Finite Group Databasebeta

← C3×#78430 #11819125

Subgroups — C3×#78430 #11819125

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#401C211yesmaximal, characteristic, complemented
2C3×#4668C211yesmaximal, characteristic
3C3×#4668C211yesmaximal, characteristic
4C3×#4667C211yesmaximal, characteristic
5C3×#4666C211yesmaximal, characteristic
6C3×#4664C211yesmaximal, characteristic
7C3×#4664C211yesmaximal, characteristic
8C3×D3×#95C211yesmaximal, characteristic
9C3×#4660C211yesmaximal, characteristic, complemented
10C3×#4658C211yesmaximal, characteristic, complemented
11C3×#4658C211yesmaximal, characteristic, complemented
12C3×#4655C211yesmaximal, characteristic, complemented
13C3×#4654C211yesmaximal, characteristic, complemented
14C3×#4653C211yesmaximal, characteristic, complemented
15C3×#4651C211yesmaximal, characteristic, complemented
16C3×#2493—31nomaximal
17#78430C311yesmaximal, characteristic, direct product factor
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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
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—21no—
54C3×#401D311yescharacteristic, complemented
55C3×#401C2×C311yescharacteristic, complemented
56C3×#400—31no—
57C3×#400—31no—
58C3×#400—31no—
59C3×#387—31no—
60C3×#387—31no—
61C3×#387—31no—
62C3×#385—31no—
63C3×#385—31no—
64C3×#383—31no—
65C3×#381—31no—
66C3×#381—31no—
67C3×#380—31no—
68C3×C4×C22⋊C4—31no—
69C2×C3×#95—31no—
70#4668C2×C311yescharacteristic
71#4668C2×C311yescharacteristic
72#4667C2×C311yescharacteristic
73#4666C2×C311yescharacteristic
74#4664C2×C311yescharacteristic
75#4664C2×C311yescharacteristic
76D3×#95C2×C311yescharacteristic
77#4660C2×C311yescharacteristic, complemented
78#4658C2×C311yescharacteristic, complemented
79#4658C2×C311yescharacteristic, complemented
80#4655C2×C311yescharacteristic, complemented
81#4654C2×C311yescharacteristic, complemented
82#4653C2×C311yescharacteristic, complemented
83#4651C2×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—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—41no—
107C2×C3×C4×D3—41no—
108C3×(C2×D3)⋊C4—22no—
109C3×(C2×D3)⋊C4—22no—
110C3×(C2×D3)⋊C4—22no—
111C3×(C2×D3)⋊C4—22no—
112C3×C4⋊Dic3—22no—
113C3×C4⋊Dic3—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—41no—
116C3×Dic3⋊C4—41no—
117C3×Dic3⋊C4—41no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3—41no—
120#2493—31noSylow
121C23×C3×C4—31no—
122C23×C3×C4—31no—
123C23×C3×C4—31no—
124C22×C4×D3C22×C311yescharacteristic
125C22×C4×D3C22×C311yescharacteristic
126C22×C4×D3C22×C311yescharacteristic
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C42—31no—
138C2×C3×C42—31no—
139C2×(C2×D3)⋊C4C22×C311yescharacteristic
140C2×(C2×D3)⋊C4C22×C311yescharacteristic
141C2×(C2×D3)⋊C4C22×C311yescharacteristic
142C2×(C2×D3)⋊C4C22×C311yescharacteristic
143C2×C4⋊Dic3C22×C311yescharacteristic
144C2×C4⋊Dic3C22×C311yescharacteristic
145C2×Dic3⋊C4C22×C311yescharacteristic
146C2×Dic3⋊C4C22×C311yescharacteristic
147C2×Dic3⋊C4C22×C311yescharacteristic
148C2×Dic3⋊C4C22×C311yescharacteristic
149C2×C4×Dic3C22×C311yescharacteristic
150C2×C4×Dic3C22×C311yescharacteristic
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
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×#95C2×D311yescharacteristic
172C3×#95C2×D311yescharacteristic
173C3×#95C2×D311yescharacteristic
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×C32C2411yescharacteristic
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3#4112yes—
204C22×C3×D3#4112yes—
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—21no—
226C2×C32×C4—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—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3#4112yes—
247C2×C3×Dic3#4112yes—
248C3×C4×D3—44no—
249C3×C4×D3—44no—
250C3×C4×D3—44no—
251#401C3×D311yescharacteristic, complemented
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×#95—31no—
266C24×C3—31no—
267C23×D3C23×C311yescharacteristic
