C2×C22⋊C411yescharacteristic
237C3⋊Dic3C2×C22⋊C412yes—
238C3⋊Dic3C22×D411yescharacteristic
239C3×Dic3—24no—
240C2×#41—61no—
241C2×#41—94no—
242C2×#41—94no—
243C2×#41—181no—
244C2×#41—181no—
245C2×#41—181no—
246C2×#41—182no—
247C2×#41—182no—
248C22×Q8—91no—
249C22×D4—92no—
250C22×D4—91no—
251C23×C4—92no—
252C23×C4—91no—
253C2×M16—94no—
254C2×M16—181no—
255C2×M16—182no—
256C2×M16—181no—
257C22×C8—61no—
258C22×C8—92no—
259C22×C8—94no—
260C22×C8—92no—
261C22×C8—182no—
262C22×C8—181no—
263C22⋊C8—916no—
264C23×C3—21no—
265C23×C3—21no—
266C23×C3—62no—
267C22×D3—22no—
268C22×D3—64no—
269C22×D3—61no—
270C22×D3—62no—
271C22×D3—61no—
272C22×D3—61no—
273C22×D3—62no—
274C22×D3—61no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—64no—
278C22×D3—68no—
279C22×D3—128no—
280C22×D3—124no—
281C3×Q8—64no—
282C3×D4—64no—
283C3×D4—68no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—64no—
293C2×C3×C4—64no—
294C2×C3×C4—62no—
295#67—28no—
296#67—68no—
297#67—68no—
298C2×Dic3—22no—
299C2×Dic3—61no—
300C2×Dic3—62no—
301C2×Dic3—61no—
302C2×Dic3—62no—
303C2×Dic3—61no—
304C2×Dic3—62no—
305C2×Dic3—61no—
306C2×Dic3—62no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309D12—24no—
310D12—68no—
311C4×D3—24no—
312C4×D3—24no—
313C4×D3—64no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—61no—
321C4×D3—62no—
322C4×D3—61no—
323C4×D3—62no—
324C4×D3—61no—
325C4×D3—62no—
326C4×D3—61no—
327C4×D3—62no—
328C4×D3—61no—
329C4×D3—61no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—61no—
333C4×D3—61no—
334C4×D3—64no—
335C4×D3—64no—
336C4×D3—64no—
337Dic6—24no—
338Dic6—68no—
339C3×C8—64no—
340C3⋊C8—24no—
341C2×C32—22no—
342C2×C32#40812yescomplemented
343C2×C32C22×C22⋊C411yescharacteristic
344C3⋊D3—22no—
345C3⋊D3#40812yescomplemented
346C3⋊D3C2×#13112yes—
347C3×D3—44no—
348C24—92no—
349C24—91no—
350#41—64no—
351#41—64no—
352#41—184no—
353#41—184no—
354#41—184no—
355#41—184no—
356#41—184no—
357#41—184no—
358C2×Q8—61no—
359C2×Q8—94no—
360C2×Q8—181no—
361C2×Q8—182no—
362C2×D4—62no—
363C2×D4—61no—
364C2×D4—98no—
365C2×D4—94no—
366C2×D4—182no—
367C2×D4—182no—
368C2×D4—181no—
369C2×D4—184no—
370C22×C4—62no—
371C22×C4—94no—
372C22×C4—92no—
373C22×C4—94no—
374C22×C4—91no—
375C22×C4—92no—
376C22×C4—92no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—92no—
381C22×C4—91no—
382C22×C4—92no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4—182no—
386C22×C4GO+(4,𝔽2)11yescharacteristic
387M16—184no—
388M16—184no—
389C2×C8—64no—
390C2×C8—62no—
391C2×C8—94no—
392C2×C8—94no—
393C2×C8—182no—
394C2×C8—184no—
395C2×C8—182no—
396C2×C8—182no—
397C22×C3—24no—
398C22×C3—21no—
399C22×C3—22no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—42no—
403C22×C3—64no—
404C22×C3—124no—
405C2×D3—24no—
406C2×D3—44no—
407C2×D3—61no—
408C2×D3—61no—
409C2×D3—61no—
410C2×D3—62no—
411C2×D3—61no—
412C2×D3—64no—
413C2×D3—64no—
414C2×D3—62no—
415C2×D3—68no—
416C2×D3—68no—
417C2×D3—64no—
418C2×D3—128no—
419C2×D3—124no—
420C2×D3—124no—
421C2×D3—122no—
422C2×D3—128no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—22no—
429C3×C4—64no—
430Dic3—24no—
431Dic3—62no—
432Dic3—61no—
433Dic3—61no—
434Dic3—61no—
435Dic3—62no—
436Dic3—61no—
437C32C2×#40811yescharacteristic, complemented, Sylow
438C23—62no—
439C23—94no—
440C23—91no—
441C23—92no—
442C23—92no—
443C23—91no—
444C23—184no—
445C23—182no—
446C23—188no—
447C23D32⋊C411yescharacteristic
448Q8—64no—
449Q8—184no—
450D4—68no—
451D4—64no—
452D4—188no—
453D4—184no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—64no—
457C2×C4—94no—
458C2×C4—91no—
459C2×C4—92no—
460C2×C4—91no—
461C2×C4—92no—
462C2×C4—91no—
463C2×C4—91no—
464C2×C4—92no—
465C2×C4—91no—
466C2×C4—92no—
467C2×C4—91no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—92no—
472C2×C4—182no—
473C2×C4—184no—
474C2×C4—184no—
475C2×C4D32⋊C411yescharacteristic
476C2×C4D32⋊C412yes—
477C2×C4C2×GO+(4,𝔽2)12yes—
478C2×C4C2×GO+(4,𝔽2)11yescharacteristic
479C8—64no—
480C8—184no—
481C2×C3—24no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—42no—
487C2×C3—124no—
488D3—44no—
489D3—62no—
490D3—62no—
491D3—62no—
492D3—62no—
493D3—64no—
494D3—122no—
495C22—22no—
496C22—64no—
497C22—94no—
498C22—91no—
499C22—91no—
500C22—92no—
501C22—124no—
502C22—184no—
503C22—184no—
504C22—188no—
505C22—182no—
506C22—364no—
507C22C2×D32⋊C412yes—
508C22C2×D32⋊C411yescharacteristic
509C4—64no—
510C4—91no—
511C4—91no—
512C4—92no—
513C4C2×D32⋊C411yescharacteristic
514C4C2×D32⋊C412yes—
515C4C22×GO+(4,𝔽2)11yescharacteristic
516C3—21no—
517C3—21no—
518C2—22no—
519C2—92no—
520C2—92no—
521C2—124no—
522C2—182no—
523C2#1059330812yesdirect product factor
524C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#408
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. C2×#64283C2semidirect
3. C22×#3710C2semidirect
4. #10593308C2direct (N × H)
5. C2×D32⋊C8C2semidirect
21. #64283C22semidirect
28. C2×#3710C22semidirect
29. D32⋊C8C22semidirect
342. C2×C32#408semidirect
345. C3⋊D3#408semidirect
437. C32C2×#408semidirect
523. C2#10593308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642832
C22×#37102
#105933082
C2×D32⋊C82
C2×#4089