Finite Group Databasebeta

← C3×#77461 #11808878

Subgroups — C3×#77461 #11808878

Order 1152.

949 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#397C211yesmaximal, characteristic
2C3×#4985C211yesmaximal, characteristic, complemented
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×#4952C211yesmaximal, characteristic
5C3×#4952C211yesmaximal, characteristic
6C3×#4948C211yesmaximal, characteristic
7C3×Dic3×C22⋊C4C211yesmaximal, characteristic
8C3×Dic3×C22⋊C4C211yesmaximal, characteristic
9C3×Dic3×C22⋊C4C211yesmaximal, characteristic
10C3×C3⋊#401C211yesmaximal, characteristic, complemented
11C3×#4660C211yesmaximal, characteristic, complemented
12C3×#4658C211yesmaximal, characteristic, complemented
13C3×#4649C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4648C211yesmaximal, characteristic, complemented
16C3×#2401—31nomaximal
17#77461C311yesmaximal, characteristic, direct product factor
18C23×C3×Dic3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C32×#95C2211yescharacteristic
38C32×#95C2211yescharacteristic
39C32×#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#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×#401—31no—
54C3×#400—31no—
55C3×#400—31no—
56C3×#400—31no—
57C3×#397—21no—
58C3×#397—31no—
59C3×#397—31no—
60C3×#397D311yescharacteristic
61C3×#397C2×C311yescharacteristic
62C3×#396—31no—
63C3×C4×C4⋊C4—31no—
64C3×C4×C4⋊C4—31no—
65C3×C4×C4⋊C4—31no—
66C3×C4×C22⋊C4—31no—
67C3×C4×C22⋊C4—31no—
68C3×C4×C22⋊C4—31no—
69C3×#376—31no—
70#4985C2×C311yescharacteristic, complemented
71Dic3×C4⋊C4C2×C311yescharacteristic, complemented
72#4952C2×C311yescharacteristic
73#4952C2×C311yescharacteristic
74#4948C2×C311yescharacteristic
75Dic3×C22⋊C4C2×C311yescharacteristic
76Dic3×C22⋊C4C2×C311yescharacteristic
77Dic3×C22⋊C4C2×C311yescharacteristic
78C3⋊#401C2×C311yescharacteristic, complemented
79#4660C2×C311yescharacteristic, complemented
80#4658C2×C311yescharacteristic, complemented
81#4649C2×C311yescharacteristic, complemented
82#4649C2×C311yescharacteristic, complemented
83#4648C2×C311yescharacteristic, complemented
84C24×C32C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C3×Dic3—22no—
92C22×C3×Dic3—22no—
93C22×C3×Dic3—22no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C32×C4⋊C4—22no—
103C32×C22⋊C4—22no—
104C32×C22⋊C4—22no—
105C32×C22⋊C4—22no—
106C3×#217—22no—
107C3×#217—22no—
108C3×#217—22no—
109C3×C4⋊Dic3—22no—
110C3×Dic3⋊C4—22no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—22no—
114C3×C4×Dic3—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—22no—
120#2401—31noSylow
121C23×C3×C4—31no—
122C23×Dic3C22×C311yescharacteristic
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C22×C311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4C2×D311yescharacteristic
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C22×C311yescharacteristic
141C2×C3×C22⋊C4C22×C311yescharacteristic
142C2×C3×C22⋊C4C22×C311yescharacteristic
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C3×C42—31no—
147C2×C3×C42—31no—
148C2×C3×C42—31no—
149C2×#217C22×C311yescharacteristic
150C2×#217C22×C311yescharacteristic
151C2×#217C22×C311yescharacteristic
152C2×C4⋊Dic3C22×C311yescharacteristic
153C2×Dic3⋊C4C22×C311yescharacteristic
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×Dic3⋊C4C22×C311yescharacteristic
156C2×Dic3⋊C4C22×C311yescharacteristic
157C2×C4×Dic3C22×C311yescharacteristic
158C2×C4×Dic3C22×C311yescharacteristic
159C2×C4×Dic3C22×C311yescharacteristic
160C2×C4×Dic3C22×C311yescharacteristic
161C2×C4×Dic3C22×C311yescharacteristic
162C2×C4×Dic3C22×C311yescharacteristic
163C3×#95—21no—
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95—31no—
176C3×#95—31no—
177C3×#95—31no—
178C3×#95—31no—
179C3×#95C2×D311yescharacteristic
180C3×#95C2×D311yescharacteristic
181C3×#95C2×D311yescharacteristic
182C3×#95C22×C311yescharacteristic
183C3×#95C22×C311yescharacteristic
184C3×#95C22×C311yescharacteristic
185C3⋊#95C22×C311yescharacteristic
186C3⋊#95C22×C311yescharacteristic
187C3⋊#95C22×C311yescharacteristic
