Finite Group Databasebeta

← C3×#80681 #11887371

Subgroups — C3×#80681 #11887371

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5630C211yesmaximal, characteristic, complemented
2C3×#5618C211yesmaximal, characteristic, complemented
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5172C211yesmaximal, characteristic, complemented
5C3×#5165C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C3×C8×#67C211yesmaximal, characteristic, complemented
8C3×#5044C211yesmaximal, characteristic, complemented
9C3×#5036C211yesmaximal, characteristic, complemented
10C3×#4871C211yesmaximal, characteristic, complemented
11C3×#4866C211yesmaximal, characteristic, complemented
12C3×#4804C211yesmaximal, characteristic, complemented
13C3×#4800C211yesmaximal, characteristic, complemented
14C3×#4775C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#80681C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic, complemented
21C22×C32×C8C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24C3×#947C2211yescharacteristic
25C3×#939—21no—
26C3×#938C2211yescharacteristic, complemented
27C3×D4×Dic3—21no—
28C3×D4×Dic3C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34C3×#895—21no—
35C3×#895C2211yescharacteristic
36C3×#894—21no—
37C3×#893C2211yescharacteristic
38C3×#892C2211yescharacteristic, complemented
39C3×#890C2211yescharacteristic, complemented
40C3×#886—21no—
41C3×#882—21no—
42C3×D3×C22⋊C4—21no—
43C3×#879—21no—
44C32×#106C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic, 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×#807C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5630C2×C311yescharacteristic, complemented
64#5618C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#484—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#466—31no—
70C3×#465—21no—
71C3×#465D311yescharacteristic, complemented
72C3×#465C2×C311yescharacteristic, complemented
73C3×#463—31no—
74C3×#449—31no—
75C3×#447—31no—
76C3×C4×D8—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80#5172C2×C311yescharacteristic, complemented
81#5165C2×C311yescharacteristic, complemented
82C2×#821C2×C311yescharacteristic, complemented
83C8×#67C2×C311yescharacteristic, complemented
84#5044C2×C311yescharacteristic, complemented
85#5036C2×C311yescharacteristic, complemented
86#4871C2×C311yescharacteristic, complemented
87#4866C2×C311yescharacteristic, complemented
88#4804C2×C311yescharacteristic, complemented
89#4800C2×C311yescharacteristic, complemented
90#4775C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#239—22no—
102C3×#239—41no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C32×SD16—41no—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C22⋊C4—21no—
121C32×C22⋊C4—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×#213—22no—
126C3×#213—41no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3297—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#239C22×C311yescharacteristic
148C22×D12C22×C311yescharacteristic
149C2×C3×SD16—21no—
150C2×C3×SD16C2×D311yescharacteristic, complemented
151C2×C3×SD16C22×C311yescharacteristic, complemented
152C2×C3×D8—31no—
153C2×C3×D8—31no—
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×#126—61no—
159C3×#125—31no—
160C3×#124—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—21no—
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×C22⋊Q8C22×C311yescharacteristic
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—31no—
169C3×#121—61no—
170C3×#121—61no—
171C3×#121C2×D311yescharacteristic
172C3×#121C22×C311yescharacteristic
173C3×#120—61no—
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178C3×#117—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C22⋊C4—61no—
181#947C22×C311yescharacteristic
182#939—21no—
183#938C22×C311yescharacteristic, complemented
184D4×Dic3—21no—
185D4×Dic3C22×C311yescharacteristic, complemented
186C2×#213C22×C311yescharacteristic
187C2×#213C22×C311yescharacteristic
188C4×#67C22×C311yescharacteristic
189C2×C4⋊Dic3C22×C311yescharacteristic
190C2×D3×C8C22×C311yescharacteristic, complemented
191#895—21no—
192#895C22×C311yescharacteristic
193#894—21no—
194#893C22×C311yescharacteristic
195#892C22×C311yescharacteristic, complemented
196#890C22×C311yescharacteristic, complemented
197#886—21no—
198#882—21no—
199D3×C22⋊C4—21no—
200#879—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#106—21no—
204C3×#106C2×D311yescharacteristic, complemented
205C3×#106C22×C311yescharacteristic, complemented
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic, complemented
211C3×#103C22×C311yescharacteristic, complemented
212C3×#102—21no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic, complemented
220C3×#102C22×C311yescharacteristic, complemented
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#807C22×C311yescharacteristic, complemented
237#807C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—42no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258C3×#67—22no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12—42no—
272C3×D12—81no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—42no—
277C3×C4×D3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—31no—
283#546—31no—
284#488—31no—
285#484—31no—
286#482—31no—
287#478—31no—
288#466—31no—
289#465C3×D311yescharacteristic, complemented
290#463—31no—
291#449—31no—
292#447—31no—
293C4×D8—31no—
294C8×D4—31no—
295#416—31no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—21no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—41no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—121no—
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C23×C311yescharacteristic
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4—61no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C23×C311yescharacteristic
327C2×#67—21no—
328C2×#67C3×D411yescharacteristic
329C22×Dic3—21no—
330C22×Dic3—21no—
331#239—22no—
332#239—41no—
333C2×D12—22no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12—41no—
338C2×D12C23×C311yescharacteristic
339C2×D12C23×C311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3C23×C311yescharacteristic
343C3×SD16—41no—
344C3×SD16—41no—
345C3×SD16—42no—
346C3×D8—62no—
347C3×D8—121no—
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—41no—
