Finite Group Databasebeta

← C3×#10594528 #13173946

Subgroups — C3×#10594528 #13173946

Order 1728.

1462 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#897C211yesmaximal, characteristic, complemented
5C32×#895C211yesmaximal, characteristic, complemented
6C3×#63916C212yesmaximal, complemented
7C3×#63912C212yesmaximal, complemented
8C3×#63908C211yesmaximal, characteristic, complemented
9C3×#63899C212yesmaximal, complemented
10C3×#63885C212yesmaximal, complemented
11C3×#63856C211yesmaximal, characteristic, complemented
12C3×#5629—31nomaximal
13C3×#5608—31nomaximal
14#10594528C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2212yes—
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×D12C2212yes—
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×Dic6C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×#626C2211yescharacteristic
24C2×C3×#626C2212yes—
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2212yes—
28C2×C3×D3×Dic3C2212yes—
29C3×#3798—24no—
30C3×#3796—24no—
31C33×C4⋊C4C2211yescharacteristic
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#3750C2212yes—
34C32×(C2×D3)⋊C4C2212yes—
35C32×(C2×D3)⋊C4C2212yes—
36C32×C4⋊Dic3C2212yes—
37C3×#3724C2212yes—
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C3×#239—31no—
41C2×C3×#237—31no—
42C2×C3×#235—31no—
43C2×C3×#235—31no—
44C2×#3798C2×C311yescharacteristic, complemented
45C2×#3796C2×C311yescharacteristic, complemented
46C32×C22⋊Q8—31no—
47C32×#121—31no—
48C4⋊C4×C3⋊D3C2×C311yescharacteristic, complemented
49C3×#946—31no—
50C3×#939—32no—
51C3×#938—31no—
52C3×#938—32no—
53C3×#930—31no—
54C3×#924—31no—
55C3×#897—21no—
56C3×#897D311yescharacteristic, complemented
57C3×#897C2×C311yescharacteristic, complemented
58C3×#896—32no—
59C3×#895—21no—
60C3×#895—32no—
61C3×#895D311yescharacteristic, complemented
62C3×#895C2×C311yescharacteristic, complemented
63C3×D3×C4⋊C4—31no—
64C3×D3×C4⋊C4—31no—
65C3×D3×C4⋊C4—61no—
66C3×#884—32no—
67C3×#884—32no—
68C3×#884—32no—
69C3×#878—32no—
70#63916C2×C312yescomplemented
71#63912C2×C312yescomplemented
72#63908C2×C311yescharacteristic, complemented
73#63899C2×C312yescomplemented
74#63885C2×C312yescomplemented
75#63856C2×C311yescharacteristic, complemented
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2312yes—
78C22×C32×D3C2311yescharacteristic
79C22×C32×D3C2311yescharacteristic
80C2×C33×C4C2312yes—
81C2×C33×C4C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C3×C4×C3⋊D3—42no—
85C3×C4×C3⋊D3D414yescomplemented
86C2×C32×Dic3C2312yes—
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2311yescharacteristic
89C32×D12—22no—
90C32×D12—42no—
91C32×C4×D3—22no—
92C32×C4×D3—22no—
93C32×Dic6—22no—
94C3×#627—22no—
95C3×#626—24no—
96C3×#626—22no—
97C3×#626—22no—
98C3×#625—22no—
99C3×#625—42no—
100C3×D3×Dic3—24no—
101C3×#537—91no—
102#5629—31no—
103#5608—31no—
104C2×C32×Q8—31no—
105C2×C32×D4—31no—
106C2×C32×D4—32no—
107C22×C32×C4—31no—
108C22×C32×C4—31no—
109C2×C4×C3⋊D3C22×C312yes—
110C2×C4×C3⋊D3C22×C311yescharacteristic
