Finite Group Databasebeta

← C3×#73778 #11808664

Subgroups — C3×#73778 #11808664

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
3C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#4994C211yesmaximal, characteristic
5C3×#4993C211yesmaximal, characteristic
6C3×#4983C211yesmaximal, characteristic, complemented
7C3×#4979C211yesmaximal, characteristic, complemented
8C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
9C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
10C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#4676C211yesmaximal, characteristic
13C3×#4673C211yesmaximal, characteristic
14C3×#4658C211yesmaximal, characteristic, complemented
15C3×#4657C211yesmaximal, characteristic, complemented
16C3×#2396—31nomaximal
17#73778C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#872—24no—
44C3×C4×Dic6—24no—
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C2×C3×C4×Q8—31no—
56C2×C3×#117—31no—
57C2×#872C2×C311yescharacteristic
58C2×C4×Dic6C2×C311yescharacteristic, complemented
59C3×#400—31no—
60C3×#399—31no—
61C3×#398—31no—
62C3×#398—31no—
63C3×#396—31no—
64C3×#396—31no—
65C3×#395—31no—
66C3×#393—31no—
67C3×C4×C4⋊C4—21no—
68C3×C4×C4⋊C4—31no—
69C3×C4×C4⋊C4—31no—
70C3×C4×C4⋊C4D311yescharacteristic, complemented
71C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
72C3×C4×C22⋊C4—31no—
73C3×C4×C22⋊C4—31no—
74#4994C2×C311yescharacteristic
75#4993C2×C311yescharacteristic
76#4983C2×C311yescharacteristic, complemented
77#4979C2×C311yescharacteristic, complemented
78C4×(C2×D3)⋊C4C2×C311yescharacteristic
79C4×(C2×D3)⋊C4C2×C311yescharacteristic
80C4×Dic3⋊C4C2×C311yescharacteristic, complemented
81C4×Dic3⋊C4C2×C311yescharacteristic, complemented
82#4676C2×C311yescharacteristic
83#4673C2×C311yescharacteristic
84#4658C2×C311yescharacteristic, complemented
85#4657C2×C311yescharacteristic, complemented
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3Q814yescomplemented
104C2×C3×Dic6—22no—
105C2×C3×Dic6—22no—
106C2×C3×Dic6—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×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×Dic3⋊C4—22no—
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×Dic3⋊C4—22no—
126C3×Dic3⋊C4—22no—
127C3×C4×Dic3—22no—
128C3×C4×Dic3—22no—
129C3×C4×Dic3D414yes—
130#2396—31noSylow
131C22×C3×Q8—31no—
132C23×C3×C4—31no—
133C22×C4×D3C22×C311yescharacteristic
134C22×Dic6C22×C311yescharacteristic
135C3×C4×Q8—64no—
136C3×#117—64no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
149C2×C3×C4⋊C4C2×D311yescharacteristic
150C2×C3×C4⋊C4C22×C311yescharacteristic
151C2×C3×C4⋊C4C22×C311yescharacteristic
152C2×C3×C22⋊C4—31no—
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×C42—21no—
159C2×C3×C42—21no—
160C2×C3×C42—21no—
161C2×C3×C42—31no—
162C2×C3×C42—31no—
163C2×C3×C42—31no—
164C2×C3×C42C2×D311yescharacteristic
165C2×C3×C42C2×D311yescharacteristic
166C2×C3×C42C2×D311yescharacteristic
167C2×C3×C42C22×C311yescharacteristic
168C2×C3×C42C22×C311yescharacteristic
169C2×C3×C42C22×C311yescharacteristic
170C2×(C2×D3)⋊C4C22×C311yescharacteristic
171C2×(C2×D3)⋊C4C22×C311yescharacteristic
172C2×(C2×D3)⋊C4C22×C311yescharacteristic
173C2×(C2×D3)⋊C4C22×C311yescharacteristic
174C2×(C2×D3)⋊C4C22×C311yescharacteristic
