Finite Group Databasebeta

← C3×#78845 #11887202

Subgroups — C3×#78845 #11887202

Order 1152.

895 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic
2C3×#5529C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic, complemented
7C3×#5003C211yesmaximal, characteristic, complemented
8C3×#4813C211yesmaximal, characteristic, complemented
9C3×#4805C211yesmaximal, characteristic, complemented
10C3×#4800C211yesmaximal, characteristic, complemented
11C3×#4798C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4763C211yesmaximal, characteristic, complemented
15C3×#4758C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#78845C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21C32×#117C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic, complemented
25C3×#939—21no—
26C3×#937—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#929—21no—
31C3×C4×#67C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4—21no—
33C3×#924C2211yescharacteristic, complemented
34C2×C3×#204C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36C3×#897C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890C2211yescharacteristic, complemented
39C3×#887C2211yescharacteristic, complemented
40C3×#883—21no—
41C3×#879—21no—
42C3×#872—21no—
43C3×#870—21no—
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×#817C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—31no—
63#5829C2×C311yescharacteristic
64#5529C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#483—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#450—31no—
74C3×C4×SD16—31no—
75C3×C8×D4—31no—
76C3×#416—21no—
77C3×#416D311yescharacteristic, complemented
78C3×#416C2×C311yescharacteristic, complemented
79C2×C3×#102—31no—
80#5239C2×C311yescharacteristic, complemented
81#5114C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic, complemented
83#5003C2×C311yescharacteristic, complemented
84#4813C2×C311yescharacteristic, complemented
85#4805C2×C311yescharacteristic, complemented
86#4800C2×C311yescharacteristic, complemented
87#4798C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic, complemented
89D3×#102C2×C311yescharacteristic, complemented
90#4763C2×C311yescharacteristic, complemented
91#4758C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×#214—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—41no—
143C3×D3×C8—41no—
144#3296—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×D4—31no—
149C2×D3×D4C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—21no—
154C22×C3×C8—31no—
155C22×C3×C8C2×D311yescharacteristic, complemented
156C22×C3×C8C22×C311yescharacteristic, complemented
157C3×#126—61no—
158C3×#125—31no—
159C3×#125—61no—
160C3×#124—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×#121—31no—
167C3×#121—61no—
168C3×#120—61no—
169C3×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×#117—21no—
173C3×#117—61no—
174C3×#117C2×D311yescharacteristic, complemented
175C3×#117C22×C311yescharacteristic, complemented
176C2×C3×C4⋊C4—31no—
177C2×C3×C22⋊C4—61no—
178#947C22×C311yescharacteristic
179#946C22×C311yescharacteristic
180C2×#216C22×C311yescharacteristic, complemented
181#939—21no—
182#937—21no—
183D4×Dic3C22×C311yescharacteristic
184C2×#214C22×C311yescharacteristic
185#930C22×C311yescharacteristic
186#929—21no—
187C4×#67C22×C311yescharacteristic
188C2×(C2×D3)⋊C4—21no—
189#924C22×C311yescharacteristic, complemented
190C2×#204C22×C311yescharacteristic
191C2×D3×C8C22×C311yescharacteristic
192#897C22×C311yescharacteristic
193D3×C4⋊C4C22×C311yescharacteristic
194#890C22×C311yescharacteristic, complemented
195#887C22×C311yescharacteristic, complemented
196#883—21no—
197#879—21no—
198#872—21no—
199#870—21no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C2×D311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#103C22×C311yescharacteristic, complemented
212C3×#102—21no—
213C3×#102—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic
219C3×#102C2×D311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#835C22×C311yescharacteristic, complemented
226#832C22×C311yescharacteristic
227#830C22×C311yescharacteristic, complemented
228#821C22×C311yescharacteristic
229(C2×D3)⋊C8C22×C311yescharacteristic
230#817C22×C311yescharacteristic, complemented
231#816C22×C311yescharacteristic, complemented
232Dic3⋊C8C22×C311yescharacteristic, complemented
233C8×Dic3C22×C311yescharacteristic, complemented
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#808C22×C311yescharacteristic, complemented
237#807C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
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×D4—21no—
248C32×D4—42no—
249C32×D4#4112yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—42no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258C3×#67—22no—
259C3×#67—42no—
260C3×#67—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272C3×C4×D3—42no—
273C3×Dic6—21no—
274C3×Dic6—21no—
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#467—31no—
286#465—31no—
287#464—31no—
288#452—31no—
289#450—31no—
290C4×SD16—31no—
291C8×D4—31no—
292#416C3×D311yescharacteristic, complemented
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C3×#41—24no—
297C3×#41—22no—
298C3×#41—22no—
299C3×#41—41no—
300C3×#41—41no—
301C3×#41—42no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C23×C311yescharacteristic
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—41no—
312C2×C3×D4—61no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—121no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C23×C311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C23×C311yescharacteristic
327C2×#67—21no—
328C2×#67—21no—
329C2×#67C3×D411yescharacteristic
330C22×Dic3—21no—
331D3×D4—22no—
332D3×D4—41no—
333C2×D12C23×C311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3C23×C311yescharacteristic
336C2×Dic6C23×C311yescharacteristic
337C3×Q16—121no—
338C3×SD16—62no—
339C3×SD16—121no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—41no—
345C2×C3×C8—41no—
346C2×C3×C8—42no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C23×C311yescharacteristic
351C2×C3×C8C23×C311yescharacteristic
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4C22×D311yescharacteristic
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C23×C311yescharacteristic
367C3×C4⋊C4C23×C311yescharacteristic
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C22⋊C4—41no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—31no—
