Finite Group Databasebeta

← C2×#10593338 #11801392

Subgroups — C2×#10593338 #11801392

Order 1152.

1170 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 215 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×#3773C211yesmaximal, characteristic
2C2×#63883C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic
4C2×#63781C211yesmaximal, characteristic
5C2×#63737C211yesmaximal, characteristic
6C2×#63737C211yesmaximal, characteristic
7C2×#63737C211yesmaximal, characteristic
8#10593338C218yesmaximal, direct product factor
9C23×#157C2211yescharacteristic
10C23×#157C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#624C2211yescharacteristic
13C22×#624C2211yescharacteristic
14C22×#624C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C2×#3773C418yescomplemented
17C2×#3773C2214yes—
18C2×C3×Dic3⋊C4—21no—
19C2×C3×C4×Dic3—21no—
20C2×Dic3⋊Dic3—21no—
21C2×Dic32—21no—
22#63883—22no—
23#63883C2214yes—
24C4×#624—22no—
25C4×#624C2214yes—
26#63781C2214yes—
27#63737C2214yes—
28#63737C2214yes—
29#63737C2214yes—
30C2×D3×C4⋊C4—61no—
31C2×C42×D3—61no—
32C23×C3⋊D3C2311yescharacteristic
33C22×#157—22no—
34C22×#157—22no—
35C22×#157—22no—
36C22×#157—22no—
37C22×#157—22no—
38C22×#157C2×C414yes—
39C22×#157C2312yes—
40C22×#157C2312yes—
41C22×C32×C4D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C2×C4×C3⋊D3—22no—
44C2×C4×C3⋊D3—22no—
45C2×C4×C3⋊D3D412yes—
46C2×C4×C3⋊D3C2312yes—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C2×#624—21no—
52C2×#624—21no—
53C2×#624—21no—
54C2×#624—22no—
55C2×#624—22no—
56C2×#624—22no—
57C2×#624—22no—
58C2×#624—22no—
59C2×#624—21no—
60C2×#624C2×C414yes—
61C2×#624C2×C414yes—
62C2×#624Q814yes—
63C2×#624C2312yes—
64C2×#624C2312yes—
65C2×#624C2312yes—
66C2×#624C2312yes—
67#3773C2×C4116yescomplemented
68C3×Dic3⋊C4—24no—
69C3×C4×Dic3—24no—
70Dic3⋊Dic3—24no—
71Dic32—24no—
72C2×#387—91nomaximal, Sylow
73C22×C4×D3—61no—
74C22×C4×D3—61no—
75C22×C4×D3—61no—
76C22×C4×D3—61no—
77C22×C4×D3—61no—
78C22×C4×D3—61no—
79C2×C3×C4⋊C4—61no—
80C2×C3×C42—61no—
81C2×C4⋊Dic3—61no—
82C2×Dic3⋊C4—21no—
83C2×Dic3⋊C4—61no—
84C2×C4×Dic3—21no—
85C2×C4×Dic3—61no—
86C2×C4×Dic3—61no—
87D3×C4⋊C4—64no—
88D3×C4⋊C4—64no—
89C42×D3—64no—
90C42×D3—64no—
91C23×C32C2×D411yescharacteristic
92C22×C3⋊D3C22×C412yes—
93C22×C3⋊D3C2×D411yescharacteristic
94C22×C3⋊D3C2×Q812yes—
95C22×C3⋊D3#4112yes—
96C22×C3⋊D3#4112yes—
97C22×C3⋊D3#4112yes—
98C22×C3⋊D3#4112yes—
99C22×C3⋊D3C2411yescharacteristic
100C2×#157—28no—
101C2×#157—22no—
102C2×#157—22no—
103C2×#157—22no—
104C2×#157—22no—
105C2×#157—22no—
106C2×#157—44no—
107C2×#157C22×C414yes—
108C2×C32×C4—22no—
109C2×C32×C4C2×D412yes—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3C2×D412yes—
112C4×C3⋊D3—24no—
113C4×C3⋊D3—22no—
114C4×C3⋊D3—22no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—42no—
123#624—24no—
124#624—24no—
125#624—24no—
126#624—22no—
127#624—22no—
128#624—22no—
129#624—22no—
130#624—22no—
131#624—42no—
132#624C22×C414yes—
133#624C22×C414yes—
134#624C2×Q814yes—
135C22×C4⋊C4—91no—
136C22×C4⋊C4—91no—
137C22×C42—91no—
138#387—98no—
139C2×#95—91no—
140C2×#95—91no—
141C2×#95—91no—
142C2×#95—91no—
143C23×D3—61no—
