Finite Group Databasebeta

← C3×#73681 #11817720

Subgroups — C3×#73681 #11817720

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#876C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#4993C211yesmaximal, characteristic, complemented
5C3×#4993C211yesmaximal, characteristic, complemented
6C3×#4990C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8C3×#4940C211yesmaximal, characteristic, complemented
9C3×#4940C211yesmaximal, characteristic, complemented
10C3×#4939C211yesmaximal, characteristic
11C3×#4933C211yesmaximal, characteristic, complemented
12C3×#4672C211yesmaximal, characteristic
13C3×#4665C211yesmaximal, characteristic
14C3×#4657C211yesmaximal, characteristic, complemented
15C3×#4647C211yesmaximal, characteristic, complemented
16C3×#2479—31nomaximal
17#73681C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C42C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#876—24no—
46C3×#872—24no—
47C32×#95C2211yescharacteristic
48C32×#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×#126—31no—
56C2×C3×#117—31no—
57C2×#876C2×C311yescharacteristic, complemented
58C2×#872C2×C311yescharacteristic, complemented
59C3×#399—31no—
60C3×#399—31no—
61C3×#398—31no—
62C3×#394—31no—
63C3×#390—31no—
64C3×#389—31no—
65C3×#388—31no—
66C3×#388—31no—
67C3×#388—31no—
68C3×#387—31no—
69C3×#386—31no—
70C3×#385—31no—
71C3×C4×C4⋊C4—21no—
72C3×C4×C4⋊C4D311yescharacteristic, complemented
73C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
74#4993C2×C311yescharacteristic, complemented
75#4993C2×C311yescharacteristic, complemented
76#4990C2×C311yescharacteristic, complemented
77#4989C2×C311yescharacteristic, complemented
78#4940C2×C311yescharacteristic, complemented
79#4940C2×C311yescharacteristic, complemented
80#4939C2×C311yescharacteristic
81#4933C2×C311yescharacteristic, complemented
82#4672C2×C311yescharacteristic
83#4665C2×C311yescharacteristic
84#4657C2×C311yescharacteristic, complemented
85#4647C2×C311yescharacteristic, complemented
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12—41no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C32×C4⋊C4—22no—
108C32×C4⋊C4—22no—
109C32×C42—22no—
110C32×C42—22no—
111C32×C42—22no—
112C3×(C2×D3)⋊C4—22no—
113C3×(C2×D3)⋊C4—22no—
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—22no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—41no—
122C3×(C2×D3)⋊C4—41no—
123C3×C4⋊Dic3—41no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×Dic3⋊C4—22no—
128C3×Dic3⋊C4—41no—
129C3×Dic3⋊C4—41no—
130C3×Dic3⋊C4D414yescomplemented
131C3×C4×Dic3—22no—
132#2479—31noSylow
133C22×C3×D4—31no—
134C23×C3×C4—31no—
135C22×D12C22×C311yescharacteristic
136C22×C4×D3C22×C311yescharacteristic
137C3×#126—64no—
138C3×#117—64no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C2×D311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C4⋊C4C22×C311yescharacteristic
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—21no—
165C2×C3×C42—21no—
166C2×C3×C42—21no—
167C2×C3×C42—31no—
168C2×C3×C42C2×D311yescharacteristic
169C2×C3×C42C2×D311yescharacteristic
170C2×C3×C42C2×D311yescharacteristic
171C2×C3×C42C22×C311yescharacteristic
172C2×C3×C42C22×C311yescharacteristic
173C2×C3×C42C22×C311yescharacteristic
174C2×(C2×D3)⋊C4C22×C311yescharacteristic
175C2×(C2×D3)⋊C4C22×C311yescharacteristic
