Finite Group Databasebeta

← C3×#80775 #11887217

Subgroups — C3×#80775 #11887217

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5642C211yesmaximal, characteristic, complemented
2C3×#5630C211yesmaximal, characteristic
3C32×#467C211yesmaximal, characteristic, complemented
4C3×#5187C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C3×C8×#67C211yesmaximal, characteristic, complemented
8C3×#5046C211yesmaximal, characteristic, complemented
9C3×#5043C211yesmaximal, characteristic, complemented
10C3×#4891C211yesmaximal, characteristic, complemented
11C3×#4885C211yesmaximal, characteristic, complemented
12C3×#4807C211yesmaximal, characteristic, complemented
13C3×#4804C211yesmaximal, characteristic, complemented
14C3×#4800C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#80775C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic, complemented
21C22×C32×C8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×#946C2211yescharacteristic, complemented
26C3×Q8×Dic3C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C3×C4×#67C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#898—21no—
33C3×#895—21no—
34C3×#895C2211yescharacteristic
35C3×#894—21no—
36C3×#893C2211yescharacteristic
37C3×#892C2211yescharacteristic, complemented
38C3×#890—21no—
39C3×#890C2211yescharacteristic, complemented
40C3×#886—21no—
41C3×#882—21no—
42C3×D3×C22⋊C4—21no—
43C3×#877—21no—
44C32×#107C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#830C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#808C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5642C2×C311yescharacteristic, complemented
64#5630C2×C311yescharacteristic
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—21no—
70C3×#467D311yescharacteristic, complemented
71C3×#467C2×C311yescharacteristic, complemented
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#450—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5187C2×C311yescharacteristic, complemented
81#5185C2×C311yescharacteristic, complemented
82C2×#821C2×C311yescharacteristic, complemented
83C8×#67C2×C311yescharacteristic, complemented
84#5046C2×C311yescharacteristic, complemented
85#5043C2×C311yescharacteristic, complemented
86#4891C2×C311yescharacteristic, complemented
87#4885C2×C311yescharacteristic, complemented
88#4807C2×C311yescharacteristic, complemented
89#4804C2×C311yescharacteristic, complemented
90#4800C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C32×Q16—41no—
111C2×C32×C8—41no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4—21no—
115C32×C4⋊C4—21no—
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C3×#217D411yescharacteristic
121C3×#215—22no—
122C3×#215—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C22×C311yescharacteristic
148C22×D12C22×C311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16C2×D311yescharacteristic, complemented
151C2×C3×Q16C22×C311yescharacteristic, complemented
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×#126—61no—
159C3×#125—31no—
160C3×#125—61no—
161C3×#124—31no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8C2×D311yescharacteristic
168C3×C22⋊Q8C2×D311yescharacteristic
169C3×C22⋊Q8C22×C311yescharacteristic
170C3×C22⋊Q8C22×C311yescharacteristic
171C3×#121—31no—
172C3×#121—61no—
173C3×#120—61no—
174C3×C4×Q8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×#117—31no—
178C3×#117—61no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—61no—
181#947C22×C311yescharacteristic
182#946C22×C311yescharacteristic, complemented
183Q8×Dic3C22×C311yescharacteristic, complemented
184C2×#215C22×C311yescharacteristic
185C2×#215C22×C311yescharacteristic
186C4×#67C22×C311yescharacteristic
187C2×C4⋊Dic3C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic, complemented
189#898—21no—
190#895—21no—
191#895C22×C311yescharacteristic
192#894—21no—
193#893C22×C311yescharacteristic
194#892C22×C311yescharacteristic, complemented
195#890—21no—
196#890C22×C311yescharacteristic, complemented
197#886—21no—
198#882—21no—
199D3×C22⋊C4—21no—
200#877—21no—
201C3×#107—21no—
202C3×#107C2×D311yescharacteristic, complemented
203C3×#107C22×C311yescharacteristic, complemented
204C3×#106—31no—
205C3×#106—31no—
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103C2×D311yescharacteristic, complemented
212C3×#103C2×D311yescharacteristic, complemented
213C3×#103C22×C311yescharacteristic, complemented
214C3×#103C22×C311yescharacteristic, complemented
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—31no—
222C3×C22⋊C8—31no—
223C3×C4×C8—31no—
224#835C22×C311yescharacteristic, complemented
225#835C22×C311yescharacteristic, complemented
226#830C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic, complemented
232Dic3⋊C8C22×C311yescharacteristic, complemented
233C8×Dic3C22×C311yescharacteristic, complemented
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic, complemented
237#808C22×C311yescharacteristic, complemented
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12—42no—
269C3×D12—81no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—31no—
281#488—31no—
282#483—31no—
283#482—31no—
284#478—31no—
285#467C3×D311yescharacteristic, complemented
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416—31no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C23×C311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—62no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C2×#67C3×D411yescharacteristic
320C22×Dic3—21no—
321#239—22no—
322#239—41no—
323C2×D12—22no—
324C2×D12—21no—
325C2×D12—21no—
326C2×D12—21no—
327C2×D12—41no—
328C2×D12C23×C311yescharacteristic
329C2×D12C23×C311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3C23×C311yescharacteristic
