Finite Group Databasebeta

← C3×#80670 #11878543

Subgroups — C3×#80670 #11878543

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5629C211yesmaximal, characteristic, complemented
2C3×#5608C211yesmaximal, characteristic, complemented
3C32×#465C211yesmaximal, characteristic, complemented
4C3×#5173C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6C3×#5114C211yesmaximal, characteristic, complemented
7C3×#5110C211yesmaximal, characteristic, complemented
8C3×#5052C211yesmaximal, characteristic, complemented
9C3×#5039C211yesmaximal, characteristic, complemented
10C3×#4863C211yesmaximal, characteristic, complemented
11C3×#4862C211yesmaximal, characteristic, complemented
12C3×#4808C211yesmaximal, characteristic, complemented
13C3×#4805C211yesmaximal, characteristic, complemented
14C3×#4781C211yesmaximal, characteristic, complemented
15C3×#4777C211yesmaximal, characteristic, complemented
16C3×#3204—31nomaximal
17#80670C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C2×C32×SD16C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C3×#939—21no—
28C3×#938—21no—
29C3×#938C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C2×C3×#204C2211yescharacteristic
35C3×#897C2211yescharacteristic
36C3×#896—21no—
37C3×#895—21no—
38C3×#895C2211yescharacteristic
39C3×D3×C4⋊C4C2211yescharacteristic
40C3×D3×C4⋊C4C2211yescharacteristic
41C3×#884—21no—
42C3×#884—21no—
43C3×#884—21no—
44C3×#878—21no—
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×(C2×D3)⋊C8C2211yescharacteristic
55C3×#817C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#537—31no—
62C3×#537—31no—
63#5629C2×C311yescharacteristic, complemented
64#5608C2×C311yescharacteristic, complemented
65C3×#483—31no—
66C3×#483—31no—
67C3×#481—31no—
68C3×#481—31no—
69C3×#470—31no—
70C3×#469—31no—
71C3×#465—21no—
72C3×#465—31no—
73C3×#465D311yescharacteristic, complemented
74C3×#465C2×C311yescharacteristic, complemented
75C3×#452—31no—
76C3×#452—31no—
77C3×#449—31no—
78C3×#449—31no—
79C3×#408—31no—
80#5173C2×C311yescharacteristic, complemented
81#5172C2×C311yescharacteristic, complemented
82#5114C2×C311yescharacteristic, complemented
83#5110C2×C311yescharacteristic, complemented
84#5052C2×C311yescharacteristic, complemented
85#5039C2×C311yescharacteristic, complemented
86#4863C2×C311yescharacteristic, complemented
87#4862C2×C311yescharacteristic, complemented
88#4808C2×C311yescharacteristic, complemented
89#4805C2×C311yescharacteristic, complemented
90#4781C2×C311yescharacteristic, complemented
91#4777C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C3×#239—41no—
103C3×#239—41no—
104C3×#237—41no—
105C3×#237—41no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×Dic6D411yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C32×SD16—41no—
120C2×C32×C8—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4—21no—
124C32×C4⋊C4C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127C32×C22⋊C4—21no—
128C3×#217—21no—
129C3×#217—21no—
130C3×#216—41no—
131C3×#213—41no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×#208—41no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C3×#204—41no—
147#3204—31noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×#239C22×C311yescharacteristic
152C2×#237C22×C311yescharacteristic
153C2×#235C22×C311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×SD16—21no—
156C2×C3×SD16—31no—
157C2×C3×SD16C2×D311yescharacteristic
158C2×C3×SD16C22×C311yescharacteristic
159C2×C3×D8—31no—
160C2×C3×M16—31no—
161C22×C3×C8—21no—
162C22×C3×C8C2×D311yescharacteristic
163C22×C3×C8C22×C311yescharacteristic
164C3×C22⋊Q8—21no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8C2×D311yescharacteristic
171C3×C22⋊Q8C22×C311yescharacteristic
172C3×#121—21no—
173C3×#121—31no—
174C3×#121—31no—