111C2×C3×#67—31no—
112C2×C3×#67—31no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—31no—
116C2×C3×#67—32no—
117C2×C3×#67—31no—
118C22×C3×Dic3—32no—
119C3×#239—64no—
120C3×#237—64no—
121C3×#235—64no—
122C3×#235—64no—
123C2×C3×D12—21no—
124C2×C3×D12—22no—
125C2×C3×D12—31no—
126C2×C3×D12—32no—
127C2×C3×D12—31no—
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×D12C2×D312yes—
130C2×C3×D12C22×C311yescharacteristic
131C2×C3×D12C22×C312yes—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3—32no—
137C2×C3×C4×D3—32no—
138C2×C3×C4×D3—32no—
139C2×C3×C4×D3—61no—
140C2×C3×C4×D3—62no—
141C2×C3×C4×D3C2×D311yescharacteristic
142C2×C3×C4×D3C2×D311yescharacteristic
143C2×C3×C4×D3C22×C311yescharacteristic
144C2×C3×C4×D3C22×C311yescharacteristic
145C2×C3×Dic6—21no—
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×C3×Dic6C2×D311yescharacteristic
149C2×C3×Dic6C22×C311yescharacteristic
150C2×#627C22×C311yescharacteristic
151C2×#626C22×C312yes—
152C2×#626C22×C311yescharacteristic
153C2×#626C22×C311yescharacteristic
154C2×#625C22×C311yescharacteristic
155C2×#625C22×C312yes—
156C2×D3×Dic3C22×C312yes—
157#3798—24no—
158#3796—24no—
159C32×C4⋊C4—21no—
160C32×C4⋊C4—21no—
161C32×C4⋊C4—21no—
162C32×C4⋊C4—32no—
163C32×C4⋊C4—41no—
164C32×C4⋊C4C2×D311yescharacteristic
165C32×C4⋊C4C2×D311yescharacteristic
166C32×C4⋊C4C22×C311yescharacteristic
167C32×C22⋊C4—32no—
168C32×C22⋊C4—32no—
169C4⋊(C3⋊Dic3)C22×C311yescharacteristic
170#3750C22×C312yes—
171C3×#217—32no—
172C3×#217—32no—
173C3×(C2×D3)⋊C4—22no—
174C3×(C2×D3)⋊C4—22no—
175C3×(C2×D3)⋊C4—32no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4C2×D312yes—
178C3×(C2×D3)⋊C4C2×D312yes—
179C3×(C2×D3)⋊C4C22×C312yes—
180C3×(C2×D3)⋊C4C22×C312yes—
181C3×C4⋊Dic3—22no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—61no—
185C3×C4⋊Dic3C2×D312yes—
186C3×C4⋊Dic3C22×C312yes—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—32no—
189C3×Dic3⋊C4—32no—
190C3×Dic3⋊C4—32no—
191C3×Dic3⋊C4—62no—
192#3724C22×C312yes—
193(C2×D3)⋊Dic3C22×C312yes—
194(C2×D3)⋊Dic3C22×C312yes—
195C22×C33C2411yescharacteristic
196C2×C3×C3⋊D3—21no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3C2×D412yes—
199C2×C32×D3—22no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C33×C4—22no—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—22no—
211C3×C3⋊Dic3C2×D412yes—
212C32×Dic3—22no—
213C32×Dic3—21no—
214C32×Dic3—21no—
215C2×C3×#41—91no—
216C2×C3×#41—91no—
217C2×#239—31no—
218C2×#237—31no—
219C2×#235—31no—
220C2×#235—31no—
221C3×C22⋊Q8—31no—
222C3×C22⋊Q8—31no—
223C3×C22⋊Q8—61no—
224C3×C22⋊Q8—92no—
225C3×C22⋊Q8—91no—
226C3×#121—31no—
227C3×#121—31no—
228C3×#121—61no—
229C3×#121—92no—
230C3×#121—92no—
231C3×#121—92no—
232C3×#121—91no—
233C2×C3×C4⋊C4—91no—
234#946—31no—
235#939—32no—
236#938—31no—
237#938—32no—
238#930—31no—
239#924—31no—
240#897C3×D311yescharacteristic, complemented
241#896—32no—
242#895—32no—
243#895C3×D311yescharacteristic, complemented
244D3×C4⋊C4—31no—
245D3×C4⋊C4—31no—
246D3×C4⋊C4—61no—
247#884—32no—
