Finite Group Databasebeta

← C3×#83535 #11887864

Subgroups — C3×#83535 #11887864

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#548C211yesmaximal, characteristic, complemented
2C3×#5565C211yesmaximal, characteristic, complemented
3C3×#5238C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5C3×#5227C211yesmaximal, characteristic, complemented
6C2×C3×#835C211yesmaximal, characteristic, complemented
7C3×#5057C211yesmaximal, characteristic, complemented
8C3×#5056C211yesmaximal, characteristic, complemented
9C3×#5048C211yesmaximal, characteristic, complemented
10C3×#5045C211yesmaximal, characteristic, complemented
11C3×#5038C211yesmaximal, characteristic, complemented
12C3×#5034C211yesmaximal, characteristic, complemented
13C3×C4×#215C211yesmaximal, characteristic, complemented
14C3×#5022C211yesmaximal, characteristic, complemented
15C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
16C3×#3301—31nomaximal
17#83535C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C32×#124—21no—
21C32×#124C2211yescharacteristic
22C32×C22⋊Q8—21no—
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121—21no—
25C32×#121C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4—21no—
28C32×C4×D4C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#939—21no—
32C2×C3×#213C2211yescharacteristic
33C3×#930C2211yescharacteristic
34C3×#930C2211yescharacteristic
35C3×#926C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C22×C3×C3⋊C8C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#898—21no—
40C3×#883—21no—
41C3×#67⋊C4—21no—
42C3×C4×D12C2211yescharacteristic
43C3×#870C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#830C2211yescharacteristic
54C3×#830C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#553—31no—
62C3×#548—21no—
63C3×#548D311yescharacteristic, complemented
64C3×#548C2×C311yescharacteristic, complemented
65#5565C2×C311yescharacteristic, complemented
66C3×#488—31no—
67C3×#485—31no—
68C3×#481—31no—
69C3×#479—31no—
70C3×#466—31no—
71C3×#465—31no—
72C3×#463—31no—
73C3×#449—31no—
74C3×#448—31no—
75C3×C4×SD16—31no—
76C3×C8×D4—31no—
77C3×#416—31no—
78C2×C3×#103—31no—
79#5238C2×C311yescharacteristic, complemented
80#5233C2×C311yescharacteristic, complemented
81#5227C2×C311yescharacteristic, complemented
82C2×#835C2×C311yescharacteristic, complemented
83#5057C2×C311yescharacteristic, complemented
84#5056C2×C311yescharacteristic, complemented
85#5048C2×C311yescharacteristic, complemented
86#5045C2×C311yescharacteristic, complemented
87#5038C2×C311yescharacteristic, complemented
88#5034C2×C311yescharacteristic, complemented
89C4×#215C2×C311yescharacteristic, complemented
90#5022C2×C311yescharacteristic, complemented
91D4×C3⋊C8C2×C311yescharacteristic, complemented
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8—21no—
95C2×C32×Q8—22no—
96C2×C32×Q8—41no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×Q8C2311yescharacteristic
99C2×C32×D4—21no—
100C2×C32×D4—21no—
101C2×C32×D4D411yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4—21no—
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4D411yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C22⋊C4—21no—
119C32×C22⋊C4—21no—
120C32×C22⋊C4D411yescharacteristic
121C32×C22⋊C4D411yescharacteristic
122C32×C42—21no—
123C32×C42C2311yescharacteristic
124C3×#217—21no—
125C3×#215—22no—
126C3×#215—41no—
127C3×#213—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—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#3301—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×Q8—21no—
149C22×C3×Q8C2×D311yescharacteristic
150C22×C3×Q8C22×C311yescharacteristic
151C2×C3×SD16—31no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C22×C3×C8—31no—
155C22×C3×C8—31no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#124—22no—
159C3×#124—21no—
160C3×#124—21no—
161C3×#124—21no—
162C3×#124C2×D311yescharacteristic
