Finite Group Databasebeta

← C3×#80015 #11887365

Subgroups — C3×#80015 #11887365

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5806C211yesmaximal, characteristic, complemented
2C3×#5618C211yesmaximal, characteristic, complemented
3C32×#447C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5C3×#5158C211yesmaximal, characteristic, complemented
6C3×#5157C211yesmaximal, characteristic, complemented
7C3×#5153C211yesmaximal, characteristic, complemented
8C3×Dic3×D8C211yesmaximal, characteristic, complemented
9C3×#5041C211yesmaximal, characteristic, complemented
10C3×#4784C211yesmaximal, characteristic, complemented
11C3×#4772C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4766C211yesmaximal, characteristic, complemented
14C3×#67⋊C8C211yesmaximal, characteristic, complemented
15C3×#4722C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#80015C311yesmaximal, characteristic, direct product factor
18C22×C32×D4C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C2×C32×D8C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C3×#953—21no—
24C2×C3×#217—21no—
25C3×#939—21no—
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C3×#938C2211yescharacteristic, complemented
29C3×#936C2211yescharacteristic
30C3×#935—21no—
31C3×D4×Dic3—21no—
32C3×D4×Dic3C2211yescharacteristic
33C3×D4×Dic3C2211yescharacteristic, complemented
34C2×C3×#214C2211yescharacteristic, complemented
35C3×C4×#67C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C3×#924C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C2×C3×D3×C8C2211yescharacteristic, complemented
40C3×#892C2211yescharacteristic, complemented
41C3×#890C2211yescharacteristic, complemented
42C3×#886—21no—
43C3×#879—21no—
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#818C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#808C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5806C2×C311yescharacteristic, complemented
64#5618C2×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—21no—
74C3×#447D311yescharacteristic, complemented
75C3×#447C2×C311yescharacteristic, complemented
76C3×C4×D8—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#102—31no—
80C2×#832C2×C311yescharacteristic, complemented
81#5158C2×C311yescharacteristic, complemented
82#5157C2×C311yescharacteristic, complemented
83#5153C2×C311yescharacteristic, complemented
84Dic3×D8C2×C311yescharacteristic, complemented
85#5041C2×C311yescharacteristic, complemented
86#4784C2×C311yescharacteristic, complemented
87#4772C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4766C2×C311yescharacteristic, complemented
90#67⋊C8C2×C311yescharacteristic, complemented
91#4722C2×C311yescharacteristic, complemented
92C24×C32—21no—
93C2×C32×D4—22no—
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C22×C3×Dic3—21no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C3×#237—22no—
110C3×#237—41no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×D8—22no—
114C32×D8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#217—21no—
126C3×#217D411yescharacteristic
127C3×#214—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8—41no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×D3×C8—41no—
144#3297—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—21no—
147C22×C3×D4C2×D311yescharacteristic
148C22×C3×D4C22×C311yescharacteristic
149C2×#237C22×C311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×D8—21no—
152C2×C3×D8—21no—
153C2×C3×D8C2×D311yescharacteristic
154C2×C3×D8C2×D311yescharacteristic
155C2×C3×D8C22×C311yescharacteristic
156C2×C3×D8C22×C311yescharacteristic
157C22×C3×C8—31no—
158C22×C3×C8—31no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#124—31no—
162C3×#123—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×#121—21no—
166C3×#121—31no—
167C3×#121—31no—
168C3×#121—61no—
169C3×#121—61no—
170C3×#121C2×D311yescharacteristic
171C3×#121C22×C311yescharacteristic
172C3×#120—61no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4—31no—
