Finite Group Databasebeta

← C3×#78132 #11808884

Subgroups — C3×#78132 #11808884

Order 1152.

931 conjugacy classes of subgroups.

The subgroup lattice has 761 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#400C211yesmaximal, characteristic, complemented
2C3×#4994C211yesmaximal, characteristic
3C3×#4992C211yesmaximal, characteristic
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6C3×#4675C211yesmaximal, characteristic
7C3×#4674C211yesmaximal, characteristic
8C3×#4666C211yesmaximal, characteristic
9C3×#4666C211yesmaximal, characteristic
10C3×#4666C211yesmaximal, characteristic
11C3×C3⋊#401C211yesmaximal, characteristic, complemented
12C3×#4660C211yesmaximal, characteristic, complemented
13C3×#4659C211yesmaximal, characteristic, complemented
14C3×#4649C211yesmaximal, characteristic, complemented
15C3×#4648C211yesmaximal, characteristic, complemented
16C3×#2401—31nomaximal
17#78132C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
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
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×#401—31no—
54C3×#400—21no—
55C3×#400—31no—
56C3×#400—31no—
57C3×#400D311yescharacteristic, complemented
58C3×#400C2×C311yescharacteristic, complemented
59C3×#397—31no—
60C3×#397—31no—
61C3×#397—31no—
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#4994C2×C311yescharacteristic
71#4992C2×C311yescharacteristic
72Dic3×C4⋊C4C2×C311yescharacteristic, complemented
73Dic3×C4⋊C4C2×C311yescharacteristic, complemented
74#4675C2×C311yescharacteristic
75#4674C2×C311yescharacteristic
76#4666C2×C311yescharacteristic
77#4666C2×C311yescharacteristic
78#4666C2×C311yescharacteristic
79C3⋊#401C2×C311yescharacteristic, complemented
80#4660C2×C311yescharacteristic, complemented
81#4659C2×C311yescharacteristic, complemented
82#4649C2×C311yescharacteristic, complemented
83#4648C2×C311yescharacteristic, complemented
84C23×C3×D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C32×C4⋊C4—22no—
103C32×C4⋊C4—22no—
104C3×(C2×D3)⋊C4—22no—
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×C4⋊Dic3—22no—
111C3×C4⋊Dic3—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—
122C22×C4×D3C22×C311yescharacteristic
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
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⋊C4C2×D311yescharacteristic
131C2×C3×C4⋊C4C22×C311yescharacteristic
132C2×C3×C4⋊C4C22×C311yescharacteristic
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×(C2×D3)⋊C4C22×C311yescharacteristic
146C2×(C2×D3)⋊C4C22×C311yescharacteristic
147C2×(C2×D3)⋊C4C22×C311yescharacteristic
148C2×(C2×D3)⋊C4C22×C311yescharacteristic
149C2×(C2×D3)⋊C4C22×C311yescharacteristic
150C2×(C2×D3)⋊C4C22×C311yescharacteristic
151C2×C4⋊Dic3C22×C311yescharacteristic
152C2×C4⋊Dic3C22×C311yescharacteristic
153C2×Dic3⋊C4C22×C311yescharacteristic
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×C4×Dic3C22×C311yescharacteristic
156C2×C4×Dic3C22×C311yescharacteristic
157C2×C4×Dic3C22×C311yescharacteristic
158C2×C4×Dic3C22×C311yescharacteristic
159C2×C4×Dic3C22×C311yescharacteristic
160C2×C4×Dic3C22×C311yescharacteristic
161C3×#95—21no—
162C3×#95—21no—
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×#95C2×D311yescharacteristic
178C3×#95C2×D311yescharacteristic
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×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3#4112yes—
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—21no—
224C2×C32×C4—21no—
225C2×C32×C4#4112yes—
226C2×C32×C4#4112yes—
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—21no—
244C2×C3×Dic3#4112yes—
245C2×C3×Dic3#4112yes—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248C3×C4×D3—44no—
249#401—31no—
250#400—31no—
251#400—31no—
252#400C3×D311yescharacteristic, complemented
253#397—31no—
254#397—31no—
255#397—31no—
