Finite Group Databasebeta

← C3×#73353 #11819140

Subgroups — C3×#73353 #11819140

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#95C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C3×#5211C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic
5C3×#5210C211yesmaximal, characteristic
6C3×#5210C211yesmaximal, characteristic
7C3×C4×#217C211yesmaximal, characteristic
8C3×C3⋊#401C211yesmaximal, characteristic, complemented
9C3×#4660C211yesmaximal, characteristic, complemented
10C3×#4659C211yesmaximal, characteristic, complemented
11C3×#4658C211yesmaximal, characteristic, complemented
12C3×#4655C211yesmaximal, characteristic, complemented
13C3×#4653C211yesmaximal, characteristic, complemented
14C3×#4652C211yesmaximal, characteristic, complemented
15C3×#4651C211yesmaximal, characteristic, complemented
16C3×#2493—31nomaximal
17#73353C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
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
33C32×#95C2211yescharacteristic
34C32×#95C2211yescharacteristic
35C32×#95C2211yescharacteristic
36C32×#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#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×#387—31no—
58C3×#387—31no—
59C3×#387—31no—
60C3×#385—31no—
61C3×#385—31no—
62C3×#383—31no—
63C3×#381—31no—
64C3×#381—31no—
65C3×#380—31no—
66C3×C4×C22⋊C4—31no—
67C2×C3×#95—21no—
68C2×C3×#95D311yescharacteristic
69C2×C3×#95C2×C311yescharacteristic
70#5212C2×C311yescharacteristic
71#5211C2×C311yescharacteristic
72#5211C2×C311yescharacteristic
73#5210C2×C311yescharacteristic
74#5210C2×C311yescharacteristic
75C4×#217C2×C311yescharacteristic
76C3⋊#401C2×C311yescharacteristic, complemented
77#4660C2×C311yescharacteristic, complemented
78#4659C2×C311yescharacteristic, complemented
79#4658C2×C311yescharacteristic, complemented
80#4655C2×C311yescharacteristic, complemented
81#4653C2×C311yescharacteristic, complemented
82#4652C2×C311yescharacteristic, complemented
83#4651C2×C311yescharacteristic, complemented
84C24×C32C2311yescharacteristic
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—22no—
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4—22no—
92C22×C32×C4—41no—
93C22×C32×C4—41no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C3×#217—22no—
109C3×#217—22no—
110C3×#217—22no—
111C3×#217—22no—
112C3×C4⋊Dic3—22no—
113C3×C4⋊Dic3—41no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—41no—
117C3×Dic3⋊C4—41no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—41no—
120#2493—31noSylow
121C23×C3×C4—21no—
122C23×C3×C4—21no—
123C23×C3×C4—21no—
124C23×C3×C4C2×D311yescharacteristic
125C23×C3×C4C2×D311yescharacteristic
126C23×C3×C4C2×D311yescharacteristic
127C23×C3×C4C22×C311yescharacteristic
128C23×C3×C4C22×C311yescharacteristic
129C23×C3×C4C22×C311yescharacteristic
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×#217C22×C311yescharacteristic
143C2×#217C22×C311yescharacteristic
144C2×#217C22×C311yescharacteristic
145C2×#217C22×C311yescharacteristic
146C2×C4⋊Dic3C22×C311yescharacteristic
147C2×C4⋊Dic3C22×C311yescharacteristic
148C2×Dic3⋊C4C22×C311yescharacteristic
149C2×Dic3⋊C4C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C311yescharacteristic
151C2×Dic3⋊C4C22×C311yescharacteristic
152C2×C4×Dic3C22×C311yescharacteristic
153C2×C4×Dic3C22×C311yescharacteristic
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—31no—
159C3×#95—31no—
160C3×#95—31no—
161C3×#95—31no—
162C3×#95—31no—
163C3×#95—31no—
164C3×#95—31no—
165C3×#95—31no—
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×#95C2×D311yescharacteristic
175C3×#95C2×D311yescharacteristic
176C3×#95C2×D311yescharacteristic
177C3×#95C2×D311yescharacteristic
178C3×#95C22×C311yescharacteristic
179C3×#95C22×C311yescharacteristic
180C3×#95C22×C311yescharacteristic
181C3×#95C22×C311yescharacteristic