176C3×C4×D4—61no—
177C3×#117—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C22⋊C4—61no—
180#953—21no—
181C2×#217—21no—
182#939—21no—
183#939—21no—
184#938C22×C311yescharacteristic
185#938C22×C311yescharacteristic, complemented
186#936C22×C311yescharacteristic
187#935—21no—
188D4×Dic3—21no—
189D4×Dic3C22×C311yescharacteristic
190D4×Dic3C22×C311yescharacteristic, complemented
191C2×#214C22×C311yescharacteristic, complemented
192C4×#67C22×C311yescharacteristic
193C2×C4⋊Dic3C22×C311yescharacteristic
194#924C22×C311yescharacteristic
195C22×C3⋊C8C22×C311yescharacteristic
196C2×D3×C8C22×C311yescharacteristic, complemented
197#892C22×C311yescharacteristic, complemented
198#890C22×C311yescharacteristic, complemented
199#886—21no—
200#879—21no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—21no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102C2×D311yescharacteristic
216C3×#102C2×D311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×#102C22×C311yescharacteristic
219C3×C22⋊C8—21no—
220C3×C22⋊C8—31no—
221C3×C22⋊C8C2×D311yescharacteristic
222C3×C22⋊C8C22×C311yescharacteristic
223C3×C4×C8—31no—
224#832C22×C311yescharacteristic
225#832C22×C311yescharacteristic
226#832C22×C311yescharacteristic
227#832C22×C311yescharacteristic
228#832C22×C311yescharacteristic, complemented
229(C2×D3)⋊C8C22×C311yescharacteristic, complemented
230#818C22×C311yescharacteristic, complemented
231#818C22×C311yescharacteristic, complemented
232#816C22×C311yescharacteristic, complemented
233#816C22×C311yescharacteristic, complemented
234Dic3⋊C8C22×C311yescharacteristic, complemented
235C8×Dic3C22×C311yescharacteristic, complemented
236#810C22×C311yescharacteristic, complemented
237#808C22×C311yescharacteristic, complemented
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—21no—
251C32×D4—42no—
252C32×D4—42no—
253C32×D4#4112yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
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—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3—81no—
269C2×C3×Dic3—81no—
270C2×C3×Dic3—81no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
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#447C3×D311yescharacteristic, complemented
293C4×D8—31no—
294C8×D4—31no—
295#416—31no—
296C2×#102—31no—
297C24×C3—21no—
298C24×C3—21no—
299C24×C3—41no—
300C3×#41—62no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—41no—
314C2×C3×D4—42no—
315C2×C3×D4—41no—
316C2×C3×D4—41no—
317C2×C3×D4—41no—
318C2×C3×D4—42no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4C22×D311yescharacteristic
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C23×C311yescharacteristic
326C2×C3×D4C23×C311yescharacteristic
327C2×C3×D4C23×C311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C23×C311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67C3×D411yescharacteristic
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344#237—22no—
345#237—41no—
346C2×C4×D3C23×C311yescharacteristic
347C2×Dic6C23×C311yescharacteristic
348C3×SD16—121no—
349C3×D8—22no—
350C3×D8—22no—
351C3×D8—42no—
352C3×D8—41no—
353C3×D8—41no—
354C3×D8—42no—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8—31no—
358C2×C3×C8—31no—
359C2×C3×C8—121no—
360C2×C3×C8—121no—
361C2×C3×C8C22×D311yescharacteristic
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C23×C311yescharacteristic
364C2×C3×C8C23×C311yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C23×C311yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—41no—
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×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—31no—
390C3×C42—61no—
391#217—21no—
392#217—21no—
393#217—21no—
394#217—21no—
395#217—21no—
396#217—21no—
397#217—21no—
398#217C3×D411yescharacteristic
399#214—41no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4C3×D411yescharacteristic
402C4⋊Dic3—21no—
403C4⋊Dic3—21no—
404C4⋊Dic3C23×C311yescharacteristic
405C4⋊Dic3C23×C311yescharacteristic
