Finite Group Databasebeta

← C3×#78846 #11887356

Subgroups — C3×#78846 #11887356

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2C3×#5530C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5C3×#5115C211yesmaximal, characteristic, complemented
6C3×C8×#67C211yesmaximal, characteristic, complemented
7C3×#5003C211yesmaximal, characteristic, complemented
8C3×#4819C211yesmaximal, characteristic, complemented
9C3×#4811C211yesmaximal, characteristic, complemented
10C3×#4807C211yesmaximal, characteristic, complemented
11C3×#4800C211yesmaximal, characteristic, complemented
12C3×#4773C211yesmaximal, characteristic, complemented
13C3×D3×#102C211yesmaximal, characteristic, complemented
14C3×#4766C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#78846C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21C32×#117C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic, complemented
25C3×#939—21no—
26C3×#937—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic, complemented
31C3×#929—21no—
32C3×C4×#67C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4—21no—
34C2×C3×D24C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36C3×#895C2211yescharacteristic
37C3×#893C2211yescharacteristic, complemented
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#890C2211yescharacteristic, complemented
40C3×#884—21no—
41C3×#883—21no—
42C3×#876—21no—
43C3×C4×D12—21no—
44C32×#103C2211yescharacteristic, complemented
45C32×#103C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic, complemented
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5829C2×C311yescharacteristic, complemented
64#5530C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#484—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#466—31no—
70C3×#465—31no—
71C3×#463—31no—
72C3×#449—31no—
73C3×#447—31no—
74C3×C4×D8—31no—
75C3×C8×D4—31no—
76C3×#416—21no—
77C3×#416D311yescharacteristic, complemented
78C3×#416C2×C311yescharacteristic, complemented
79C2×C3×#102—31no—
80#5238C2×C311yescharacteristic, complemented
81#5115C2×C311yescharacteristic, complemented
82C8×#67C2×C311yescharacteristic, complemented
83#5003C2×C311yescharacteristic, complemented
84#4819C2×C311yescharacteristic, complemented
85#4811C2×C311yescharacteristic, complemented
86#4807C2×C311yescharacteristic, complemented
87#4800C2×C311yescharacteristic, complemented
88#4773C2×C311yescharacteristic, complemented
89D3×#102C2×C311yescharacteristic, complemented
90#4766C2×C311yescharacteristic, complemented
91#4756C2×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×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C32×C8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42—21no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×#213—22no—
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)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4D411yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143C3×D3×C8—41no—
144#3297—31noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C22×C311yescharacteristic
148C22×C3×D4—31no—
149C2×D3×D4C22×C311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×D8—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×#124—31no—
160C3×#123—61no—
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×#121—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—61no—
167C3×#121—61no—
168C3×#120—61no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×#117—21no—
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×#215C22×C311yescharacteristic, complemented
181#939—21no—
182#937—21no—
183D4×Dic3C22×C311yescharacteristic
184C2×#213C22×C311yescharacteristic
185#930C22×C311yescharacteristic
186#930C22×C311yescharacteristic, complemented
187#929—21no—
188C4×#67C22×C311yescharacteristic
189C2×(C2×D3)⋊C4—21no—
190C2×D24C22×C311yescharacteristic
191C2×D3×C8C22×C311yescharacteristic
192#895C22×C311yescharacteristic
193#893C22×C311yescharacteristic, complemented
194D3×C4⋊C4C22×C311yescharacteristic
195#890C22×C311yescharacteristic, complemented
196#884—21no—
197#883—21no—
198#876—21no—
199C4×D12—21no—
200C3×#107—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103C2×D311yescharacteristic, complemented
208C3×#103C2×D311yescharacteristic, complemented
209C3×#103C22×C311yescharacteristic, complemented
210C3×#103C22×C311yescharacteristic, complemented
211C3×#102—21no—
212C3×#102—21no—
213C3×#102—31no—
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#821C22×C311yescharacteristic, complemented
230(C2×D3)⋊C8C22×C311yescharacteristic
231#818C22×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—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—42no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—42no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C3×#67—22no—
260C3×#67—42no—
261C3×#67—81no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—42no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—81no—
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#465—31no—
290#463—31no—
291#449—31no—