333C3×Q16—41no—
334C3×Q16—41no—
335C3×Q16—42no—
336C3×SD16—62no—
337C3×SD16—121no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—41no—
343C2×C3×C8—41no—
344C2×C3×C8—42no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C2×C3×C8C23×C311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—41no—
360C3×C4⋊C4—41no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4—61no—
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C23×C311yescharacteristic
369C3×C4⋊C4C23×C311yescharacteristic
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—41no—
377C3×C22⋊C4—41no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385C3×C42—61no—
386C3×C42—61no—
387#217C3×D411yescharacteristic
388#215—22no—
389#215—41no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4C3×D411yescharacteristic
397C4⋊Dic3—21no—
398C4⋊Dic3—21no—
399C4⋊Dic3—21no—
400C4⋊Dic3C23×C311yescharacteristic
401C4⋊Dic3C23×C311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4C3×D411yescharacteristic
405C4×Dic3—21no—
406C4×Dic3—21no—
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13512yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—31no—
439C2×Q16C2×C3×D311yescharacteristic, complemented
440C2×SD16—31no—
441C2×SD16—31no—
442C22×C8—31no—
443C22×C8C2×C3×D311yescharacteristic
444#126—61no—
445#125—31no—
446#125—61no—
447#124—31no—
448#123—61no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8C2×C3×D311yescharacteristic
452C22⋊Q8C2×C3×D311yescharacteristic
453#121—31no—
454#121—61no—
455#120—61no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—31no—
459#117—31no—
460#117—61no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—61no—
463#107C2×C3×D311yescharacteristic, complemented
464#106—31no—
465#106—31no—
466C4⋊C8—31no—
467#103—31no—
468#103—31no—
469#103C2×C3×D311yescharacteristic, complemented
470#103C2×C3×D311yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477C22⋊C8—31no—
478C22⋊C8—31no—
479C4×C8—31no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×C3×D411yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×C3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×D4—32no—
508C3×D4—62no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—122no—
513C3×D4—122no—
514C3×D4—241no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4—122no—
544C2×C3×C4—241no—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C2×C3×D411yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548C2×C3×C4C24×C311yescharacteristic
549#67—22no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—42no—
553C2×Dic3C2×C3×D411yescharacteristic
554C2×Dic3C2×C3×D411yescharacteristic
555C2×Dic3C2×C3×D411yescharacteristic
556D12—21no—
557D12—21no—
558D12—21no—
559D12—42no—
560D12—42no—
561D12—81no—
562D12C3×#4112yes—
563C4×D3—21no—
564C4×D3—21no—
565C4×D3—42no—
566C4×D3—81no—
567C3×C8—22no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—22no—
578C2×C32#54611yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—42no—
583C3×D3—81no—
584C24—61no—
585#41—62no—
586#41—121no—
587C2×Q8C22×C3×D311yescharacteristic
588C2×Q8C22×C3×D311yescharacteristic
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—121no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4C22×C3×D311yescharacteristic
602Q16—41no—
603SD16—62no—
604SD16—121no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—41no—
608C2×C8—121no—
609C2×C8C22×C3×D311yescharacteristic
610C2×C8C22×C3×D311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4C22×C3×D311yescharacteristic
622C4⋊C4C22×C3×D311yescharacteristic
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C42—31no—
634C42—61no—
635C42—61no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—22no—
641C22×C3—21no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3#91912yes—
655C22×C3C3×#13512yes—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×C3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—22no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4#100411yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4C2×C3×#4111yescharacteristic
693C3×C4C3×H(5,𝔽2)11yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699C32#329611yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—122no—
704C23—122no—
705C23—241no—
706C23C3×D3×D411yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—21no—
710Q8—21no—
711D4—32no—
712D4—62no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—122no—
718D4—241no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4—241no—
735C2×C4C3×D3×D411yescharacteristic
736C2×C4C23×C3×D311yescharacteristic
737C8—21no—
738C8—21no—
739C8—61no—
740C8—61no—
741C2×C3—22no—
742C2×C3—22no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—121no—
748C2×C3—122no—
749C2×C3—241no—
750C2×C3#561011yescharacteristic
751C2×C3C2×#91911yescharacteristic
752C2×C3#577011yescharacteristic
753C2×C3C3×#54611yescharacteristic
754C2×C3C2×C3×#13511yescharacteristic
755C2×C3C3×#57711yescharacteristic
756D3—41no—
757D3—42no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—62no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—244no—
771C22C3×#91912yes—
772C22C2×C3×D3×D411yescharacteristic
773C4—21no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4C3×#100411yescharacteristic
784C4C3×D3×#4111yescharacteristic
785C3—21no—
786C3#8077511yescharacteristic, direct product factor
787C3C3×#329611yescharacteristic, complemented
788C2—22no—
789C2—121no—
790C2—122no—
791C2—241no—
792C2C3×#561011yescharacteristic
793C2C2×C3×#91911yescharacteristic
794C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#467C2
socleC22×C32C22×D4
prime radicalC3×#5630C2
hypercenterC3×#467D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#467