188C3⋊#95C22×C311yescharacteristic
189C3⋊#95C22×C311yescharacteristic
190C3⋊#95C22×C311yescharacteristic
191C3⋊#95C22×C311yescharacteristic
192C3⋊#95C22×C311yescharacteristic
193C3⋊#95C22×C311yescharacteristic
194C3⋊#95C22×C311yescharacteristic
195C3⋊#95C22×C311yescharacteristic
196C3⋊#95C22×C311yescharacteristic
197C3⋊#95C22×C311yescharacteristic
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32#4112yes—
205C23×C32C2411yescharacteristic
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
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#4112yes—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
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—44no—
244C2×C3×Dic3#4112yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248C2×C3×Dic3#4112yes—
249#401—31no—
250#400—31no—
251#400—31no—
252#400—31no—
253#397—31no—
254#397—31no—
255#397C3×D311yescharacteristic
256#396—31no—
257C4×C4⋊C4—31no—
258C4×C4⋊C4—31no—
259C4×C4⋊C4—31no—
260C4×C22⋊C4—31no—
261C4×C22⋊C4—31no—
262C4×C22⋊C4—31no—
263#376—31no—
264C24×C3—21no—
265C24×C3C22×D311yescharacteristic
266C24×C3C23×C311yescharacteristic
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—62no—
282C22×C3×C4—62no—
283C22×C3×C4—62no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C23×C311yescharacteristic
291C22×C3×C4C23×C311yescharacteristic
292C22×C3×C4C23×C311yescharacteristic
293C22×C3×C4C23×C311yescharacteristic
294C22×C3×C4C23×C311yescharacteristic
295C22×C3×C4C23×C311yescharacteristic
296C22×Dic3—22no—
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C311yescharacteristic
301C22×Dic3C23×C311yescharacteristic
302C22×Dic3C23×C311yescharacteristic
303C22×Dic3C23×C311yescharacteristic
304C22×Dic3C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C311yescharacteristic
307C3×C4⋊C4—22no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—42no—
310C3×C4⋊C4—62no—
311C3×C4⋊C4—62no—
312C3×C4⋊C4—62no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—62no—
326C3×C22⋊C4—62no—
327C3×C42—62no—
328C3×C42—62no—
329C3×C42—62no—
330C3×C42—62no—
331C3×C42—62no—
332C3×C42—62no—
333#217—22no—
334#217—22no—
335#217—22no—
336C4⋊Dic3—22no—
337Dic3⋊C4—22no—
338Dic3⋊C4—22no—
339Dic3⋊C4—22no—
340Dic3⋊C4—22no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—41no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C32×C4—22no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C32×C4—41no—
367C3×Dic3—22no—
368C3×Dic3—22no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3#12614yes—
375C23×C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4C2×C3×D311yescharacteristic
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4C2×C3×D311yescharacteristic
386C2×C22⋊C4C2×C3×D311yescharacteristic
387C2×C22⋊C4C2×C3×D311yescharacteristic
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—31no—
392C2×C42—31no—
393C2×C42—31no—
394#95—31no—
395#95—31no—
396#95—31no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—31no—
403#95—31no—
404#95—31no—
405#95—31no—
406#95—31no—
407#95C2×C3×D311yescharacteristic
408#95C2×C3×D311yescharacteristic
409#95C2×C3×D311yescharacteristic
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—22no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3#23712yes—
431C23×C3C3×#4112yes—
432C23×C3C23×D311yescharacteristic
433C23×C3C24×C311yescharacteristic
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
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—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
473C2×C3×C4—32no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—124no—
511C2×C3×C4#23712yes—
512C2×C3×C4C3×#4112yes—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—44no—
533C2×Dic3C3×#4112yes—
534C2×Dic3C3×#4112yes—
535C2×Dic3C3×#4112yes—
536C2×Dic3C3×#4112yes—
537C2×Dic3C3×#4112yes—
538C2×C32—42no—
539C2×C32C2×#12611yescharacteristic
540C2×C32#52911yescharacteristic
541C2×C32#52911yescharacteristic
542C2×C32#52911yescharacteristic
543C2×C32#52911yescharacteristic
544C2×C32#52911yescharacteristic
545C2×C32#52911yescharacteristic
546C24C22×C3×D311yescharacteristic