175C3×#121—31no—
176C3×#121—61no—
177C3×#121—61no—
178C3×#121—61no—
179C3×#121—61no—
180C3×#121—61no—
181C3×#121—61no—
182C3×#121C2×D311yescharacteristic
183C3×#121C22×C311yescharacteristic
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186#946C22×C311yescharacteristic
187C2×#216C22×C311yescharacteristic
188#939—21no—
189#938—21no—
190#938C22×C311yescharacteristic
191C2×#213C22×C311yescharacteristic
192#930C22×C311yescharacteristic
193#924C22×C311yescharacteristic
194C2×#208C22×C311yescharacteristic
195C2×#204C22×C311yescharacteristic
196#897C22×C311yescharacteristic
197#896—21no—
198#895—21no—
199#895C22×C311yescharacteristic
200D3×C4⋊C4C22×C311yescharacteristic
201D3×C4⋊C4C22×C311yescharacteristic
202#884—21no—
203#884—21no—
204#884—21no—
205#878—21no—
206C3×#106—21no—
207C3×#106—31no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#106C2×D311yescharacteristic
211C3×#106C22×C311yescharacteristic
212C3×#103—21no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103C2×D311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#102—21no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×C22⋊C8—31no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8—31no—
227C3×C22⋊C8—31no—
228#835C22×C311yescharacteristic
229#832C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231(C2×D3)⋊C8C22×C311yescharacteristic
232(C2×D3)⋊C8C22×C311yescharacteristic
233(C2×D3)⋊C8C22×C311yescharacteristic
234(C2×D3)⋊C8C22×C311yescharacteristic
235#817C22×C311yescharacteristic
236#816C22×C311yescharacteristic
237#810C22×C311yescharacteristic
238#809C22×C311yescharacteristic
239#808C22×C311yescharacteristic
240#808C22×C311yescharacteristic
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—81no—
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—41no—
259C3×#67—41no—
260C3×#67—42no—
261C3×#67—81no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—42no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—41no—
272C3×D12—42no—
273C3×D12—81no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—42no—
279C3×C4×D3—81no—
280C3×C4×D3—81no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—41no—
284C32×C8—21no—
285C32×C8—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—31no—
290#483—31no—
291#483—31no—
292#481—31no—
293#481—31no—
294#470—31no—
295#469—31no—
296#465—31no—
297#465C3×D311yescharacteristic, complemented
298#452—31no—
299#452—31no—
300#449—31no—
301#449—31no—
302#408—31no—
303C3×#41—121no—
304C3×#41—121no—
305C3×#41—121no—
306C3×#41—121no—
307C3×#41—121no—
308C3×#41—121no—
309C2×C3×Q8—21no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C23×C311yescharacteristic
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—41no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C23×C311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C23×C311yescharacteristic
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67C3×D411yescharacteristic
342C2×#67C3×D411yescharacteristic
343C22×Dic3—21no—
344#239—41no—
345#239—41no—
346#237—41no—
347#237—41no—
348#235—41no—
349#235—41no—
350C2×D12—21no—
351C2×D12—21no—
352C2×D12C3×D411yescharacteristic
353C2×D12C23×C311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×C4×D3C23×C311yescharacteristic
358C2×C4×D3C23×C311yescharacteristic
359C2×Dic6C3×D411yescharacteristic
360C2×Dic6C23×C311yescharacteristic
361C3×Q16—121no—
362C3×SD16—41no—
363C3×SD16—41no—
364C3×SD16—42no—
365C3×SD16—121no—
366C3×D8—121no—
367C3×M16—121no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—31no—
371C2×C3×C8—31no—
372C2×C3×C8—41no—
373C2×C3×C8—41no—
374C2×C3×C8—42no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C2×C3×C8C23×C311yescharacteristic
378C2×C3×C8C23×C311yescharacteristic
379C3×C4⋊C4—21no—
