Finite Group Databasebeta

← C2×#10593506 #11858170

Subgroups — C2×#10593506 #11858170

Order 1152.

1382 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C22×#3805C211yesmaximal, characteristic
2C22×#3792C211yesmaximal, characteristic, complemented
3C2×#63957C211yesmaximal, characteristic, complemented
4#10593506C218yesmaximal, direct product factor
5C2×#63741C214yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C22×C3×#67—21no—
8C22×#627C411yescharacteristic, complemented
9C22×#625C411yescharacteristic, complemented
10C2×#3805—22no—
11C2×#3805—21no—
12C2×#3805—21no—
13C2×#3805—22no—
14C2×#3805C414yescomplemented
15C2×#3805C412yescomplemented
16C2×#3805C2212yes—
17C2×#3805C2214yes—
18C22×D3×Dic3—21no—
19C2×#3792—21no—
20C2×#3792—22no—
21C2×#3792C2212yescomplemented
22C2×#3792C2214yescomplemented
23C22×#622—21no—
24C2×C3×#217—21no—
25C2×#3724—21no—
26#63957—22no—
27#63957C2214yescomplemented
28C2×Dic32C2212yescomplemented
29#63741C22116yescomplemented
30C22×#237—61no—
31C2×#877—61no—
32C24×C32D411yescharacteristic
33C23×C3×D3—21no—
34C22×C3⋊Dic3C2×C412yes—
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3D412yes—
38C22×C3⋊Dic3D411yescharacteristic
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D412yes—
42C22×C3⋊Dic3C2311yescharacteristic
43C22×C3⋊Dic3C2312yes—
44C2×C3×#67—22no—
45C2×C3×#67—24no—
46C2×C3×#67—22no—
47C2×C3×#67—24no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—22no—
50C2×#627—22no—
51C2×#627—21no—
52C2×#627C2×C412yes—
53C2×#627C2×C414yescomplemented
54C2×#625—22no—
55C2×#625—21no—
56C2×#625C2×C412yes—
57C2×#625C2×C414yescomplemented
58#3805—24no—
59#3805—24no—
60#3805—24no—
61#3805—22no—
62#3805—24no—
63#3805—22no—
64#3805—24no—
65#3805C2×C414yes—
66#3805C2×C418yescomplemented
67#3805C2314yes—
68C2×D3×Dic3—24no—
69C2×D3×Dic3—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3—24no—
72#3792—24no—
73#3792—22no—
74#3792C2314yescomplemented
75C2×#622—22no—
76C2×#622—24no—
77C3×#217—24no—
78#3724—24no—
79Dic32—22no—
80Dic32C2314yescomplemented
81C2×#421—91nomaximal, Sylow
82C22×C3×D4—61no—
83C22×#67—21no—
84C22×#67—61no—
85C23×Dic3—61no—
86C23×Dic3—61no—
87C23×Dic3—61no—
88C2×#237—62no—
89C2×#237—64no—
90C2×#237—62no—
91C2×#237—64no—
92C2×#237—62no—
93C2×#237—64no—
94C2×#237—62no—
95C2×#237—64no—
96C22×C4×D3—61no—
97C22×Dic6—61no—
98C2×C3×C22⋊C4—61no—
99C2×#217—21no—
100C2×Dic3⋊C4—62no—
101C2×C4×Dic3—62no—
102#877—64no—
103#877—64no—
104C23×C32—42no—
105C23×C32C22⋊C411yescharacteristic
106C23×C32C22⋊C411yescharacteristic
107C23×C32C22⋊C412yes—
108C23×C32C2×D411yescharacteristic
109C23×C32C2×D412yes—
110C22×C3×D3—22no—
111C22×C3×D3—24no—
112C22×C3×D3—44no—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3C22⋊C411yescharacteristic
115C2×C3⋊Dic3C22⋊C412yes—
116C2×C3⋊Dic3C22⋊C412yes—
117C2×C3⋊Dic3C22⋊C412yes—
118C2×C3⋊Dic3C22⋊C412yes—
119C2×C3⋊Dic3C22⋊C411yescharacteristic
120C2×C3⋊Dic3C22×C411yescharacteristic
121C2×C3⋊Dic3C22×C412yes—
122C2×C3⋊Dic3C22×C411yescharacteristic
123C2×C3⋊Dic3C22×C412yes—
124C2×C3⋊Dic3C2×D411yescharacteristic
125C2×C3⋊Dic3C2×D412yes—
126C2×C3⋊Dic3C2×D411yescharacteristic
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129C2×C3⋊Dic3C2×D411yescharacteristic
130C2×C3⋊Dic3C2411yescharacteristic
131C3×#67—24no—
132C3×#67—28no—
133C3×#67—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—44no—