176C2×(C2×D3)⋊C4C22×C311yescharacteristic
177C2×(C2×D3)⋊C4C22×C311yescharacteristic
178C2×(C2×D3)⋊C4C22×C311yescharacteristic
179C2×(C2×D3)⋊C4C22×C311yescharacteristic
180C2×(C2×D3)⋊C4C22×C311yescharacteristic
181C2×(C2×D3)⋊C4C22×C311yescharacteristic
182C2×(C2×D3)⋊C4C22×C311yescharacteristic
183C2×(C2×D3)⋊C4C22×C311yescharacteristic
184C2×(C2×D3)⋊C4C22×C311yescharacteristic
185C2×C4⋊Dic3C22×C311yescharacteristic
186C2×Dic3⋊C4C22×C311yescharacteristic
187C2×Dic3⋊C4C22×C311yescharacteristic
188C2×Dic3⋊C4C22×C311yescharacteristic
189C2×Dic3⋊C4C22×C311yescharacteristic
190C2×Dic3⋊C4C22×C311yescharacteristic
191C2×Dic3⋊C4C22×C311yescharacteristic
192C2×Dic3⋊C4C22×C311yescharacteristic
193C2×C4×Dic3C22×C311yescharacteristic
194#876—24no—
195#872—24no—
196C3×#95—21no—
197C3×#95—21no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95C2×D311yescharacteristic
205C3×#95C2×D311yescharacteristic
206C3×#95C22×C311yescharacteristic
207C3×#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C3⋊#95C22×C311yescharacteristic
213C3⋊#95C22×C311yescharacteristic
214C23×C32C2411yescharacteristic
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3#4112yes—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D412yes—
247C2×C32×C4#4112yes—
248C2×C32×C4#4112yes—
249C2×C32×C4#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D412yes—
267C2×C3×Dic3C2×D412yes—
268C3×D12—44no—
269C3×C4×D3—28no—
270C2×#126—31no—
271C2×#117—31no—
272#399—31no—
273#399—31no—
274#398—31no—
275#394—31no—
276#390—31no—
277#389—31no—
278#388—31no—
279#388—31no—
280#388—31no—
281#387—31no—
282#386—31no—
283#385—31no—
284C4×C4⋊C4C3×D311yescharacteristic, complemented
285C24×C3—31no—
286C24×C3—31no—
287C23×D3C23×C311yescharacteristic
288C23×D3C23×C311yescharacteristic
289C2×C3×D4—62no—
290C2×C3×D4—62no—
291C2×C3×D4—121no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—62no—
306C22×C3×C4—62no—
307C22×C3×C4—62no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C22×C3×C4C23×C311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C311yescharacteristic
327C22×Dic3C23×C311yescharacteristic
328C2×D12—22no—
329C2×D12—22no—
330C2×D12—41no—
331C2×C4×D3—22no—
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—22no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C4⋊C4—22no—
340C3×C4⋊C4—34no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C4⋊C4—121no—
346C3×C4⋊C4—121no—
347C3×C4⋊C4—121no—
348C3×C22⋊C4—62no—
349C3×C22⋊C4—62no—
350C3×C22⋊C4—62no—
351C3×C22⋊C4—62no—
352C3×C22⋊C4—62no—
353C3×C22⋊C4—62no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—62no—
356C3×C22⋊C4—62no—
357C3×C22⋊C4—121no—
358C3×C22⋊C4—121no—
359C3×C42—24no—
360C3×C42—22no—
361C3×C42—22no—
362C3×C42—22no—
363C3×C42—22no—
364C3×C42—22no—
365C3×C42—22no—
366C3×C42—42no—
367C3×C42—42no—
368C3×C42—62no—
369(C2×D3)⋊C4—22no—
370(C2×D3)⋊C4—22no—
371(C2×D3)⋊C4—22no—
372(C2×D3)⋊C4—22no—
373(C2×D3)⋊C4—22no—
374(C2×D3)⋊C4—22no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—22no—
378(C2×D3)⋊C4—41no—
379(C2×D3)⋊C4—41no—
380C4⋊Dic3—41no—
381Dic3⋊C4—22no—
382Dic3⋊C4—22no—
383Dic3⋊C4—22no—
384Dic3⋊C4—22no—
385Dic3⋊C4—41no—
386Dic3⋊C4—41no—
387Dic3⋊C4C3×D414yescomplemented
388C4×Dic3—22no—
389C22×C32C22×D411yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32H(5,𝔽2)11yescharacteristic
395C22×C322−1+411yescharacteristic
