Finite Group Databasebeta

← C3×#81147 #11872807

Subgroups — C3×#81147 #11872807

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5698C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5019C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4888C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4841C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic
13C3×#4776C211yesmaximal, characteristic
14C3×#4758C211yesmaximal, characteristic, complemented
15C3×#4757C211yesmaximal, characteristic, complemented
16C3×#3123—31nomaximal
17#81147C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C32×#125C2211yescharacteristic, complemented
20C32×C4×D4C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#898—21no—
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×#890—21no—
35C3×#890—21no—
36C3×#887C2211yescharacteristic, complemented
37C3×#887C2211yescharacteristic, complemented
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×#869C2211yescharacteristic, complemented
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×C4⋊C8C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#541—31no—
62C3×#518—31no—
63#5698C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic
65C3×#485—31no—
66C3×#485—31no—
67C3×#478—21no—
68C3×#478—31no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#461—31no—
72C3×#461—31no—
73C3×#450—31no—
74C3×#450—31no—
75C3×#440—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×SD16—31no—
79C3×#433—31no—
80#5066C2×C311yescharacteristic, complemented
81#5019C2×C311yescharacteristic, complemented
82#4889C2×C311yescharacteristic, complemented
83#4888C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4841C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic
89#4776C2×C311yescharacteristic
90#4758C2×C311yescharacteristic, complemented
91#4757C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106C2×C32×C8C2311yescharacteristic
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C3×#217—21no—
115C3×#214—22no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141#3123—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×SD16—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#126—61no—
151C3×#125—21no—
152C3×#125—61no—
153C3×#125—61no—
154C3×#125C2×D311yescharacteristic, complemented
155C3×#125C22×C311yescharacteristic, complemented
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C22×C311yescharacteristic
168C3×#117—31no—
169C3×#117—31no—
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—61no—
172D4×Dic3C22×C311yescharacteristic
173C2×#214C22×C311yescharacteristic
174C2×#214C22×C311yescharacteristic
175C4×#67—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×#204C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179#898—21no—
180#898—21no—
181#897C22×C311yescharacteristic
182#897C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#892C22×C311yescharacteristic
185#890—21no—
186#890—21no—
187#887C22×C311yescharacteristic, complemented
188#887C22×C311yescharacteristic, complemented
189#67⋊C4—21no—
190D3×C22⋊C4—21no—
191C4×D12C22×C311yescharacteristic
192#872C22×C311yescharacteristic
193#869C22×C311yescharacteristic, complemented
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C22×C311yescharacteristic, complemented
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic, complemented
201C3×#106C22×C311yescharacteristic, complemented
202C3×C4⋊C8—21no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C22×C311yescharacteristic, complemented
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C2×D311yescharacteristic
216C3×#102C22×C311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222(C2×D3)⋊C8C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224#816C22×C311yescharacteristic, complemented
225#816C22×C311yescharacteristic, complemented
226#815C22×C311yescharacteristic, complemented
227C8×Dic3C22×C311yescharacteristic, complemented
228#810C22×C311yescharacteristic, complemented
229#810C22×C311yescharacteristic, complemented
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—24no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12#4112yes—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—81no—