380C3×C4⋊C4—21no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—41no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C23×C311yescharacteristic
394C3×C4⋊C4C23×C311yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—41no—
400C3×C22⋊C4—41no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407#217—21no—
408#217—21no—
409#216—41no—
410#213—41no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415C4⋊Dic3—21no—
416C4⋊Dic3C23×C311yescharacteristic
417C4⋊Dic3C23×C311yescharacteristic
418Dic3⋊C4—21no—
419Dic3⋊C4—21no—
420Dic3⋊C4—21no—
421Dic3⋊C4—21no—
422#208—41no—
423C2×C3⋊C8C23×C311yescharacteristic
424C2×C3⋊C8C23×C311yescharacteristic
425#204—41no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C22×D411yescharacteristic
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C32×C4—21no—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4—41no—
446C32×C4H(5,𝔽2)11yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C2×#41—31no—
454C2×#41—31no—
455C2×#41—31no—
456C2×Q16—31no—
457C2×SD16—31no—
458C2×SD16C2×C3×D311yescharacteristic
459C2×D8—31no—
460C2×M16—31no—
461C22×C8C2×C3×D311yescharacteristic
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465C22⋊Q8—61no—
466C22⋊Q8—61no—
467C22⋊Q8C2×C3×D311yescharacteristic
468#121—31no—
469#121—31no—
470#121—31no—
471#121—61no—
472#121—61no—
473#121—61no—
474#121—61no—
475#121—61no—
476#121—61no—
477#121C2×C3×D311yescharacteristic
478C2×C4⋊C4—31no—
479C2×C4⋊C4—31no—
480#106—31no—
481#106—31no—
482#106—31no—
483#106C2×C3×D311yescharacteristic
484#103—31no—
485#103—31no—
486#103—31no—
487#103C2×C3×D311yescharacteristic
488#102—31no—
489#102—31no—
490#102—31no—
491#102C2×C3×D311yescharacteristic
492C22⋊C8—31no—
493C22⋊C8—31no—
494C22⋊C8—31no—
495C22⋊C8—31no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—31no—
500C23×C3—31no—
501C23×C3—41no—
502C23×C3—61no—
503C23×C3D3×D411yescharacteristic
504C23×C3C2×C3×D411yescharacteristic
505C22×D3—21no—
506C22×D3C2×C3×D411yescharacteristic
507C22×D3C2×C3×D411yescharacteristic
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—41no—
513C3×Q8—41no—
514C3×Q8—61no—
515C3×Q8—61no—
516C3×Q8—121no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—61no—
524C3×D4—61no—
525C3×D4—81no—
526C3×D4—81no—
527C3×D4—82no—
528C3×D4—121no—
529C3×D4—122no—
530C3×D4—121no—
531C3×D4—121no—
532C3×D4—122no—
533C3×D4—241no—
534C3×D4—241no—
535C3×D4—241no—
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—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—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4—122no—
564C2×C3×C4—241no—
565C2×C3×C4—241no—
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4C2×C3×D411yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C24×C311yescharacteristic
570#67—41no—
571#67—41no—
572#67—42no—
573#67—81no—
574#67—81no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—42no—
579C2×Dic3C2×C3×D411yescharacteristic
580C2×Dic3C2×C3×D411yescharacteristic
581D12—21no—
582D12—21no—
583D12—41no—
584D12—42no—
585D12—81no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—42no—
591C4×D3—81no—
592C4×D3—81no—
593Dic6—21no—
594Dic6—21no—
595Dic6—41no—
596C3×C8—22no—
597C3×C8—21no—
598C3×C8—21no—
599C3×C8—21no—
600C3×C8—21no—
601C3×C8—41no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C2×C32—41no—
607C2×C32—81no—
608C2×C32#53411yescharacteristic
609C2×C32#57711yescharacteristic
610C2×C32#57711yescharacteristic
611C3×D3—41no—
612C3×D3—41no—
613C3×D3—81no—
614#41—121no—
615#41—121no—
616#41—121no—
617#41—121no—
618#41—121no—
619#41—121no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8C22×C3×D311yescharacteristic
623C2×D4—21no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4C22×C3×D311yescharacteristic
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4C22×C3×D311yescharacteristic
