Finite Group Databasebeta

← C3×#69409 #11773349

Subgroups — C3×#69409 #11773349

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C32×#95C211yesmaximal, characteristic
4C2×C3×C3⋊#95C211yesmaximal, characteristic
5C2×C3×C3⋊#95C211yesmaximal, characteristic
6C2×C3×C3⋊#95C211yesmaximal, characteristic
7C2×C3×C3⋊#95C211yesmaximal, characteristic
8C3×#1441—31nomaximal
9#69409C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C3×Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—22no—
18C2×C3×Dic3⋊C4—22no—
19C2×C3×Dic3⋊C4—22no—
20C2×C3×Dic3⋊C4—22no—
21C2×C3×Dic3⋊C4—22no—
22C2×C3×Dic3⋊C4C414yescomplemented
23C32×#95—22no—
24C3×C3⋊#95—22no—
25C3×C3⋊#95—22no—
26C3×C3⋊#95—22no—
27C3×C3⋊#95—22no—
28C22×C3×C4⋊C4—31no—
29C22×C3×C4⋊C4—31no—
30C22×Dic3⋊C4C2×C311yescharacteristic
31C22×Dic3⋊C4C2×C311yescharacteristic
32C2×C3×#95—21no—
33C2×C3×#95—31no—
34C2×C3×#95—31no—
35C2×C3×#95—31no—
36C2×C3×#95—31no—
37C2×C3×#95D311yescharacteristic
38C2×C3×#95C2×C311yescharacteristic
39C2×C3⋊#95C2×C311yescharacteristic
40C2×C3⋊#95C2×C311yescharacteristic
41C2×C3⋊#95C2×C311yescharacteristic
42C2×C3⋊#95C2×C311yescharacteristic
43C24×C32C2311yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4—21no—
61C22×C32×C4—21no—
62C22×C32×C4C2×C412yes—
63C22×C32×C4D412yes—
64C22×C32×C4Q812yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—21no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—21no—
71C22×C3×Dic3—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3C2×C412yes—
86C22×C3×Dic3C2×C412yes—
87C22×C3×Dic3D412yes—
88C22×C3×Dic3D412yes—
89C22×C3×Dic3D412yes—
90C22×C3×Dic3D412yes—
91C22×C3×Dic3Q812yes—
92C22×C3×Dic3Q812yes—
93C3×Dic3⋊C4—28no—
94C3×Dic3⋊C4—28no—
95#1441—31noSylow
96C23×C3×C4—21no—
97C23×C3×C4—21no—
98C23×C3×C4—21no—
99C23×C3×C4—31no—
100C23×C3×C4—31no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C23×C3×C4C2×D311yescharacteristic
106C23×C3×C4C22×C311yescharacteristic
107C23×C3×C4C22×C311yescharacteristic
108C23×C3×C4C22×C311yescharacteristic
109C23×Dic3C22×C311yescharacteristic
110C23×Dic3C22×C311yescharacteristic
111C23×Dic3C22×C311yescharacteristic
112C23×Dic3C22×C311yescharacteristic
113C2×C3×C4⋊C4—34no—
114C2×C3×C4⋊C4—62no—
115C2×C3×C4⋊C4—62no—
116C2×C3×C4⋊C4—62no—
117C2×C3×C4⋊C4—62no—
118C2×C3×C4⋊C4—62no—
119C2×Dic3⋊C4—22no—
120C2×Dic3⋊C4—22no—
121C2×Dic3⋊C4—22no—
122C2×Dic3⋊C4—22no—
123C2×Dic3⋊C4—22no—
124C2×Dic3⋊C4C3×C414yescomplemented
125C3×#95—24no—
126C3×#95—22no—
127C3×#95—22no—
128C3×#95—62no—
129C3×#95—62no—
130C3×#95—62no—
131C3×#95—62no—
132C3⋊#95—22no—
133C3⋊#95—22no—
134C3⋊#95—22no—
135C3⋊#95—22no—
136C23×C32C22×C411yescharacteristic
137C23×C32C2×D411yescharacteristic
138C23×C32C2×D411yescharacteristic
139C23×C32C2×D411yescharacteristic
140C23×C32C2×D411yescharacteristic
141C23×C32C2×D411yescharacteristic
142C23×C32C2×Q811yescharacteristic
143C23×C32C2×Q811yescharacteristic
144C23×C32C2×Q811yescharacteristic
145C23×C32#4111yescharacteristic
146C23×C32#4111yescharacteristic
147C23×C32#4111yescharacteristic
148C23×C32#4111yescharacteristic
149C23×C32#4111yescharacteristic
150C23×C32#4111yescharacteristic
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4—41no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C32×C4—41no—
166C2×C32×C4—41no—
167C2×C32×C4—41no—
168C2×C32×C4—41no—
169C2×C32×C4—41no—
170C2×C32×C4—41no—
171C2×C32×C4—41no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—41no—