263C3×C4×D3—81no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
273#518—31no—
274#485—31no—
275#485—31no—
276#478—31no—
277#478C3×D311yescharacteristic, complemented
278#461—31no—
279#461—31no—
280#450—31no—
281#450—31no—
282#440—31no—
283#440—31no—
284C4×SD16—31no—
285C4×SD16—31no—
286#433—31no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—62no—
295C2×C3×D4—62no—
296C2×C3×D4C22×D311yescharacteristic
297C2×C3×D4C23×C311yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C22×Dic3—21no—
307D3×D4—22no—
308D3×D4—22no—
309C2×D12C23×C311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3C23×C311yescharacteristic
313C2×Dic6C23×C311yescharacteristic
314C2×Dic6C23×C311yescharacteristic
315C3×SD16—62no—
316C3×SD16—62no—
317C3×SD16—62no—
318C3×SD16—62no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8C22×D311yescharacteristic
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C23×C311yescharacteristic
326C2×C3×C8C23×C311yescharacteristic
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—41no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—31no—
364C3×C42—61no—
365C3×C42—61no—
366C3×C42—61no—
367C3×C42C22×D311yescharacteristic
368C3×C42C23×C311yescharacteristic
369#217—21no—
370#214—22no—
371#214—22no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4C3×D411yescharacteristic
378(C2×D3)⋊C4C3×D411yescharacteristic
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4C3×D411yescharacteristic
387Dic3⋊C4C3×D411yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394#204—22no—
395#204—22no—
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—84no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×D4—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×SD16—31no—
424C2×SD16—31no—
425C4⋊Q8—31no—
426#126—61no—
427#126—61no—
428#125—61no—
429#125—61no—
430#125C2×C3×D311yescharacteristic, complemented
431C22⋊Q8—31no—
432C22⋊Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—31no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4C2×C3×D311yescharacteristic
441#117—31no—
442#117—31no—
443C2×C22⋊C4—61no—
444C2×C22⋊C4—61no—
445#107—31no—
446#107C2×C3×D311yescharacteristic, complemented
447#106—31no—
448#106C2×C3×D311yescharacteristic, complemented
449C4⋊C8—31no—
450C4⋊C8C2×C3×D311yescharacteristic, complemented
451#103—31no—
452#103—31no—
453#103—31no—
454#103—31no—
455#102—31no—
456#102—31no—
457#102C2×C3×D311yescharacteristic
458#102C2×C3×D311yescharacteristic
459C22⋊C8—31no—
460C22⋊C8—31no—
461#97—31no—
462C4×C8—31no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—31no—
466C23×C3—41no—
467C23×C3—64no—
468C23×C3—61no—
469C23×C3—241no—
470C23×C3—241no—
471C22×D3—21no—
472C22×D3—24no—
473C22×D3—81no—
474C22×D3—81no—
475C22×D3C2×C3×D411yescharacteristic
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—22no—
483C3×D4—32no—
484C3×D4—41no—
485C3×D4—64no—
486C3×D4—61no—
487C3×D4#23912yes—
488C3×D4C3×#4112yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—81no—
510C2×C3×C4—81no—
511C2×C3×C4—82no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C24×C311yescharacteristic
521#67—24no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—81no—
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529D12—21no—
530D12C3×#4112yes—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—81no—
534C4×D3—81no—
535Dic6—21no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—21no—
543C3×C8—41no—
544C3×C8—41no—
545C3×C8—61no—
546C3×C8—61no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C2×C32—42no—
550C2×C32#52511yescharacteristic
551C2×C32#57711yescharacteristic
552C2×C32#57711yescharacteristic
553C3×D3—41no—
554C3×D3—42no—
555C24—61no—
556C2×Q8—31no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—62no—
561C2×D4—62no—
562C2×D4C22×C3×D311yescharacteristic
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568SD16—62no—
569SD16—62no—
570SD16—62no—
571SD16—62no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8C22×C3×D311yescharacteristic
575C2×C8C22×C3×D311yescharacteristic
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4C22×C3×D311yescharacteristic
588C4⋊C4C22×C3×D311yescharacteristic