163C3×#124C22×C311yescharacteristic
164C3×#123—61no—
165C3×C22⋊Q8—22no—
166C3×C22⋊Q8—21no—
167C3×C22⋊Q8—21no—
168C3×C22⋊Q8—21no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C22×C311yescharacteristic
171C3×#121—22no—
172C3×#121—21no—
173C3×#121—21no—
174C3×#121—21no—
175C3×#121—31no—
176C3×#121—31no—
177C3×#121—61no—
178C3×#121C2×D311yescharacteristic
179C3×#121C22×C311yescharacteristic
180C3×C4×Q8—21no—
181C3×C4×Q8C2×D311yescharacteristic
182C3×C4×Q8C22×C311yescharacteristic
183C3×C4×D4—22no—
184C3×C4×D4—21no—
185C3×C4×D4—21no—
186C3×C4×D4—21no—
187C3×C4×D4—31no—
188C3×C4×D4—61no—
189C3×C4×D4C2×D311yescharacteristic
190C3×C4×D4C22×C311yescharacteristic
191C3×#117—31no—
192C2×C3×C4⋊C4—31no—
193C2×#215C22×C311yescharacteristic
194C2×#215C22×C311yescharacteristic
195#939—21no—
196C2×#213C22×C311yescharacteristic
197#930C22×C311yescharacteristic
198#930C22×C311yescharacteristic
199#926C22×C311yescharacteristic
200C2×C4⋊Dic3C22×C311yescharacteristic
201C22×C3⋊C8C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203#898—21no—
204#883—21no—
205#67⋊C4—21no—
206C4×D12C22×C311yescharacteristic
207#870C22×C311yescharacteristic
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×#103—31no—
217C3×#103—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
226#835C22×C311yescharacteristic
227#835C22×C311yescharacteristic
228#835C22×C311yescharacteristic
229#835C22×C311yescharacteristic
230#835C22×C311yescharacteristic
231#832C22×C311yescharacteristic
232#832C22×C311yescharacteristic
233#832C22×C311yescharacteristic
234#830C22×C311yescharacteristic
235#830C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238#808C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241C4×C3⋊C8C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—42no—
250C32×Q8#4112yes—
251C32×D4—22no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C32×D4—42no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—42no—
264C2×C32×C4—42no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2411yescharacteristic
270C3×#67—42no—
271C3×#67—81no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—81no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—81no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#553—31no—
284#548C3×D311yescharacteristic, complemented
285#488—31no—
286#485—31no—
287#481—31no—
288#479—31no—
289#466—31no—
290#465—31no—
291#463—31no—
292#449—31no—
293#448—31no—
294C4×SD16—31no—
295C8×D4—31no—
296#416—31no—
297C2×#103—31no—
298C3×#41—22no—
299C3×#41—22no—
300C3×#41—42no—
301C3×#41—41no—
302C3×#41—41no—
303C3×#41—42no—
304C2×C3×Q8—22no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—22no—
308C2×C3×Q8—22no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—42no—
312C2×C3×Q8—41no—
313C2×C3×Q8—41no—
314C2×C3×Q8—42no—
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C23×C311yescharacteristic
318C2×C3×Q8C23×C311yescharacteristic
319C2×C3×D4—22no—
320C2×C3×D4—22no—
321C2×C3×D4—21no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4#6711yescharacteristic
331C2×C3×D4C3×D411yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C23×C311yescharacteristic
334C22×C3×C4—22no—
335C22×C3×C4—22no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—61no—
343C22×C3×C4—61no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C23×C311yescharacteristic
347C22×C3×C4C23×C311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C22×Dic3—21no—
351C2×D12C23×C311yescharacteristic
352C2×C4×D3—21no—
353C3×SD16—62no—
354C3×SD16—121no—
355C3×D8—121no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—121no—
361C2×C3×C8—121no—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—22no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4#6711yescharacteristic
377C3×C4⋊C4C3×D411yescharacteristic
378C3×C4⋊C4C22×D311yescharacteristic
379C3×C4⋊C4C23×C311yescharacteristic
380C3×C22⋊C4—22no—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
