Finite Group Databasebeta

← D3×#4994 #11808265

Subgroups — D3×#4994 #11808265

Order 1152.

1909 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7#10592693C211yesmaximal, characteristic, complemented
8C3×#4994C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10#10591347C211yesmaximal, characteristic, complemented
11#10591319C211yesmaximal, characteristic, complemented
12#10591311C211yesmaximal, characteristic, complemented
13#10591311C211yesmaximal, characteristic, complemented
14#10591308C211yesmaximal, characteristic, complemented
15#10591306C211yesmaximal, characteristic, complemented
16C2×#4994—31nomaximal
17D3×#396—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic, complemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C2×#3750C2211yescharacteristic, complemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
35C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
36C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C3×D3×C4⋊C4—24no—
40C2×#3724C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×Dic3⋊Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50D3×(C2×D3)⋊C4—24no—
51D3×(C2×D3)⋊C4—24no—
52D3×(C2×D3)⋊C4—24no—
53D3×C4⋊Dic3—24no—
54D3×Dic3⋊C4—24no—
55#63658C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C22×C3×C4⋊C4—31no—
60C22×(C2×D3)⋊C4—31no—
61C22×(C2×D3)⋊C4—31no—
62C22×(C2×D3)⋊C4—31no—
63C22×C4⋊Dic3—31no—
64C22×Dic3⋊C4—31no—
65C2×D3×C4⋊C4—31no—
66C2×D3×C4⋊C4—31no—
67C2×D3×C4⋊C4D311yescharacteristic, complemented
68C2×D3×C22⋊C4—31no—
69C2×D3×C22⋊C4—31no—
70C2×D3×C22⋊C4—31no—
71C3×#396—31no—
72C2×C3⋊#95—31no—
73#4994—31no—
74#4994—31no—
75#4994—31no—
76#4994—31no—
77#4994—31no—
78#4994—31no—
79#4994—31no—
80#4994—31no—
81#4994—31no—
82#4994—31no—
83#4994—61no—
84#4994D311yescharacteristic, direct product factor
85#4948—31no—
86#4948—31no—
87#4948—31no—
88#4676—31no—
89D3×#95—31no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32—22no—
99C22×D32Q814yes—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3D414yes—
120C2×C3×C4×D3D414yes—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3D414yes—
130C32×C4⋊C4—22no—
131#3752—22no—
132#3752—22no—
133#3752—22no—
134C4⋊(C3⋊Dic3)—22no—
135#3750—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×C4⋊Dic3—22no—
140C3×C4⋊Dic3—22no—
141C3×Dic3⋊C4—22no—
142C3×Dic3⋊C4—22no—
143C3×Dic3⋊C4—22no—
144#3724—22no—
145Dic3⋊Dic3—22no—
146Dic3⋊Dic3—22no—
147Dic3⋊Dic3—22no—
148#3722—22no—
149#3722—22no—
150#3722—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154C2×#396—91noSylow
155C24×D3—31no—
156C24×D3—31no—
157C23×C3×C4—31no—
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C23×Dic3—31no—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3C2×D311yescharacteristic
167C22×C4×D3C2×D311yescharacteristic
168C22×C4×D3C2×D311yescharacteristic
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—31no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—64no—
176C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
177C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—61no—
200C2×(C2×D3)⋊C4—61no—
201C2×(C2×D3)⋊C4—61no—
202C2×(C2×D3)⋊C4—64no—
203C2×(C2×D3)⋊C4—64no—
204C2×(C2×D3)⋊C4—64no—
205C2×(C2×D3)⋊C4C2×D311yescharacteristic
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—61no—
214C2×C4⋊Dic3—64no—
215C2×C4⋊Dic3C2×D311yescharacteristic, complemented
216C2×C4⋊Dic3C2×D311yescharacteristic, complemented