191C2×C3×Dic3—41no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—41no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—41no—
196C2×C3×Dic3—41no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3C22⋊C414yes—
199C2×C3×Dic3C4⋊C414yescomplemented
200C22×C4⋊C4—31no—
201C22×C4⋊C4—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95C3×D311yescharacteristic
207C24×C3—21no—
208C24×C3C22×D311yescharacteristic
209C24×C3C23×C311yescharacteristic
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—32no—
256C22×C3×C4—32no—
257C22×C3×C4—32no—
258C22×C3×C4—32no—
259C22×C3×C4—32no—
260C22×C3×C4—32no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—41no—
264C22×C3×C4—41no—
265C22×C3×C4—41no—
266C22×C3×C4—41no—
267C22×C3×C4—41no—
268C22×C3×C4—41no—
269C22×C3×C4—41no—
270C22×C3×C4—41no—
271C22×C3×C4—41no—
272C22×C3×C4—41no—
273C22×C3×C4—41no—
274C22×C3×C4—41no—
275C22×C3×C4—61no—
276C22×C3×C4—61no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4—61no—
280C22×C3×C4—61no—
281C22×C3×C4—61no—
282C22×C3×C4—61no—
283C22×C3×C4—61no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4Dic612yes—
296C22×C3×C4C4×D312yes—
297C22×C3×C4#6712yes—
298C22×C3×C4C2×C3×C412yes—
299C22×C3×C4C3×D412yes—
300C22×C3×C4C3×Q812yes—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3C2×C3×C412yes—
322C22×Dic3C2×C3×C412yes—
323C22×Dic3C3×D412yes—
324C22×Dic3C3×D412yes—
325C22×Dic3C3×D412yes—
326C22×Dic3C3×D412yes—
327C22×Dic3C3×Q812yes—
328C22×Dic3C3×Q812yes—
329C3×C4⋊C4—68no—
330C3×C4⋊C4—68no—
331Dic3⋊C4—28no—
332Dic3⋊C4—28no—
333C22×C32C2×C22⋊C411yescharacteristic
334C22×C32C2×C4⋊C411yescharacteristic
335C22×C32#11711yescharacteristic
336C22×C32C4×D411yescharacteristic
337C22×C32C4×D411yescharacteristic
338C22×C32C4×Q811yescharacteristic
339C22×C32C4×Q811yescharacteristic
340C22×C32#12011yescharacteristic
341C22×C32#12111yescharacteristic
342C22×C32#12111yescharacteristic
343C22×C32#12111yescharacteristic
344C22×C32#12111yescharacteristic
345C22×C32#12111yescharacteristic
346C22×C32#12111yescharacteristic
347C22×C32C22⋊Q811yescharacteristic
348C22×C32C22⋊Q811yescharacteristic
349C22×C32C22⋊Q811yescharacteristic
350C22×C32C22⋊Q811yescharacteristic
351C22×C32C22⋊Q811yescharacteristic
352C22×C32C22⋊Q811yescharacteristic
353C22×C32C22⋊Q811yescharacteristic
354C22×C32C22⋊Q811yescharacteristic
355C22×C32#12311yescharacteristic
356C22×C32#12311yescharacteristic
357C22×C32#12311yescharacteristic
358C22×C32#12411yescharacteristic
359C22×C32#12511yescharacteristic
360C22×C32#12511yescharacteristic
361C22×C32#12511yescharacteristic
362C22×C32#12511yescharacteristic
363C22×C32#12611yescharacteristic
364C22×C32#12611yescharacteristic
365C22×C32C4⋊Q811yescharacteristic
366C22×C32C4⋊Q811yescharacteristic
367C22×C32C4⋊Q811yescharacteristic
368C32×C4—42no—
369C32×C4—42no—
370C32×C4—42no—
371C3×Dic3—24no—
372C3×Dic3—24no—
373C3×Dic3—42no—
374C3×Dic3—42no—
375C23×C4—31no—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C23×C4C2×C3×D311yescharacteristic
380C23×C4C2×C3×D311yescharacteristic
381C23×C4C2×C3×D311yescharacteristic
382C2×C4⋊C4—34no—
383C2×C4⋊C4—62no—
384C2×C4⋊C4—62no—
385C2×C4⋊C4—62no—
386C2×C4⋊C4—62no—
387C2×C4⋊C4—62no—
388#95—22no—
389#95—62no—
390#95—62no—
391#95—62no—
392#95—62no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3C2×Dic611yescharacteristic
