Finite Group Databasebeta

← C3×#73509 #11819122

Subgroups — C3×#73509 #11819122

Order 1152.

1009 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C22⋊C4C211yesmaximal, characteristic
2C3×#5210C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4C3×#4946C211yesmaximal, characteristic
5C3×#4943C211yesmaximal, characteristic
6C3×#4943C211yesmaximal, characteristic
7C3×#4942C211yesmaximal, characteristic
8C3×#4937C211yesmaximal, characteristic, complemented
9C3×#4933C211yesmaximal, characteristic, complemented
10C3×#4933C211yesmaximal, characteristic, complemented
11C3×#4933C211yesmaximal, characteristic, complemented
12C3×C3⋊#401C211yesmaximal, characteristic, complemented
13C3×#4658C211yesmaximal, characteristic, complemented
14C3×#4658C211yesmaximal, characteristic, complemented
15C3×#4658C211yesmaximal, characteristic, complemented
16C3×#2493—31nomaximal
17#73509C311yesmaximal, characteristic, direct product factor
18C23×C32×C4C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C42C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C32×#95C2211yescharacteristic
34C32×#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#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—21no—
67C3×C4×C22⋊C4D311yescharacteristic
68C3×C4×C22⋊C4C2×C311yescharacteristic
69C2×C3×#95—31no—
70#5210C2×C311yescharacteristic
71C2×C3⋊#95C2×C311yescharacteristic
72#4946C2×C311yescharacteristic
73#4943C2×C311yescharacteristic
74#4943C2×C311yescharacteristic
75#4942C2×C311yescharacteristic
76#4937C2×C311yescharacteristic, complemented
77#4933C2×C311yescharacteristic, complemented
78#4933C2×C311yescharacteristic, complemented
79#4933C2×C311yescharacteristic, complemented
80C3⋊#401C2×C311yescharacteristic, complemented
81#4658C2×C311yescharacteristic, complemented
82#4658C2×C311yescharacteristic, complemented
83#4658C2×C311yescharacteristic, complemented
84C24×C32C2311yescharacteristic
85C22×C32×C4—22no—
86C22×C32×C4—22no—
87C22×C32×C4—41no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3×Dic3—22no—
95C22×C3×Dic3—22no—
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—22no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C32×C22⋊C4—22no—
109C32×C22⋊C4—22no—
110C32×C42—22no—
111C32×C42—41no—
112C3×#217—22no—
113C3×#217—22no—
114C3×Dic3⋊C4—22no—
115C3×Dic3⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×Dic3⋊C4—41no—
118C3×Dic3⋊C4—41no—
119C3×Dic3⋊C4—41no—
120#2493—31noSylow
121C23×C3×C4—21no—
122C23×C3×C4—31no—
123C23×C3×C4—31no—
124C23×C3×C4C2×D311yescharacteristic
125C23×C3×C4C22×C311yescharacteristic
126C23×Dic3C22×C311yescharacteristic
127C23×Dic3C22×C311yescharacteristic
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×C4⋊C4—31no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C22×C311yescharacteristic
141C2×C3×C22⋊C4C22×C311yescharacteristic
142C2×C3×C42—21no—
143C2×C3×C42—21no—
144C2×C3×C42C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C22×C311yescharacteristic
147C2×C3×C42C22×C311yescharacteristic
148C2×#217C22×C311yescharacteristic
149C2×#217C22×C311yescharacteristic
150C2×Dic3⋊C4C22×C311yescharacteristic
151C2×Dic3⋊C4C22×C311yescharacteristic
152C2×Dic3⋊C4C22×C311yescharacteristic
153C2×Dic3⋊C4C22×C311yescharacteristic
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×Dic3⋊C4C22×C311yescharacteristic
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×#95—31no—
175C3×#95—31no—
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—21no—
223C2×C32×C4—44no—
224C2×C32×C4#4112yes—
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—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—44no—
249C2×C3×Dic3—44no—
250C2×C3×Dic3#4112yes—
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⋊C4C3×D311yescharacteristic
265C2×#95—31no—
266C24×C3—21no—
267C24×C3C22×D311yescharacteristic