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—61no—
225C2×Dic3⋊C4—64no—
226C2×Dic3⋊C4C2×D311yescharacteristic, complemented
227C2×Dic3⋊C4C2×D311yescharacteristic, complemented
228C2×Dic3⋊C4C2×D311yescharacteristic, complemented
229D3×C4⋊C4—24no—
230D3×C4⋊C4—64no—
231D3×C4⋊C4—64no—
232D3×C22⋊C4—64no—
233D3×C22⋊C4—64no—
234D3×C22⋊C4—64no—
235C3×#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—61no—
243C3⋊#95C2×D311yescharacteristic, complemented
244C23×C32C2411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3⋊D3—21no—
247C22×C3⋊D3—21no—
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3C2×Q812yes—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D412yes—
259C22×C3×D3C2×D412yes—
260C22×C3×D3C2×D412yes—
261C22×C3×D3C2×Q812yes—
262C22×C3×D3C2×Q812yes—
263C22×C3×D3#4112yes—
264C22×C3×D3#4112yes—
265C22×C3×D3#4112yes—
266C2×D32—28no—
267C2×D32—28no—
268C2×D32—28no—
269C2×D32—44no—
270C2×D32—44no—
271C2×D32—44no—
272C2×D32—44no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4C2×D412yes—
281C2×C32×C4C2×D412yes—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3—21no—
288C2×C3⋊Dic3—21no—
289C2×C3⋊Dic3—21no—
290C2×C3⋊Dic3C2×D412yes—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D412yes—
307C2×C3×Dic3C2×D412yes—
308C2×C3×Dic3C2×D412yes—
309C3×C4×D3—28no—
310C3×C4×D3—28no—
311C3×C4×D3—44no—
312D3×Dic3—28no—
313D3×Dic3—44no—
314D3×Dic3—44no—
315C22×C4⋊C4—31no—
316C22×C4⋊C4—91no—
317C22×C4⋊C4—91no—
318C22×C22⋊C4—91no—
319C22×C22⋊C4—91no—
320C22×C22⋊C4—91no—
321#396—31no—
322#396—91no—
323#396—91no—
324#396—91no—
325#396—91no—
326#396—91no—
327#396—91no—
328#396—91no—
329C2×#95—91no—
330C24×C3—31no—
331C24×C3—31no—
332C23×D3—31no—
333C23×D3—31no—
334C23×D3—34no—
335C23×D3—34no—
336C23×D3—61no—
337C23×D3—62no—
338C23×D3—62no—
339C23×D3—62no—
340C23×D3—62no—
341C23×D3—62no—
342C23×D3—62no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—62no—
346C23×D3—62no—
347C23×D3—62no—
348C23×D3—62no—
349C23×D3C22×D311yescharacteristic
350C23×D3C22×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—34no—
358C22×C3×C4—34no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—62no—
363C22×C3×C4—62no—
364C22×C3×C4—62no—
365C22×C3×C4—62no—
366C22×C3×C4—62no—
367C22×C3×C4—62no—
368C22×C3×C4—62no—
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—34no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—61no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—62no—
386C22×Dic3—62no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—62no—
391C22×Dic3—62no—
392C22×Dic3—62no—
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×C4×D3—22no—
400C2×C4×D3—22no—
401C2×C4×D3—22no—
402C2×C4×D3—22no—
403C2×C4×D3—22no—
404C2×C4×D3—22no—
405C2×C4×D3—22no—
406C2×C4×D3—34no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3—62no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3D1214yes—
416C2×C4×D3#6714yes—
417C3×C4⋊C4—22no—
418C3×C4⋊C4—22no—
419C3×C4⋊C4—42no—
420C3×C4⋊C4—62no—
421C3×C4⋊C4—62no—
422C3×C4⋊C4—62no—
423C3×C4⋊C4—62no—
424C3×C4⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431(C2×D3)⋊C4—22no—
432(C2×D3)⋊C4—22no—
433(C2×D3)⋊C4—22no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—122no—
451(C2×D3)⋊C4—122no—
452C4⋊Dic3—22no—
453C4⋊Dic3—22no—
454C4⋊Dic3—62no—
455C4⋊Dic3—62no—
456C4⋊Dic3—62no—
457C4⋊Dic3—62no—
458C4⋊Dic3—62no—