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
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—31no—
282C22×C3×C4—62no—
283C22×C3×C4—62no—
284C22×C3×C4—62no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4—62no—
288C22×C3×C4—62no—
289C22×C3×C4—121no—
290C22×C3×C4—121no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C23×C311yescharacteristic
299C22×C3×C4C23×C311yescharacteristic
300C22×C3×C4C23×C311yescharacteristic
301C22×C3×C4C23×C311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C22×Dic3C23×C311yescharacteristic
306C22×Dic3C23×C311yescharacteristic
307C22×Dic3C23×C311yescharacteristic
308C22×Dic3C23×C311yescharacteristic
309C22×Dic3C23×C311yescharacteristic
310C22×Dic3C23×C311yescharacteristic
311C22×Dic3C23×C311yescharacteristic
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—22no—
317C2×C4×D3—22no—
318C2×C4×D3—22no—
319C2×C4×D3—41no—
320C2×C4×D3—41no—
321C3×C4⋊C4—62no—
322C3×C4⋊C4—62no—
323C3×C4⋊C4—62no—
324C3×C4⋊C4—121no—
325C3×C4⋊C4—121no—
326C3×C4⋊C4—121no—
327C3×C22⋊C4—62no—
328C3×C22⋊C4—62no—
329C3×C22⋊C4—62no—
330C3×C22⋊C4—62no—
331C3×C42—62no—
332C3×C42—121no—
333(C2×D3)⋊C4—22no—
334(C2×D3)⋊C4—22no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—22no—
337C4⋊Dic3—22no—
338C4⋊Dic3—22no—
339Dic3⋊C4—22no—
340Dic3⋊C4—41no—
341Dic3⋊C4—41no—
342Dic3⋊C4—41no—
343C4×Dic3—22no—
344C4×Dic3—41no—
345C22×C32C2×#4111yescharacteristic
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C22×C32C2×#4111yescharacteristic
350C22×C32H(5,𝔽2)11yescharacteristic
351C22×C322−1+411yescharacteristic
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—22no—
355C2×C3×D3—22no—
356C2×C3×D3—22no—
357C2×C3×D3—22no—
358C2×C3×D3#12614yes—
359C32×C4—41no—
360C32×C4—41no—
361C32×C4—41no—
362C32×C4—41no—
363C32×C4—41no—
364C32×C4—41no—
365C32×C4—41no—
366C3×Dic3—22no—
367C3×Dic3—22no—
368C3×Dic3—41no—
369C3×Dic3—41no—
370C3×Dic3—41no—
371C3×Dic3—41no—
372C3×Dic3—41no—
373C23×C4—31no—
374C23×C4—31no—
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⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C42—31no—
387C2×C42—31no—
388#95—31no—
389#95—31no—
390#95—31no—
391#95—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#95C2×C3×D311yescharacteristic
402#95C2×C3×D311yescharacteristic
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—32no—
411C23×C3—32no—
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×D3C3×#4112yes—
423C22×D3C3×#4112yes—
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—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
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—41no—
489C2×C3×C4—41no—
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—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—124no—
510C2×C3×C4—124no—
511C2×C3×C4—124no—
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×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3C3×#4112yes—
532C2×Dic3C3×#4112yes—
533C4×D3—44no—
534C4×D3—44no—
535C4×D3—44no—
536C2×C32C2×#12611yescharacteristic
537C2×C32#52911yescharacteristic
538C2×C32#53911yescharacteristic
539C2×C32#55111yescharacteristic
540C2×C32#55111yescharacteristic
541C2×C32#55211yescharacteristic
542C2×C32#55211yescharacteristic
543C3×D3—24no—
544C24—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—121no—
560C22×C4—121no—
561C22×C4C22×C3×D311yescharacteristic
562C22×C4C22×C3×D311yescharacteristic
563C22×C4C22×C3×D311yescharacteristic
564C22×C4C22×C3×D311yescharacteristic
565C22×C4C22×C3×D311yescharacteristic
566C22×C4C22×C3×D311yescharacteristic
567C22×C4C22×C3×D311yescharacteristic
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—121no—
572C4⋊C4—121no—
573C4⋊C4—121no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C42—62no—
579C42—121no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—34no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—62no—
592C22×C3—62no—
593C22×C3—62no—