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#4112yes—
203C23×C32#4112yes—
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—44no—
223C2×C32×C4—44no—
224C2×C32×C4—44no—
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—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—
251#401—31no—
252#400—31no—
253#400—31no—
254#400—31no—
255#387—31no—
256#387—31no—
257#387—31no—
258#385—31no—
259#385—31no—
260#383—31no—
261#381—31no—
262#381—31no—
263#380—31no—
264C4×C22⋊C4—31no—
265C2×#95C3×D311yescharacteristic
266C24×C3—21no—
267C24×C3C22×D311yescharacteristic
268C24×C3C23×C311yescharacteristic
269C22×C3×C4—24no—
270C22×C3×C4—24no—
271C22×C3×C4—24no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—42no—
301C22×C3×C4—42no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4—41no—
305C22×C3×C4—41no—
306C22×C3×C4—41no—
307C22×C3×C4—41no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C23×C311yescharacteristic
317C22×C3×C4C23×C311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C22×Dic3C23×C311yescharacteristic
325C22×Dic3C23×C311yescharacteristic
326C22×Dic3C23×C311yescharacteristic
327C22×Dic3C23×C311yescharacteristic
328C22×Dic3C23×C311yescharacteristic
329C22×Dic3C23×C311yescharacteristic
330C3×C4⋊C4—62no—
331C3×C4⋊C4—62no—
332C3×C4⋊C4—62no—
333C3×C4⋊C4—121no—
334C3×C4⋊C4—121no—
335C3×C4⋊C4—121no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—62no—
338C3×C22⋊C4—62no—
339C3×C22⋊C4—62no—
340C3×C42—62no—
341C3×C42—121no—
342#217—22no—
343#217—22no—
344#217—22no—
345#217—22no—
346C4⋊Dic3—22no—
347C4⋊Dic3—41no—
348Dic3⋊C4—22no—
349Dic3⋊C4—22no—
350Dic3⋊C4—41no—
351Dic3⋊C4—41no—
352C4×Dic3—22no—
353C4×Dic3—41no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32#12614yes—
361C22×C32C2×#4111yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32C2×#4111yescharacteristic
365C22×C32C2×#4111yescharacteristic
366C22×C32H(5,𝔽2)11yescharacteristic
367C22×C322−1+411yescharacteristic
368C32×C4—22no—
369C32×C4—22no—
370C32×C4—41no—
371C32×C4—41no—
372C32×C4—41no—
373C32×C4—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C3×Dic3—41no—
379C3×Dic3—41no—
380C3×Dic3—41no—
381C3×Dic3—41no—
382C23×C4C2×C3×D311yescharacteristic
383C23×C4C2×C3×D311yescharacteristic
384C23×C4C2×C3×D311yescharacteristic
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C22⋊C4—31no—
392C2×C22⋊C4—31no—
393C2×C22⋊C4—31no—
394C2×C22⋊C4—31no—
395C2×C42—31no—
396C2×C42—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#95—31no—
408#95—31no—
409#95—31no—
410#95—31no—
411#95—31no—
412#95—31no—
413#95C2×C3×D311yescharacteristic
414#95C2×C3×D311yescharacteristic
415#95C2×C3×D311yescharacteristic
416#95C2×C3×D311yescharacteristic
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3#23512yes—
434C23×C3#23712yes—
435C23×C3#23712yes—
436C23×C3C3×#4112yes—
437C23×C3C3×#4112yes—
438C23×C3C3×#4112yes—
439C23×C3C23×D311yescharacteristic
440C23×C3C24×C311yescharacteristic
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—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
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—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—22no—
478C2×C3×C4—22no—
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—44no—
492C2×C3×C4—44no—
493C2×C3×C4—44no—
494C2×C3×C4—44no—
495C2×C3×C4—48no—
496C2×C3×C4—48no—
497C2×C3×C4—48no—
498C2×C3×C4—44no—
499C2×C3×C4—44no—
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—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#23512yes—
525C2×C3×C4#23512yes—
526C2×C3×C4C3×#4112yes—
527C2×C3×C4C3×#4112yes—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
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×C32—24no—
553C2×C32C2×#12611yescharacteristic
554C2×C32#52911yescharacteristic
555C2×C32#53911yescharacteristic
556C2×C32#55111yescharacteristic
557C2×C32#55111yescharacteristic