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—61no—
398C3×C22⋊C4#6711yescharacteristic
399C3×C22⋊C4#6711yescharacteristic
400C3×C22⋊C4C3×D411yescharacteristic
401C3×C22⋊C4C3×D411yescharacteristic
402C3×C42—22no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—21no—
406C3×C42—61no—
407C3×C42C22×D311yescharacteristic
408C3×C42C23×C311yescharacteristic
409#217—21no—
410#215—22no—
411#215—41no—
412#213—41no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3C23×C311yescharacteristic
418C4⋊Dic3C23×C311yescharacteristic
419C4⋊Dic3C23×C311yescharacteristic
420Dic3⋊C4—21no—
421Dic3⋊C4—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—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32#13512yes—
438C22×C32C22×D411yescharacteristic
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—22no—
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—
454C2×#41C2×C3×D311yescharacteristic
455C22×Q8C2×C3×D311yescharacteristic
456C2×SD16—31no—
457C2×SD16—31no—
458C2×D8—31no—
459C22×C8—31no—
460C22×C8—31no—
461#126—61no—
462#125—31no—
463#124—21no—
464#124C2×C3×D311yescharacteristic
465#123—61no—
466C22⋊Q8—21no—
467C22⋊Q8C2×C3×D311yescharacteristic
468#121—21no—
469#121—31no—
470#121—31no—
471#121—61no—
472#121C2×C3×D311yescharacteristic
473C4×Q8C2×C3×D311yescharacteristic
474C4×D4—21no—
475C4×D4—31no—
476C4×D4—61no—
477C4×D4C2×C3×D311yescharacteristic
478#117—31no—
479C2×C4⋊C4—31no—
480#107—31no—
481#106—31no—
482#106—31no—
483C4⋊C8—31no—
484#103—31no—
485#103—31no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103—31no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494C22⋊C8—31no—
495C22⋊C8—31no—
496C4×C8—31no—
497C23×C3—22no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—61no—
503C23×C3C2×#6711yescharacteristic
504C23×C3C2×#6711yescharacteristic
505C23×C3C2×C3×D411yescharacteristic
506C23×C3C2×C3×D411yescharacteristic
507C22×D3—21no—
508C3×Q8—22no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—22no—
516C3×Q8—41no—
517C3×Q8—41no—
518C3×Q8—42no—
519C3×Q8—42no—
520C3×Q8—44no—
521C3×Q8#23712yes—
522C3×Q8C3×#4112yes—
523C3×D4—22no—
524C3×D4—22no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—42no—
534C3×D4—44no—
535C3×D4—44no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
541C3×D4—241no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4—42no—
571C2×C3×C4—42no—
572C2×C3×C4—44no—
573C2×C3×C4—44no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—241no—
578C2×C3×C4—241no—
579C2×C3×C4C2×#6711yescharacteristic
580C2×C3×C4C2×#6711yescharacteristic
581C2×C3×C4C2×#6711yescharacteristic
582C2×C3×C4C2×#6711yescharacteristic
583C2×C3×C4C2×C3×D411yescharacteristic
584C2×C3×C4C2×C3×D411yescharacteristic
585C2×C3×C4C2×C3×D411yescharacteristic
586C2×C3×C4C2×C3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C24×C311yescharacteristic
589#67—42no—
590#67—81no—
591C2×Dic3—21no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—81no—
595D12—21no—
596D12—21no—
597C4×D3—81no—
598C3×C8—61no—
599C3×C8—61no—
600C3×C8—61no—
601C3×C8—61no—
602C3⋊C8—21no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C2×C32—22no—
607C2×C32—41no—
608C2×C32—81no—
609C2×C32#54611yescharacteristic
610C2×C32C2×#13511yescharacteristic
611C2×C32#57711yescharacteristic
612C3×D3—81no—
613#41—22no—
614#41—41no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—41no—
618C2×Q8C22×C3×D311yescharacteristic
619C2×Q8C22×C3×D311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—31no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4C3×#6711yescharacteristic
626C2×D4C22×C3×D311yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4C22×C3×D311yescharacteristic
632C22×C4C22×C3×D311yescharacteristic
633SD16—62no—
634SD16—121no—
635D8—121no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—121no—
641C2×C8—121no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—61no—