144C23×D3—61no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—61no—
148C22×C3×C4—61no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×Dic3—21no—
152C22×Dic3—21no—
153C22×Dic3—21no—
154C22×Dic3—21no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—64no—
161C2×C4×D3—64no—
162C2×C4×D3—64no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—62no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—62no—
170C2×C4×D3—62no—
171C2×C4×D3—64no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×C4×D3—64no—
176C2×C4×D3—62no—
177C2×C4×D3—122no—
178C2×C4×D3—122no—
179C2×C4×D3—122no—
180C2×C4×D3—122no—
181C3×C4⋊C4—64no—
182C3×C42—64no—
183C4⋊Dic3—64no—
184Dic3⋊C4—24no—
185Dic3⋊C4—64no—
186C4×Dic3—24no—
187C4×Dic3—64no—
188C4×Dic3—64no—
189C22×C32C4×D412yes—
190C22×C32C22⋊Q812yes—
191C22×C32#12312yes—
192C22×C32C22×D411yescharacteristic
193C2×C3⋊D3#11714yes—
194C2×C3⋊D3C4×D412yes—
195C2×C3⋊D3C4×Q814yes—
196C2×C3⋊D3C22⋊Q812yes—
197C2×C3⋊D3#12312yes—
198C2×C3⋊D3#12514yes—
199C2×C3⋊D3#12614yes—
200C2×C3⋊D3C23×C411yescharacteristic
201C2×C3⋊D3C22×Q811yescharacteristic
202C2×C3⋊D3C2×#4111yescharacteristic
203C2×C3⋊D3C2×#4111yescharacteristic
204C2×C3⋊D3C2×#4111yescharacteristic
205C2×C3⋊D3C2×#4111yescharacteristic
206#157—24no—
207#157—42no—
208C32×C4—22no—
209C3⋊Dic3—22no—
210C3×Dic3—24no—
211C3×Dic3—24no—
212C3×Dic3—24no—
213C3×Dic3—42no—
214C23×C4—91no—
215C23×C4—91no—
216C23×C4—91no—
217C23×C4—91no—
218C23×C4—91no—
219C23×C4—91no—
220C23×C4—91no—
221C2×C4⋊C4—61no—
222C2×C4⋊C4—94no—
223C2×C4⋊C4—94no—
224C2×C4⋊C4—98no—
225C2×C4⋊C4—182no—
226C2×C4⋊C4—181no—
227C2×C42—61no—
228C2×C42—94no—
229C2×C42—182no—
230C2×C42—181no—
231#95—94no—
232#95—94no—
233#95—94no—
234#95—94no—
235C23×C3—21no—
236C23×C3—21no—
237C22×D3—62no—
238C22×D3—62no—
239C22×D3—61no—
240C22×D3—61no—
241C22×D3—62no—
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—62no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—61no—
252C22×D3—61no—
253C2×C3×C4—24no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—42no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—64no—
261C2×C3×C4—64no—
262C2×C3×C4—64no—
263C2×C3×C4—62no—
264C2×C3×C4—122no—
265C2×Dic3—22no—
266C2×Dic3—22no—
267C2×Dic3—22no—
268C2×Dic3—24no—
269C2×Dic3—24no—
270C2×Dic3—24no—
271C2×Dic3—22no—
272C2×Dic3—42no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—64no—
276C2×Dic3—122no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—64no—
280C4×D3—68no—
281C4×D3—68no—
282C4×D3—68no—
283C4×D3—64no—
284C4×D3—64no—
285C4×D3—64no—
286C4×D3—68no—
287C4×D3—64no—
288C4×D3—64no—
289C4×D3—122no—
290C4×D3—122no—
291C4×D3—124no—
292C4×D3—122no—
293C4×D3—122no—
294C4×D3—124no—
295C2×C32#38714yescomplemented
296C2×C32C2×C4×D411yescharacteristic
297C2×C32C2×C22⋊Q811yescharacteristic
298C2×C32C2×#12311yescharacteristic
299C3⋊D3#38714yescomplemented
300C3⋊D3C2×#11711yescharacteristic
301C3⋊D3C2×C4×Q811yescharacteristic
302C3⋊D3C2×#12511yescharacteristic
303C3⋊D3C2×#12611yescharacteristic
304C24—91no—
305C22×C4—61no—
306C22×C4—61no—
307C22×C4—61no—
308C22×C4—61no—
309C22×C4—92no—
310C22×C4—92no—
311C22×C4—92no—