409C23×C3C2×C4×D311yescharacteristic
410C23×C3#23511yescharacteristic
411C23×C3#23511yescharacteristic
412C23×C3#23511yescharacteristic
413C23×C3#23511yescharacteristic
414C23×C3D3×D411yescharacteristic
415C23×C3D3×D411yescharacteristic
416C23×C3D3×D411yescharacteristic
417C23×C3D3×D411yescharacteristic
418C23×C3#23711yescharacteristic
419C23×C3#23711yescharacteristic
420C23×C3D3×Q811yescharacteristic
421C23×C3D3×Q811yescharacteristic
422C23×C3C2×#6711yescharacteristic
423C23×C3C22×C3×C411yescharacteristic
424C23×C3C2×C3×D411yescharacteristic
425C23×C3C2×C3×D411yescharacteristic
426C23×C3C2×C3×D411yescharacteristic
427C23×C3C2×C3×D411yescharacteristic
428C23×C3C2×C3×D411yescharacteristic
429C23×C3C2×C3×Q811yescharacteristic
430C23×C3C2×C3×Q811yescharacteristic
431C23×C3C2×C3×Q811yescharacteristic
432C23×C3C3×#4111yescharacteristic
433C23×C3C3×#4111yescharacteristic
434C23×C3C3×#4111yescharacteristic
435C23×C3C3×#4111yescharacteristic
436C23×C3C3×#4111yescharacteristic
437C23×C3C3×#4111yescharacteristic
438C2×C3×C4—24no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—34no—
460C2×C3×C4—34no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—42no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—42no—
469C2×C3×C4—42no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—42no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
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—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—62no—
506C2×C3×C4—62no—
507C2×C3×C4—62no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—62no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—62no—
521C2×C3×C4—121no—
522C2×C3×C4—121no—
523C2×C3×C4—121no—
524C2×C3×C4—121no—
525C2×C3×C4—121no—
526C2×C3×C4—121no—
527C2×C3×C4—121no—
528C2×C3×C4—121no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—22no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—22no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—22no—
541C2×Dic3—22no—
542C2×Dic3—22no—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3C3×C22⋊C414yes—
556C2×Dic3C3×C4⋊C414yescomplemented
557C2×C32#38011yescharacteristic
558C2×C32#38611yescharacteristic
559C2×C32#38711yescharacteristic
560C2×C32#38711yescharacteristic
561C2×C32#38911yescharacteristic
562C2×C32#38911yescharacteristic
563C2×C32#39111yescharacteristic
564C2×C32#39411yescharacteristic
565C2×C32#39511yescharacteristic
566C2×C32#39611yescharacteristic
567C2×C32#39611yescharacteristic
568C2×C32#39811yescharacteristic
569C2×C32#39811yescharacteristic
570C2×C32#39811yescharacteristic
571C2×C32#40011yescharacteristic
572C24C22×C3×D311yescharacteristic
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—32no—
592C22×C4—32no—
593C22×C4—32no—
594C22×C4—32no—
595C22×C4—32no—
596C22×C4—32no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4C3×Dic612yes—
620C22×C4C3×C4×D312yes—
621C22×C4C3×#6712yes—
622C4⋊C4—68no—
623C4⋊C4—68no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3C4×Dic611yescharacteristic
660C22×C3#87011yescharacteristic
661C22×C3#87211yescharacteristic
662C22×C3#87611yescharacteristic
663C22×C3#87811yescharacteristic
664C22×C3#87811yescharacteristic
665C22×C3#87911yescharacteristic
666C22×C3D3×C22⋊C411yescharacteristic
667C22×C3#67⋊C411yescharacteristic
668C22×C3#88311yescharacteristic
669C22×C3#88311yescharacteristic
670C22×C3#88411yescharacteristic
