Finite Group Databasebeta

← C3×#81341 #11878567

Subgroups — C3×#81341 #11878567

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5608C211yesmaximal, characteristic, complemented
2C3×#5510C211yesmaximal, characteristic, complemented
3C32×#481C211yesmaximal, characteristic, complemented
4C3×#5037C211yesmaximal, characteristic, complemented
5C3×#4971C211yesmaximal, characteristic, complemented
6C3×#4867C211yesmaximal, characteristic, complemented
7C3×#4864C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4783C211yesmaximal, characteristic, complemented
11C3×#4782C211yesmaximal, characteristic, complemented
12C3×#4781C211yesmaximal, characteristic, complemented
13C3×#4778C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#4727C211yesmaximal, characteristic, complemented
16C3×#3204—31nomaximal
17#81341C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#121C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C3×#939—21no—
24C3×#938—21no—
25C3×#938C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#930—21no—
29C3×#930—21no—
30C3×#924C2211yescharacteristic
31C2×C3×Dic12C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35C3×#897—21no—
36C3×#897C2211yescharacteristic
37C3×#897C2211yescharacteristic
38C3×#897C2211yescharacteristic
39C3×#895—21no—
40C3×#895C2211yescharacteristic
41C3×#895C2211yescharacteristic
42C3×D3×C4⋊C4C2211yescharacteristic
43C3×#884—21no—
44C3×#878—21no—
45C32×#106C2211yescharacteristic
46C32×#106C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×C22⋊C8C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#537—31no—
62C3×#537—31no—
63#5608C2×C311yescharacteristic, complemented
64#5510C2×C311yescharacteristic, complemented
65C3×#483—31no—
66C3×#483—31no—
67C3×#481—21no—
68C3×#481—31no—
69C3×#481D311yescharacteristic, complemented
70C3×#481C2×C311yescharacteristic, complemented
71C3×#470—31no—
72C3×#469—31no—
73C3×#465—31no—
74C3×#465—31no—
75C3×#452—31no—
76C3×#452—31no—
77C3×#449—31no—
78C3×#449—31no—
79C3×#408—31no—
80#5037C2×C311yescharacteristic, complemented
81#4971C2×C311yescharacteristic, complemented
82#4867C2×C311yescharacteristic, complemented
83#4864C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4783C2×C311yescharacteristic, complemented
87#4782C2×C311yescharacteristic, complemented
88#4781C2×C311yescharacteristic, complemented
89#4778C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#4727C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
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×#237—41no—
103C3×#237—41no—
104C3×#235—41no—
105C3×#235—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×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6D411yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C32×C8C2311yescharacteristic
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124C32×C4⋊C4C2311yescharacteristic
125C32×C22⋊C4—21no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#214—41no—
129C3×#213—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×Dic12—41no—
144C3×#204—41no—
145C3×ΓL(1,𝔽25)—41no—
146C3×D3×C8—41no—
147#3204—31noSylow
148C2×C3×#41—31no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×#237C22×C311yescharacteristic
152C2×#235C22×C311yescharacteristic
153C2×#235C22×C311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C2×C3×D8—31no—
158C2×C3×M16—31no—
159C22×C3×C8—31no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—61no—
165C3×C22⋊Q8—61no—
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×#121—61no—
173C3×#121—61no—
174C3×#121—61no—
175C3×#121—61no—
176C3×#121C2×D311yescharacteristic
177C3×#121C22×C311yescharacteristic
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4C2×D311yescharacteristic
181C2×C3×C4⋊C4C22×C311yescharacteristic
182#939—21no—
183#938—21no—
184#938C22×C311yescharacteristic
185C2×#214C22×C311yescharacteristic
186C2×#213C22×C311yescharacteristic
187#930—21no—
188#930—21no—
189#924C22×C311yescharacteristic
190C2×Dic12C22×C311yescharacteristic
191C2×#204C22×C311yescharacteristic
192C2×ΓL(1,𝔽25)C22×C311yescharacteristic
193C2×D3×C8C22×C311yescharacteristic
194#897—21no—
195#897C22×C311yescharacteristic
196#897C22×C311yescharacteristic
197#897C22×C311yescharacteristic
198#895—21no—
199#895C22×C311yescharacteristic
200#895C22×C311yescharacteristic
201D3×C4⋊C4C22×C311yescharacteristic
202#884—21no—
203#878—21no—
204C3×#106—21no—
205C3×#106—21no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#106C2×D311yescharacteristic
209C3×#106C2×D311yescharacteristic