353C2×C3×C8—41no—
354C2×C3×C8—42no—
355C2×C3×C8—121no—
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C23×C311yescharacteristic
359C2×C3×C8C23×C311yescharacteristic
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—41no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C23×C311yescharacteristic
374C3×C4⋊C4C23×C311yescharacteristic
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—41no—
382C3×C22⋊C4—41no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C42—31no—
391C3×C42—61no—
392#217—21no—
393#217—21no—
394#217C3×D411yescharacteristic
395#213—22no—
396#213—41no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402(C2×D3)⋊C4C3×D411yescharacteristic
403C4⋊Dic3—21no—
404C4⋊Dic3—21no—
405C4⋊Dic3C23×C311yescharacteristic
406C4⋊Dic3C23×C311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4C3×D411yescharacteristic
409C4×Dic3—21no—
410C4×Dic3C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412C2×C3⋊C8C23×C311yescharacteristic
413D3×C8—41no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32#13512yes—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16C2×C3×D311yescharacteristic, complemented
445C2×D8—31no—
446C2×D8—31no—
447C22×C8—31no—
448C22×C8C2×C3×D311yescharacteristic
449#126—61no—
450#125—31no—
451#124—31no—
452#123—61no—
453#123—61no—
454C22⋊Q8C2×C3×D311yescharacteristic
455#121—31no—
456#121—31no—
457#121—61no—
458#121—61no—
459#121C2×C3×D311yescharacteristic
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—61no—
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—61no—
468#107—31no—
469#107—31no—
470#106C2×C3×D311yescharacteristic, complemented
471C4⋊C8—31no—
472#103—31no—
473#103—31no—
474#103C2×C3×D311yescharacteristic, complemented
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102C2×C3×D311yescharacteristic, complemented
482C22⋊C8—31no—
483C22⋊C8—31no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—241no—
495C23×C3D3×D411yescharacteristic
496C23×C3C2×C3×D411yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—81no—
502C22×D3C2×C3×D411yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—41no—
508C3×Q8—41no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—32no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—42no—
517C3×D4—42no—
518C3×D4—62no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—82no—
523C3×D4—122no—
524C3×D4—122no—
525C3×D4—241no—
526C3×D4—241no—
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—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—122no—
552C2×C3×C4—241no—
553C2×C3×C4—241no—
554C2×C3×C4—241no—
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C24×C311yescharacteristic
559#67—22no—
560#67—81no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—81no—
564C2×Dic3—81no—
565C2×Dic3C2×C3×D411yescharacteristic
566C2×Dic3C2×C3×D411yescharacteristic
567C2×Dic3C2×C3×D411yescharacteristic
568D12—21no—
569D12—21no—
570D12—21no—
571D12—42no—
572D12—42no—
573D12—81no—
574D12C3×#4112yes—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—42no—
578C4×D3—81no—
579C3×C8—22no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—41no—
585C3×C8—61no—
586C3×C8—61no—
587C3⋊C8—21no—
588C3⋊C8—21no—
589C2×C32—22no—
590C2×C32—81no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3×D3—41no—
595C3×D3—42no—
596C3×D3—81no—
597C24—61no—
598#41—62no—
599#41—121no—
600C2×Q8C22×C3×D311yescharacteristic
601C2×D4—21no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—62no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—121no—
611C2×D4C22×C3×D311yescharacteristic
612C22×C4—31no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4C22×C3×D311yescharacteristic
618SD16—41no—
619D8—62no—
620D8—121no—
621C2×C8—31no—
622C2×C8—31no—
623C2×C8—41no—
624C2×C8—121no—
625C2×C8C22×C3×D311yescharacteristic
626C2×C8C22×C3×D311yescharacteristic
627C4⋊C4—21no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4C22×C3×D311yescharacteristic
635C4⋊C4C22×C3×D311yescharacteristic
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C42—31no—
648C42—61no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—61no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3#91612yes—
677C22×C3C3×#13512yes—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C22×C3×D411yescharacteristic
680C2×D3—21no—
681C2×D3—21no—
682C2×D3—21no—
683C2×D3—22no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—84no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4#100411yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4C2×C3×#4111yescharacteristic
712C3×C4C3×H(5,𝔽2)11yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—21no—
716Dic3—41no—
717Dic3—41no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—61no—
722C23—61no—
723C23—122no—
724C23—122no—
725C23—241no—
726C23C3×D3×D411yescharacteristic
727Q8—21no—
728Q8—21no—
729D4—21no—
730D4—21no—
731D4—32no—
732D4—42no—
733D4—62no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—122no—
738D4—122no—
739D4—241no—
740D4—241no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—122no—
754C2×C4—241no—
755C2×C4—241no—
756C2×C4—241no—
757C2×C4C3×D3×D411yescharacteristic
758C2×C4C23×C3×D311yescharacteristic
759C8—21no—
760C8—21no—
761C8—61no—
762C8—61no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—81no—
770C2×C3—81no—
771C2×C3—121no—
772C2×C3—122no—
773C2×C3—161no—
774C2×C3—241no—
775C2×C3#561011yescharacteristic
776C2×C3C2×#91611yescharacteristic
777C2×C3#576911yescharacteristic
778C2×C3C3×#54611yescharacteristic
779C2×C3C2×C3×#13511yescharacteristic
780C2×C3C3×#57611yescharacteristic
781D3—41no—
782D3—42no—
783D3—81no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—61no—
790C22—61no—
791C22—61no—
792C22—62no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—244no—
799C22C3×#91612yes—
800C22C2×C3×D3×D411yescharacteristic
801C4—21no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—121no—
809C4—121no—
810C4C3×#100411yescharacteristic
811C4C3×D3×#4111yescharacteristic
812C3—21no—
813C3#8068111yescharacteristic, direct product factor
814C3C3×#329711yescharacteristic, complemented
815C2—22no—
816C2—81no—
817C2—121no—
818C2—122no—
819C2—241no—
820C2C3×#561011yescharacteristic
821C2C2×C3×#91611yescharacteristic
822C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#465