558C2×C32#55211yescharacteristic
559C2×C32#55211yescharacteristic
560C24C22×C3×D311yescharacteristic
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—41no—
577C22×C4—41no—
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—62no—
585C4⋊C4—62no—
586C4⋊C4—62no—
587C4⋊C4—121no—
588C4⋊C4—121no—
589C4⋊C4—121no—
590C22⋊C4—62no—
591C22⋊C4—62no—
592C22⋊C4—62no—
593C22⋊C4—62no—
594C42—62no—
595C42—121no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—24no—
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—24no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3#87914yes—
623C22×C3C3×#12614yes—
624C22×C3C2×#23511yescharacteristic
625C22×C3C2×#23511yescharacteristic
626C22×C3C2×#23511yescharacteristic
627C22×C3C2×#23711yescharacteristic
628C22×C3C2×#23711yescharacteristic
629C22×C3#100411yescharacteristic
630C22×C3#100711yescharacteristic
631C22×C3C2×C3×#4111yescharacteristic
632C22×C3C2×C3×#4111yescharacteristic
633C22×C3C2×C3×#4111yescharacteristic
634C22×C3C2×C3×#4111yescharacteristic
635C22×C3C2×C3×#4111yescharacteristic
636C22×C3C3×H(5,𝔽2)11yescharacteristic
637C22×C3C3×2−1+411yescharacteristic
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672C32#249311yescharacteristic, complemented, Sylow
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23C3×#23512yes—
678C23C3×#23712yes—
679C23C3×#23712yes—
680C23C23×C3×D311yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
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—44no—
698C2×C4—44no—
699C2×C4—44no—
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—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—61no—
723C2×C4—61no—
724C2×C4C3×#23512yes—
725C2×C4C3×#23512yes—
726C2×C3—28no—
727C2×C3—24no—
728C2×C3—24no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3#547911yescharacteristic
737C2×C3C2×#87911yescharacteristic
738C2×C3#549511yescharacteristic
739C2×C3#549511yescharacteristic
740C2×C3#551311yescharacteristic
741C2×C3#551311yescharacteristic
742C2×C3#551511yescharacteristic
743C2×C3C2×C3×#12611yescharacteristic
744C2×C3C3×#52911yescharacteristic
745C2×C3C3×#53911yescharacteristic
746C2×C3C3×#55111yescharacteristic
747C2×C3C3×#55111yescharacteristic
748C2×C3C3×#55211yescharacteristic
749C2×C3C3×#55211yescharacteristic
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22C3×#87914yes—
757C22C2×C3×#23511yescharacteristic
758C22C2×C3×#23511yescharacteristic
759C22C2×C3×#23511yescharacteristic
760C22C2×C3×#23711yescharacteristic
761C22C2×C3×#23711yescharacteristic
762C22C3×#100411yescharacteristic
763C22C3×#100711yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—121no—
778C3—21no—
779C3#7335311yescharacteristic, direct product factor
780C3C3×#249311yescharacteristic, complemented
781C2—24no—
782C2C3×#547911yescharacteristic
783C2C2×C3×#87911yescharacteristic
784C2C3×#549511yescharacteristic
785C2C3×#549511yescharacteristic
786C2C3×#551311yescharacteristic
787C2C3×#551311yescharacteristic
788C2C3×#551511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C3×#95D3
hypocenterC3C3×#2493
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. C3×C3⋊#401C2semidirect
9. C3×#4660C2semidirect
10. C3×#4659C2semidirect
11. C3×#4658C2semidirect
12. C3×#4655C2semidirect
13. C3×#4653C2semidirect
14. C3×#4652C2semidirect
15. C3×#4651C2semidirect
17. #73353C3direct (N × H)
76. C3⋊#401C2×C3semidirect
77. #4660C2×C3semidirect
78. #4659C2×C3semidirect
79. #4658C2×C3semidirect
80. #4655C2×C3semidirect
81. #4653C2×C3semidirect
82. #4652C2×C3semidirect
83. #4651C2×C3semidirect
672. C32#2493semidirect
779. C3#73353direct (N × H)
780. C3C3×#2493semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#952
C3×#52122
C3×#52112
C3×#52102
C3×C4×#2172
C3×C3⋊#4012
C3×#46602
C3×#46592
C3×#46582
C3×#46552
C3×#46532
C3×#46522
C3×#46512
C3×#24933
#733533