Finite Group Databasebeta

← C3×#83494 #11887199

Subgroups — C3×#83494 #11887199

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#546C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5C3×#5218C211yesmaximal, characteristic, complemented
6C2×C3×#832C211yesmaximal, characteristic, complemented
7C3×#5056C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5051C211yesmaximal, characteristic, complemented
10C3×#5043C211yesmaximal, characteristic, complemented
11C3×#5041C211yesmaximal, characteristic, complemented
12C3×#5035C211yesmaximal, characteristic, complemented
13C3×C4×#214C211yesmaximal, characteristic, complemented
14C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
15C3×#5009C211yesmaximal, characteristic, complemented
16C3×#3296—31nomaximal
17#83494C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C32×#123—21no—
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121—21no—
24C32×#121C2211yescharacteristic
25C32×#120—21no—
26C32×C4×D4C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C2×C32×C22⋊C4—21no—
29C2×C3×#216C2211yescharacteristic, complemented
30C3×#935—21no—
31C2×C3×#214C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C3×#926C2211yescharacteristic, complemented
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic, complemented
37C22×C3×C3⋊C8C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic, complemented
39C3×#889—21no—
40C3×#879—21no—
41C3×#877—21no—
42C3×#870C2211yescharacteristic, complemented
43C3×C4×Dic6C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#830C2211yescharacteristic
54C3×#830C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#808C2211yescharacteristic, complemented
57C3×#808C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62C3×#546—21no—
63C3×#546D311yescharacteristic
64C3×#546C2×C311yescharacteristic
65#5541C2×C311yescharacteristic, complemented
66C3×#488—31no—
67C3×#483—31no—
68C3×#482—31no—
69C3×#478—31no—
70C3×#467—31no—
71C3×#465—31no—
72C3×#464—31no—
73C3×#452—31no—
74C3×#450—31no—
75C3×C4×SD16—31no—
76C3×C8×D4—31no—
77C3×#416—31no—
78C2×C3×#102—31no—
79#5239C2×C311yescharacteristic, complemented
80#5233C2×C311yescharacteristic, complemented
81#5218C2×C311yescharacteristic, complemented
82C2×#832C2×C311yescharacteristic, complemented
83#5056C2×C311yescharacteristic, complemented
84#5054C2×C311yescharacteristic, complemented
85#5051C2×C311yescharacteristic, complemented
86#5043C2×C311yescharacteristic, complemented
87#5041C2×C311yescharacteristic, complemented
88#5035C2×C311yescharacteristic, complemented
89C4×#214C2×C311yescharacteristic, complemented
90D4×C3⋊C8C2×C311yescharacteristic, complemented
91#5009C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—22no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4D411yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4—21no—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3×Dic3—21no—
109C2×C3×Dic6C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4D411yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C22⋊C4D411yescharacteristic
119C32×C22⋊C4D411yescharacteristic
120C32×C42C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#216—41no—
125C3×#214—22no—
126C3×#214—41no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3296—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×D4—21no—
149C22×C3×D4C2×D311yescharacteristic
150C22×C3×D4C22×C311yescharacteristic
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C22×C3×C8—31no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#125—61no—
159C3×#124—21no—
160C3×#124C2×D311yescharacteristic
161C3×#124C22×C311yescharacteristic
162C3×#123—22no—
163C3×#123—21no—
164C3×#123—21no—
165C3×#123—61no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C22×C311yescharacteristic
171C3×#121—22no—
172C3×#121—21no—
173C3×#121—21no—
174C3×#121—21no—
175C3×#121C2×D311yescharacteristic
176C3×#121C22×C311yescharacteristic
177C3×#120—22no—
178C3×#120—21no—
179C3×#120—21no—
180C3×C4×Q8—31no—
181C3×C4×D4—21no—
182C3×C4×D4—21no—
183C3×C4×D4C2×D311yescharacteristic
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C22×C311yescharacteristic
186C3×C4×D4C22×C311yescharacteristic
187C3×#117—31no—
188C3×#117—61no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C22⋊C4—22no—
191C2×C3×C22⋊C4—21no—
192C2×C3×C22⋊C4—21no—
193C2×#216C22×C311yescharacteristic, complemented
194#935—21no—
195C2×#214C22×C311yescharacteristic
196C2×#214C22×C311yescharacteristic
197#926C22×C311yescharacteristic, complemented
198C2×C4⋊Dic3C22×C311yescharacteristic
199#924C22×C311yescharacteristic
200#924C22×C311yescharacteristic, complemented
201C22×C3⋊C8C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic, complemented
203#889—21no—
204#879—21no—
205#877—21no—
206#870C22×C311yescharacteristic, complemented