459C4⋊Dic3—122no—
460Dic3⋊C4—22no—
461Dic3⋊C4—22no—
462Dic3⋊C4—22no—
463Dic3⋊C4—62no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4—62no—
467Dic3⋊C4—62no—
468Dic3⋊C4—62no—
469Dic3⋊C4—62no—
470Dic3⋊C4—122no—
471C22×C32C22×D411yescharacteristic
472C22×C32C22×D411yescharacteristic
473C22×C32C22×D411yescharacteristic
474C22×C32C22×Q811yescharacteristic
475C22×C32C2×#4111yescharacteristic
476C22×C32C2×#4111yescharacteristic
477C22×C32C2×#4111yescharacteristic
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3#12114yes—
493C2×C3×D3#12114yes—
494C2×C3×D3#12114yes—
495C2×C3×D3C22⋊Q814yes—
496C2×C3×D3C22⋊Q814yes—
497C2×C3×D3C22⋊Q814yes—
498C2×C3×D3#12614yes—
499D32—416no—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—41no—
503C3⋊Dic3—22no—
504C3⋊Dic3—41no—
505C3⋊Dic3—41no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—41no—
510C3×Dic3—41no—
511C3×Dic3—41no—
512C25—91no—
513C23×C4—31no—
514C23×C4—31no—
515C23×C4—31no—
516C23×C4—91no—
517C23×C4—91no—
518C23×C4—91no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—64no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—184no—
532C2×C4⋊C4—184no—
533C2×C4⋊C4D3211yescharacteristic, complemented
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4—91no—
544C2×C22⋊C4—91no—
545C2×C22⋊C4—91no—
546C2×C22⋊C4—184no—
547C2×C22⋊C4—184no—
548C2×C22⋊C4—184no—
549#95—31no—
550#95—91no—
551#95—91no—
552#95—91no—
553C23×C3—21no—
554C23×C3—32no—
555C23×C3—32no—
556C23×C3—32no—
557C23×C3—32no—
558C23×C3—32no—
559C23×C3—32no—
560C23×C3—32no—
561C23×C3—32no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3C23×D311yescharacteristic
569C23×C3C23×D311yescharacteristic
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—32no—
577C22×D3—32no—
578C22×D3—62no—
579C22×D3—68no—
580C22×D3—68no—
581C22×D3—68no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—68no—
595C22×D3—68no—
596C22×D3—68no—
597C22×D3—121no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—124no—
604C22×D3—124no—
605C22×D3—124no—
606C22×D3—124no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3C2×D1212yes—
612C22×D3#23512yes—
613C22×D3D3×D412yes—
614C22×D3#23712yes—
615C22×D3D3×Q812yes—
616C22×D3D3×Q812yes—
617C22×D3#23912yes—
618C22×D3C2×#6712yes—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—22no—
634C2×C3×C4—22no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—32no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—41no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—68no—
646C2×C3×C4—68no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—124no—
663C2×C3×C4C2×D1212yes—
664C2×C3×C4D3×D412yes—
665C2×C3×C4D3×D412yes—
666C2×C3×C4C2×#6712yes—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—21no—
677C2×Dic3—21no—
678C2×Dic3—21no—
679C2×Dic3—21no—
680C2×Dic3—21no—
681C2×Dic3—21no—
682C2×Dic3—32no—
683C2×Dic3—32no—
684C2×Dic3—62no—
685C2×Dic3—68no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—121no—
703C2×Dic3—121no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—121no—
707C2×Dic3—121no—
708C2×Dic3—121no—
709C2×Dic3—121no—
710C2×Dic3—124no—
711C2×Dic3—124no—
712C2×Dic3C2×D1212yes—
713C2×Dic3D3×D412yes—
714C2×Dic3C2×#6712yes—
715C4×D3—28no—
716C4×D3—28no—
717C4×D3—44no—
718C4×D3—68no—
719C4×D3—124no—
720C4×D3—124no—
721C2×C32C2×#12111yescharacteristic
722C2×C32C2×#12111yescharacteristic
723C2×C32C2×#12111yescharacteristic