Complements

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

NH ≅ G/Ntype
1. C3×#5642C2semidirect
3. C32×#467C2semidirect
4. C3×#5187C2semidirect
5. C3×#5185C2semidirect
6. C2×C3×#821C2semidirect
7. C3×C8×#67C2semidirect
8. C3×#5046C2semidirect
9. C3×#5043C2semidirect
10. C3×#4891C2semidirect
11. C3×#4885C2semidirect
12. C3×#4807C2semidirect
13. C3×#4804C2semidirect
14. C3×#4800C2semidirect
15. C3×#4788C2semidirect
17. #80775C3direct (N × H)
20. C2×C32×Q16C22semidirect
25. C3×#946C22semidirect
26. C3×Q8×Dic3C22semidirect
31. C2×C3×D3×C8C22semidirect
37. C3×#892C22semidirect
39. C3×#890C22semidirect
44. C32×#107C22semidirect
45. C32×#103C22semidirect
46. C32×#103C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
59. C3×#808C22semidirect
60. C3×#808C22semidirect
63. #5642C2×C3semidirect
70. C3×#467D3semidirect
71. C3×#467C2×C3semidirect
80. #5187C2×C3semidirect
81. #5185C2×C3semidirect
82. C2×#821C2×C3semidirect
83. C8×#67C2×C3semidirect
84. #5046C2×C3semidirect
85. #5043C2×C3semidirect
86. #4891C2×C3semidirect
87. #4885C2×C3semidirect
88. #4807C2×C3semidirect
89. #4804C2×C3semidirect
90. #4800C2×C3semidirect
91. #4788C2×C3semidirect
150. C2×C3×Q16C2×D3semidirect
151. C2×C3×Q16C22×C3semidirect
182. #946C22×C3semidirect
183. Q8×Dic3C22×C3semidirect
188. C2×D3×C8C22×C3semidirect
194. #892C22×C3semidirect
196. #890C22×C3semidirect
202. C3×#107C2×D3semidirect
203. C3×#107C22×C3semidirect
211. C3×#103C2×D3semidirect
212. C3×#103C2×D3semidirect
213. C3×#103C22×C3semidirect
214. C3×#103C22×C3semidirect
224. #835C22×C3semidirect
225. #835C22×C3semidirect
231. (C2×D3)⋊C8C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
236. #808C22×C3semidirect
237. #808C22×C3semidirect
285. #467C3×D3semidirect
439. C2×Q16C2×C3×D3semidirect
463. #107C2×C3×D3semidirect
469. #103C2×C3×D3semidirect
470. #103C2×C3×D3semidirect
699. C32#3296semidirect
786. C3#80775direct (N × H)
787. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#56422
C3×#56302
C32×#4672
C3×#51872
C3×#51852
C2×C3×#8212
C3×C8×#672
C3×#50462
C3×#50432
C3×#48912
C3×#48852
C3×#48072
C3×#48042
C3×#48002
C3×#47882
C3×#32963
#807753