Finite Group Databasebeta

← C3×#74663 #11803003

Subgroups — C3×#74663 #11803003

Order 1152.

1279 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C32×#386C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4946C211yesmaximal, characteristic, complemented
7C3×#4945C211yesmaximal, characteristic, complemented
8C3×#4944C211yesmaximal, characteristic, complemented
9C3×#4943C211yesmaximal, characteristic, complemented
10C3×#4942C211yesmaximal, characteristic, complemented
11C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12C3×#4654C211yesmaximal, characteristic, complemented
13C3×#4653C211yesmaximal, characteristic, complemented
14C3×#4651C211yesmaximal, characteristic, complemented
15C3×#4650C211yesmaximal, characteristic, complemented
16C3×#2318—31nomaximal
17#74663C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C3×D4×Dic3C418yescomplemented
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C32×#95C2211yescharacteristic
41C32×#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C2×C3×C4×D4—31no—
55C2×D4×Dic3C2×C311yescharacteristic
56C3×#388—31no—
57C3×#388—31no—
58C3×#387—31no—
59C3×#387—31no—
60C3×#386—21no—
61C3×#386—31no—
62C3×#386D311yescharacteristic
63C3×#386C2×C311yescharacteristic
64C3×#385—31no—
65C3×#385—31no—
66C3×#383—31no—
67C3×#382—31no—
68C3×#381—31no—
69C3×#380—31no—
70C3×C4×C22⋊C4—31no—
71C2×C3×#95—31no—
72#5220C2×C311yescharacteristic
73#5210C2×C311yescharacteristic, complemented
74C2×C3⋊#95C2×C311yescharacteristic, complemented
75#4946C2×C311yescharacteristic, complemented
76#4945C2×C311yescharacteristic, complemented
77#4944C2×C311yescharacteristic, complemented
78#4943C2×C311yescharacteristic, complemented
79#4942C2×C311yescharacteristic, complemented
80Dic3×C22⋊C4C2×C311yescharacteristic, complemented
81#4654C2×C311yescharacteristic, complemented
82#4653C2×C311yescharacteristic, complemented
83#4651C2×C311yescharacteristic, complemented
84#4650C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C24×C32C2311yescharacteristic
87C2×C32×D4—22no—
88C2×C32×D4—22no—
89C2×C32×D4C2×C414yes—
90C22×C32×C4—22no—
91C22×C32×C4—41no—
92C22×C32×C4—41no—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C3×Dic3—22no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3—41no—
101C22×C3×Dic3—41no—
102C22×C3×Dic3—41no—
103C22×C3×Dic3—41no—
104C22×C3×Dic3—41no—
105C22×C3×Dic3C2×C414yes—
106C22×C3×Dic3C2×C414yescomplemented
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C32×C22⋊C4—22no—
116C32×C22⋊C4—41no—
117C32×C22⋊C4—41no—
118C3×#217—22no—
119C3×#217—41no—
120C3×#217—41no—
121C3×#217C2×C414yes—
122C3×#217C2×C414yescomplemented
123C3×C4⋊Dic3C2×C414yescomplemented
124C3×Dic3⋊C4—41no—
125C3×Dic3⋊C4—41no—
126C3×Dic3⋊C4—41no—
127C3×Dic3⋊C4—41no—
128C3×C4×Dic3—41no—
129C3×C4×Dic3—41no—
130C3×C4×Dic3C2×C414yescomplemented
131#2318—31noSylow
132C22×C3×D4—21no—
133C22×C3×D4C2×D311yescharacteristic
134C22×C3×D4C22×C311yescharacteristic
135C23×C3×C4—21no—
136C23×C3×C4—31no—
137C23×C3×C4—31no—
138C23×C3×C4—31no—
139C23×C3×C4C2×D311yescharacteristic
140C23×C3×C4C22×C311yescharacteristic
141C23×Dic3C22×C311yescharacteristic
142C23×Dic3C22×C311yescharacteristic
143C23×Dic3C22×C311yescharacteristic
144C3×C4×D4—38no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C4⋊C4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
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⋊C4C2×D311yescharacteristic
159C2×C3×C22⋊C4C2×D311yescharacteristic
160C2×C3×C22⋊C4C2×D311yescharacteristic
161C2×C3×C22⋊C4C22×C311yescharacteristic
162C2×C3×C22⋊C4C22×C311yescharacteristic
163C2×C3×C22⋊C4C22×C311yescharacteristic
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×C3×C42—31no—
167C2×#217C22×C311yescharacteristic
168C2×#217C22×C311yescharacteristic