207C4×Dic6C22×C311yescharacteristic, complemented
208C3×#107—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×C4×C8—31no—
225#835C22×C311yescharacteristic, complemented
226#835C22×C311yescharacteristic, complemented
227#835C22×C311yescharacteristic, complemented
228#832C22×C311yescharacteristic
229#832C22×C311yescharacteristic
230#832C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#832C22×C311yescharacteristic
234#830C22×C311yescharacteristic
235#830C22×C311yescharacteristic, complemented
236#810C22×C311yescharacteristic, complemented
237#808C22×C311yescharacteristic, complemented
238#808C22×C311yescharacteristic, complemented
239#807C22×C311yescharacteristic, complemented
240C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
241C4×C3⋊C8C22×C311yescharacteristic, complemented
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—42no—
245C23×C32—42no—
246C23×C32—81no—
247C23×C32C2×D411yescharacteristic
248C23×C32C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8—21no—
251C32×D4—21no—
252C32×D4—22no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—42no—
256C32×D4—42no—
257C32×D4—81no—
258C32×D4#4112yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—42no—
266C2×C32×C4—81no—
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—42no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—31no—
284#546C3×D311yescharacteristic
285#488—31no—
286#483—31no—
287#482—31no—
288#478—31no—
289#467—31no—
290#465—31no—
291#464—31no—
292#452—31no—
293#450—31no—
294C4×SD16—31no—
295C8×D4—31no—
296#416—31no—
297C2×#102—31no—
298C24×C3—22no—
299C24×C3—21no—
300C24×C3—21no—
301C3×#41—22no—
302C3×#41—22no—
303C3×#41—42no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—42no—
307C2×C3×Q8—21no—
308C2×C3×Q8—31no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C23×C311yescharacteristic
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—22no—
314C2×C3×D4—22no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—22no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—42no—
326C2×C3×D4—41no—
327C2×C3×D4—41no—
328C2×C3×D4—42no—
329C2×C3×D4#6711yescharacteristic
330C2×C3×D4C3×D411yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C23×C311yescharacteristic
334C2×C3×D4C23×C311yescharacteristic
335C22×C3×C4—22no—
336C22×C3×C4—22no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C22×Dic3—21no—
349C2×Dic6C23×C311yescharacteristic
350C3×Q16—121no—
351C3×SD16—62no—
352C3×SD16—121no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—31no—
357C2×C3×C8—121no—
358C2×C3×C8—121no—
359C3×C4⋊C4—22no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4#6711yescharacteristic
374C3×C4⋊C4C3×D411yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C23×C311yescharacteristic
377C3×C22⋊C4—22no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—22no—
380C3×C22⋊C4—22no—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4#6711yescharacteristic
398C3×C22⋊C4#6711yescharacteristic
399C3×C22⋊C4C3×D411yescharacteristic
400C3×C22⋊C4C3×D411yescharacteristic
401C3×C42—21no—
402C3×C42—61no—
403C3×C42—61no—
404C3×C42C22×D311yescharacteristic
405C3×C42C23×C311yescharacteristic
406#217—21no—
407#217—21no—
408#217—21no—
409#216—41no—
410#214—22no—
411#214—41no—
412C4⋊Dic3—21no—
413C4⋊Dic3C23×C311yescharacteristic
414C4⋊Dic3C23×C311yescharacteristic
415C4⋊Dic3C23×C311yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421C4×Dic3—21no—
422C4×Dic3—21no—
423C2×C3⋊C8—41no—
424C2×C3⋊C8—41no—
425C2×C3⋊C8C23×C311yescharacteristic
426C2×C3⋊C8C23×C311yescharacteristic
427C2×C3⋊C8C23×C311yescharacteristic
428C2×C3⋊C8C23×C311yescharacteristic
429C22×C32—22no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—84no—
441C22×C32#13512yes—
442C22×C32C22×D411yescharacteristic
443C32×C4—21no—
444C32×C4—21no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—41no—
448C32×C4—41no—
449C32×C4C2×#4111yescharacteristic
450C32×C4H(5,𝔽2)11yescharacteristic
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41C2×C3×D311yescharacteristic
456C22×D4C2×C3×D311yescharacteristic
457C2×Q16—31no—
458C2×SD16—31no—
459C2×SD16—31no—
460C22×C8—31no—
461C22×C8—31no—
462#126—61no—
463#125—31no—
464#125—61no—
465#124C2×C3×D311yescharacteristic
466#123—21no—
467#123—61no—
468C22⋊Q8—31no—
469C22⋊Q8—31no—
470C22⋊Q8C2×C3×D311yescharacteristic
471#121—21no—
472#121C2×C3×D311yescharacteristic
473#120—21no—
474C4×Q8—31no—
475C4×D4C2×C3×D311yescharacteristic
476C4×D4C2×C3×D311yescharacteristic
477#117—31no—
478#117—61no—
479C2×C4⋊C4—31no—
480C2×C22⋊C4—21no—
481#107—31no—
482#106—31no—
483#106—31no—
484C4⋊C8—31no—
485#103—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—31no—
495C22⋊C8—31no—
496C22⋊C8—31no—
497C4×C8—31no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—22no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—44no—
509C23×C3—44no—