594C22×C3D3×#4111yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C22×C3D3×#4111yescharacteristic
597C22×C3D3×#4111yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3#100911yescharacteristic
600C22×C3#101011yescharacteristic
601C22×C3C2×C3×#4111yescharacteristic
602C22×C3C2×C3×#4111yescharacteristic
603C22×C3C2×C3×#4111yescharacteristic
604C22×C3C2×C3×#4111yescharacteristic
605C22×C3C2×C3×#4111yescharacteristic
606C22×C3C3×H(5,𝔽2)11yescharacteristic
607C22×C3C3×2−1+411yescharacteristic
608C2×D3—22no—
609C2×D3—22no—
610C2×D3—22no—
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3C3×#12614yes—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—41no—
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—41no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—81no—
632C3×C4—81no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—81no—
637C3×C4—81no—
638C3×C4—121no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643Dic3—22no—
644Dic3—22no—
645Dic3—41no—
646Dic3—41no—
647Dic3—41no—
648Dic3—41no—
649Dic3—41no—
650C32#249311yescharacteristic, complemented, Sylow
651C23—32no—
652C23—32no—
653C23—32no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23C23×C3×D311yescharacteristic
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—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—32no—
681C2×C4—32no—
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—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—124no—
702C2×C4—124no—
703C2×C4—124no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—21no—
711C2×C3—64no—
712C2×C3D3×#12611yescharacteristic
713C2×C3#570511yescharacteristic
714C2×C3#570511yescharacteristic
715C2×C3#570611yescharacteristic
716C2×C3#570711yescharacteristic
717C2×C3#570811yescharacteristic
718C2×C3#570811yescharacteristic
719C2×C3C2×C3×#12611yescharacteristic
720C2×C3C3×#52911yescharacteristic
721C2×C3C3×#53911yescharacteristic
722C2×C3C3×#55111yescharacteristic
723C2×C3C3×#55111yescharacteristic
724C2×C3C3×#55211yescharacteristic
725C2×C3C3×#55211yescharacteristic
726D3—24no—
727C22—34no—
728C22—62no—
729C22—62no—
730C22—62no—
731C22—62no—
732C22—62no—
733C22—62no—
734C22C3×D3×#4111yescharacteristic
735C22C3×D3×#4111yescharacteristic
736C22C3×D3×#4111yescharacteristic
737C22C3×D3×#4111yescharacteristic
738C22C3×D3×#4111yescharacteristic
739C22C3×#100911yescharacteristic
740C22C3×#101011yescharacteristic
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—41no—
748C4—62no—
749C4—62no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—121no—
755C3—21no—
756C3#7843011yescharacteristic, direct product factor
757C3C3×#249311yescharacteristic, complemented
758C2—64no—
759C2C3×D3×#12611yescharacteristic
760C2C3×#570511yescharacteristic
761C2C3×#570511yescharacteristic
762C2C3×#570611yescharacteristic
763C2C3×#570711yescharacteristic
764C2C3×#570811yescharacteristic
765C2C3×#570811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#401C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC3×#401D3
hypocenterC3C3×#2493
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#401

Complements

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

NH ≅ G/Ntype
1. C32×#401C2semidirect
9. C3×#4660C2semidirect
10. C3×#4658C2semidirect
11. C3×#4658C2semidirect
12. C3×#4655C2semidirect
13. C3×#4654C2semidirect
14. C3×#4653C2semidirect
15. C3×#4651C2semidirect
17. #78430C3direct (N × H)
54. C3×#401D3semidirect
55. C3×#401C2×C3semidirect
77. #4660C2×C3semidirect
78. #4658C2×C3semidirect
79. #4658C2×C3semidirect
80. #4655C2×C3semidirect
81. #4654C2×C3semidirect
82. #4653C2×C3semidirect
83. #4651C2×C3semidirect
251. #401C3×D3semidirect
650. C32#2493semidirect
756. C3#78430direct (N × H)
757. C3C3×#2493semidirect

Maximal subgroups

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

subgroupindex
C32×#4012
C3×#46682
C3×#46672
C3×#46662
C3×#46642
C3×D3×#952
C3×#46602
C3×#46582
C3×#46552
C3×#46542
C3×#46532
C3×#46512
C3×#24933
#784303