Finite Group Databasebeta

← C3×#76617 #11807791

Subgroups — C3×#76617 #11807791

Order 1152.

1021 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#946C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic, complemented
3C3×#5229C211yesmaximal, characteristic, complemented
4C3×#4990C211yesmaximal, characteristic
5C3×#4976C211yesmaximal, characteristic, complemented
6C3×#4940C211yesmaximal, characteristic
7C3×#4933C211yesmaximal, characteristic, complemented
8C3×#4670C211yesmaximal, characteristic
9C3×#4669C211yesmaximal, characteristic
10C3×#4667C211yesmaximal, characteristic
11C3×#4664C211yesmaximal, characteristic
12C3×#4654C211yesmaximal, characteristic, complemented
13C3×#4653C211yesmaximal, characteristic, complemented
14C3×#4652C211yesmaximal, characteristic, complemented
15C3×#4647C211yesmaximal, characteristic, complemented
16C3×#2378—31nomaximal
17#76617C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C3×#946C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
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
42C32×#95C2211yescharacteristic
43C32×#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×#946C2×C311yescharacteristic
56C3×#391—21no—
57C3×#391—31no—
58C3×#391D311yescharacteristic, complemented
59C3×#391C2×C311yescharacteristic, complemented
60C3×#389—31no—
61C3×#389—31no—
62C3×#388—31no—
63C3×#388—31no—
64C3×#388—31no—
65C3×#388—31no—
66C3×#387—31no—
67C3×#387—31no—
68C3×#387—31no—
69C3×#387—31no—
70C3×#381—31no—
71C3×#380—31no—
72#5229C2×C311yescharacteristic, complemented
73#4990C2×C311yescharacteristic
74#4976C2×C311yescharacteristic, complemented
75#4940C2×C311yescharacteristic
76#4933C2×C311yescharacteristic, complemented
77#4670C2×C311yescharacteristic
78#4669C2×C311yescharacteristic
79#4667C2×C311yescharacteristic
80#4664C2×C311yescharacteristic
81#4654C2×C311yescharacteristic, complemented
82#4653C2×C311yescharacteristic, complemented
83#4652C2×C311yescharacteristic, complemented
84#4647C2×C311yescharacteristic, complemented
85C23×C3×D3C2311yescharacteristic
86C2×C32×Q8—41no—
87C2×C32×Q8—41no—
88C2×C32×Q8C2×C414yes—
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3C2×C414yes—
106C32×C4⋊C4—41no—
107C32×C42—41no—
108C3×(C2×D3)⋊C4—41no—
109C3×(C2×D3)⋊C4—41no—
110C3×(C2×D3)⋊C4—41no—
111C3×(C2×D3)⋊C4—41no—
112C3×(C2×D3)⋊C4C2×C414yes—
113C3×(C2×D3)⋊C4C2×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—21no—
127C22×C3×Q8C2×D311yescharacteristic
128C22×C3×Q8C22×C311yescharacteristic
129C23×C3×C4—31no—
130C22×C4×D3C22×C311yescharacteristic
131C3×C22⋊Q8—38no—
132C2×C3×C4⋊C4—21no—
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⋊C4—31no—
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C4⋊C4C22×C311yescharacteristic
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C42—21no—
150C2×C3×C42—31no—
151C2×C3×C42—31no—
152C2×C3×C42—31no—
153C2×C3×C42C2×D311yescharacteristic
154C2×C3×C42C22×C311yescharacteristic
155#946C3×C418yescomplemented
156C2×(C2×D3)⋊C4C22×C311yescharacteristic
157C2×(C2×D3)⋊C4C22×C311yescharacteristic
158C2×(C2×D3)⋊C4C22×C311yescharacteristic
159C2×(C2×D3)⋊C4C22×C311yescharacteristic
160C2×(C2×D3)⋊C4C22×C311yescharacteristic
161C2×(C2×D3)⋊C4C22×C311yescharacteristic
162C2×C4⋊Dic3C22×C311yescharacteristic
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×Dic3⋊C4C22×C311yescharacteristic
165C2×Dic3⋊C4C22×C311yescharacteristic
166C2×Dic3⋊C4C22×C311yescharacteristic
167C2×Dic3⋊C4C22×C311yescharacteristic
168C2×Dic3⋊C4C22×C311yescharacteristic
169C2×Dic3⋊C4C22×C311yescharacteristic
170C2×C4×Dic3C22×C311yescharacteristic
171C2×C4×Dic3C22×C311yescharacteristic
172C2×C4×Dic3C22×C311yescharacteristic
173C3×#95—21no—
174C3×#95—21no—
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×#95C2×D311yescharacteristic
188C3×#95C2×D311yescharacteristic
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×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C32×Q8—44no—
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×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4C22×C412yes—
233C2×C32×C4C22×C412yes—
234C2×C32×C4C22×C412yes—