510C23×C3—42no—
511C23×C3—42no—
512C23×C3—81no—
513C23×C3—81no—
514C23×C3—82no—
515C23×C3C2×#6711yescharacteristic
516C23×C3C2×#6711yescharacteristic
517C23×C3C2×C3×D411yescharacteristic
518C23×C3C2×C3×D411yescharacteristic
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—41no—
524C3×Q8—41no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—22no—
528C3×D4—22no—
529C3×D4—22no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—21no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—22no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—42no—
540C3×D4—42no—
541C3×D4—42no—
542C3×D4—42no—
543C3×D4—42no—
544C3×D4—44no—
545C3×D4—44no—
546C3×D4—81no—
547C3×D4—81no—
548C3×D4—82no—
549C3×D4#23712yes—
550C3×D4C3×#4112yes—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—42no—
575C2×C3×C4—42no—
576C2×C3×C4—44no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—81no—
582C2×C3×C4—81no—
583C2×C3×C4—82no—
584C2×C3×C4—122no—
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C2×#6711yescharacteristic
587C2×C3×C4C2×#6711yescharacteristic
588C2×C3×C4C2×#6711yescharacteristic
589C2×C3×C4C2×C3×D411yescharacteristic
590C2×C3×C4C2×C3×D411yescharacteristic
591C2×C3×C4C2×C3×D411yescharacteristic
592C2×C3×C4C2×C3×D411yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C24×C311yescharacteristic
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—42no—
600Dic6—21no—
601Dic6—21no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—22no—
611C2×C32—42no—
612C2×C32—41no—
613C2×C32—81no—
614C2×C32#54611yescharacteristic
615C2×C32C2×#13511yescharacteristic
616C2×C32#57711yescharacteristic
617C24—21no—
618#41—22no—
619#41—41no—
620C2×Q8—31no—
621C2×Q8C22×C3×D311yescharacteristic
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—41no—
627C2×D4C3×#6711yescharacteristic
628C2×D4C22×C3×D311yescharacteristic
629C2×D4C22×C3×D311yescharacteristic
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—61no—
633C22×C4C22×C3×D311yescharacteristic
634C22×C4C22×C3×D311yescharacteristic
635Q16—121no—
636SD16—62no—
637SD16—121no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8—121no—
644C4⋊C4—21no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4C3×#6711yescharacteristic
655C4⋊C4C22×C3×D311yescharacteristic
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4C3×#6711yescharacteristic
665C22⋊C4C3×#6711yescharacteristic
666C42—61no—
667C42—61no—
668C42C22×C3×D311yescharacteristic
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—42no—
690C22×C3—42no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—84no—
705C22×C3—84no—
706C22×C3—88no—
707C22×C3#95012yes—
708C22×C3C3×#13512yes—
709C22×C3C22×#6711yescharacteristic
710C22×C3C22×C3×D411yescharacteristic
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734C3×C4—121no—
735C3×C4C2×#23711yescharacteristic
736C3×C4#100411yescharacteristic
737C3×C4C2×C3×#4111yescharacteristic
738C3×C4C3×H(5,𝔽2)11yescharacteristic
739Dic3—41no—
740Dic3—41no—
741Dic3—41no—
742Dic3—41no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—21no—
745C23—21no—
746C23—42no—
747C23—42no—
748C23—81no—
749C23C2×C3×#6711yescharacteristic
750C23C2×C3×#6711yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—61no—
754Q8—61no—
755D4—22no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—42no—
760D4—42no—
761D4—81no—
762D4C3×#23712yes—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—42no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—81no—
775C2×C4—122no—
776C2×C4C2×C3×#6711yescharacteristic
777C2×C4C2×C3×#6711yescharacteristic
778C2×C4C2×C3×#6711yescharacteristic
779C2×C4C2×C3×#6711yescharacteristic
780C2×C4C23×C3×D311yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—42no—
791C2×C3—44no—
792C2×C3—41no—
793C2×C3—42no—
794C2×C3—41no—
795C2×C3—42no—
796C2×C3—81no—
797C2×C3—82no—
798C2×C3—81no—
799C2×C3—81no—
800C2×C3#580611yescharacteristic
801C2×C3C2×#95011yescharacteristic
802C2×C3#583611yescharacteristic
803C2×C3C3×#54611yescharacteristic
804C2×C3C2×C3×#13511yescharacteristic
805C2×C3C3×#57711yescharacteristic
806C22—21no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—84no—
818C22C3×#95012yes—
819C22C22×C3×#6711yescharacteristic
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—121no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4C2×C3×#23711yescharacteristic
831C4C3×#100411yescharacteristic
832C3—21no—
833C3#8349411yescharacteristic, direct product factor
834C3C3×#329611yescharacteristic, complemented
835C2—22no—
836C2—41no—
837C2—42no—
838C2—81no—
839C2C3×#580611yescharacteristic
840C2C2×C3×#95011yescharacteristic
841C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
Fitting, prime radicalC32×#546C2
socleC22×C32C22×D4
hypercenterC3×#546D3
hypocenterC3C3×#3296
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#546