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C32×C4—22no—
411C32×C4—22no—
412C32×C4—22no—
413C32×C4—22no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C22×D4—31no—
424C23×C4—31no—
425#126—64no—
426#117—64no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4C2×C3×D311yescharacteristic
436C2×C4⋊C4C2×C3×D311yescharacteristic
437C2×C22⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C42—31no—
449C2×C42C2×C3×D311yescharacteristic
450C2×C42C2×C3×D311yescharacteristic
451C2×C42C2×C3×D311yescharacteristic
452#95—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95C2×C3×D311yescharacteristic
459#95C2×C3×D311yescharacteristic
460C23×C3—21no—
461C23×C3—32no—
462C23×C3—61no—
463C23×C3—61no—
464C23×C3—61no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—61no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3C23×D311yescharacteristic
476C23×C3C24×C311yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3C3×#4112yes—
491C3×D4—124no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—68no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4#23512yes—
567C2×C3×C4#23512yes—
568C2×C3×C4#23512yes—
569C2×C3×C4D3×D412yes—
570C2×C3×C4C2×C3×D412yes—
571C2×C3×C4C3×#4112yes—
572C2×C3×C4C3×#4112yes—
573C2×C3×C4C3×#4112yes—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3C2×C3×D412yes—
591C2×Dic3C2×C3×D412yes—
592D12—44no—
593C4×D3—28no—
594C2×C32#52511yescharacteristic
595C2×C32#52911yescharacteristic
596C2×C32#54211yescharacteristic
597C2×C32#54711yescharacteristic
598C2×C32#55011yescharacteristic
599C2×C32#55111yescharacteristic
600C2×C32#55211yescharacteristic
601C3×D3—42no—
602C3×D3—81no—
603C24—31no—
604C24—31no—
605C2×D4—62no—
606C2×D4—62no—
607C2×D4—121no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—62no—
615C22×C4—62no—
616C22×C4—62no—
617C22×C4C22×C3×D311yescharacteristic
618C22×C4C22×C3×D311yescharacteristic
619C22×C4C22×C3×D311yescharacteristic
620C22×C4C22×C3×D311yescharacteristic
621C22×C4C22×C3×D311yescharacteristic
622C22×C4C22×C3×D311yescharacteristic
623C22×C4C22×C3×D311yescharacteristic
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—34no—
627C4⋊C4—62no—
628C4⋊C4—62no—
629C4⋊C4—62no—
630C4⋊C4—62no—
631C4⋊C4—121no—
632C4⋊C4—121no—
633C4⋊C4—121no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—62no—
637C22⋊C4—62no—
638C22⋊C4—62no—
639C22⋊C4—62no—
640C22⋊C4—62no—
641C22⋊C4—62no—
642C22⋊C4—62no—
643C22⋊C4—121no—
644C22⋊C4—121no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—62no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—62no—
657C22×C3—62no—
658C22×C3—62no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×#23511yescharacteristic
671C22×C3C2×#23511yescharacteristic
672C22×C3C2×#23511yescharacteristic
673C22×C3C2×D3×D411yescharacteristic
674C22×C3#100711yescharacteristic
675C22×C3D3×#4111yescharacteristic
676C22×C3#100911yescharacteristic
677C22×C3C22×C3×D411yescharacteristic
678C22×C3C2×C3×#4111yescharacteristic
679C22×C3C2×C3×#4111yescharacteristic
680C22×C3C2×C3×#4111yescharacteristic
681C22×C3C2×C3×#4111yescharacteristic
682C22×C3C3×H(5,𝔽2)11yescharacteristic
683C22×C3C3×2−1+411yescharacteristic
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—22no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C3×C4—24no—
