Finite Group Databasebeta

← C3×#75491 #11807788

Subgroups — C3×#75491 #11807788

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic
2C32×#388C211yesmaximal, characteristic
3C3×#4976C211yesmaximal, characteristic, complemented
4C3×#4973C211yesmaximal, characteristic, complemented
5C3×#4951C211yesmaximal, characteristic
6C3×#4944C211yesmaximal, characteristic
7C3×#4944C211yesmaximal, characteristic
8C3×#4943C211yesmaximal, characteristic
9C3×#4942C211yesmaximal, characteristic
10C3×#4933C211yesmaximal, characteristic, complemented
11C3×#4928C211yesmaximal, characteristic, complemented
12C3×#4655C211yesmaximal, characteristic, complemented
13C3×#4654C211yesmaximal, characteristic, complemented
14C3×#4652C211yesmaximal, characteristic, complemented
15C3×#4646C211yesmaximal, characteristic, complemented
16C3×#2378—31nomaximal
17#75491C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#878C418yescomplemented
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×C22⋊Q8—31no—
55C2×#878C2×C311yescharacteristic
56C3×#391—31no—
57C3×#391—31no—
58C3×#389—31no—
59C3×#389—31no—
60C3×#388—21no—
61C3×#388—31no—
62C3×#388—31no—
63C3×#388—31no—
64C3×#388D311yescharacteristic
65C3×#388C2×C311yescharacteristic
66C3×#387—31no—
67C3×#387—31no—
68C3×#387—31no—
69C3×#387—31no—
70C3×#381—31no—
71C3×#380—31no—
72#4976C2×C311yescharacteristic, complemented
73#4973C2×C311yescharacteristic, complemented
74#4951C2×C311yescharacteristic
75#4944C2×C311yescharacteristic
76#4944C2×C311yescharacteristic
77#4943C2×C311yescharacteristic
78#4942C2×C311yescharacteristic
79#4933C2×C311yescharacteristic, complemented
80#4928C2×C311yescharacteristic, complemented
81#4655C2×C311yescharacteristic, complemented
82#4654C2×C311yescharacteristic, complemented
83#4652C2×C311yescharacteristic, complemented
84#4646C2×C311yescharacteristic, complemented
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3×Dic3—41no—
93C22×C3×Dic3—41no—
94C22×C3×Dic3C2×C414yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2×C414yes—
106C32×C4⋊C4—41no—
107C32×C22⋊C4—41no—
108C32×C22⋊C4—41no—
109C32×C22⋊C4C2×C414yes—
110C32×C42—41no—
111C3×#217—41no—
112C3×#217—41no—
113C3×#217C2×C414yes—
114C3×C4⋊Dic3—41no—
115C3×C4⋊Dic3C2×C414yes—
116C3×Dic3⋊C4—41no—
117C3×Dic3⋊C4—41no—
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4—41no—
120C3×Dic3⋊C4C2×C414yes—
121C3×Dic3⋊C4C2×C414yes—
122C3×C4×Dic3—41no—
123C3×C4×Dic3—41no—
124C3×C4×Dic3—41no—
125#2378—31noSylow
126C22×C3×Q8—31no—
127C23×C3×C4—31no—
128C23×Dic3C22×C311yescharacteristic
129C22×Dic6C22×C311yescharacteristic
130C3×C22⋊Q8—38no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×C3×C4⋊C4C22×C311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C22⋊C4C2×D311yescharacteristic
150C2×C3×C22⋊C4C2×D311yescharacteristic
151C2×C3×C22⋊C4C22×C311yescharacteristic
152C2×C3×C22⋊C4C22×C311yescharacteristic
153C2×C3×C22⋊C4C22×C311yescharacteristic
154C2×C3×C42—21no—
155C2×C3×C42—31no—
156C2×C3×C42—31no—
157C2×C3×C42—31no—
158C2×C3×C42C2×D311yescharacteristic
159C2×C3×C42C22×C311yescharacteristic
160C2×#217C22×C311yescharacteristic
161C2×#217C22×C311yescharacteristic
162C2×#217C22×C311yescharacteristic
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×C4⋊Dic3C22×C311yescharacteristic
165C2×Dic3⋊C4C22×C311yescharacteristic
166C2×Dic3⋊C4C22×C311yescharacteristic
167C2×Dic3⋊C4C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C311yescharacteristic
169C2×Dic3⋊C4C22×C311yescharacteristic
170C2×Dic3⋊C4C22×C311yescharacteristic
171C2×C4×Dic3C22×C311yescharacteristic
172C2×C4×Dic3C22×C311yescharacteristic
173C2×C4×Dic3C22×C311yescharacteristic
174#878C3×C418yescomplemented
175C3×#95—21no—
176C3×#95—21no—
177C3×#95—31no—
178C3×#95—31no—
179C3×#95—31no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95C2×D311yescharacteristic
190C3×#95C2×D311yescharacteristic
191C3×#95C22×C311yescharacteristic
192C3×#95C22×C311yescharacteristic
193C3⋊#95C22×C311yescharacteristic
194C3⋊#95C22×C311yescharacteristic
195C3⋊#95C22×C311yescharacteristic
196C3⋊#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C3⋊#95C22×C311yescharacteristic
199C3⋊#95C22×C311yescharacteristic
200C3⋊#95C22×C311yescharacteristic
201C3⋊#95C22×C311yescharacteristic
202C3⋊#95C22×C311yescharacteristic
203C3⋊#95C22×C311yescharacteristic
204C3⋊#95C22×C311yescharacteristic