292#447—31no—
293C4×D8—31no—
294C8×D4—31no—
295#416C3×D311yescharacteristic, complemented
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—24no—
300C3×#41—22no—
301C3×#41—22no—
302C3×#41—41no—
303C3×#41—41no—
304C3×#41—42no—
305C2×C3×Q8—21no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C23×C311yescharacteristic
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—41no—
315C2×C3×D4—61no—
316C2×C3×D4—61no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—121no—
321C2×C3×D4C22×D311yescharacteristic
322C2×C3×D4C23×C311yescharacteristic
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—41no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C23×C311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67C3×D411yescharacteristic
337C22×Dic3—21no—
338D3×D4—22no—
339D3×D4—41no—
340C2×D12—21no—
341C2×D12C23×C311yescharacteristic
342C2×D12C23×C311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3C23×C311yescharacteristic
346C3×SD16—121no—
347C3×D8—62no—
348C3×D8—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—41no—
354C2×C3×C8—41no—
355C2×C3×C8—42no—
356C2×C3×C8—121no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C23×C311yescharacteristic
360C2×C3×C8C23×C311yescharacteristic
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C23×C311yescharacteristic
373C3×C4⋊C4C23×C311yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—41no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42—31no—
390C3×C42—41no—
391#217—21no—
392#217C3×D411yescharacteristic
393#215—41no—
394#213—22no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
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⋊Dic3C23×C311yescharacteristic
405C4⋊Dic3C23×C311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4C3×D411yescharacteristic
410C4×Dic3C23×C311yescharacteristic
411C2×C3⋊C8C23×C311yescharacteristic
412C2×C3⋊C8C23×C311yescharacteristic
413D24—41no—
414D3×C8—41no—
415C22×C32—21no—
416C22×C32—22no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C2×C3×D3#13512yes—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4—41no—
436C32×C4C2×#4111yescharacteristic
437C32×C4H(5,𝔽2)11yescharacteristic
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41C2×C3×D311yescharacteristic
444C22×D4—31no—
445C2×SD16—31no—
446C2×D8—31no—
447C2×D8—31no—
448C22×C8—31no—
449C22×C8C2×C3×D311yescharacteristic, complemented
450#126—61no—
451#125—31no—
452#124—31no—
453#123—61no—
454#123—61no—
455C22⋊Q8—31no—
456#121—31no—
457#121—31no—
458#121—31no—
459#121—61no—
460#121—61no—
461#120—61no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—61no—
466#117C2×C3×D311yescharacteristic, complemented
467C2×C4⋊C4—31no—
468C2×C22⋊C4—61no—
469#107—31no—
470#107—31no—
471#106—31no—
472C4⋊C8—31no—
473#103—31no—
474#103C2×C3×D311yescharacteristic, complemented
475#103C2×C3×D311yescharacteristic, complemented
476#102—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102C2×C3×D311yescharacteristic
482#102C2×C3×D311yescharacteristic
483C22⋊C8—31no—
484C22⋊C8—31no—
485C4×C8—31no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×C3×D411yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—81no—
503C22×D3C2×C3×D411yescharacteristic
504C3×Q8—22no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—42no—
515C3×D4—42no—
516C3×D4—44no—
517C3×D4—62no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—122no—
524C3×D4—241no—
525C3×D4—241no—
526C3×D4#23512yes—
527C3×D4C3×#4112yes—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
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—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—42no—
549C2×C3×C4—42no—
550C2×C3×C4—44no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—241no—
556C2×C3×C4—241no—
557C2×C3×C4—241no—
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C2×C3×D411yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C24×C311yescharacteristic
562#67—22no—
563#67—42no—
564#67—81no—
565#67—81no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—81no—
569C2×Dic3C2×C3×D411yescharacteristic
570C2×Dic3C2×C3×D411yescharacteristic
571C2×Dic3C2×C3×D411yescharacteristic
572D12—21no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12—42no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—81no—
580C4×D3—81no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—41no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32—42no—
593C2×C32#54611yescharacteristic
594C2×C32C2×#13511yescharacteristic
595C2×C32#57611yescharacteristic
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—61no—
600#41—22no—
601#41—41no—
602C2×Q8C22×C3×D311yescharacteristic
603C2×D4—21no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—121no—
613C2×D4C22×C3×D311yescharacteristic
614C22×C4—21no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4C22×C3×D311yescharacteristic
620SD16—121no—
621D8—62no—
622D8—121no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—41no—
626C2×C8—121no—
627C2×C8C22×C3×D311yescharacteristic
628C2×C8C22×C3×D311yescharacteristic