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—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C412yes—
256C3×C4×D3—44no—
257C2×C22⋊Q8—31no—
258#391—31no—
259#391C3×D311yescharacteristic, complemented
260#389—31no—
261#389—31no—
262#388—31no—
263#388—31no—
264#388—31no—
265#388—31no—
266#387—31no—
267#387—31no—
268#387—31no—
269#387—31no—
270#381—31no—
271#380—31no—
272C24×C3—31no—
273C23×D3C23×C311yescharacteristic
274C2×C3×Q8—24no—
275C2×C3×Q8—41no—
276C2×C3×Q8—41no—
277C2×C3×Q8—41no—
278C2×C3×Q8—41no—
279C2×C3×Q8—42no—
280C2×C3×Q8—42no—
281C2×C3×Q8C4×D314yes—
282C2×C3×Q8C2×C3×C414yes—
283C22×C3×C4—21no—
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—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—34no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—121no—
299C22×C3×C4—121no—
300C22×C3×C4C22×D311yescharacteristic
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×C4C23×C311yescharacteristic
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×Dic3C23×C311yescharacteristic
315C22×Dic3C23×C311yescharacteristic
316C22×Dic3C23×C311yescharacteristic
317C22×Dic3C23×C311yescharacteristic
318C22×Dic3C23×C311yescharacteristic
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C2×C4×D3—41no—
322C2×C4×D3—41no—
323C2×C4×D3C2×C3×C414yes—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—41no—
328C3×C4⋊C4—41no—
329C3×C4⋊C4—42no—
330C3×C4⋊C4—121no—
331C3×C4⋊C4—121no—
332C3×C4⋊C4—121no—
333C3×C4⋊C4—121no—
334C3×C4⋊C4—121no—
335C3×C22⋊C4—34no—
336C3×C22⋊C4—34no—
337C3×C22⋊C4—121no—
338C3×C22⋊C4—121no—
339C3×C22⋊C4—121no—
340C3×C22⋊C4—121no—
341C3×C42—41no—
342C3×C42—41no—
343C3×C42—42no—
344C3×C42—121no—
345C3×C42—121no—
346C3×C42—121no—
347(C2×D3)⋊C4—41no—
348(C2×D3)⋊C4—41no—
349(C2×D3)⋊C4—41no—
350(C2×D3)⋊C4—41no—
351(C2×D3)⋊C4C2×C3×C414yes—
352(C2×D3)⋊C4C2×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×C32C23×C411yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C22×C32H(5,𝔽2)11yescharacteristic
367C22×C32H(5,𝔽2)11yescharacteristic
368C22×C322−1+411yescharacteristic
369C22×C322−1+411yescharacteristic
370C22×C322−1+411yescharacteristic
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—41no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C2×C3×D3—41no—
378C32×C4—22no—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4—41no—
382C32×C4—41no—
383C32×C4—41no—
384C32×C4—41no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C22×Q8C2×C3×D311yescharacteristic
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⋊C4—31no—
408C2×C22⋊C4—31no—
409C2×C22⋊C4—31no—
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#95C2×C3×D311yescharacteristic
425#95C2×C3×D311yescharacteristic
426#95C2×C3×D311yescharacteristic
427#95C2×C3×D311yescharacteristic
428C23×C3—21no—
429C23×C3—32no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3—61no—
436C23×C3C23×D311yescharacteristic
437C23×C3C24×C311yescharacteristic
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3C22×C3×C412yes—
445C3×Q8—44no—
446C3×Q8—44no—
447C3×Q8—48no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
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—21no—
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—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—21no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
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—41no—
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—124no—
527C2×C3×C4C2×C4×D312yes—
528C2×C3×C4C2×C4×D312yes—
529C2×C3×C4C2×C4×D312yes—
530C2×C3×C4C22×C3×C412yes—
531C2×C3×C4C22×C3×C412yes—
532C2×C3×C4C22×C3×C412yes—
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×Dic3C22×C3×C412yes—
552C2×Dic3C22×C3×C412yes—
553C2×Dic3C22×C3×C412yes—
554C4×D3—44no—
555C2×C32#51811yescharacteristic
556C2×C32#51911yescharacteristic
557C2×C32#52011yescharacteristic
558C2×C32#56211yescharacteristic
559C2×C32#56211yescharacteristic
560C2×C32#56311yescharacteristic
561C2×C32#56311yescharacteristic
562C3×D3—42no—
563C24—31no—
564C2×Q8—41no—
565C2×Q8—41no—
566C2×Q8C3×C4×D314yes—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—34no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—121no—
576C22×C4—121no—
577C22×C4C22×C3×D311yescharacteristic