724C2×C32C2×C22⋊Q811yescharacteristic
725C2×C32C2×C22⋊Q811yescharacteristic
726C2×C32C2×C22⋊Q811yescharacteristic
727C2×C32C2×#12611yescharacteristic
728C3⋊D3—42no—
729C3×D3—42no—
730C3×D3#39618yescomplemented
731C24—31no—
732C24—31no—
733C24—94no—
734C24—91no—
735C24—182no—
736C24—182no—
737C24—182no—
738C24—182no—
739C24—182no—
740C24—182no—
741C22×C4—31no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—34no—
745C22×C4—34no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—62no—
750C22×C4—62no—
751C22×C4—62no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—62no—
755C22×C4—62no—
756C22×C4—94no—
757C22×C4—91no—
758C22×C4—91no—
759C22×C4—91no—
760C22×C4—182no—
761C22×C4—182no—
762C22×C4—182no—
763C22×C4—182no—
764C22×C4—182no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—182no—
768C22×C4C2×D3211yescharacteristic
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—22no—
772C4⋊C4—62no—
773C4⋊C4—62no—
774C4⋊C4—62no—
775C4⋊C4—62no—
776C4⋊C4—62no—
777C4⋊C4—182no—
778C4⋊C4—182no—
779C4⋊C4—182no—
780C4⋊C4—182no—
781C4⋊C4—182no—
782C4⋊C4—182no—
783C22⋊C4—62no—
784C22⋊C4—62no—
785C22⋊C4—62no—
786C22⋊C4—182no—
787C22⋊C4—182no—
788C22⋊C4—182no—
789C22⋊C4—182no—
790C22⋊C4—182no—
791C22⋊C4—182no—
792C22⋊C4—182no—
793C22⋊C4—182no—
794C22⋊C4—182no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—34no—
803C22×C3—34no—
804C22×C3—34no—
805C22×C3—34no—
806C22×C3—34no—
807C22×C3—34no—
808C22×C3—34no—
809C22×C3—62no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3C22×D1211yescharacteristic
817C22×C3C2×#23511yescharacteristic
818C22×C3C2×D3×D411yescharacteristic
819C22×C3C2×D3×D411yescharacteristic
820C22×C3C2×D3×D411yescharacteristic
821C22×C3C2×D3×D411yescharacteristic
822C22×C3C2×#23711yescharacteristic
823C22×C3C2×D3×Q811yescharacteristic
824C22×C3C2×D3×Q811yescharacteristic
825C22×C3C2×#23911yescharacteristic
826C22×C3D3×#4111yescharacteristic
827C22×C3D3×#4111yescharacteristic
828C22×C3D3×#4111yescharacteristic
829C22×C3C22×#6711yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—1216no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—1216no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3#89514yes—
861C2×D3#89614yes—
862C2×D3#89714yes—
863C2×D3#89814yes—
864C2×D3#93014yes—
865C2×D3#93914yes—
866C2×D3#94614yes—
867C3×C4—22no—
868C3×C4—22no—
869C3×C4—22no—
870C3×C4—22no—
871C3×C4—42no—
872C3×C4—42no—
873C3×C4—41no—
874C3×C4—41no—
875C3×C4—62no—
876C3×C4—62no—
877C3×C4—62no—
878C3×C4—81no—
879C3×C4—121no—
880C3×C4—121no—
881C3×C4—121no—
882Dic3—22no—
883Dic3—22no—
884Dic3—22no—
885Dic3—41no—
886Dic3—41no—
887Dic3—41no—
888Dic3—62no—
889Dic3—62no—
890Dic3—122no—
891Dic3—121no—
892Dic3—121no—
893Dic3—121no—
894Dic3—121no—
895Dic3—241no—
896Dic3—241no—
897C32C2×#39611yescharacteristic, complemented, Sylow
898C23—32no—
899C23—32no—
900C23—32no—
901C23—32no—
902C23—32no—
903C23—32no—
904C23—32no—
905C23—32no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—92no—
913C23—188no—
914C23—188no—
915C23—188no—
916C23—181no—
917C23—181no—
918C23—181no—
919C23—181no—
920C23—181no—
921C23—181no—
922C23—364no—
923C23—364no—
924C23—364no—
925C23—364no—
926C23C22×D3211yescharacteristic
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—32no—
937C2×C4—68no—
938C2×C4—68no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—61no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—61no—