138#627—22no—
139#627—24no—
140#627C22×C414yes—
141#625—22no—
142#625—24no—
143#625C22×C414yes—
144D3×Dic3—24no—
145D3×Dic3—28no—
146D3×Dic3—24no—
147#622—24no—
148C22×#41—91no—
149C22×M16—91no—
150C2×#117—91no—
151#421—98no—
152C2×#104—94no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—64no—
158C2×C3×D4—62no—
159C2×C3×D4—64no—
160C2×C3×D4—62no—
161C22×C3×C4—61no—
162C22×C3×C4—62no—
163C2×#67—24no—
164C2×#67—22no—
165C2×#67—24no—
166C2×#67—22no—
167C2×#67—62no—
168C2×#67—64no—
169C2×#67—64no—
170C2×#67—62no—
171C22×Dic3—21no—
172C22×Dic3—22no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—62no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—62no—
183C22×Dic3—61no—
184C22×Dic3—62no—
185C22×Dic3—61no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—62no—
193C22×Dic3—64no—
194C22×Dic3—62no—
195C22×Dic3—64no—
196C22×Dic3—62no—
197#237—64no—
198#237—68no—
199#237—64no—
200#237—68no—
201#237—68no—
202#237—68no—
203#237—64no—
204#237—68no—
205#237—68no—
206#237—64no—
207C2×C4×D3—64no—
208C2×C4×D3—62no—
209C2×C4×D3—64no—
210C2×C4×D3—62no—
211C2×Dic6—62no—
212C2×Dic6—64no—
213C2×Dic6—64no—
214C2×Dic6—62no—
215C3×C22⋊C4—64no—
216#217—24no—
217Dic3⋊C4—68no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C22×C32—22no—
221C22×C32—22no—
222C22×C32—22no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32C2×C22⋊C412yes—
226C22×C32C2×C22⋊C411yescharacteristic
227C22×C32C2×C22⋊C412yes—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—24no—
231C2×C3×D3—48no—
232C2×C3×D3—44no—
233C3⋊Dic3C2×C22⋊C411yescharacteristic
234C3⋊Dic3C2×C22⋊C412yes—
235C3⋊Dic3C2×C22⋊C411yescharacteristic
236C3⋊Dic3C2×C22⋊C412yes—
237C3⋊Dic3C23×C411yescharacteristic
238C3⋊Dic3C22×D411yescharacteristic
239C3×Dic3—24no—
240C3×Dic3—44no—
241C2×#41—92no—
242C2×#41—94no—
243C2×#41—94no—
244C2×#41—92no—
245C2×#41—181no—
246C2×#41—182no—
247C2×#41—181no—
248C2×#41—182no—
249C22×Q8—91no—
250C22×D4—61no—
251C22×D4—91no—
252C23×C4—91no—
253C23×C4—181no—
254C2×M16—92no—
255C2×M16—94no—
256C2×M16—181no—
257C2×M16—182no—
258C22×C8—181no—
259#117—94no—
260#117—182no—
261C2×C4⋊C4—181no—
262C2×C22⋊C4—61no—
263C2×C42—92no—
264#104—916no—
265C23×C3—21no—
266C23×C3—22no—
267C23×C3—21no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—21no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—22no—
275C23×C3—44no—
276C23×C3—44no—
277C23×C3—64no—
278C23×C3—62no—
279C23×C3—124no—
280C22×D3—24no—
281C22×D3—22no—
282C22×D3—44no—
283C3×D4—64no—
284C3×D4—64no—
285C3×D4—68no—
286C2×C3×C4—64no—
287C2×C3×C4—62no—
288C2×C3×C4—64no—
289C2×C3×C4—124no—
290#67—24no—
291#67—24no—
292#67—28no—
293#67—64no—
294#67—64no—
295#67—68no—
296C2×Dic3—24no—
297C2×Dic3—22no—
298C2×Dic3—24no—
299C2×Dic3—44no—
300C2×Dic3—62no—
301C2×Dic3—61no—
302C2×Dic3—62no—
303C2×Dic3—61no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—61no—
320C2×Dic3—62no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—64no—
337C2×Dic3—68no—
338C2×Dic3—64no—
339C4×D3—64no—
340C4×D3—68no—
341C4×D3—64no—
342Dic6—64no—
343Dic6—64no—
344Dic6—68no—
345C2×C32—21no—
346C2×C32—22no—
347C2×C32—21no—
348C2×C32—22no—
349C2×C32#42112yescomplemented
350C2×C32C22×C22⋊C411yescharacteristic
351C3×D3—44no—
352C24—61no—
353C24GO+(4,𝔽2)11yescharacteristic
354#41—94no—
355#41—94no—
356#41—98no—
357#41—182no—
358#41—184no—