248#884—32no—
249#884—32no—
250#878—32no—
251C23×C32—31no—
252C23×C32—32no—
253C23×C32—31no—
254C22×C3⋊D3C23×C311yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—22no—
258C22×C3×D3—31no—
259C22×C3×D3—31no—
260C22×C3×D3—61no—
261C22×C3×D3C22×D311yescharacteristic
262C22×C3×D3C22×D312yes—
263C22×C3×D3C22×D311yescharacteristic
264C22×C3×D3C23×C311yescharacteristic
265C22×C3×D3C23×C312yes—
266C22×C3×D3C23×C311yescharacteristic
267C32×Q8—62no—
268C32×D4—62no—
269C32×D4—122no—
270C2×C32×C4—21no—
271C2×C32×C4—22no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4—31no—
277C2×C32×C4—32no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4—42no—
281C2×C32×C4—62no—
282C2×C32×C4—62no—
283C2×C32×C4C22×D312yes—
284C2×C32×C4C22×D312yes—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C23×C312yes—
288C2×C32×C4C23×C311yescharacteristic
289C2×C3⋊Dic3C23×C312yes—
290C2×C3⋊Dic3C23×C311yescharacteristic
291C4×C3⋊D3—42no—
292C4×C3⋊D3C3×D414yescomplemented
293C3×#67—62no—
294C3×#67—62no—
295C3×#67—64no—
296C3×#67—62no—
297C3×#67—62no—
298C3×#67—122no—
299C3×#67—122no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—32no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—62no—
309C2×C3×Dic3—64no—
310C2×C3×Dic3C22×D311yescharacteristic
311C2×C3×Dic3C22×D312yes—
312C2×C3×Dic3C22×D311yescharacteristic
313C2×C3×Dic3C23×C311yescharacteristic
314C2×C3×Dic3C23×C312yes—
315C2×C3×Dic3C23×C311yescharacteristic
316C3×D12—22no—
317C3×D12—22no—
318C3×D12—42no—
319C3×D12—42no—
320C3×D12—42no—
321C3×D12—44no—
322C3×D12—62no—
323C3×D12—62no—
324C3×D12—64no—
325C3×C4×D3—22no—
326C3×C4×D3—22no—
327C3×C4×D3—22no—
328C3×C4×D3—22no—
329C3×C4×D3—34no—
330C3×C4×D3—34no—
331C3×C4×D3—42no—
332C3×C4×D3—42no—
333C3×C4×D3—64no—
334C3×C4×D3—64no—
335C3×C4×D3—122no—
336C3×C4×D3—122no—
337C3×C4×D3—124no—
338C3×Dic6—22no—
339C3×Dic6—22no—
340C3×Dic6—42no—
341C3×Dic6—62no—
342C3×Dic6—62no—
343#627—22no—
344#626—24no—
345#626—22no—
346#626—22no—
347#625—22no—
348#625—42no—
349D3×Dic3—24no—
350#537—91noSylow
351C2×C33C22×D411yescharacteristic
352C2×C33H(5,𝔽2)11yescharacteristic
353C2×C332−1+411yescharacteristic
354C3×C3⋊D3—22no—
355C32×D3—41no—
356C32×D3—41no—
357C32×D3—42no—
358C3×#41—184no—
359C3×#41—184no—
360C2×C3×Q8—31no—
361C2×C3×Q8—31no—
362C2×C3×Q8—61no—
363C2×C3×Q8—91no—
364C2×C3×D4—31no—
365C2×C3×D4—32no—
366C2×C3×D4—31no—
367C2×C3×D4—32no—
368C2×C3×D4—61no—
369C2×C3×D4—62no—
370C2×C3×D4—91no—
371C2×C3×D4—92no—
372C2×C3×D4—91no—
373C2×C3×D4—91no—
374C2×C3×D4—92no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—61no—
380C22×C3×C4—61no—
381C22×C3×C4—92no—
382C22×C3×C4—91no—
383C22×C3×C4—92no—
384C2×#67—31no—
385C2×#67—31no—
386C2×#67—32no—
387C2×#67—32no—
388C2×#67—31no—
389C2×#67—32no—
390C2×#67—31no—
391C22×Dic3—32no—
392#239—64no—
393#237—64no—
394#235—64no—
395#235—64no—
396C2×D12—31no—
397C2×D12—32no—
398C2×D12—31no—
399C2×D12C2×C3×D311yescharacteristic
400C2×D12C2×C3×D312yes—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—61no—
407C2×C4×D3—62no—