175C2×(C2×D3)⋊C4C22×C311yescharacteristic
176C2×C4⋊Dic3C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×Dic3⋊C4C22×C311yescharacteristic
179C2×Dic3⋊C4C22×C311yescharacteristic
180C2×Dic3⋊C4C22×C311yescharacteristic
181C2×Dic3⋊C4C22×C311yescharacteristic
182C2×Dic3⋊C4C22×C311yescharacteristic
183C2×Dic3⋊C4C22×C311yescharacteristic
184C2×Dic3⋊C4C22×C311yescharacteristic
185C2×C4×Dic3C22×C311yescharacteristic
186C2×C4×Dic3C22×C311yescharacteristic
187C2×C4×Dic3C22×C311yescharacteristic
188#872—24no—
189C4×Dic6—24no—
190C3×#95—21no—
191C3×#95—21no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95—31no—
196C3×#95—31no—
197C3×#95—31no—
198C3×#95—31no—
199C3×#95—31no—
200C3×#95C2×D311yescharacteristic
201C3×#95C2×D311yescharacteristic
202C3×#95C22×C311yescharacteristic
203C3×#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C3⋊#95C22×C311yescharacteristic
206C3⋊#95C22×C311yescharacteristic
207C3⋊#95C22×C311yescharacteristic
208C3⋊#95C22×C311yescharacteristic
209C3⋊#95C22×C311yescharacteristic
210C3⋊#95C22×C311yescharacteristic
211C3⋊#95C22×C311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3C2×Q812yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
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×C4C2×D412yes—
237C2×C32×C4C2×Q812yes—
238C2×C32×C4#4112yes—
239C2×C32×C4#4112yes—
240C2×C32×C4#4112yes—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×Q812yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262C3×C4×D3—28no—
263C3×Dic6—28no—
264C2×C4×Q8—31no—
265C2×#117—31no—
266#400—31no—
267#399—31no—
268#398—31no—
269#398—31no—
270#396—31no—
271#396—31no—
272#395—31no—
273#393—31no—
274C4×C4⋊C4—31no—
275C4×C4⋊C4—31no—
276C4×C4⋊C4C3×D311yescharacteristic, complemented
277C4×C22⋊C4—31no—
278C4×C22⋊C4—31no—
279C24×C3—31no—
280C23×D3C23×C311yescharacteristic
281C2×C3×Q8—62no—
282C2×C3×Q8—62no—
283C2×C3×Q8—62no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—34no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C22×C3×C4C23×C311yescharacteristic
315C22×Dic3C23×C311yescharacteristic
316C22×Dic3C23×C311yescharacteristic
317C22×Dic3C23×C311yescharacteristic
318C22×Dic3C23×C311yescharacteristic
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3C3×Q814yescomplemented
325C2×Dic6—22no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C3×C4⋊C4—24no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—62no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—62no—
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C4⋊C4—62no—
341C3×C4⋊C4—62no—
342C3×C4⋊C4—62no—
343C3×C22⋊C4—62no—
344C3×C22⋊C4—62no—
345C3×C22⋊C4—62no—
346C3×C22⋊C4—62no—
347C3×C22⋊C4—62no—
348C3×C22⋊C4—62no—
349C3×C42—24no—
350C3×C42—22no—
351C3×C42—22no—
352C3×C42—22no—
353C3×C42—22no—
354C3×C42—22no—
355C3×C42—22no—
356C3×C42—34no—
357C3×C42—42no—
358C3×C42—42no—
359C3×C42—62no—
360C3×C42—62no—
361(C2×D3)⋊C4—22no—
362(C2×D3)⋊C4—22no—
363(C2×D3)⋊C4—22no—
364(C2×D3)⋊C4—22no—
365(C2×D3)⋊C4—22no—
366(C2×D3)⋊C4—22no—
367C4⋊Dic3—22no—
368Dic3⋊C4—22no—
369Dic3⋊C4—22no—
370Dic3⋊C4—22no—
371Dic3⋊C4—22no—
372Dic3⋊C4—22no—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376C4×Dic3—22no—
377C4×Dic3—22no—
378C4×Dic3C3×D414yes—
379C22×C32C22×D411yescharacteristic