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C3×#5239C2semidirect
4. C3×#5233C2semidirect
5. C3×#5218C2semidirect
6. C2×C3×#832C2semidirect
7. C3×#5056C2semidirect
8. C3×#5054C2semidirect
9. C3×#5051C2semidirect
10. C3×#5043C2semidirect
11. C3×#5041C2semidirect
12. C3×#5035C2semidirect
13. C3×C4×#214C2semidirect
14. C3×D4×C3⋊C8C2semidirect
15. C3×#5009C2semidirect
17. #83494C3direct (N × H)
29. C2×C3×#216C22semidirect
33. C3×#926C22semidirect
36. C3×#924C22semidirect
38. C22×C3×C3⋊C8C22semidirect
42. C3×#870C22semidirect
43. C3×C4×Dic6C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
54. C3×#830C22semidirect
55. C3×#810C22semidirect
56. C3×#808C22semidirect
57. C3×#808C22semidirect
58. C3×#807C22semidirect
59. C3×C4⋊(C3⋊C8)C22semidirect
60. C3×C4×C3⋊C8C22semidirect
65. #5541C2×C3semidirect
79. #5239C2×C3semidirect
80. #5233C2×C3semidirect
81. #5218C2×C3semidirect
82. C2×#832C2×C3semidirect
83. #5056C2×C3semidirect
84. #5054C2×C3semidirect
85. #5051C2×C3semidirect
86. #5043C2×C3semidirect
87. #5041C2×C3semidirect
88. #5035C2×C3semidirect
89. C4×#214C2×C3semidirect
90. D4×C3⋊C8C2×C3semidirect
91. #5009C2×C3semidirect
193. C2×#216C22×C3semidirect
197. #926C22×C3semidirect
200. #924C22×C3semidirect
202. C22×C3⋊C8C22×C3semidirect
206. #870C22×C3semidirect
207. C4×Dic6C22×C3semidirect
225. #835C22×C3semidirect
226. #835C22×C3semidirect
227. #835C22×C3semidirect
235. #830C22×C3semidirect
236. #810C22×C3semidirect
237. #808C22×C3semidirect
238. #808C22×C3semidirect
239. #807C22×C3semidirect
240. C4⋊(C3⋊C8)C22×C3semidirect
241. C4×C3⋊C8C22×C3semidirect
743. C32#3296semidirect
833. C3#83494direct (N × H)
834. C3C3×#3296semidirect

Maximal subgroups

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

subgroupindex
C32×#5462
C3×#55412
C3×#52392
C3×#52332
C3×#52182
C2×C3×#8322
C3×#50562
C3×#50542
C3×#50512
C3×#50432
C3×#50412
C3×#50352
C3×C4×#2142
C3×D4×C3⋊C82
C3×#50092
C3×#32963
#834943