210C3×#106C22×C311yescharacteristic
211C3×#106C22×C311yescharacteristic
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#102—21no—
217C3×#102—21no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102C2×D311yescharacteristic
221C3×#102C2×D311yescharacteristic
222C3×#102C22×C311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×C22⋊C8—21no—
225C3×C22⋊C8—31no—
226C3×C22⋊C8—31no—
227C3×C22⋊C8—31no—
228C3×C22⋊C8C2×D311yescharacteristic
229C3×C22⋊C8C22×C311yescharacteristic
230#830C22×C311yescharacteristic
231#821C22×C311yescharacteristic
232(C2×D3)⋊C8C22×C311yescharacteristic
233(C2×D3)⋊C8C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#810C22×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×D4—21no—
247C32×D4—21no—
248C32×D4—81no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—81no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C3×#67—41no—
258C3×#67—41no—
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—42no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—41no—
271C3×D12—81no—
272C3×D12—81no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—42no—
278C3×C4×D3—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
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#481C3×D311yescharacteristic, complemented
294#470—31no—
295#469—31no—
296#465—31no—
297#465—31no—
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—31no—
310C2×C3×Q8—31no—
311C2×C3×Q8—31no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—41no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C23×C311yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—41no—
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#237—41no—
345#237—41no—
346#235—41no—
347#235—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×D3C23×C311yescharacteristic
357C2×C4×D3C23×C311yescharacteristic
358C2×Dic6C3×D411yescharacteristic
359C2×Dic6C23×C311yescharacteristic
360C2×Dic6C23×C311yescharacteristic
361C3×Q16—121no—
362C3×SD16—121no—
363C3×SD16—121no—
364C3×D8—121no—
365C3×M16—121no—
366C2×C3×C8—21no—
367C2×C3×C8—21no—
368C2×C3×C8—31no—
369C2×C3×C8—31no—
370C2×C3×C8—121no—
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C2×C3×C8C23×C311yescharacteristic
374C2×C3×C8C23×C311yescharacteristic
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—21no—
380C3×C4⋊C4—31no—
381C3×C4⋊C4—41no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4—61no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C4⋊C4C23×C311yescharacteristic
391C3×C4⋊C4C23×C311yescharacteristic
392C3×C4⋊C4C23×C311yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—41no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403#217—21no—
404#217—21no—
405#214—41no—
406#213—41no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412C4⋊Dic3—21no—
413C4⋊Dic3—21no—
414C4⋊Dic3—21no—
415C4⋊Dic3C23×C311yescharacteristic
416Dic3⋊C4—21no—
417Dic3⋊C4—21no—
418C2×C3⋊C8C23×C311yescharacteristic
419C2×C3⋊C8C23×C311yescharacteristic
420Dic12—41no—
421#204—41no—
422ΓL(1,𝔽25)—41no—
423D3×C8—41no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32C22×D411yescharacteristic
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C32×C4—21no—
441C32×C4—41no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4H(5,𝔽2)11yescharacteristic
445C32×C4H(5,𝔽2)11yescharacteristic
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—31no—
454C2×Q16—31no—
455C2×SD16—31no—
456C2×SD16—31no—
457C2×D8—31no—
458C2×M16—31no—
459C22×C8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—31no—
462C22⋊Q8—31no—
463C22⋊Q8—31no—
464C22⋊Q8—61no—
465C22⋊Q8—61no—
466#121—31no—
467#121—31no—
468#121—31no—
469#121—61no—
470#121—61no—
471#121—61no—
472#121—61no—
473#121—61no—
474#121—61no—
475#121C2×C3×D311yescharacteristic
476C2×C4⋊C4—31no—
477C2×C4⋊C4C2×C3×D311yescharacteristic
478#106—31no—
479#106—31no—
480#106C2×C3×D311yescharacteristic
481#106C2×C3×D311yescharacteristic
482#103—31no—
483#103—31no—
484#103—31no—
485#103—31no—
486#102—31no—
487#102—31no—
488#102C2×C3×D311yescharacteristic
489#102C2×C3×D311yescharacteristic
490C22⋊C8—31no—
491C22⋊C8—31no—
492C22⋊C8—31no—
493C22⋊C8C2×C3×D311yescharacteristic
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—31no—
498C23×C3—31no—
499C23×C3—41no—
500C23×C3—61no—
501C23×C3D3×D411yescharacteristic
502C23×C3C2×C3×D411yescharacteristic
503C22×D3—21no—
504C22×D3C2×C3×D411yescharacteristic
505C22×D3C2×C3×D411yescharacteristic
506C3×Q8—61no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8—121no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—81no—