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32C22×C412yes—
212C23×C32C2411yescharacteristic
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
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×C4C22×C412yes—
230C2×C32×C4C22×C412yes—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
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—44no—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C412yes—
256C3×Dic6—44no—
257C2×C22⋊Q8—31no—
258#391—31no—
259#391—31no—
260#389—31no—
261#389—31no—
262#388—31no—
263#388—31no—
264#388—31no—
265#388C3×D311yescharacteristic
266#387—31no—
267#387—31no—
268#387—31no—
269#387—31no—
270#381—31no—
271#380—31no—
272C24×C3—21no—
273C24×C3C22×D311yescharacteristic
274C24×C3C23×C311yescharacteristic
275C2×C3×Q8—34no—
276C2×C3×Q8—121no—
277C2×C3×Q8—121no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—34no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—121no—
294C22×C3×C4—121no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C22×C3×C4C23×C311yescharacteristic
306C22×C3×C4C23×C311yescharacteristic
307C22×Dic3—41no—
308C22×Dic3—41no—
309C22×Dic3C2×C3×C414yes—
310C22×Dic3C23×C311yescharacteristic
311C22×Dic3C23×C311yescharacteristic
312C22×Dic3C23×C311yescharacteristic
313C22×Dic3C23×C311yescharacteristic
314C22×Dic3C23×C311yescharacteristic
315C22×Dic3C23×C311yescharacteristic
316C22×Dic3C23×C311yescharacteristic
317C22×Dic3C23×C311yescharacteristic
318C2×Dic6—41no—
319C2×Dic6—41no—
320C2×Dic6C2×C3×C414yes—
321C3×C4⋊C4—34no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—41no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4—42no—
327C3×C4⋊C4—121no—
328C3×C4⋊C4—121no—
329C3×C4⋊C4—121no—
330C3×C4⋊C4—121no—
331C3×C4⋊C4—121no—
332C3×C22⋊C4—24no—
333C3×C22⋊C4—34no—
334C3×C22⋊C4—41no—
335C3×C22⋊C4—41no—
336C3×C22⋊C4—41no—
337C3×C22⋊C4—41no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—121no—
341C3×C22⋊C4—121no—
342C3×C22⋊C4C4×D314yes—
343C3×C22⋊C4C2×C3×C414yes—
344C3×C42—41no—
345C3×C42—41no—
346C3×C42—42no—
347C3×C42—121no—
348C3×C42—121no—
349C3×C42—121no—
350#217—41no—
351#217—41no—
352#217C2×C3×C414yes—
353C4⋊Dic3—41no—
354C4⋊Dic3C2×C3×C414yes—
355Dic3⋊C4—41no—
356Dic3⋊C4—41no—
357Dic3⋊C4—41no—
358Dic3⋊C4—41no—
359Dic3⋊C4C2×C3×C414yes—
360Dic3⋊C4C2×C3×C414yes—
361C4×Dic3—41no—
362C4×Dic3—41no—
363C4×Dic3—41no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32C23×C411yescharacteristic
372C22×C32H(5,𝔽2)11yescharacteristic
373C22×C32H(5,𝔽2)11yescharacteristic
374C22×C32H(5,𝔽2)11yescharacteristic
375C22×C322−1+411yescharacteristic
376C22×C322−1+411yescharacteristic
377C22×C322−1+411yescharacteristic
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—41no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—41no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C22×Q8—31no—
393C23×C4—31no—
394C22⋊Q8—38no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—31no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4C2×C3×D311yescharacteristic
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4C2×C3×D311yescharacteristic
408C2×C22⋊C4C2×C3×D311yescharacteristic
409C2×C22⋊C4C2×C3×D311yescharacteristic
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42C2×C3×D311yescharacteristic
414#95—31no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95—31no—
426#95C2×C3×D311yescharacteristic
427#95C2×C3×D311yescharacteristic
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3C2×C4×D312yes—
449C23×C3C22×C3×C412yes—
450C23×C3C23×D311yescharacteristic
451C23×C3C24×C311yescharacteristic
452C3×Q8—124no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—21no—
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—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
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—22no—
488C2×C3×C4—22no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
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—124no—
528C2×C3×C4C2×C4×D312yes—
529C2×C3×C4C2×C4×D312yes—
530C2×C3×C4C22×C3×C412yes—
531C2×C3×C4C22×C3×C412yes—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—44no—
553C2×Dic3C22×C3×C412yes—
554C2×Dic3C22×C3×C412yes—
555C2×Dic3C22×C3×C412yes—
556C2×Dic3C22×C3×C412yes—
557Dic6—44no—
558C2×C32—42no—
559C2×C32#51811yescharacteristic
560C2×C32#51911yescharacteristic
561C2×C32#52011yescharacteristic