380C22×C32C22×Q811yescharacteristic
381C22×C32C2×#4111yescharacteristic
382C22×C32C2×#4111yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C32×C4—22no—
394C32×C4—22no—
395C32×C4—41no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4—41no—
399C32×C4C22⋊Q814yes—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C22×Q8—31no—
408C23×C4—31no—
409C4×Q8—64no—
410#117—64no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4C2×C3×D311yescharacteristic
421C2×C4⋊C4C2×C3×D311yescharacteristic
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42C2×C3×D311yescharacteristic
432C2×C42C2×C3×D311yescharacteristic
433C2×C42C2×C3×D311yescharacteristic
434#95—31no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—31no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95C2×C3×D311yescharacteristic
443#95C2×C3×D311yescharacteristic
444C23×C3—21no—
445C23×C3—32no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3C23×D311yescharacteristic
453C23×C3C24×C311yescharacteristic
454C22×D3—21no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3C2×C3×Q812yes—
461C3×Q8—68no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—68no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4#23512yes—
538C2×C3×C4#23512yes—
539C2×C3×C4#23512yes—
540C2×C3×C4D3×D412yes—
541C2×C3×C4D3×Q812yes—
542C2×C3×C4C2×C3×D412yes—
543C2×C3×C4C2×C3×Q812yes—
544C2×C3×C4C3×#4112yes—
545C2×C3×C4C3×#4112yes—
546C2×C3×C4C3×#4112yes—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3C2×C3×D412yes—
564C2×Dic3C2×C3×D412yes—
565C2×Dic3C2×C3×Q812yes—
566C2×Dic3C3×#4112yes—
567C2×Dic3C3×#4112yes—
568C4×D3—28no—
569Dic6—28no—
570C2×C32C2×C22⋊Q811yescharacteristic
571C2×C32#52511yescharacteristic
572C2×C32#52911yescharacteristic
573C2×C32#52911yescharacteristic
574C2×C32#53211yescharacteristic
575C2×C32#53311yescharacteristic
576C2×C32#53311yescharacteristic
577C3×D3—42no—
578C24—31no—
579C2×Q8—62no—
580C2×Q8—62no—
581C2×Q8—62no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—34no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—62no—
591C22×C4—62no—
592C22×C4C22×C3×D311yescharacteristic
593C22×C4C22×C3×D311yescharacteristic
594C22×C4C22×C3×D311yescharacteristic
595C22×C4C22×C3×D311yescharacteristic
596C22×C4C22×C3×D311yescharacteristic
597C22×C4C22×C3×D311yescharacteristic
598C22×C4C22×C3×D311yescharacteristic
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—62no—
602C4⋊C4—62no—
603C4⋊C4—62no—
604C4⋊C4—62no—
605C4⋊C4—62no—
606C4⋊C4—62no—
607C4⋊C4—62no—
608C4⋊C4—62no—
609C4⋊C4—62no—
610C22⋊C4—62no—
611C22⋊C4—62no—
612C22⋊C4—62no—
613C22⋊C4—62no—
614C22⋊C4—62no—
615C22⋊C4—62no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—34no—
620C42—62no—
621C42—62no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—62no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C2×#23511yescharacteristic
637C22×C3C2×#23511yescharacteristic
638C22×C3C2×#23511yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C2×D3×Q811yescharacteristic
641C22×C3D3×#4111yescharacteristic
642C22×C3D3×#4111yescharacteristic
643C22×C3C22×C3×D411yescharacteristic
644C22×C3C22×C3×Q811yescharacteristic
645C22×C3C2×C3×#4111yescharacteristic
646C22×C3C2×C3×#4111yescharacteristic
647C22×C3C2×C3×#4111yescharacteristic