268C24×C3C23×C311yescharacteristic
269C22×C3×C4—24no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—42no—
289C22×C3×C4—41no—
290C22×C3×C4—41no—
291C22×C3×C4—42no—
292C22×C3×C4—62no—
293C22×C3×C4—62no—
294C22×C3×C4—62no—
295C22×C3×C4—62no—
296C22×C3×C4—62no—
297C22×C3×C4—121no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C22×C3×C4C23×C311yescharacteristic
306C22×C3×C4C23×C311yescharacteristic
307C22×C3×C4C23×C311yescharacteristic
308C22×C3×C4C23×C311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—41no—
316C22×Dic3C23×C311yescharacteristic
317C22×Dic3C23×C311yescharacteristic
318C22×Dic3C23×C311yescharacteristic
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C311yescharacteristic
323C22×Dic3C23×C311yescharacteristic
324C3×C4⋊C4—62no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—62no—
327C3×C4⋊C4—121no—
328C3×C4⋊C4—121no—
329C3×C4⋊C4—121no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—22no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—22no—
335C3×C22⋊C4—22no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—62no—
338C3×C42—22no—
339C3×C42—22no—
340C3×C42—42no—
341C3×C42—41no—
342C3×C42—41no—
343C3×C42—42no—
344#217—22no—
345#217—22no—
346Dic3⋊C4—22no—
347Dic3⋊C4—22no—
348Dic3⋊C4—22no—
349Dic3⋊C4—41no—
350Dic3⋊C4—41no—
351Dic3⋊C4—41no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32#12614yes—
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32C2×#4111yescharacteristic
363C22×C32C2×#4111yescharacteristic
364C22×C32H(5,𝔽2)11yescharacteristic
365C22×C322−1+411yescharacteristic
366C32×C4—22no—
367C32×C4—41no—
368C32×C4—41no—
369C32×C4—41no—
370C32×C4—41no—
371C32×C4—41no—
372C3×Dic3—22no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C3×Dic3—41no—
379C3×Dic3—41no—
380C23×C4—31no—
381C23×C4—31no—
382C23×C4C2×C3×D311yescharacteristic
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—31no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C22⋊C4—31no—
390C2×C22⋊C4—31no—
391C2×C22⋊C4C2×C3×D311yescharacteristic
392C2×C22⋊C4C2×C3×D311yescharacteristic
393C2×C42C2×C3×D311yescharacteristic
394C2×C42C2×C3×D311yescharacteristic
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#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
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—21no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3#23512yes—
432C23×C3#23512yes—
433C23×C3#23512yes—
434C23×C3C3×#4112yes—
435C23×C3C3×#4112yes—
436C23×C3C3×#4112yes—
437C23×C3C23×D311yescharacteristic
438C23×C3C24×C311yescharacteristic
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
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—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—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—32no—
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—41no—
492C2×C3×C4—44no—
493C2×C3×C4—44no—
494C2×C3×C4—48no—
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—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—124no—
519C2×C3×C4—124no—
520C2×C3×C4#23712yes—
521C2×C3×C4C3×#4112yes—
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—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—44no—
546C2×Dic3—44no—
547C2×Dic3C3×#4112yes—
548C2×C32—24no—
549C2×C32C2×#12611yescharacteristic
550C2×C32#52911yescharacteristic
551C2×C32#53911yescharacteristic
552C2×C32#55111yescharacteristic
553C2×C32#55111yescharacteristic
554C2×C32#55211yescharacteristic
555C2×C32#55211yescharacteristic
556C24C22×C3×D311yescharacteristic
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—41no—
568C22×C4—62no—
569C22×C4—62no—
570C22×C4—62no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—121no—
574C22×C4C22×C3×D311yescharacteristic
575C22×C4C22×C3×D311yescharacteristic
576C22×C4C22×C3×D311yescharacteristic