406C4⋊Dic3C23×C311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4C3×D411yescharacteristic
410C4×Dic3—21no—
411C4×Dic3C23×C311yescharacteristic
412C2×C3⋊C8—41no—
413C2×C3⋊C8C23×C311yescharacteristic
414C2×C3⋊C8C23×C311yescharacteristic
415D3×C8—41no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—84no—
428C22×C32#13512yes—
429C22×C32C22×D411yescharacteristic
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C32×C4—21no—
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—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—31no—
445C22×D4C2×C3×D311yescharacteristic
446C2×SD16—31no—
447C2×D8C2×C3×D311yescharacteristic
448C2×D8C2×C3×D311yescharacteristic
449C22×C8—31no—
450C22×C8—31no—
451#126—61no—
452#125—31no—
453#124—31no—
454#123—61no—
455#123—61no—
456C22⋊Q8—31no—
457#121—31no—
458#121—31no—
459#121—61no—
460#121—61no—
461#121C2×C3×D311yescharacteristic
462#120—61no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—31no—
466C4×D4—61no—
467#117—31no—
468C2×C4⋊C4—31no—
469C2×C22⋊C4—61no—
470#107—31no—
471#107—31no—
472#106—31no—
473C4⋊C8—31no—
474#103—31no—
475#103—31no—
476#103—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102C2×C3×D311yescharacteristic
483#102C2×C3×D311yescharacteristic
484C22⋊C8—31no—
485C22⋊C8C2×C3×D311yescharacteristic
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—41no—
497C23×C3—41no—
498C23×C3—42no—
499C23×C3—42no—
500C23×C3—44no—
501C23×C3—42no—
502C23×C3—42no—
503C23×C3—82no—
504C23×C3—81no—
505C23×C3—81no—
506C23×C3—82no—
507C23×C3D3×D411yescharacteristic
508C23×C3C2×C3×D411yescharacteristic
509C22×D3C2×C3×D411yescharacteristic
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—22no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—42no—
529C3×D4—42no—
530C3×D4—44no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—62no—
534C3×D4—82no—
535C3×D4—122no—
536C3×D4—241no—
537C3×D4—241no—
538C3×D4#23712yes—
539C3×D4C3×#4112yes—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—122no—
561C2×C3×C4—241no—
562C2×C3×C4—241no—
563C2×C3×C4—241no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C2×C3×D411yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C24×C311yescharacteristic
568#67—22no—
569#67—42no—
570#67—81no—
571#67—81no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—42no—
577C2×Dic3—81no—
578C2×Dic3—81no—
579C2×Dic3—81no—
580C2×Dic3C2×C3×D411yescharacteristic
581C2×Dic3C2×C3×D411yescharacteristic
582C2×Dic3C2×C3×D411yescharacteristic
583C4×D3—21no—
584C4×D3—21no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C2×C32—22no—
598C2×C32—42no—
599C2×C32—81no—
600C2×C32—81no—
601C2×C32#54611yescharacteristic
602C2×C32C2×#13511yescharacteristic
603C2×C32#57611yescharacteristic
604C3×D3—41no—
605C24—21no—
606#41—62no—
607#41—121no—
608C2×Q8—31no—
609C2×D4—22no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—31no—
613C2×D4—41no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4C22×C3×D311yescharacteristic
618C2×D4C22×C3×D311yescharacteristic
619C2×D4C22×C3×D311yescharacteristic
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4C22×C3×D311yescharacteristic
626SD16—121no—
627D8—22no—
628D8—41no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—121no—
632C2×C8—121no—
633C2×C8C22×C3×D311yescharacteristic
634C2×C8C22×C3×D311yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—61no—
642C4⋊C4—61no—
643C4⋊C4C22×C3×D311yescharacteristic
644C22⋊C4—21no—
645C22⋊C4—31no—
646C22⋊C4—31no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C42—31no—
656C42—61no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—21no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—84no—
696C22×C3—84no—
697C22×C3—88no—
698C22×C3#91212yes—
699C22×C3C3×#13512yes—
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C22×C3×D411yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4C2×#23711yescharacteristic
721C3×C4#100411yescharacteristic
722C3×C4C2×C3×#4111yescharacteristic
723C3×C4C3×H(5,𝔽2)11yescharacteristic