169C2×#217C22×C311yescharacteristic
170C2×#217C22×C311yescharacteristic
171C2×#217C22×C311yescharacteristic
172D4×Dic3C3×C418yescomplemented
173C2×C4⋊Dic3C22×C311yescharacteristic
174C2×Dic3⋊C4C22×C311yescharacteristic
175C2×Dic3⋊C4C22×C311yescharacteristic
176C2×Dic3⋊C4C22×C311yescharacteristic
177C2×Dic3⋊C4C22×C311yescharacteristic
178C2×C4×Dic3C22×C311yescharacteristic
179C2×C4×Dic3C22×C311yescharacteristic
180C2×C4×Dic3C22×C311yescharacteristic
181C3×#95—21no—
182C3×#95—21no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95—31no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—31no—
194C3×#95—31no—
195C3×#95C2×D311yescharacteristic
196C3×#95C2×D311yescharacteristic
197C3×#95C22×C311yescharacteristic
198C3×#95C22×C311yescharacteristic
199C3⋊#95C22×C311yescharacteristic
200C3⋊#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
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
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32C22×C412yes—
222C23×C32C22×C412yes—
223C23×C32#4112yes—
224C23×C32#4112yes—
225C23×C32C2411yescharacteristic
226C32×D4—28no—
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×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—44no—
242C2×C32×C4C22×C412yes—
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×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—44no—
264C2×C3×Dic3—44no—
265C2×C3×Dic3—44no—
266C2×C3×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269C2×C3×Dic3C22×C412yes—
270C2×C4×D4—31no—
271#388—31no—
272#388—31no—
273#387—31no—
274#387—31no—
275#386—31no—
276#386C3×D311yescharacteristic
277#385—31no—
278#385—31no—
279#383—31no—
280#382—31no—
281#381—31no—
282#380—31no—
283C4×C22⋊C4—31no—
284C2×#95—31no—
285C24×C3—21no—
286C24×C3—21no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C24×C3C23×C311yescharacteristic
290C24×C3C23×C311yescharacteristic
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—24no—
296C2×C3×D4—42no—
297C2×C3×D4—42no—
298C2×C3×D4C4×D314yes—
299C2×C3×D4C2×C3×C414yes—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—34no—
312C22×C3×C4—34no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—42no—
318C22×C3×C4—41no—
319C22×C3×C4—41no—
320C22×C3×C4—41no—
321C22×C3×C4—41no—
322C22×C3×C4—42no—
323C22×C3×C4—42no—
324C22×C3×C4—62no—
325C22×C3×C4—121no—
326C22×C3×C4—121no—
327C22×C3×C4—121no—
328C22×C3×C4—121no—
329C22×C3×C4—121no—
330C22×C3×C4—121no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C23×C311yescharacteristic
337C22×C3×C4C23×C311yescharacteristic
338C22×C3×C4C23×C311yescharacteristic
339C22×C3×C4C23×C311yescharacteristic
340C22×C3×C4C23×C311yescharacteristic
341C22×Dic3—22no—
342C22×Dic3—41no—
343C22×Dic3—41no—
344C22×Dic3—41no—
345C22×Dic3—41no—
346C22×Dic3—41no—
347C22×Dic3—41no—
348C22×Dic3C2×C3×C414yes—
349C22×Dic3C2×C3×C414yescomplemented
350C22×Dic3C23×C311yescharacteristic
351C22×Dic3C23×C311yescharacteristic
352C22×Dic3C23×C311yescharacteristic
353C22×Dic3C23×C311yescharacteristic
354C22×Dic3C23×C311yescharacteristic
355C22×Dic3C23×C311yescharacteristic
356C22×Dic3C23×C311yescharacteristic
357C22×Dic3C23×C311yescharacteristic
358C3×C4⋊C4—34no—
359C3×C4⋊C4—121no—
360C3×C4⋊C4—121no—
361C3×C4⋊C4—121no—
362C3×C4⋊C4—121no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—22no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—42no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—41no—
371C3×C22⋊C4—41no—
372C3×C22⋊C4—42no—
373C3×C22⋊C4—42no—
374C3×C22⋊C4—62no—
375C3×C22⋊C4—121no—
376C3×C22⋊C4—121no—
377C3×C42—34no—
378C3×C42—121no—
379C3×C42—121no—
380#217—22no—
381#217—41no—
382#217—41no—
383#217C2×C3×C414yes—
384#217C2×C3×C414yescomplemented
385C4⋊Dic3C2×C3×C414yescomplemented
386Dic3⋊C4—41no—
387Dic3⋊C4—41no—