578C22×C4C22×C3×D311yescharacteristic
579C22×C4C22×C3×D311yescharacteristic
580C22×C4C22×C3×D311yescharacteristic
581C22×C4C22×C3×D311yescharacteristic
582C22×C4C22×C3×D311yescharacteristic
583C22×C4C22×C3×D311yescharacteristic
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—41no—
588C4⋊C4—121no—
589C4⋊C4—121no—
590C4⋊C4—121no—
591C4⋊C4—121no—
592C4⋊C4—121no—
593C22⋊C4—34no—
594C22⋊C4—34no—
595C22⋊C4—121no—
596C22⋊C4—121no—
597C22⋊C4—121no—
598C22⋊C4—121no—
599C42—41no—
600C42—121no—
601C42—121no—
602C42—121no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3C22×C4×D311yescharacteristic
618C22×C3#100411yescharacteristic
619C22×C3#100411yescharacteristic
620C22×C3#100711yescharacteristic
621C22×C3#100711yescharacteristic
622C22×C3#100911yescharacteristic
623C22×C3#101011yescharacteristic
624C22×C3C23×C3×C411yescharacteristic
625C22×C3C3×H(5,𝔽2)11yescharacteristic
626C22×C3C3×H(5,𝔽2)11yescharacteristic
627C22×C3C3×H(5,𝔽2)11yescharacteristic
628C22×C3C3×2−1+411yescharacteristic
629C22×C3C3×2−1+411yescharacteristic
630C22×C3C3×2−1+411yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—62no—
658C3×C4—62no—
659C3×C4—62no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666Dic3—22no—
667Dic3—22no—
668Dic3—22no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673C32#237811yescharacteristic, complemented, Sylow
674C23—32no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23C23×C3×D311yescharacteristic
682Q8—44no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
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—32no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
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—124no—
723C2×C4C2×C3×C4×D312yes—
724C2×C4C2×C3×C4×D312yes—
725C2×C4C2×C3×C4×D312yes—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—122no—
734C2×C3#548611yescharacteristic
735C2×C3#557211yescharacteristic
736C2×C3#557411yescharacteristic
737C2×C3#564611yescharacteristic
738C2×C3#564711yescharacteristic
739C2×C3#568411yescharacteristic
740C2×C3#573511yescharacteristic
741C2×C3C3×#51811yescharacteristic
742C2×C3C3×#51911yescharacteristic
743C2×C3C3×#52011yescharacteristic
744C2×C3C3×#56211yescharacteristic
745C2×C3C3×#56211yescharacteristic
746C2×C3C3×#56311yescharacteristic
747C2×C3C3×#56311yescharacteristic
748D3—42no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22C22×C3×C4×D311yescharacteristic
757C22C3×#100411yescharacteristic
758C22C3×#100411yescharacteristic
759C22C3×#100711yescharacteristic
760C22C3×#100711yescharacteristic
761C22C3×#100911yescharacteristic
762C22C3×#101011yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—62no—
771C4—62no—
772C4—62no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C3—21no—
778C3#7661711yescharacteristic, direct product factor
779C3C3×#237811yescharacteristic, complemented
780C2—122no—
781C2C3×#548611yescharacteristic
782C2C3×#557211yescharacteristic
783C2C3×#557411yescharacteristic
784C2C3×#564611yescharacteristic
785C2C3×#564711yescharacteristic
786C2C3×#568411yescharacteristic
787C2C3×#573511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#391C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#391D3
hypocenterC3C3×#2378
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#391

Complements

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

NH ≅ G/Ntype
2. C32×#391C2semidirect
3. C3×#5229C2semidirect
5. C3×#4976C2semidirect
7. C3×#4933C2semidirect
12. C3×#4654C2semidirect
13. C3×#4653C2semidirect
14. C3×#4652C2semidirect
15. C3×#4647C2semidirect
17. #76617C3direct (N × H)
22. C3×#946C4semidirect
58. C3×#391D3semidirect
59. C3×#391C2×C3semidirect
72. #5229C2×C3semidirect
74. #4976C2×C3semidirect
76. #4933C2×C3semidirect
81. #4654C2×C3semidirect
82. #4653C2×C3semidirect
83. #4652C2×C3semidirect
84. #4647C2×C3semidirect
155. #946C3×C4semidirect
259. #391C3×D3semidirect
673. C32#2378semidirect
778. C3#76617direct (N × H)
779. C3C3×#2378semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C32×#3912
C3×#52292
C3×#49902
C3×#49762
C3×#49402
C3×#49332
C3×#46702
C3×#46692
C3×#46672
C3×#46642
C3×#46542
C3×#46532
C3×#46522
C3×#46472
C3×#23783
#766173