520C3×D4—81no—
521C3×D4—82no—
522C3×D4—121no—
523C3×D4—121no—
524C3×D4—121no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
528C3×D4—241no—
529C3×D4—241no—
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—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—81no—
557C2×C3×C4—81no—
558C2×C3×C4—82no—
559C2×C3×C4—122no—
560C2×C3×C4—122no—
561C2×C3×C4—241no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4C2×C3×D411yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C24×C311yescharacteristic
566#67—41no—
567#67—41no—
568#67—42no—
569#67—42no—
570#67—81no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—42no—
575C2×Dic3C2×C3×D411yescharacteristic
576C2×Dic3C2×C3×D411yescharacteristic
577D12—21no—
578D12—21no—
579D12—41no—
580D12—81no—
581D12—81no—
582C4×D3—21no—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—42no—
587C4×D3—81no—
588Dic6—21no—
589Dic6—21no—
590Dic6—21no—
591Dic6—21no—
592Dic6—41no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—21no—
597C3×C8—41no—
598C3×C8—41no—
599C3×C8—61no—
600C3×C8—61no—
601C3⋊C8—21no—
602C3⋊C8—21no—
603C2×C32—41no—
604C2×C32—81no—
605C2×C32#53411yescharacteristic
606C2×C32#57711yescharacteristic
607C2×C32#57711yescharacteristic
608C3×D3—41no—
609C3×D3—41no—
610C3×D3—81no—
611#41—121no—
612#41—121no—
613#41—121no—
614#41—121no—
615#41—121no—
616#41—121no—
617C2×Q8—31no—
618C2×Q8—31no—
619C2×Q8—31no—
620C2×D4—21no—
621C2×D4—31no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—31no—
625C2×D4—61no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4C22×C3×D311yescharacteristic
631C22×C4—21no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4C22×C3×D311yescharacteristic
638Q16—121no—
639SD16—121no—
640SD16—121no—
641D8—121no—
642M16—121no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—121no—
646C2×C8C22×C3×D311yescharacteristic
647C2×C8C22×C3×D311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—31no—
650C4⋊C4—61no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—61no—
655C4⋊C4C22×C3×D311yescharacteristic
656C4⋊C4C22×C3×D311yescharacteristic
657C4⋊C4C22×C3×D311yescharacteristic
658C22⋊C4—21no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22×C3—22no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
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—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C22×C3×D411yescharacteristic
696C2×D3—21no—
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—61no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4#100911yescharacteristic
725C3×C4#100911yescharacteristic
726C3×C4C3×H(5,𝔽2)11yescharacteristic
727C3×C4C3×H(5,𝔽2)11yescharacteristic
728Dic3—21no—
729Dic3—21no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733C32#320411yescharacteristic, complemented, Sylow
734C23—21no—
735C23—31no—
736C23—31no—
737C23—61no—
738C23C3×D3×D411yescharacteristic
739Q8—61no—
740Q8—61no—
741Q8—61no—
742Q8—61no—
743Q8—121no—
744D4—21no—
745D4—21no—
746D4—61no—
747D4—61no—
748D4—81no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—122no—
753D4—122no—
754D4—241no—
755D4—241no—
756D4—241no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—81no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4—241no—
775C2×C4C3×D3×D411yescharacteristic
776C2×C4C23×C3×D311yescharacteristic
777C8—21no—
778C8—21no—
779C8—61no—
780C8—61no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—42no—
785C2×C3—41no—
786C2×C3—41no—
787C2×C3—81no—
788C2×C3—81no—
789C2×C3—121no—
790C2×C3—121no—
791C2×C3—161no—
792C2×C3—241no—
793C2×C3#565311yescharacteristic
794C2×C3#576211yescharacteristic
795C2×C3#577511yescharacteristic
796C2×C3C3×#53411yescharacteristic
797C2×C3C3×#57711yescharacteristic
798C2×C3C3×#57711yescharacteristic
799D3—41no—
800D3—41no—
801D3—81no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22C2×C3×D3×D411yescharacteristic
818C4—21no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—61no—
823C4—61no—
824C4—121no—
825C4—121no—
826C4—121no—
827C4C3×#100911yescharacteristic
828C4C3×#100911yescharacteristic
829C3—21no—
830C3#8134111yescharacteristic, direct product factor
831C3C3×#320411yescharacteristic, complemented
832C2—41no—
833C2—81no—
834C2—121no—
835C2—121no—
836C2—241no—
837C2C3×#565311yescharacteristic
838C2C3×#576211yescharacteristic
839C2C3×#577511yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#481C2
socleC22×C32C22×D4
hypercenterC3×#481D3
hypocenterC3C3×#3204
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#481