383C3×C42—41no—
384C3×C42—61no—
385#217—21no—
386#217—21no—
387#217C3×D411yescharacteristic
388#216—41no—
389#214—22no—
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)⋊C4C3×D411yescharacteristic
396C4⋊Dic3—21no—
397C4⋊Dic3—21no—
398C4⋊Dic3C23×C311yescharacteristic
399C4⋊Dic3C23×C311yescharacteristic
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—21no—
405Dic3⋊C4C3×D411yescharacteristic
406C4×Dic3—21no—
407C4×Dic3C23×C311yescharacteristic
408C2×C3⋊C8C23×C311yescharacteristic
409C2×C3⋊C8C23×C311yescharacteristic
410#204—41no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—22no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32C22×D411yescharacteristic
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C2×C3×D3#13512yes—
426C32×C4—21no—
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—
437C3×Dic3—41no—
438C2×#41C2×C3×D311yescharacteristic
439C22×D4—31no—
440C2×Q16—31no—
441C2×SD16—31no—
442C2×SD16—31no—
443C22×C8—31no—
444C22×C8C2×C3×D311yescharacteristic, complemented
445#126—61no—
446#125—31no—
447#125—61no—
448#124—31no—
449#123—61no—
450#123—61no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454#121—31no—
455#121—61no—
456#120—61no—
457C4×Q8—31no—
458C4×D4—31no—
459C4×D4—31no—
460#117—61no—
461#117C2×C3×D311yescharacteristic, complemented
462C2×C4⋊C4—31no—
463C2×C22⋊C4—61no—
464#107—31no—
465#106—31no—
466#106—31no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103C2×C3×D311yescharacteristic, complemented
471#103C2×C3×D311yescharacteristic, complemented
472#102—31no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102C2×C3×D311yescharacteristic
477#102C2×C3×D311yescharacteristic
478C22⋊C8—31no—
479C22⋊C8—31no—
480C4×C8—31no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—122no—
488C23×C3—122no—
489C23×C3—241no—
490C23×C3D3×D411yescharacteristic
491C23×C3C2×C3×D411yescharacteristic
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C22×D3C2×C3×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—41no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—44no—
512C3×D4—62no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—122no—
516C3×D4—241no—
517C3×D4#23512yes—
518C3×D4C3×#4112yes—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
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—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—31no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—44no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—122no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×C3×D411yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C24×C311yescharacteristic
553#67—22no—
554#67—42no—
555#67—81no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—81no—
560C2×Dic3C2×C3×D411yescharacteristic
561C2×Dic3C2×C3×D411yescharacteristic
562C2×Dic3C2×C3×D411yescharacteristic
563D12—21no—
564D12—21no—
565C4×D3—21no—
566C4×D3—21no—
567C4×D3—42no—
568Dic6—21no—
569Dic6—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C2×C32—41no—
581C2×C32—42no—
582C2×C32#54611yescharacteristic
583C2×C32C2×#13511yescharacteristic
584C2×C32#57711yescharacteristic
585C3×D3—22no—
586C3×D3—81no—
587C24—61no—
588#41—22no—
589#41—41no—
590C2×Q8—31no—
591C2×Q8C22×C3×D311yescharacteristic
592C2×D4—21no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—62no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4C22×C3×D311yescharacteristic
600C22×C4—21no—
601C22×C4—31no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4C22×C3×D311yescharacteristic
605Q16—121no—
606SD16—62no—
607SD16—121no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—41no—
611C2×C8—121no—
612C2×C8C22×C3×D311yescharacteristic
613C2×C8C22×C3×D311yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4C22×C3×D311yescharacteristic
625C4⋊C4C22×C3×D311yescharacteristic
626C22⋊C4—21no—
627C22⋊C4—31no—
628C22⋊C4—31no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C42—21no—
637C42—31no—
638C42—61no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—22no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—244no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C22×C3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C2×D3C3×#13512yes—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—42no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—41no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—81no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4C2×#23511yescharacteristic
695C3×C4#100411yescharacteristic
696C3×C4C2×C3×#4111yescharacteristic
697C3×C4C3×H(5,𝔽2)11yescharacteristic
698Dic3—21no—
699Dic3—21no—
700Dic3—21no—
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704C32#329611yescharacteristic, complemented, Sylow
705C23—21no—
706C23—31no—
707C23—61no—
708C23—122no—
709C23—122no—
710C23—241no—
711C23C3×D3×D411yescharacteristic
712Q8—21no—
713Q8—21no—
714Q8—61no—
715Q8—61no—
716D4—21no—
717D4—42no—
718D4—62no—
719D4—61no—
720D4—61no—
721D4—122no—
722D4—241no—
723D4C3×#23512yes—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—31no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—42no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—122no—
739C2×C4—241no—
740C2×C4C3×D3×D411yescharacteristic
741C2×C4C23×C3×D311yescharacteristic
742C8—21no—
743C8—21no—
744C8—61no—
745C8—61no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—42no—
751C2×C3—41no—
752C2×C3—41no—
753C2×C3—42no—
754C2×C3—62no—
755C2×C3—82no—
756C2×C3—241no—
757C2×C3#549011yescharacteristic
758C2×C3D3×#13511yescharacteristic
759C2×C3#577011yescharacteristic
760C2×C3C3×#54611yescharacteristic
761C2×C3C2×C3×#13511yescharacteristic
762C2×C3C3×#57711yescharacteristic
763D3—22no—
764D3—81no—
765C22—21no—
766C22—22no—
767C22—21no—
768C22—21no—
769C22—32no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—61no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—244no—
778C22C2×C3×D3×D411yescharacteristic
779C4—21no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4C2×C3×#23511yescharacteristic
790C4C3×#100411yescharacteristic
791C3—21no—
792C3#7884511yescharacteristic, direct product factor
793C3C3×#329611yescharacteristic, complemented
794C2—41no—
795C2—42no—
796C2—62no—
797C2—241no—
798C2C3×#549011yescharacteristic
799C2C3×D3×#13511yescharacteristic
800C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radicalC3×#5829C2
hypercenterC3×#416D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#416