724Dic3—21no—
725Dic3—21no—
726Dic3—21no—
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731C32#329711yescharacteristic, complemented, Sylow
732C23—21no—
733C23—21no—
734C23—21no—
735C23—31no—
736C23—42no—
737C23—42no—
738C23—81no—
739C23C3×D3×D411yescharacteristic
740Q8—61no—
741Q8—61no—
742D4—21no—
743D4—21no—
744D4—21no—
745D4—21no—
746D4—21no—
747D4—42no—
748D4—42no—
749D4—62no—
750D4—122no—
751D4—241no—
752D4—241no—
753D4C3×#23712yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—122no—
767C2×C4—241no—
768C2×C4—241no—
769C2×C4—241no—
770C2×C4C3×D3×D411yescharacteristic
771C2×C4C23×C3×D311yescharacteristic
772C8—21no—
773C8—21no—
774C8—61no—
775C8—61no—
776C2×C3—22no—
777C2×C3—22no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—42no—
783C2×C3—42no—
784C2×C3—82no—
785C2×C3—82no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—81no—
789C2×C3—81no—
790C2×C3—121no—
791C2×C3—161no—
792C2×C3#559111yescharacteristic
793C2×C3C2×#91211yescharacteristic
794C2×C3#577411yescharacteristic
795C2×C3C3×#54611yescharacteristic
796C2×C3C2×C3×#13511yescharacteristic
797C2×C3C3×#57611yescharacteristic
798D3—41no—
799C22—21no—
800C22—21no—
801C22—22no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—84no—
814C22C3×#91212yes—
815C22C2×C3×D3×D411yescharacteristic
816C4—21no—
817C4—41no—
818C4—61no—
819C4—61no—
820C4—61no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4C2×C3×#23711yescharacteristic
826C4C3×#100411yescharacteristic
827C3—21no—
828C3#8001511yescharacteristic, direct product factor
829C3C3×#329711yescharacteristic, complemented
830C2—22no—
831C2—42no—
832C2—81no—
833C2—81no—
834C2—121no—
835C2C3×#559111yescharacteristic
836C2C2×C3×#91211yescharacteristic
837C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#447C2
socleC22×C32C22×D4
hypercenterC3×#447D3
hypocenterC3C3×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#447

Complements

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

NH ≅ G/Ntype
1. C3×#5806C2semidirect
2. C3×#5618C2semidirect
3. C32×#447C2semidirect
4. C2×C3×#832C2semidirect
5. C3×#5158C2semidirect
6. C3×#5157C2semidirect
7. C3×#5153C2semidirect
8. C3×Dic3×D8C2semidirect
9. C3×#5041C2semidirect
10. C3×#4784C2semidirect
11. C3×#4772C2semidirect
12. C3×#4768C2semidirect
13. C3×#4766C2semidirect
14. C3×#67⋊C8C2semidirect
15. C3×#4722C2semidirect
17. #80015C3direct (N × H)
28. C3×#938C22semidirect
33. C3×D4×Dic3C22semidirect
34. C2×C3×#214C22semidirect
39. C2×C3×D3×C8C22semidirect
40. C3×#892C22semidirect
41. C3×#890C22semidirect
51. C3×#832C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#818C22semidirect
54. C3×#818C22semidirect
55. C3×#816C22semidirect
56. C3×#816C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C8×Dic3C22semidirect
59. C3×#810C22semidirect
60. C3×#808C22semidirect
63. #5806C2×C3semidirect
64. #5618C2×C3semidirect
74. C3×#447D3semidirect
75. C3×#447C2×C3semidirect
80. C2×#832C2×C3semidirect
81. #5158C2×C3semidirect
82. #5157C2×C3semidirect
83. #5153C2×C3semidirect
84. Dic3×D8C2×C3semidirect
85. #5041C2×C3semidirect
86. #4784C2×C3semidirect
87. #4772C2×C3semidirect
88. #4768C2×C3semidirect
89. #4766C2×C3semidirect
90. #67⋊C8C2×C3semidirect
91. #4722C2×C3semidirect
185. #938C22×C3semidirect
190. D4×Dic3C22×C3semidirect
191. C2×#214C22×C3semidirect
196. C2×D3×C8C22×C3semidirect
197. #892C22×C3semidirect
198. #890C22×C3semidirect
228. #832C22×C3semidirect
229. (C2×D3)⋊C8C22×C3semidirect
230. #818C22×C3semidirect
231. #818C22×C3semidirect
232. #816C22×C3semidirect
233. #816C22×C3semidirect
234. Dic3⋊C8C22×C3semidirect
235. C8×Dic3C22×C3semidirect
236. #810C22×C3semidirect
237. #808C22×C3semidirect
292. #447C3×D3semidirect
731. C32#3297semidirect
828. C3#80015direct (N × H)
829. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#58062
C3×#56182
C32×#4472
C2×C3×#8322
C3×#51582
C3×#51572
C3×#51532
C3×Dic3×D82
C3×#50412
C3×#47842
C3×#47722
C3×#47682
C3×#47662
C3×#67⋊C82
C3×#47222
C3×#32973
#800153