671C22×C3#88411yescharacteristic
672C22×C3#88411yescharacteristic
673C22×C3#88411yescharacteristic
674C22×C3#88511yescharacteristic
675C22×C3#88711yescharacteristic
676C22×C3#88811yescharacteristic
677C22×C3#88811yescharacteristic
678C22×C3#88911yescharacteristic
679C22×C3#88911yescharacteristic
680C22×C3#88911yescharacteristic
681C22×C3D3×C4⋊C411yescharacteristic
682C22×C3#89611yescharacteristic
683C22×C3#89611yescharacteristic
684C22×C3#89611yescharacteristic
685C22×C3#89611yescharacteristic
686C22×C3#89611yescharacteristic
687C22×C3#92411yescharacteristic
688C22×C3C4×#6711yescharacteristic
689C22×C3#92911yescharacteristic
690C22×C3#93711yescharacteristic
691C22×C3#93811yescharacteristic
692C22×C3#93911yescharacteristic
693C22×C3#94411yescharacteristic
694C22×C3C2×C3×C22⋊C411yescharacteristic
695C22×C3C2×C3×C4⋊C411yescharacteristic
696C22×C3C3×#11711yescharacteristic
697C22×C3C3×C4×D411yescharacteristic
698C22×C3C3×C4×D411yescharacteristic
699C22×C3C3×C4×Q811yescharacteristic
700C22×C3C3×C4×Q811yescharacteristic
701C22×C3C3×#12011yescharacteristic
702C22×C3C3×#12111yescharacteristic
703C22×C3C3×#12111yescharacteristic
704C22×C3C3×#12111yescharacteristic
705C22×C3C3×#12111yescharacteristic
706C22×C3C3×#12111yescharacteristic
707C22×C3C3×#12111yescharacteristic
708C22×C3C3×C22⋊Q811yescharacteristic
709C22×C3C3×C22⋊Q811yescharacteristic
710C22×C3C3×C22⋊Q811yescharacteristic
711C22×C3C3×C22⋊Q811yescharacteristic
712C22×C3C3×C22⋊Q811yescharacteristic
713C22×C3C3×C22⋊Q811yescharacteristic
714C22×C3C3×C22⋊Q811yescharacteristic
715C22×C3C3×C22⋊Q811yescharacteristic
716C22×C3C3×#12311yescharacteristic
717C22×C3C3×#12311yescharacteristic
718C22×C3C3×#12311yescharacteristic
719C22×C3C3×#12411yescharacteristic
720C22×C3C3×#12511yescharacteristic
721C22×C3C3×#12511yescharacteristic
722C22×C3C3×#12511yescharacteristic
723C22×C3C3×#12511yescharacteristic
724C22×C3C3×#12611yescharacteristic
725C22×C3C3×#12611yescharacteristic
726C22×C3C3×C4⋊Q811yescharacteristic
727C22×C3C3×C4⋊Q811yescharacteristic
728C22×C3C3×C4⋊Q811yescharacteristic
729C3×C4—44no—
730C3×C4—44no—
731C3×C4—44no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—42no—
738C3×C4—64no—
739C3×C4—64no—
740C3×C4—122no—
741C3×C4—122no—
742Dic3—24no—
743Dic3—24no—
744Dic3—42no—
745Dic3—42no—
746C32#144111yescharacteristic, complemented, Sylow
747C23C2×C3×Dic611yescharacteristic
748C23C2×C3×C4×D311yescharacteristic
749C23C3×#23511yescharacteristic
750C23C3×#23511yescharacteristic
751C23C3×#23511yescharacteristic
752C23C3×#23511yescharacteristic
753C23C3×D3×D411yescharacteristic
754C23C3×D3×D411yescharacteristic
755C23C3×D3×D411yescharacteristic
756C23C3×D3×D411yescharacteristic
757C23C3×#23711yescharacteristic
758C23C3×#23711yescharacteristic
759C23C3×D3×Q811yescharacteristic
760C23C3×D3×Q811yescharacteristic
761C23C2×C3×#6711yescharacteristic
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—34no—
772C2×C4—34no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—62no—
794C2×C4—62no—
795C2×C4—62no—
796C2×C4—62no—
797C2×C4—62no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—62no—
801C2×C4—62no—
802C2×C4—62no—
803C2×C4—121no—
804C2×C4—121no—
805C2×C4—121no—
806C2×C4—121no—
807C2×C4—121no—
808C2×C4—121no—
809C2×C4—121no—
810C2×C4—121no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3#464611yescharacteristic
827C2×C3#464711yescharacteristic