Complements

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

NH ≅ G/Ntype
1. C3×#5630C2semidirect
2. C3×#5618C2semidirect
3. C32×#465C2semidirect
4. C3×#5172C2semidirect
5. C3×#5165C2semidirect
6. C2×C3×#821C2semidirect
7. C3×C8×#67C2semidirect
8. C3×#5044C2semidirect
9. C3×#5036C2semidirect
10. C3×#4871C2semidirect
11. C3×#4866C2semidirect
12. C3×#4804C2semidirect
13. C3×#4800C2semidirect
14. C3×#4775C2semidirect
15. C3×#4756C2semidirect
17. #80681C3direct (N × H)
20. C2×C32×SD16C22semidirect
26. C3×#938C22semidirect
28. C3×D4×Dic3C22semidirect
33. C2×C3×D3×C8C22semidirect
38. C3×#892C22semidirect
39. C3×#890C22semidirect
44. C32×#106C22semidirect
45. C32×#103C22semidirect
46. C32×#102C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
54. C3×(C2×D3)⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
59. C3×#807C22semidirect
60. C3×#807C22semidirect
63. #5630C2×C3semidirect
64. #5618C2×C3semidirect
71. C3×#465D3semidirect
72. C3×#465C2×C3semidirect
80. #5172C2×C3semidirect
81. #5165C2×C3semidirect
82. C2×#821C2×C3semidirect
83. C8×#67C2×C3semidirect
84. #5044C2×C3semidirect
85. #5036C2×C3semidirect
86. #4871C2×C3semidirect
87. #4866C2×C3semidirect
88. #4804C2×C3semidirect
89. #4800C2×C3semidirect
90. #4775C2×C3semidirect
91. #4756C2×C3semidirect
150. C2×C3×SD16C2×D3semidirect
151. C2×C3×SD16C22×C3semidirect
183. #938C22×C3semidirect
185. D4×Dic3C22×C3semidirect
190. C2×D3×C8C22×C3semidirect
195. #892C22×C3semidirect
196. #890C22×C3semidirect
204. C3×#106C2×D3semidirect
205. C3×#106C22×C3semidirect
210. C3×#103C2×D3semidirect
211. C3×#103C22×C3semidirect
219. C3×#102C2×D3semidirect
220. C3×#102C22×C3semidirect
224. #835C22×C3semidirect
225. #835C22×C3semidirect
231. (C2×D3)⋊C8C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
236. #807C22×C3semidirect
237. #807C22×C3semidirect
289. #465C3×D3semidirect
444. C2×SD16C2×C3×D3semidirect
470. #106C2×C3×D3semidirect
474. #103C2×C3×D3semidirect
481. #102C2×C3×D3semidirect
718. C32#3297semidirect
813. C3#80681direct (N × H)
814. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#56302
C3×#56182
C32×#4652
C3×#51722
C3×#51652
C2×C3×#8212
C3×C8×#672
C3×#50442
C3×#50362
C3×#48712
C3×#48662
C3×#48042
C3×#48002
C3×#47752
C3×#47562
C3×#32973
#806813