577C22×C4C22×C3×D311yescharacteristic
578C22×C4C22×C3×D311yescharacteristic
579C22×C4C22×C3×D311yescharacteristic
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—121no—
584C4⋊C4—121no—
585C4⋊C4—121no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—62no—
589C22⋊C4—62no—
590C42—22no—
591C42—41no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—24no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3#87614yes—
619C22×C3C3×#12614yes—
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×#23511yescharacteristic
622C22×C3C2×#23511yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3#100411yescharacteristic
625C22×C3D3×#4111yescharacteristic
626C22×C3#101011yescharacteristic
627C22×C3C2×C3×#4111yescharacteristic
628C22×C3C2×C3×#4111yescharacteristic
629C22×C3C2×C3×#4111yescharacteristic
630C22×C3C2×C3×#4111yescharacteristic
631C22×C3C2×C3×#4111yescharacteristic
632C22×C3C3×H(5,𝔽2)11yescharacteristic
633C22×C3C3×2−1+411yescharacteristic
634C3×C4—24no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—62no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668C32#249311yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23C3×#23512yes—
674C23C3×#23512yes—
675C23C3×#23512yes—
676C23C23×C3×D311yescharacteristic
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
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—32no—
695C2×C4—44no—
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—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—124no—
720C2×C4—124no—
721C2×C4C3×#23712yes—
722C2×C3—24no—
723C2×C3—24no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—44no—
732C2×C3C2×#87611yescharacteristic
733C2×C3#549511yescharacteristic
734C2×C3#553111yescharacteristic
735C2×C3#553811yescharacteristic
736C2×C3#554111yescharacteristic
737C2×C3#555611yescharacteristic
738C2×C3#556411yescharacteristic
739C2×C3C2×C3×#12611yescharacteristic
740C2×C3C3×#52911yescharacteristic
741C2×C3C3×#53911yescharacteristic
742C2×C3C3×#55111yescharacteristic
743C2×C3C3×#55111yescharacteristic
744C2×C3C3×#55211yescharacteristic
745C2×C3C3×#55211yescharacteristic
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22C3×#87614yes—
753C22C2×C3×#23511yescharacteristic
754C22C2×C3×#23511yescharacteristic
755C22C2×C3×#23511yescharacteristic
756C22C2×C3×#23711yescharacteristic
757C22C3×#100411yescharacteristic
758C22C3×D3×#4111yescharacteristic
759C22C3×#101011yescharacteristic
760C4—22no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—62no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—121no—
774C3—21no—
775C3#7350911yescharacteristic, direct product factor
776C3C3×#249311yescharacteristic, complemented
777C2—24no—
778C2C2×C3×#87611yescharacteristic
779C2C3×#549511yescharacteristic
780C2C3×#553111yescharacteristic
781C2C3×#553811yescharacteristic
782C2C3×#554111yescharacteristic
783C2C3×#555611yescharacteristic
784C2C3×#556411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×C4×C22⋊C4C2
socleC23×C32C24
prime radicalC24×C32C23
hypercenterC3×C4×C22⋊C4D3
hypocenterC3C3×#2493
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×#4937C2semidirect
9. C3×#4933C2semidirect
10. C3×#4933C2semidirect
11. C3×#4933C2semidirect
12. C3×C3⋊#401C2semidirect
13. C3×#4658C2semidirect
14. C3×#4658C2semidirect
15. C3×#4658C2semidirect
17. #73509C3direct (N × H)
76. #4937C2×C3semidirect
77. #4933C2×C3semidirect
78. #4933C2×C3semidirect
79. #4933C2×C3semidirect
80. C3⋊#401C2×C3semidirect
81. #4658C2×C3semidirect
82. #4658C2×C3semidirect
83. #4658C2×C3semidirect
668. C32#2493semidirect
775. C3#73509direct (N × H)
776. C3C3×#2493semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C22⋊C42
C3×#52102
C2×C3×C3⋊#952
C3×#49462
C3×#49432
C3×#49422
C3×#49372
C3×#49332
C3×C3⋊#4012
C3×#46582
C3×#24933
#735093