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—31no—
265C23×D3C23×C311yescharacteristic
266C22×C3×C4—21no—
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—62no—
281C22×C3×C4—62no—
282C22×C3×C4—62no—
283C22×C3×C4C22×D311yescharacteristic
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×C3×C4C23×C311yescharacteristic
297C22×Dic3C23×C311yescharacteristic
298C22×Dic3C23×C311yescharacteristic
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C311yescharacteristic
301C22×Dic3C23×C311yescharacteristic
302C22×Dic3C23×C311yescharacteristic
303C22×Dic3C23×C311yescharacteristic
304C2×C4×D3—22no—
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C3×C4⋊C4—22no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4—42no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4—62no—
315C3×C4⋊C4—62no—
316C3×C4⋊C4—62no—
317C3×C22⋊C4—62no—
318C3×C22⋊C4—62no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—62no—
323C3×C42—62no—
324C3×C42—62no—
325C3×C42—62no—
326C3×C42—62no—
327C3×C42—62no—
328C3×C42—62no—
329(C2×D3)⋊C4—22no—
330(C2×D3)⋊C4—22no—
331(C2×D3)⋊C4—22no—
332(C2×D3)⋊C4—22no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—22no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337Dic3⋊C4—22no—
338Dic3⋊C4—22no—
339C4×Dic3—22no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—22no—
343C4×Dic3—22no—
344C4×Dic3—22no—
345C22×C32C2×#4111yescharacteristic
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—41no—
356C2×C3×D3—41no—
357C2×C3×D3—41no—
358C2×C3×D3—41no—
359C32×C4—22no—
360C32×C4—22no—
361C32×C4—41no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C3×Dic3—22no—
367C3×Dic3—41no—
368C3×Dic3—41no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3#12614yes—
373C23×C4—31no—
374C2×C4⋊C4—31no—
375C2×C4⋊C4—31no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4C2×C3×D311yescharacteristic
379C2×C4⋊C4C2×C3×D311yescharacteristic
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C42—31no—
387C2×C42—31no—
388C2×C42—31no—
389C2×C42—31no—
390C2×C42—31no—
391C2×C42—31no—
392#95—31no—
393#95—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#95C2×C3×D311yescharacteristic
404#95C2×C3×D311yescharacteristic
405#95C2×C3×D311yescharacteristic
406#95C2×C3×D311yescharacteristic
407#95C2×C3×D311yescharacteristic
408C23×C3—21no—
409C23×C3—32no—
410C23×C3—61no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3C23×D311yescharacteristic
417C23×C3C24×C311yescharacteristic
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3C3×#4112yes—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
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—22no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
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—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
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—124no—
506C2×C3×C4#23712yes—
507C2×C3×C4#23912yes—
508C2×C3×C4C3×#4112yes—
509C2×C3×C4C3×#4112yes—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
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×Dic3C3×#4112yes—
528C2×Dic3C3×#4112yes—
529C2×Dic3C3×#4112yes—
530C2×Dic3C3×#4112yes—
531C4×D3—44no—
532C2×C32C2×#12611yescharacteristic
533C2×C32#52911yescharacteristic
534C2×C32#52911yescharacteristic
535C2×C32#52911yescharacteristic
536C2×C32#52911yescharacteristic
537C2×C32#52911yescharacteristic
538C2×C32#52911yescharacteristic
539C3×D3—42no—
540C24—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4C22×C3×D311yescharacteristic
552C22×C4C22×C3×D311yescharacteristic
553C22×C4C22×C3×D311yescharacteristic
554C22×C4C22×C3×D311yescharacteristic
555C22×C4C22×C3×D311yescharacteristic
556C22×C4C22×C3×D311yescharacteristic
557C22×C4C22×C3×D311yescharacteristic
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—62no—
563C4⋊C4—62no—
564C22⋊C4—62no—
565C22⋊C4—62no—