562C2×C32#56211yescharacteristic
563C2×C32#56211yescharacteristic
564C2×C32#56311yescharacteristic
565C2×C32#56311yescharacteristic
566C24C22×C3×D311yescharacteristic
567C2×Q8—34no—
568C2×Q8—121no—
569C2×Q8—121no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—34no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—121no—
580C22×C4—121no—
581C22×C4C22×C3×D311yescharacteristic
582C22×C4C22×C3×D311yescharacteristic
583C22×C4C22×C3×D311yescharacteristic
584C22×C4C22×C3×D311yescharacteristic
585C22×C4C22×C3×D311yescharacteristic
586C22×C4C22×C3×D311yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—34no—
590C4⋊C4—41no—
591C4⋊C4—121no—
592C4⋊C4—121no—
593C4⋊C4—121no—
594C4⋊C4—121no—
595C4⋊C4—121no—
596C22⋊C4—34no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—121no—
600C22⋊C4—121no—
601C22⋊C4C3×C4×D314yes—
602C42—41no—
603C42—121no—
604C42—121no—
605C42—121no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C22×C4×D311yescharacteristic
635C22×C3#100411yescharacteristic
636C22×C3#100411yescharacteristic
637C22×C3#100911yescharacteristic
638C22×C3#101011yescharacteristic
639C22×C3#101011yescharacteristic
640C22×C3#101011yescharacteristic
641C22×C3C23×C3×C411yescharacteristic
642C22×C3C3×H(5,𝔽2)11yescharacteristic
643C22×C3C3×H(5,𝔽2)11yescharacteristic
644C22×C3C3×H(5,𝔽2)11yescharacteristic
645C22×C3C3×2−1+411yescharacteristic
646C22×C3C3×2−1+411yescharacteristic
647C22×C3C3×2−1+411yescharacteristic
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—62no—
665C3×C4—62no—
666C3×C4—62no—
667C3×C4—62no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674Dic3—22no—
675Dic3—22no—
676Dic3—22no—
677Dic3—22no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682C32#237811yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23C2×C3×C4×D312yes—
690C23C23×C3×D311yescharacteristic
691Q8—124no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—32no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
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—124no—
733C2×C4C2×C3×C4×D312yes—
734C2×C4C2×C3×C4×D312yes—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3#551611yescharacteristic
746C2×C3#554511yescharacteristic
747C2×C3#554611yescharacteristic
748C2×C3#562111yescharacteristic
749C2×C3#566711yescharacteristic
750C2×C3#567211yescharacteristic
751C2×C3#571211yescharacteristic
752C2×C3C3×#51811yescharacteristic
753C2×C3C3×#51911yescharacteristic
754C2×C3C3×#52011yescharacteristic
755C2×C3C3×#56211yescharacteristic
756C2×C3C3×#56211yescharacteristic
757C2×C3C3×#56311yescharacteristic
758C2×C3C3×#56311yescharacteristic
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22C22×C3×C4×D311yescharacteristic
767C22C3×#100411yescharacteristic
768C22C3×#100411yescharacteristic
769C22C3×#100911yescharacteristic
770C22C3×#101011yescharacteristic
771C22C3×#101011yescharacteristic
772C22C3×#101011yescharacteristic
773C4—22no—
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—62no—
780C4—62no—
781C4—62no—
782C4—62no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—121no—
787C3—21no—
788C3#7549111yescharacteristic, direct product factor
789C3C3×#237811yescharacteristic, complemented
790C2—42no—
791C2C3×#551611yescharacteristic
792C2C3×#554511yescharacteristic
793C2C3×#554611yescharacteristic
794C2C3×#562111yescharacteristic
795C2C3×#566711yescharacteristic
796C2C3×#567211yescharacteristic
797C2C3×#571211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#388C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#388D3
hypocenterC3C3×#2378
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C3×#4976C2semidirect
4. C3×#4973C2semidirect
10. C3×#4933C2semidirect
11. C3×#4928C2semidirect
12. C3×#4655C2semidirect
13. C3×#4654C2semidirect
14. C3×#4652C2semidirect
15. C3×#4646C2semidirect
17. #75491C3direct (N × H)
39. C3×#878C4semidirect
72. #4976C2×C3semidirect
73. #4973C2×C3semidirect
79. #4933C2×C3semidirect
80. #4928C2×C3semidirect
81. #4655C2×C3semidirect
82. #4654C2×C3semidirect
83. #4652C2×C3semidirect
84. #4646C2×C3semidirect
174. #878C3×C4semidirect
682. C32#2378semidirect
788. C3#75491direct (N × H)
789. C3C3×#2378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
C32×#3882
C3×#49762
C3×#49732
C3×#49512
C3×#49442
C3×#49432
C3×#49422
C3×#49332
C3×#49282
C3×#46552
C3×#46542
C3×#46522
C3×#46462
C3×#23783
#754913