947C2×C4—61no—
948C2×C4—61no—
949C2×C4—61no—
950C2×C4—61no—
951C2×C4—61no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—92no—
955C2×C4—124no—
956C2×C4—188no—
957C2×C4—181no—
958C2×C4—181no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—364no—
966C2×C4—364no—
967C2×C4D3×D1212yes—
968C2×C4D3×#6712yes—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—38no—
977C2×C3—122no—
978C2×C3C2×#89511yescharacteristic
979C2×C3C2×#89611yescharacteristic
980C2×C3C2×#89711yescharacteristic
981C2×C3C2×#89811yescharacteristic
982C2×C3D3×#12111yescharacteristic
983C2×C3D3×#12111yescharacteristic
984C2×C3D3×#12111yescharacteristic
985C2×C3D3×C22⋊Q811yescharacteristic
986C2×C3D3×C22⋊Q811yescharacteristic
987C2×C3D3×C22⋊Q811yescharacteristic
988C2×C3D3×#12611yescharacteristic
989C2×C3C2×#93011yescharacteristic
990C2×C3C2×#93911yescharacteristic
991C2×C3C2×#94611yescharacteristic
992D3—42no—
993D3—122no—
994D3—122no—
995D3—242no—
996D3#499418yesdirect product factor
997C22—34no—
998C22—34no—
999C22—34no—
1000C22—34no—
1001C22—34no—
1002C22—34no—
1003C22—34no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—182no—
1012C22—182no—
1013C22—182no—
1014C22—3616no—
1015C22—361no—
1016C22—361no—
1017C22—361no—
1018C22—361no—
1019C22C2×D3×D1211yescharacteristic
1020C22D3×#23511yescharacteristic
1021C22D32×D411yescharacteristic
1022C22D3×#23711yescharacteristic
1023C22D32×Q811yescharacteristic
1024C22D3×#23911yescharacteristic
1025C22C2×D3×#6711yescharacteristic
1026C4—22no—
1027C4—22no—
1028C4—41no—
1029C4—62no—
1030C4—62no—
1031C4—62no—
1032C4—121no—
1033C4—121no—
1034C4—121no—
1035C4—182no—
1036C4—361no—
1037C4—361no—
1038C3—21no—
1039C3D3×#39611yescharacteristic, complemented
1040C3C2×#499411yescharacteristic, complemented
1041C2—38no—
1042C2—122no—
1043C2—362no—
1044C2D3×#89511yescharacteristic
1045C2D3×#89611yescharacteristic
1046C2D3×#89711yescharacteristic
1047C2D3×#89811yescharacteristic
1048C2D3×#93011yescharacteristic
1049C2D3×#93911yescharacteristic
1050C2D3×#94611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×D32C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×C4⋊C4C2semidirect
5. C2×D3×C4⋊Dic3C2semidirect
6. C2×D3×Dic3⋊C4C2semidirect
7. #10592693C2semidirect
8. C3×#4994C2semidirect
9. D3×C3⋊#95C2semidirect
10. #10591347C2semidirect
11. #10591319C2semidirect
12. #10591311C2semidirect
13. #10591311C2semidirect
14. #10591308C2semidirect
15. #10591306C2semidirect
25. C2×C32×C4⋊C4C22semidirect
29. C2×C4⋊(C3⋊Dic3)C22semidirect
30. C2×#3750C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×C4⋊Dic3C22semidirect
36. C2×C3×Dic3⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
67. C2×D3×C4⋊C4D3semidirect
84. #4994D3direct (N × H)
176. C2×C3×C4⋊C4C2×D3semidirect
177. C2×C3×C4⋊C4C2×D3semidirect
215. C2×C4⋊Dic3C2×D3semidirect
216. C2×C4⋊Dic3C2×D3semidirect
226. C2×Dic3⋊C4C2×D3semidirect
227. C2×Dic3⋊C4C2×D3semidirect
228. C2×Dic3⋊C4C2×D3semidirect
243. C3⋊#95C2×D3semidirect
533. C2×C4⋊C4D32semidirect
730. C3×D3#396semidirect
897. C32C2×#396semidirect
996. D3#4994direct (N × H)
1039. C3D3×#396semidirect
1040. C3C2×#4994semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×D3×(C2×D3)⋊C42
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
#105926932
C3×#49942
D3×C3⋊#952
#105913472
#105913192
#105913112
#105913082
#105913062
C2×#49943
D3×#3963