312C22×C4—94no—
313C22×C4—94no—
314C22×C4—94no—
315C22×C4—92no—
316C22×C4—94no—
317C22×C4—92no—
318C22×C4—91no—
319C22×C4—92no—
320C22×C4—92no—
321C22×C4—92no—
322C22×C4—182no—
323C22×C4—182no—
324C22×C4—181no—
325C22×C4—181no—
326C22×C4—181no—
327C22×C4—182no—
328C22×C4—182no—
329C22×C4—182no—
330C22×C4—181no—
331C22×C4—182no—
332C22×C4—182no—
333C22×C4—182no—
334C22×C4—182no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4—182no—
338C22×C4GO+(4,𝔽2)11yescharacteristic
339C4⋊C4—64no—
340C4⋊C4—916no—
341C4⋊C4—184no—
342C42—64no—
343C42—184no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C2×D3—62no—
353C2×D3—62no—
354C2×D3—62no—
355C2×D3—62no—
356C2×D3—61no—
357C2×D3—61no—
358C2×D3—61no—
359C2×D3—61no—
360C2×D3—61no—
361C2×D3—61no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—62no—
365C2×D3—61no—
366C2×D3—61no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—62no—
372C2×D3—64no—
373C2×D3—64no—
374C2×D3—64no—
375C2×D3—64no—
376C2×D3—61no—
377C2×D3—61no—
378C3×C4—24no—
379C3×C4—42no—
380C3×C4—64no—
381C3×C4—64no—
382C3×C4—64no—
383C3×C4—122no—
384Dic3—24no—
385Dic3—24no—
386Dic3—24no—
387Dic3—42no—
388Dic3—64no—
389Dic3—122no—
390C32C2×#38711yescharacteristic, complemented, Sylow
391C23—91no—
392C23—91no—
393C23—92no—
394C23—92no—
395C23—92no—
396C23—92no—
397C23—92no—
398C23—92no—
399C23C2×GO+(4,𝔽2)11yescharacteristic
400C2×C4—22no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—64no—
405C2×C4—64no—
406C2×C4—64no—
407C2×C4—62no—
408C2×C4—94no—
409C2×C4—94no—
410C2×C4—94no—
411C2×C4—94no—
412C2×C4—92no—
413C2×C4—122no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—184no—
417C2×C4—182no—
418C2×C4—184no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—184no—
422C2×C4—184no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—188no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—362no—
433C2×C4—364no—
434C2×C4C2×GO+(4,𝔽2)12yes—
435C2×C3—24no—
436C2×C3—24no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443D3—61no—
444D3—61no—
445D3—61no—
446D3—61no—
447D3—61no—
448D3—61no—
449D3—61no—
450D3—61no—
451D3—64no—
452D3—64no—
453C22—94no—
454C22—94no—
455C22—94no—
456C22—94no—
457C22—91no—
458C22—91no—
459C22—92no—
460C22—91no—
461C22—91no—
462C22—92no—
463C22—91no—
464C22—91no—
465C22—92no—
466C22D32⋊Q812yes—
467C22C4×GO+(4,𝔽2)12yes—
468C22#6423312yes—
469C22C22×GO+(4,𝔽2)11yescharacteristic
470C4—22no—
471C4—64no—
472C4—64no—
473C4—64no—
474C4—122no—
475C4—184no—
476C4—182no—
477C4—362no—
478C3—21no—
479C3—21no—
480C2—91no—
481C2—91no—
482C2—94no—
483C2—91no—
484C2—91no—
485C2#1059333814yesdirect product factor
486C2C2×D32⋊Q811yescharacteristic
487C2C2×C4×GO+(4,𝔽2)11yescharacteristic
488C2C2×#6423311yescharacteristic
subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#387
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. #10593338C2direct (N × H)
16. C2×#3773C4semidirect
67. #3773C2×C4semidirect
295. C2×C32#387semidirect
299. C3⋊D3#387semidirect
390. C32C2×#387semidirect
485. C2#10593338direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37732
C2×#638832
C2×C4×#6242
C2×#637812
C2×#637372
#105933382
C2×#3879