566C22⋊C4—62no—
567C22⋊C4—62no—
568C22⋊C4—62no—
569C22⋊C4—62no—
570C42—62no—
571C42—62no—
572C42—62no—
573C42—62no—
574C42—62no—
575C42—62no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—62no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3C2×#23711yescharacteristic
591C22×C3C2×#23911yescharacteristic
592C22×C3D3×#4111yescharacteristic
593C22×C3D3×#4111yescharacteristic
594C22×C3D3×#4111yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C22×C3C2×C3×#4111yescharacteristic
598C22×C3C2×C3×#4111yescharacteristic
599C22×C3C2×C3×#4111yescharacteristic
600C22×C3C2×C3×#4111yescharacteristic
601C22×C3C2×C3×#4111yescharacteristic
602C22×C3C2×C3×#4111yescharacteristic
603C22×C3C2×C3×#4111yescharacteristic
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—34no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—62no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—81no—
634C3×C4—121no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4—121no—
639Dic3—22no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—41no—
644Dic3—41no—
645Dic3C3×#12614yes—
646C32#240111yescharacteristic, complemented, Sylow
647C23—32no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23C23×C3×D311yescharacteristic
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—124no—
696C2×C4C3×#23712yes—
697C2×C4C3×#23912yes—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—122no—
706C2×C3#562411yescharacteristic
707C2×C3#564911yescharacteristic
708C2×C3#568011yescharacteristic
709C2×C3#569111yescharacteristic
710C2×C3#569111yescharacteristic
711C2×C3D3×#12611yescharacteristic
712C2×C3#570611yescharacteristic
713C2×C3C2×C3×#12611yescharacteristic
714C2×C3C3×#52911yescharacteristic
715C2×C3C3×#52911yescharacteristic
716C2×C3C3×#52911yescharacteristic
717C2×C3C3×#52911yescharacteristic
718C2×C3C3×#52911yescharacteristic
719C2×C3C3×#52911yescharacteristic
720D3—42no—
721C22—62no—
722C22—62no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22C2×C3×#23711yescharacteristic
729C22C2×C3×#23911yescharacteristic
730C22C3×D3×#4111yescharacteristic
731C22C3×D3×#4111yescharacteristic
732C22C3×D3×#4111yescharacteristic
733C22C3×D3×#4111yescharacteristic
734C22C3×D3×#4111yescharacteristic
735C4—22no—
736C4—22no—
737C4—34no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—62no—
744C4—121no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C3—21no—
750C3#7813211yescharacteristic, direct product factor
751C3C3×#240111yescharacteristic, complemented
752C2—122no—
753C2C3×#562411yescharacteristic
754C2C3×#564911yescharacteristic
755C2C3×#568011yescharacteristic
756C2C3×#569111yescharacteristic
757C2C3×#569111yescharacteristic
758C2C3×D3×#12611yescharacteristic
759C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#400C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×#400D3
hypocenterC3C3×#2401
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#400

Complements

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

NH ≅ G/Ntype
1. C32×#400C2semidirect
4. C3×Dic3×C4⋊C4C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
11. C3×C3⋊#401C2semidirect
12. C3×#4660C2semidirect
13. C3×#4659C2semidirect
14. C3×#4649C2semidirect
15. C3×#4648C2semidirect
17. #78132C3direct (N × H)
57. C3×#400D3semidirect
58. C3×#400C2×C3semidirect
72. Dic3×C4⋊C4C2×C3semidirect
73. Dic3×C4⋊C4C2×C3semidirect
79. C3⋊#401C2×C3semidirect
80. #4660C2×C3semidirect
81. #4659C2×C3semidirect
82. #4649C2×C3semidirect
83. #4648C2×C3semidirect
252. #400C3×D3semidirect
646. C32#2401semidirect
750. C3#78132direct (N × H)
751. C3C3×#2401semidirect

Maximal subgroups

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

subgroupindex
C32×#4002
C3×#49942
C3×#49922
C3×Dic3×C4⋊C42
C3×#46752
C3×#46742
C3×#46662
C3×C3⋊#4012
C3×#46602
C3×#46592
C3×#46492
C3×#46482
C3×#24013
#781323