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4C22×C3×D311yescharacteristic
559C22×C4C22×C3×D311yescharacteristic
560C22×C4C22×C3×D311yescharacteristic
561C22×C4C22×C3×D311yescharacteristic
562C22×C4C22×C3×D311yescharacteristic
563C22×C4C22×C3×D311yescharacteristic
564C4⋊C4—22no—
565C4⋊C4—62no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C42—62no—
577C42—62no—
578C42—62no—
579C42—62no—
580C42—62no—
581C42—62no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—81no—
607C22×C3—81no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3C2×#23711yescharacteristic
611C22×C3C2×#23711yescharacteristic
612C22×C3D3×#4111yescharacteristic
613C22×C3D3×#4111yescharacteristic
614C22×C3D3×#4111yescharacteristic
615C22×C3D3×#4111yescharacteristic
616C22×C3D3×#4111yescharacteristic
617C22×C3C2×C3×#4111yescharacteristic
618C22×C3C2×C3×#4111yescharacteristic
619C22×C3C2×C3×#4111yescharacteristic
620C22×C3C2×C3×#4111yescharacteristic
621C22×C3C2×C3×#4111yescharacteristic
622C22×C3C2×C3×#4111yescharacteristic
623C22×C3C2×C3×#4111yescharacteristic
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—34no—
627C3×C4—42no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—62no—
639C3×C4—62no—
640C3×C4—81no—
641C3×C4—81no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4—81no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650Dic3—22no—
651Dic3—22no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3C3×#12614yes—
658C32#240111yescharacteristic, complemented, Sylow
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23C3×#23712yes—
666C23C23×C3×D311yescharacteristic
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—124no—
709C2×C4C3×#23712yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—42no—
719C2×C3—82no—
720C2×C3#560011yescharacteristic
721C2×C3#564911yescharacteristic
722C2×C3#564911yescharacteristic
723C2×C3#564911yescharacteristic
724C2×C3#568011yescharacteristic
725C2×C3D3×#12611yescharacteristic
726C2×C3#570611yescharacteristic
727C2×C3C2×C3×#12611yescharacteristic
728C2×C3C3×#52911yescharacteristic
729C2×C3C3×#52911yescharacteristic
730C2×C3C3×#52911yescharacteristic
731C2×C3C3×#52911yescharacteristic
732C2×C3C3×#52911yescharacteristic
733C2×C3C3×#52911yescharacteristic
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22C2×C3×#23711yescharacteristic
742C22C2×C3×#23711yescharacteristic
743C22C3×D3×#4111yescharacteristic
744C22C3×D3×#4111yescharacteristic
745C22C3×D3×#4111yescharacteristic
746C22C3×D3×#4111yescharacteristic
747C22C3×D3×#4111yescharacteristic
748C4—22no—
749C4—34no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—62no—
756C4—62no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C3—21no—
763C3#7746111yescharacteristic, direct product factor
764C3C3×#240111yescharacteristic, complemented
765C2—42no—
766C2C3×#560011yescharacteristic
767C2C3×#564911yescharacteristic
768C2C3×#564911yescharacteristic
769C2C3×#564911yescharacteristic
770C2C3×#568011yescharacteristic
771C2C3×D3×#12611yescharacteristic
772C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#397C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×#397D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#397

Complements

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

NH ≅ G/Ntype
2. C3×#4985C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
10. C3×C3⋊#401C2semidirect
11. C3×#4660C2semidirect
12. C3×#4658C2semidirect
13. C3×#4649C2semidirect
14. C3×#4649C2semidirect
15. C3×#4648C2semidirect
17. #77461C3direct (N × H)
70. #4985C2×C3semidirect
71. Dic3×C4⋊C4C2×C3semidirect
78. C3⋊#401C2×C3semidirect
79. #4660C2×C3semidirect
80. #4658C2×C3semidirect
81. #4649C2×C3semidirect
82. #4649C2×C3semidirect
83. #4648C2×C3semidirect
658. C32#2401semidirect
763. C3#77461direct (N × H)
764. C3C3×#2401semidirect

Maximal subgroups

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

subgroupindex
C32×#3972
C3×#49852
C3×Dic3×C4⋊C42
C3×#49522
C3×#49482
C3×Dic3×C22⋊C42
C3×C3⋊#4012
C3×#46602
C3×#46582
C3×#46492
C3×#46482
C3×#24013
#774613