359#41—184no—
360#41—182no—
361#41—184no—
362#41—184no—
363#41—184no—
364C2×Q8—94no—
365C2×Q8—92no—
366C2×Q8—182no—
367C2×Q8—181no—
368C2×D4—64no—
369C2×D4—62no—
370C2×D4—64no—
371C2×D4—62no—
372C2×D4—94no—
373C2×D4—92no—
374C2×D4—182no—
375C2×D4—181no—
376C22×C4—61no—
377C22×C4—62no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—92no—
385C22×C4—91no—
386C22×C4—92no—
387C22×C4—91no—
388C22×C4—184no—
389C22×C4—184no—
390C22×C4—182no—
391C22×C4—182no—
392M16—94no—
393M16—184no—
394M16—182no—
395C2×C8—184no—
396C2×C8—182no—
397C4⋊C4—184no—
398C22⋊C4—64no—
399C42—94no—
400C42—182no—
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—22no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—44no—
418C22×C3—44no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—64no—
422C22×C3—128no—
423C22×C3—124no—
424C2×D3—24no—
425C2×D3—48no—
426C2×D3—44no—
427C3×C4—64no—
428C3×C4—124no—
429Dic3—24no—
430Dic3—44no—
431Dic3—61no—
432Dic3—62no—
433Dic3—61no—
434Dic3—61no—
435Dic3—62no—
436Dic3—61no—
437Dic3—61no—
438Dic3—62no—
439Dic3—61no—
440Dic3—62no—
441Dic3—61no—
442Dic3—61no—
443C32C2×#42111yescharacteristic, complemented, Sylow
444C23—42no—
445C23—64no—
446C23—62no—
447C23—124no—
448C23D32⋊C411yescharacteristic
449C23D32⋊C411yescharacteristic
450C23D32⋊C412yes—
451C23C2×GO+(4,𝔽2)11yescharacteristic
452C23C2×GO+(4,𝔽2)12yes—
453Q8—94no—
454Q8—182no—
455Q8—184no—
456D4—64no—
457D4—64no—
458D4—68no—
459D4—94no—
460D4—182no—
461D4—184no—
462C2×C4—64no—
463C2×C4—62no—
464C2×C4—64no—
465C2×C4—91no—
466C2×C4—91no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—91no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—91no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—124no—
484C2×C4—184no—
485C2×C4—184no—
486C2×C4—188no—
487C8—184no—
488C2×C3—22no—
489C2×C3—24no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—22no—
494C2×C3—22no—
495C2×C3—41no—
496C2×C3—42no—
497C2×C3—41no—
498C2×C3—42no—
499C2×C3—42no—
500C2×C3—124no—
501D3—44no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—42no—
507C22—64no—
508C22—128no—
509C22—124no—
510C22C2×D32⋊C412yes—
511C22C2×D32⋊C411yescharacteristic
512C22C2×D32⋊C412yes—
513C22C2×D32⋊C411yescharacteristic
514C22C22×GO+(4,𝔽2)11yescharacteristic
515C4—64no—
516C4—91no—
517C4—91no—
518C4—92no—
519C4—91no—
520C4—91no—
521C4—92no—
522C4—124no—
523C3—21no—
524C3—21no—
525C2—21no—
526C2—22no—
527C2—21no—
528C2—22no—
529C2—124no—
530C2#1059350612yesdirect product factor
531C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC24×C32D4
socleC22×C32C2×C22⋊C4
prime radicalC22×#3805C2
cosocleC2×C3⋊Dic3C24
hypercenterC24GO+(4,𝔽2)
hypocenterC32C2×#421
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#3792C2semidirect
3. C2×#63957C2semidirect
4. #10593506C2direct (N × H)
5. C2×#63741C2semidirect
8. C22×#627C4semidirect
9. C22×#625C4semidirect
14. C2×#3805C4semidirect
15. C2×#3805C4semidirect
21. C2×#3792C22semidirect
22. C2×#3792C22semidirect
27. #63957C22semidirect
28. C2×Dic32C22semidirect
29. #63741C22semidirect
53. C2×#627C2×C4semidirect
57. C2×#625C2×C4semidirect
66. #3805C2×C4semidirect
74. #3792C23semidirect
80. Dic32C23semidirect
349. C2×C32#421semidirect
443. C32C2×#421semidirect
530. C2#10593506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38052
C22×#37922
C2×#639572
#105935062
C2×#637412
C2×#4219