589C4⋊C4C22×C3×D311yescharacteristic
590C22⋊C4—21no—
591C22⋊C4—31no—
592C22⋊C4—31no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C42—31no—
600C42—61no—
601C42—61no—
602C42—61no—
603C42C22×C3×D311yescharacteristic
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—21no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—62no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—244no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C22×C3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—22no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—84no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23911yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4C2×C3×#4111yescharacteristic
656C3×C4C2×C3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663C32#312311yescharacteristic, complemented, Sylow
664C23—21no—
665C23—31no—
666C23—64no—
667C23—61no—
668C23—241no—
669C23—241no—
670Q8—61no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674D4—21no—
675D4—32no—
676D4—64no—
677D4—61no—
678D4C3×#23912yes—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—31no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—81no—
691C2×C4—241no—
692C2×C4—241no—
693C2×C4—241no—
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C3×D3×D411yescharacteristic
696C2×C4C23×C3×D311yescharacteristic
697C8—21no—
698C8—21no—
699C8—61no—
700C8—61no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—82no—
707C2×C3—121no—
708C2×C3—122no—
709C2×C3#562711yescharacteristic
710C2×C3#577011yescharacteristic
711C2×C3#577511yescharacteristic
712C2×C3C3×#52511yescharacteristic
713C2×C3C3×#57711yescharacteristic
714C2×C3C3×#57711yescharacteristic
715D3—41no—
716D3—42no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22—244no—
727C22C2×C3×D3×D411yescharacteristic
728C4—21no—
729C4—21no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—61no—
734C4—61no—
735C4—61no—
736C4—121no—
737C4—121no—
738C4—121no—
739C4C2×C3×#23911yescharacteristic
740C4C3×D3×#4111yescharacteristic
741C3—21no—
742C3#8114711yescharacteristic, direct product factor
743C3C3×#312311yescharacteristic, complemented
744C2—42no—
745C2—121no—
746C2—122no—
747C2C3×#562711yescharacteristic
748C2C3×#577011yescharacteristic
749C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC3×#478D3
hypocenterC3C3×#3123
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5698C2semidirect
3. C32×#478C2semidirect
4. C3×#5066C2semidirect
5. C3×#5019C2semidirect
6. C3×#4889C2semidirect
7. C3×#4888C2semidirect
8. C3×#4868C2semidirect
9. C3×#4852C2semidirect
10. C3×#4841C2semidirect
11. C3×#4840C2semidirect
14. C3×#4758C2semidirect
15. C3×#4757C2semidirect
17. #81147C3direct (N × H)
19. C32×#125C22semidirect
36. C3×#887C22semidirect
37. C3×#887C22semidirect
42. C3×#869C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
45. C32×C4⋊C8C22semidirect
50. C3×#816C22semidirect
51. C3×#816C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5698C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5066C2×C3semidirect
81. #5019C2×C3semidirect
82. #4889C2×C3semidirect
83. #4888C2×C3semidirect
84. #4868C2×C3semidirect
85. #4852C2×C3semidirect
86. #4841C2×C3semidirect
87. #4840C2×C3semidirect
90. #4758C2×C3semidirect
91. #4757C2×C3semidirect
154. C3×#125C2×D3semidirect
155. C3×#125C22×C3semidirect
187. #887C22×C3semidirect
188. #887C22×C3semidirect
193. #869C22×C3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C22×C3semidirect
224. #816C22×C3semidirect
225. #816C22×C3semidirect
226. #815C22×C3semidirect
227. C8×Dic3C22×C3semidirect
228. #810C22×C3semidirect
229. #810C22×C3semidirect
232. #808C22×C3semidirect
233. #807C22×C3semidirect
234. C4⋊(C3⋊C8)C22×C3semidirect
277. #478C3×D3semidirect
430. #125C2×C3×D3semidirect
446. #107C2×C3×D3semidirect
448. #106C2×C3×D3semidirect
450. C4⋊C8C2×C3×D3semidirect
663. C32#3123semidirect
742. C3#81147direct (N × H)
743. C3C3×#3123semidirect

Maximal subgroups

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

subgroupindex
C3×#56982
C3×#55452
C32×#4782
C3×#50662
C3×#50192
C3×#48892
C3×#48882
C3×#48682
C3×#48522
C3×#48412
C3×#48402
C3×#47762
C3×#47582
C3×#47572
C3×#31233
#811473