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4—61no—
636C4⋊C4C22×C3×D311yescharacteristic
637C4⋊C4C22×C3×D311yescharacteristic
638C22⋊C4—21no—
639C22⋊C4—31no—
640C22⋊C4—31no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C42—21no—
650C42—31no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—22no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—42no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—244no—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C22×C3×D411yescharacteristic
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—84no—
691C2×D3C3×#13512yes—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—42no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—81no—
708C3×C4—81no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4C2×#23511yescharacteristic
712C3×C4#100411yescharacteristic
713C3×C4C2×C3×#4111yescharacteristic
714C3×C4C3×H(5,𝔽2)11yescharacteristic
715Dic3—21no—
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—21no—
722C23—31no—
723C23—61no—
724C23—61no—
725C23—122no—
726C23—122no—
727C23—241no—
728C23C3×D3×D411yescharacteristic
729Q8—21no—
730Q8—21no—
731D4—21no—
732D4—42no—
733D4—62no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—61no—
738D4—122no—
739D4—122no—
740D4—241no—
741D4—241no—
742D4C3×#23512yes—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—31no—
751C2×C4—42no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—241no—
757C2×C4—241no—
758C2×C4—241no—
759C2×C4C3×D3×D411yescharacteristic
760C2×C4C23×C3×D311yescharacteristic
761C8—21no—
762C8—21no—
763C8—61no—
764C8—61no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—42no—
773C2×C3—62no—
774C2×C3—82no—
775C2×C3—241no—
776C2×C3—241no—
777C2×C3#549011yescharacteristic
778C2×C3D3×#13511yescharacteristic
779C2×C3#576911yescharacteristic
780C2×C3C3×#54611yescharacteristic
781C2×C3C2×C3×#13511yescharacteristic
782C2×C3C3×#57611yescharacteristic
783D3—22no—
784D3—81no—
785D3—81no—
786C22—21no—
787C22—22no—
788C22—21no—
789C22—21no—
790C22—32no—
791C22—41no—
792C22—41no—
793C22—61no—
794C22—61no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—244no—
802C22C2×C3×D3×D411yescharacteristic
803C4—21no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—61no—
808C4—61no—
809C4—61no—
810C4—121no—
811C4—121no—
812C4C2×C3×#23511yescharacteristic
813C4C3×#100411yescharacteristic
814C3—21no—
815C3#7884611yescharacteristic, direct product factor
816C3C3×#329711yescharacteristic, complemented
817C2—41no—
818C2—42no—
819C2—62no—
820C2—241no—
821C2—241no—
822C2C3×#549011yescharacteristic
823C2C3×D3×#13511yescharacteristic
824C2C3×#576911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#416C2
socleC22×C32C22×D4
hypercenterC3×#416D3
hypocenterC3C3×#3297
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
1. C3×#5829C2semidirect
2. C3×#5530C2semidirect
3. C32×#416C2semidirect
4. C3×#5238C2semidirect
5. C3×#5115C2semidirect
6. C3×C8×#67C2semidirect
7. C3×#5003C2semidirect
8. C3×#4819C2semidirect
9. C3×#4811C2semidirect
10. C3×#4807C2semidirect
11. C3×#4800C2semidirect
12. C3×#4773C2semidirect
13. C3×D3×#102C2semidirect
14. C3×#4766C2semidirect
15. C3×#4756C2semidirect
17. #78846C3direct (N × H)
20. C22×C32×C8C22semidirect
21. C32×#117C22semidirect
24. C2×C3×#215C22semidirect
30. C3×#930C22semidirect
37. C3×#893C22semidirect
39. C3×#890C22semidirect
44. C32×#103C22semidirect
45. C32×#103C22semidirect
48. C3×#835C22semidirect
50. C3×#830C22semidirect
52. C3×#821C22semidirect
54. C3×#818C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×C8×Dic3C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5829C2×C3semidirect
64. #5530C2×C3semidirect
77. C3×#416D3semidirect
78. C3×#416C2×C3semidirect
80. #5238C2×C3semidirect
81. #5115C2×C3semidirect
82. C8×#67C2×C3semidirect
83. #5003C2×C3semidirect
84. #4819C2×C3semidirect
85. #4811C2×C3semidirect
86. #4807C2×C3semidirect
87. #4800C2×C3semidirect
88. #4773C2×C3semidirect
89. D3×#102C2×C3semidirect
90. #4766C2×C3semidirect
91. #4756C2×C3semidirect
155. C22×C3×C8C2×D3semidirect
156. C22×C3×C8C22×C3semidirect
174. C3×#117C2×D3semidirect
175. C3×#117C22×C3semidirect
180. C2×#215C22×C3semidirect
186. #930C22×C3semidirect
193. #893C22×C3semidirect
195. #890C22×C3semidirect
207. C3×#103C2×D3semidirect
208. C3×#103C2×D3semidirect
209. C3×#103C22×C3semidirect
210. C3×#103C22×C3semidirect
225. #835C22×C3semidirect
227. #830C22×C3semidirect
229. #821C22×C3semidirect
231. #818C22×C3semidirect
232. Dic3⋊C8C22×C3semidirect
233. C8×Dic3C22×C3semidirect
236. #808C22×C3semidirect
237. #807C22×C3semidirect
295. #416C3×D3semidirect
449. C22×C8C2×C3×D3semidirect
466. #117C2×C3×D3semidirect
474. #103C2×C3×D3semidirect
475. #103C2×C3×D3semidirect
720. C32#3297semidirect
815. C3#78846direct (N × H)
816. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
C3×#55302
C32×#4162
C3×#52382
C3×#51152
C3×C8×#672
C3×#50032
C3×#48192
C3×#48112
C3×#48072
C3×#48002
C3×#47732
C3×D3×#1022
C3×#47662
C3×#47562
C3×#32973
#788463