648C22×C3C2×C3×#4111yescharacteristic
649C22×C3C2×C3×#4111yescharacteristic
650C2×D3—22no—
651C2×D3—22no—
652C2×D3—22no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C3×C4—24no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—24no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—62no—
677C3×C4—62no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4#89614yes—
684C3×C4C3×C22⋊Q814yes—
685Dic3—22no—
686Dic3—22no—
687Dic3—22no—
688Dic3—22no—
689Dic3—22no—
690Dic3—41no—
691Dic3—41no—
692C32#239611yescharacteristic, complemented, Sylow
693C23—32no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23C23×C3×D311yescharacteristic
701Q8—68no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—68no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4C3×#23512yes—
741C2×C4C3×#23512yes—
742C2×C4C3×#23512yes—
743C2×C4C3×D3×D412yes—
744C2×C4C3×D3×Q812yes—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—122no—
753C2×C3#547911yescharacteristic
754C2×C3C2×#89611yescharacteristic
755C2×C3#552811yescharacteristic
756C2×C3#554711yescharacteristic
757C2×C3#554811yescharacteristic
758C2×C3#557811yescharacteristic
759C2×C3#557811yescharacteristic
760C2×C3C2×C3×C22⋊Q811yescharacteristic
761C2×C3C3×#52511yescharacteristic
762C2×C3C3×#52911yescharacteristic
763C2×C3C3×#52911yescharacteristic
764C2×C3C3×#53211yescharacteristic
765C2×C3C3×#53311yescharacteristic
766C2×C3C3×#53311yescharacteristic
767D3—42no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22C2×C3×#23511yescharacteristic
776C22C2×C3×#23511yescharacteristic
777C22C2×C3×#23511yescharacteristic
778C22C2×C3×D3×D411yescharacteristic
779C22C2×C3×D3×Q811yescharacteristic
780C22C3×D3×#4111yescharacteristic
781C22C3×D3×#4111yescharacteristic
782C4—22no—
783C4—22no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—62no—
789C4—62no—
790C4—62no—
791C4—62no—
792C4—62no—
793C4—121no—
794C4—121no—
795C4C3×#89614yes—
796C3—21no—
797C3#7377811yescharacteristic, direct product factor
798C3C3×#239611yescharacteristic, complemented
799C2—122no—
800C2C3×#547911yescharacteristic
801C2C2×C3×#89611yescharacteristic
802C2C3×#552811yescharacteristic
803C2C3×#554711yescharacteristic
804C2C3×#554811yescharacteristic
805C2C3×#557811yescharacteristic
806C2C3×#557811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2396
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×Dic6C2semidirect
3. C32×C4×C4⋊C4C2semidirect
6. C3×#4983C2semidirect
7. C3×#4979C2semidirect
10. C3×C4×Dic3⋊C4C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
14. C3×#4658C2semidirect
15. C3×#4657C2semidirect
17. #73778C3direct (N × H)
58. C2×C4×Dic6C2×C3semidirect
70. C3×C4×C4⋊C4D3semidirect
71. C3×C4×C4⋊C4C2×C3semidirect
76. #4983C2×C3semidirect
77. #4979C2×C3semidirect
80. C4×Dic3⋊C4C2×C3semidirect
81. C4×Dic3⋊C4C2×C3semidirect
84. #4658C2×C3semidirect
85. #4657C2×C3semidirect
103. C2×C3×C4×D3Q8semidirect
276. C4×C4⋊C4C3×D3semidirect
324. C2×C4×D3C3×Q8semidirect
692. C32#2396semidirect
797. C3#73778direct (N × H)
798. C3C3×#2396semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C3×C4×Dic62
C32×C4×C4⋊C42
C3×#49942
C3×#49932
C3×#49832
C3×#49792
C3×C4×(C2×D3)⋊C42
C3×C4×Dic3⋊C42
C3×#46762
C3×#46732
C3×#46582
C3×#46572
C3×#23963
#737783