641Q16—121no—
642SD16—41no—
643SD16—121no—
644D8—121no—
645M16—121no—
646C2×C8—31no—
647C2×C8—31no—
648C2×C8—41no—
649C2×C8C22×C3×D311yescharacteristic
650C2×C8C22×C3×D311yescharacteristic
651C4⋊C4—21no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—61no—
655C4⋊C4—61no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4—61no—
659C4⋊C4C22×C3×D311yescharacteristic
660C4⋊C4C22×C3×D311yescharacteristic
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
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—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C22×C3×D411yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—81no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4#100411yescharacteristic
728C3×C4#100911yescharacteristic
729C3×C4C3×H(5,𝔽2)11yescharacteristic
730C3×C4C3×H(5,𝔽2)11yescharacteristic
731Dic3—21no—
732Dic3—21no—
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736C32#320411yescharacteristic, complemented, Sylow
737C23—21no—
738C23—31no—
739C23—31no—
740C23—61no—
741C23C3×D3×D411yescharacteristic
742Q8—21no—
743Q8—21no—
744Q8—61no—
745Q8—61no—
746Q8—121no—
747D4—21no—
748D4—21no—
749D4—61no—
750D4—61no—
751D4—81no—
752D4—121no—
753D4—122no—
754D4—121no—
755D4—121no—
756D4—122no—
757D4—241no—
758D4—241no—
759D4—241no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—241no—
777C2×C4—241no—
778C2×C4C3×D3×D411yescharacteristic
779C2×C4C23×C3×D311yescharacteristic
780C8—21no—
781C8—21no—
782C8—61no—
783C8—61no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—42no—
788C2×C3—41no—
789C2×C3—41no—
790C2×C3—81no—
791C2×C3—81no—
792C2×C3—121no—
793C2×C3—121no—
794C2×C3—161no—
795C2×C3—241no—
796C2×C3#560511yescharacteristic
797C2×C3#576211yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3C3×#53411yescharacteristic
800C2×C3C3×#57711yescharacteristic
801C2×C3C3×#57711yescharacteristic
802D3—41no—
803D3—41no—
804D3—81no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22C2×C3×D3×D411yescharacteristic
821C4—21no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—61no—
826C4—61no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4C3×#100411yescharacteristic
831C4C3×#100911yescharacteristic
832C3—21no—
833C3#8067011yescharacteristic, direct product factor
834C3C3×#320411yescharacteristic, complemented
835C2—41no—
836C2—81no—
837C2—121no—
838C2—121no—
839C2—241no—
840C2C3×#560511yescharacteristic
841C2C3×#576211yescharacteristic
842C2C3×#577011yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#465C2
socleC22×C32C22×D4
hypercenterC3×#465D3
hypocenterC3C3×#3204
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×#5629C2semidirect
2. C3×#5608C2semidirect
3. C32×#465C2semidirect
4. C3×#5173C2semidirect
5. C3×#5172C2semidirect
6. C3×#5114C2semidirect
7. C3×#5110C2semidirect
8. C3×#5052C2semidirect
9. C3×#5039C2semidirect
10. C3×#4863C2semidirect
11. C3×#4862C2semidirect
12. C3×#4808C2semidirect
13. C3×#4805C2semidirect
14. C3×#4781C2semidirect
15. C3×#4777C2semidirect
17. #80670C3direct (N × H)
63. #5629C2×C3semidirect
64. #5608C2×C3semidirect
73. C3×#465D3semidirect
74. C3×#465C2×C3semidirect
80. #5173C2×C3semidirect
81. #5172C2×C3semidirect
82. #5114C2×C3semidirect
83. #5110C2×C3semidirect
84. #5052C2×C3semidirect
85. #5039C2×C3semidirect
86. #4863C2×C3semidirect
87. #4862C2×C3semidirect
88. #4808C2×C3semidirect
89. #4805C2×C3semidirect
90. #4781C2×C3semidirect
91. #4777C2×C3semidirect
297. #465C3×D3semidirect
736. C32#3204semidirect
833. C3#80670direct (N × H)
834. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C3×#56292
C3×#56082
C32×#4652
C3×#51732
C3×#51722
C3×#51142
C3×#51102
C3×#50522
C3×#50392
C3×#48632
C3×#48622
C3×#48082
C3×#48052
C3×#47812
C3×#47772
C3×#32043
#806703