828C2×C3#465211yescharacteristic
829C2×C3#465711yescharacteristic
830C2×C3#465711yescharacteristic
831C2×C3#465811yescharacteristic
832C2×C3#466711yescharacteristic
833C2×C3#467611yescharacteristic
834C2×C3#493311yescharacteristic
835C2×C3#494811yescharacteristic
836C2×C3#495611yescharacteristic
837C2×C3#495911yescharacteristic
838C2×C3#497611yescharacteristic
839C2×C3#497911yescharacteristic
840C2×C3#498311yescharacteristic
841C2×C3C3×#38011yescharacteristic
842C2×C3C3×#38611yescharacteristic
843C2×C3C3×#38711yescharacteristic
844C2×C3C3×#38711yescharacteristic
845C2×C3C3×#38911yescharacteristic
846C2×C3C3×#38911yescharacteristic
847C2×C3C3×#39111yescharacteristic
848C2×C3C3×#39411yescharacteristic
849C2×C3C3×#39511yescharacteristic
850C2×C3C3×#39611yescharacteristic
851C2×C3C3×#39611yescharacteristic
852C2×C3C3×#39811yescharacteristic
853C2×C3C3×#39811yescharacteristic
854C2×C3C3×#39811yescharacteristic
855C2×C3C3×#40011yescharacteristic
856C22C3×C4×Dic611yescharacteristic
857C22C3×#87011yescharacteristic
858C22C3×#87211yescharacteristic
859C22C3×#87611yescharacteristic
860C22C3×#87811yescharacteristic
861C22C3×#87811yescharacteristic
862C22C3×#87911yescharacteristic
863C22C3×D3×C22⋊C411yescharacteristic
864C22C3×#67⋊C411yescharacteristic
865C22C3×#88311yescharacteristic
866C22C3×#88311yescharacteristic
867C22C3×#88411yescharacteristic
868C22C3×#88411yescharacteristic
869C22C3×#88411yescharacteristic
870C22C3×#88411yescharacteristic
871C22C3×#88511yescharacteristic
872C22C3×#88711yescharacteristic
873C22C3×#88811yescharacteristic
874C22C3×#88811yescharacteristic
875C22C3×#88911yescharacteristic
876C22C3×#88911yescharacteristic
877C22C3×#88911yescharacteristic
878C22C3×D3×C4⋊C411yescharacteristic
879C22C3×#89611yescharacteristic
880C22C3×#89611yescharacteristic
881C22C3×#89611yescharacteristic
882C22C3×#89611yescharacteristic
883C22C3×#89611yescharacteristic
884C22C3×#92411yescharacteristic
885C22C3×C4×#6711yescharacteristic
886C22C3×#92911yescharacteristic
887C22C3×#93711yescharacteristic
888C22C3×#93811yescharacteristic
889C22C3×#93911yescharacteristic
890C22C3×#94411yescharacteristic
891C4—42no—
892C4—42no—
893C4—42no—
894C4—64no—
895C4—64no—
896C4—122no—
897C4—122no—
898C3—21no—
899C3#6940911yescharacteristic, direct product factor
900C3C3×#144111yescharacteristic, complemented
901C2C3×#464611yescharacteristic
902C2C3×#464711yescharacteristic
903C2C3×#465211yescharacteristic
904C2C3×#465711yescharacteristic
905C2C3×#465711yescharacteristic
906C2C3×#465811yescharacteristic
907C2C3×#466711yescharacteristic
908C2C3×#467611yescharacteristic
909C2C3×#493311yescharacteristic
910C2C3×#494811yescharacteristic
911C2C3×#495611yescharacteristic
912C2C3×#495911yescharacteristic
913C2C3×#497611yescharacteristic
914C2C3×#497911yescharacteristic
915C2C3×#498311yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC2×C32×#95C2
socle, prime radicalC24×C32C23
cosocleC24×C3C23×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#1441
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
9. #69409C3direct (N × H)
22. C2×C3×Dic3⋊C4C4semidirect
124. C2×Dic3⋊C4C3×C4semidirect
199. C2×C3×Dic3C4⋊C4semidirect
556. C2×Dic3C3×C4⋊C4semidirect
746. C32#1441semidirect
899. C3#69409direct (N × H)
900. C3C3×#1441semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×C32×#952
C2×C3×C3⋊#952
C3×#14413
#694093