Complements

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

NH ≅ G/Ntype
1. C3×#5608C2semidirect
2. C3×#5510C2semidirect
3. C32×#481C2semidirect
4. C3×#5037C2semidirect
5. C3×#4971C2semidirect
6. C3×#4867C2semidirect
7. C3×#4864C2semidirect
8. C3×#4863C2semidirect
9. C3×#4862C2semidirect
10. C3×#4783C2semidirect
11. C3×#4782C2semidirect
12. C3×#4781C2semidirect
13. C3×#4778C2semidirect
14. C3×#4733C2semidirect
15. C3×#4727C2semidirect
17. #81341C3direct (N × H)
63. #5608C2×C3semidirect
64. #5510C2×C3semidirect
69. C3×#481D3semidirect
70. C3×#481C2×C3semidirect
80. #5037C2×C3semidirect
81. #4971C2×C3semidirect
82. #4867C2×C3semidirect
83. #4864C2×C3semidirect
84. #4863C2×C3semidirect
85. #4862C2×C3semidirect
86. #4783C2×C3semidirect
87. #4782C2×C3semidirect
88. #4781C2×C3semidirect
89. #4778C2×C3semidirect
90. #4733C2×C3semidirect
91. #4727C2×C3semidirect
293. #481C3×D3semidirect
733. C32#3204semidirect
830. C3#81341direct (N × H)
831. C3C3×#3204semidirect

Maximal subgroups

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

subgroupindex
C3×#56082
C3×#55102
C32×#4812
C3×#50372
C3×#49712
C3×#48672
C3×#48642
C3×#48632
C3×#48622
C3×#47832
C3×#47822
C3×#47812
C3×#47782
C3×#47332
C3×#47272
C3×#32043
#813413