650C4⋊C4C3×#6711yescharacteristic
651C4⋊C4C22×C3×D311yescharacteristic
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4C3×#6711yescharacteristic
661C22⋊C4C3×#6711yescharacteristic
662C42—21no—
663C42—61no—
664C42C22×C3×D311yescharacteristic
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—22no—
676C22×C3—21no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3#95012yes—
695C22×C3C3×#13512yes—
696C22×C3C22×#6711yescharacteristic
697C22×C3C22×C3×D411yescharacteristic
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C3×C4—24no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—22no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—22no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C2×#23711yescharacteristic
728C3×C4#100411yescharacteristic
729C3×C4C2×C3×#4111yescharacteristic
730C3×C4C3×H(5,𝔽2)11yescharacteristic
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734C32#330111yescharacteristic, complemented, Sylow
735C23—21no—
736C23—61no—
737C23C2×C3×#6711yescharacteristic
738C23C2×C3×#6711yescharacteristic
739Q8—21no—
740Q8—21no—
741Q8—21no—
742Q8—42no—
743Q8C3×#23712yes—
744D4—22no—
745D4—21no—
746D4—21no—
747D4—42no—
748D4—42no—
749D4—61no—
750D4—61no—
751D4—122no—
752D4—241no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—241no—
766C2×C4—241no—
767C2×C4C2×C3×#6711yescharacteristic
768C2×C4C2×C3×#6711yescharacteristic
769C2×C4C2×C3×#6711yescharacteristic
770C2×C4C2×C3×#6711yescharacteristic
771C2×C4C23×C3×D311yescharacteristic
772C8—61no—
773C8—61no—
774C8—61no—
775C8—61no—
776C2×C3—22no—
777C2×C3—22no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—41no—
783C2×C3—41no—
784C2×C3—81no—
785C2×C3—82no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—241no—
789C2×C3#580611yescharacteristic
790C2×C3C2×#95011yescharacteristic
791C2×C3#583711yescharacteristic
792C2×C3C3×#54611yescharacteristic
793C2×C3C2×C3×#13511yescharacteristic
794C2×C3C3×#57711yescharacteristic
795D3—81no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22C3×#95012yes—
808C22C22×C3×#6711yescharacteristic
809C4—21no—
810C4—21no—
811C4—22no—
812C4—21no—
813C4—21no—
814C4—41no—
815C4—41no—
816C4—121no—
817C4—121no—
818C4—121no—
819C4C2×C3×#23711yescharacteristic
820C4C3×#100411yescharacteristic
821C3—21no—
822C3#8353511yescharacteristic, direct product factor
823C3C3×#330111yescharacteristic, complemented
824C2—22no—
825C2—41no—
826C2—81no—
827C2—241no—
828C2C3×#580611yescharacteristic
829C2C2×C3×#95011yescharacteristic
830C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#548C2
socleC22×C32C22×D4
hypercenterC3×#548D3
hypocenterC3C3×#3301
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C32×#548C2semidirect
2. C3×#5565C2semidirect
3. C3×#5238C2semidirect
4. C3×#5233C2semidirect
5. C3×#5227C2semidirect
6. C2×C3×#835C2semidirect
7. C3×#5057C2semidirect
8. C3×#5056C2semidirect
9. C3×#5048C2semidirect
10. C3×#5045C2semidirect
11. C3×#5038C2semidirect
12. C3×#5034C2semidirect
13. C3×C4×#215C2semidirect
14. C3×#5022C2semidirect
15. C3×D4×C3⋊C8C2semidirect
17. #83535C3direct (N × H)
63. C3×#548D3semidirect
64. C3×#548C2×C3semidirect
65. #5565C2×C3semidirect
79. #5238C2×C3semidirect
80. #5233C2×C3semidirect
81. #5227C2×C3semidirect
82. C2×#835C2×C3semidirect
83. #5057C2×C3semidirect
84. #5056C2×C3semidirect
85. #5048C2×C3semidirect
86. #5045C2×C3semidirect
87. #5038C2×C3semidirect
88. #5034C2×C3semidirect
89. C4×#215C2×C3semidirect
90. #5022C2×C3semidirect
91. D4×C3⋊C8C2×C3semidirect
284. #548C3×D3semidirect
734. C32#3301semidirect
822. C3#83535direct (N × H)
823. C3C3×#3301semidirect

Maximal subgroups

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

subgroupindex
C32×#5482
C3×#55652
C3×#52382
C3×#52332
C3×#52272
C2×C3×#8352
C3×#50572
C3×#50562
C3×#50482
C3×#50452
C3×#50382
C3×#50342
C3×C4×#2152
C3×#50222
C3×D4×C3⋊C82
C3×#33013
#835353