Complements

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

NH ≅ G/Ntype
2. C3×#5529C2semidirect
3. C32×#416C2semidirect
4. C3×#5239C2semidirect
5. C3×#5114C2semidirect
6. C3×C8×#67C2semidirect
7. C3×#5003C2semidirect
8. C3×#4813C2semidirect
9. C3×#4805C2semidirect
10. C3×#4800C2semidirect
11. C3×#4798C2semidirect
12. C3×#4776C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4763C2semidirect
15. C3×#4758C2semidirect
17. #78845C3direct (N × H)
20. C22×C32×C8C22semidirect
21. C32×#117C22semidirect
24. C2×C3×#216C22semidirect
33. C3×#924C22semidirect
38. C3×#890C22semidirect
39. C3×#887C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
48. C3×#835C22semidirect
50. C3×#830C22semidirect
53. C3×#817C22semidirect
54. C3×#816C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
64. #5529C2×C3semidirect
77. C3×#416D3semidirect
78. C3×#416C2×C3semidirect
80. #5239C2×C3semidirect
81. #5114C2×C3semidirect
82. C8×#67C2×C3semidirect
83. #5003C2×C3semidirect
84. #4813C2×C3semidirect
85. #4805C2×C3semidirect
86. #4800C2×C3semidirect
87. #4798C2×C3semidirect
88. #4776C2×C3semidirect
89. D3×#102C2×C3semidirect
90. #4763C2×C3semidirect
91. #4758C2×C3semidirect
155. C22×C3×C8C2×D3semidirect
156. C22×C3×C8C22×C3semidirect
174. C3×#117C2×D3semidirect
175. C3×#117C22×C3semidirect
180. C2×#216C22×C3semidirect
189. #924C22×C3semidirect
194. #890C22×C3semidirect
195. #887C22×C3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C2×D3semidirect
210. C3×#103C22×C3semidirect
211. C3×#103C22×C3semidirect
225. #835C22×C3semidirect
227. #830C22×C3semidirect
230. #817C22×C3semidirect
231. #816C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
236. #808C22×C3semidirect
237. #807C22×C3semidirect
292. #416C3×D3semidirect
444. C22×C8C2×C3×D3semidirect
461. #117C2×C3×D3semidirect
470. #103C2×C3×D3semidirect
471. #103C2×C3×D3semidirect
704. C32#3296semidirect
792. C3#78845direct (N × H)
793. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C3×#55292
C32×#4162
C3×#52392
C3×#51142
C3×C8×#672
C3×#50032
C3×#48132
C3×#48052
C3×#48002
C3×#47982
C3×#47762
C3×D3×#1022
C3×#47632
C3×#47582
C3×#32963
#788453