699C3×C4—24no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—22no—
703C3×C4—22no—
704C3×C4—22no—
705C3×C4—22no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4—42no—
711C3×C4—42no—
712C3×C4—42no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725Dic3—22no—
726Dic3—22no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731C32#247911yescharacteristic, complemented, Sylow
732C23—32no—
733C23—61no—
734C23—61no—
735C23—61no—
736C23—61no—
737C23—61no—
738C23—61no—
739C23—61no—
740C23—61no—
741C23—61no—
742C23—61no—
743C23—61no—
744C23—61no—
745C23—61no—
746C23C23×C3×D311yescharacteristic
747D4—124no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—68no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4C3×#23512yes—
785C2×C4C3×#23512yes—
786C2×C4C3×#23512yes—
787C2×C4C3×D3×D412yes—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3#547911yescharacteristic
798C2×C3#550711yescharacteristic
799C2×C3#552711yescharacteristic
800C2×C3#554711yescharacteristic
801C2×C3#555311yescharacteristic
802C2×C3#558111yescharacteristic
803C2×C3#558211yescharacteristic
804C2×C3C3×#52511yescharacteristic
805C2×C3C3×#52911yescharacteristic
806C2×C3C3×#54211yescharacteristic
807C2×C3C3×#54711yescharacteristic
808C2×C3C3×#55011yescharacteristic
809C2×C3C3×#55111yescharacteristic
810C2×C3C3×#55211yescharacteristic
811D3—42no—
812D3—81no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—121no—
826C22—121no—
827C22C2×C3×#23511yescharacteristic
828C22C2×C3×#23511yescharacteristic
829C22C2×C3×#23511yescharacteristic
830C22C2×C3×D3×D411yescharacteristic
831C22C3×#100711yescharacteristic
832C22C3×D3×#4111yescharacteristic
833C22C3×#100911yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—22no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—62no—
842C4—62no—
843C4—121no—
844C4—121no—
845C4—121no—
846C4—121no—
847C3—21no—
848C3#7368111yescharacteristic, direct product factor
849C3C3×#247911yescharacteristic, complemented
850C2—122no—
851C2—241no—
852C2C3×#547911yescharacteristic
853C2C3×#550711yescharacteristic
854C2C3×#552711yescharacteristic
855C2C3×#554711yescharacteristic
856C2C3×#555311yescharacteristic
857C2C3×#558111yescharacteristic
858C2C3×#558211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2479
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#876C2semidirect
2. C2×C3×#872C2semidirect
3. C32×C4×C4⋊C4C2semidirect
4. C3×#4993C2semidirect
5. C3×#4993C2semidirect
6. C3×#4990C2semidirect
7. C3×#4989C2semidirect
8. C3×#4940C2semidirect
9. C3×#4940C2semidirect
11. C3×#4933C2semidirect
14. C3×#4657C2semidirect
15. C3×#4647C2semidirect
17. #73681C3direct (N × H)
57. C2×#876C2×C3semidirect
58. C2×#872C2×C3semidirect
72. C3×C4×C4⋊C4D3semidirect
73. C3×C4×C4⋊C4C2×C3semidirect
74. #4993C2×C3semidirect
75. #4993C2×C3semidirect
76. #4990C2×C3semidirect
77. #4989C2×C3semidirect
78. #4940C2×C3semidirect
79. #4940C2×C3semidirect
81. #4933C2×C3semidirect
84. #4657C2×C3semidirect
85. #4647C2×C3semidirect
130. C3×Dic3⋊C4D4semidirect
284. C4×C4⋊C4C3×D3semidirect
387. Dic3⋊C4C3×D4semidirect
731. C32#2479semidirect
848. C3#73681direct (N × H)
849. C3C3×#2479semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8762
C2×C3×#8722
C32×C4×C4⋊C42
C3×#49932
C3×#49902
C3×#49892
C3×#49402
C3×#49392
C3×#49332
C3×#46722
C3×#46652
C3×#46572
C3×#46472
C3×#24793
#736813