388Dic3⋊C4—41no—
389Dic3⋊C4—41no—
390C4×Dic3—41no—
391C4×Dic3—41no—
392C4×Dic3C2×C3×C414yescomplemented
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32#11714yes—
407C22×C32C23×C411yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32H(5,𝔽2)11yescharacteristic
411C22×C32H(5,𝔽2)11yescharacteristic
412C22×C32H(5,𝔽2)11yescharacteristic
413C22×C322−1+411yescharacteristic
414C32×C4—22no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4C2×C3×D311yescharacteristic
428C23×C4—31no—
429C23×C4—31no—
430C23×C4—31no—
431C23×C4C2×C3×D311yescharacteristic
432C4×D4—38no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4C2×C3×D311yescharacteristic
444C2×C22⋊C4C2×C3×D311yescharacteristic
445C2×C22⋊C4C2×C3×D311yescharacteristic
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—31no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—31no—
454#95—31no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95C2×C3×D311yescharacteristic
462#95C2×C3×D311yescharacteristic
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—22no—
485C23×C3—22no—
486C23×C3—22no—
487C23×C3—22no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3C2×C4×D312yes—
499C23×C3C2×C4×D312yes—
500C23×C3#23712yes—
501C23×C3#23712yes—
502C23×C3C22×C3×C412yes—
503C23×C3C22×C3×C412yes—
504C23×C3C3×#4112yes—
505C23×C3C3×#4112yes—
506C23×C3C23×D311yescharacteristic
507C23×C3C24×C311yescharacteristic
508C3×D4—28no—
509C3×D4—28no—
510C3×D4—48no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
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—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—22no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—32no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—44no—
559C2×C3×C4—44no—
560C2×C3×C4—48no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—124no—
582C2×C3×C4—124no—
583C2×C3×C4—124no—
584C2×C3×C4C2×C4×D312yes—
585C2×C3×C4C22×C3×C412yes—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—44no—
607C2×Dic3—44no—
608C2×Dic3—44no—
609C2×Dic3C22×C3×C412yes—
610C2×Dic3C22×C3×C412yes—
611C2×Dic3C22×C3×C412yes—
612C2×Dic3C22×C3×C412yes—
613C2×C32—24no—
614C2×C32—42no—
615C2×C32C2×#11711yescharacteristic
616C2×C32#51811yescharacteristic
617C2×C32#52011yescharacteristic
618C2×C32#53811yescharacteristic
619C2×C32#53811yescharacteristic
620C2×C32#53911yescharacteristic
621C2×C32#53911yescharacteristic
622C24C22×C3×D311yescharacteristic
623C24C22×C3×D311yescharacteristic
624C2×D4—22no—
625C2×D4—22no—
626C2×D4C3×C4×D314yes—
627C22×C4—22no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—34no—
633C22×C4—34no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—62no—
641C22×C4—121no—
642C22×C4—121no—
643C22×C4—121no—
644C22×C4—121no—
645C22×C4—121no—
646C22×C4—121no—
647C22×C4C22×C3×D311yescharacteristic
648C22×C4C22×C3×D311yescharacteristic
649C22×C4C22×C3×D311yescharacteristic
650C22×C4C22×C3×D311yescharacteristic
651C22×C4C22×C3×D311yescharacteristic
652C4⋊C4—34no—
653C4⋊C4—121no—
654C4⋊C4—121no—
655C4⋊C4—121no—
656C4⋊C4—121no—
657C22⋊C4—22no—
658C22⋊C4—34no—
659C22⋊C4—34no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—62no—
663C22⋊C4—121no—
664C22⋊C4—121no—
665C42—34no—
666C42—121no—
667C42—121no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—24no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3#87714yes—
716C22×C3C3×#11714yes—
717C22×C3C22×C4×D311yescharacteristic
718C22×C3C2×#23711yescharacteristic
719C22×C3C2×#23711yescharacteristic
720C22×C3#100411yescharacteristic
721C22×C3#100411yescharacteristic
722C22×C3#100911yescharacteristic
723C22×C3#101011yescharacteristic
724C22×C3C23×C3×C411yescharacteristic
725C22×C3C2×C3×#4111yescharacteristic
726C22×C3C2×C3×#4111yescharacteristic
727C22×C3C3×H(5,𝔽2)11yescharacteristic
728C22×C3C3×H(5,𝔽2)11yescharacteristic
729C22×C3C3×H(5,𝔽2)11yescharacteristic
730C22×C3C3×2−1+411yescharacteristic
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—41no—
744C3×C4—62no—
745C3×C4—62no—
746C3×C4—62no—
747C3×C4—62no—
748C3×C4—81no—
749C3×C4—81no—
750C3×C4—121no—
751C3×C4—121no—
752C3×C4—121no—
753C3×C4—121no—
754Dic3—22no—
755Dic3—22no—
756Dic3—22no—
757Dic3—22no—
758Dic3—41no—
759Dic3—41no—
760Dic3—41no—
761Dic3—41no—
762C32#231811yescharacteristic, complemented, Sylow
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23C2×C3×C4×D312yes—
774C23C2×C3×C4×D312yes—
775C23C3×#23712yes—
776C23C3×#23712yes—
777C23C23×C3×D311yescharacteristic
778D4—28no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—32no—
794C2×C4—32no—
795C2×C4—32no—
796C2×C4—32no—
797C2×C4—44no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—124no—
819C2×C4—124no—
820C2×C4—124no—
821C2×C4C2×C3×C4×D312yes—
822C2×C3—24no—
823C2×C3—24no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—44no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3C2×#87711yescharacteristic
836C2×C3#554511yescharacteristic
837C2×C3#554611yescharacteristic
838C2×C3#559311yescharacteristic
839C2×C3#560211yescharacteristic
840C2×C3#561711yescharacteristic
841C2×C3#566511yescharacteristic
842C2×C3C2×C3×#11711yescharacteristic
843C2×C3C3×#51811yescharacteristic
844C2×C3C3×#52011yescharacteristic
845C2×C3C3×#53811yescharacteristic
846C2×C3C3×#53811yescharacteristic
847C2×C3C3×#53911yescharacteristic
848C2×C3C3×#53911yescharacteristic
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22C3×#87714yes—
863C22C22×C3×C4×D311yescharacteristic
864C22C2×C3×#23711yescharacteristic
865C22C2×C3×#23711yescharacteristic
866C22C3×#100411yescharacteristic
867C22C3×#100411yescharacteristic
868C22C3×#100911yescharacteristic
869C22C3×#101011yescharacteristic
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—62no—
879C4—121no—
880C4—121no—
881C4—121no—
882C4—121no—
883C3—21no—
884C3#7466311yescharacteristic, direct product factor
885C3C3×#231811yescharacteristic, complemented
886C2—24no—
887C2—42no—
888C2C2×C3×#87711yescharacteristic
889C2C3×#554511yescharacteristic
890C2C3×#554611yescharacteristic
891C2C3×#559311yescharacteristic
892C2C3×#560211yescharacteristic
893C2C3×#561711yescharacteristic
894C2C3×#566511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC22×C32×D4C22
cosocleC23×C3C24×C3
hypercenterC3×#386D3
hypocenterC3C3×#2318
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
4. C3×#5210C2semidirect
5. C2×C3×C3⋊#95C2semidirect
6. C3×#4946C2semidirect
7. C3×#4945C2semidirect
8. C3×#4944C2semidirect
9. C3×#4943C2semidirect
10. C3×#4942C2semidirect
11. C3×Dic3×C22⋊C4C2semidirect
12. C3×#4654C2semidirect
13. C3×#4653C2semidirect
14. C3×#4651C2semidirect
15. C3×#4650C2semidirect
17. #74663C3direct (N × H)
31. C3×D4×Dic3C4semidirect
73. #5210C2×C3semidirect
74. C2×C3⋊#95C2×C3semidirect
75. #4946C2×C3semidirect
76. #4945C2×C3semidirect
77. #4944C2×C3semidirect
78. #4943C2×C3semidirect
79. #4942C2×C3semidirect
80. Dic3×C22⋊C4C2×C3semidirect
81. #4654C2×C3semidirect
82. #4653C2×C3semidirect
83. #4651C2×C3semidirect
84. #4650C2×C3semidirect
106. C22×C3×Dic3C2×C4semidirect
122. C3×#217C2×C4semidirect
123. C3×C4⋊Dic3C2×C4semidirect
130. C3×C4×Dic3C2×C4semidirect
172. D4×Dic3C3×C4semidirect
349. C22×Dic3C2×C3×C4semidirect
384. #217C2×C3×C4semidirect
385. C4⋊Dic3C2×C3×C4semidirect
392. C4×Dic3C2×C3×C4semidirect
762. C32#2318semidirect
884. C3#74663direct (N × H)
885. C3C3×#2318semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C32×#3862
C3×#52202
C3×#52102
C2×C3×C3⋊#952
C3×#49462
C3×#49452
C3×#49442
C3×#49432
C3×#49422
C3×Dic3×C22⋊C42
C3×#46542
C3×#46532
C3×#46512
C3×#46502
C3×#23183
#746633