408C2×C4×D3C2×C3×D311yescharacteristic
409C2×C4×D3C2×C3×D311yescharacteristic
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6C2×C3×D311yescharacteristic
413C3×C4⋊C4—21no—
414C3×C4⋊C4—21no—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—32no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—41no—
419C3×C4⋊C4—62no—
420C3×C4⋊C4—92no—
421C3×C4⋊C4—92no—
422C3×C4⋊C4—91no—
423C3×C4⋊C4D3211yescharacteristic
424C3×C4⋊C4C2×C3×D311yescharacteristic
425C3×C4⋊C4C2×C3×D311yescharacteristic
426C3×C22⋊C4—32no—
427C3×C22⋊C4—32no—
428C3×C22⋊C4—32no—
429C3×C22⋊C4—32no—
430C3×C22⋊C4—62no—
431C3×C22⋊C4—62no—
432C3×C22⋊C4—92no—
433C3×C22⋊C4—92no—
434#217—32no—
435#217—32no—
436(C2×D3)⋊C4—32no—
437(C2×D3)⋊C4—32no—
438(C2×D3)⋊C4C2×C3×D312yes—
439(C2×D3)⋊C4C2×C3×D312yes—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3C2×C3×D312yes—
444Dic3⋊C4—32no—
445Dic3⋊C4—32no—
446Dic3⋊C4—32no—
447Dic3⋊C4—32no—
448Dic3⋊C4—62no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32—62no—
456C22×C32—61no—
457C22×C32—61no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32—62no—
461C22×C32—62no—
462C22×C32C23×D311yescharacteristic
463C22×C32C23×D311yescharacteristic
464C22×C32C24×C311yescharacteristic
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3C2×C3×D412yes—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—21no—
474C2×C3×D3—22no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—22no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—22no—
488C2×C3×D3—32no—
489C2×C3×D3—32no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—42no—
495C2×C3×D3—42no—
496C2×C3×D3—42no—
497C2×C3×D3—62no—
498C2×C3×D3—62no—
499C2×C3×D3—62no—
500C2×C3×D3—61no—
501C2×C3×D3—61no—
502C2×C3×D3—61no—
503C2×C3×D3—61no—
504C32×C4—22no—
505C32×C4—22no—
506C32×C4—22no—
507C32×C4—22no—
508C32×C4—22no—
509C32×C4—22no—
510C32×C4—42no—
511C32×C4—42no—
512C32×C4—42no—
513C32×C4—42no—
514C32×C4—61no—
515C32×C4—61no—
516C32×C4—62no—
517C32×C4—82no—
518C32×C4D3×D412yes—
519C32×C4D3×D412yes—
520C32×C4C2×C3×D412yes—
521C3⋊Dic3—22no—
522C3⋊Dic3C2×C3×D412yes—
523C3×Dic3—22no—
524C3×Dic3—21no—
525C3×Dic3—21no—
526C3×Dic3—22no—
527C3×Dic3—21no—
528C3×Dic3—21no—
529C3×Dic3—32no—
530C3×Dic3—32no—
531C3×Dic3—42no—
532C3×Dic3—41no—
533C3×Dic3—41no—
534C3×Dic3—62no—
535C3×Dic3—62no—
536C3×Dic3—62no—
537C3×Dic3—122no—
538C2×#41—91no—
539C2×#41—91no—
540C22⋊Q8—31no—
541C22⋊Q8—92no—
542C22⋊Q8—91no—
543#121—31no—
544#121—92no—
545#121—92no—
546#121—92no—
547#121—91no—
548C2×C4⋊C4—91no—
549C33#53711yescharacteristic, complemented, Sylow
550C23×C3—31no—
551C23×C3—32no—
552C23×C3—31no—
553C23×C3—31no—
554C23×C3—32no—
555C23×C3—31no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—62no—
559C23×C3—91no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—61no—
563C22×D3C22×C3×D311yescharacteristic
564C22×D3C22×C3×D312yes—
565C22×D3C22×C3×D311yescharacteristic
566C3×Q8—62no—
567C3×Q8—62no—
568C3×Q8—122no—
569C3×Q8—182no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C3×D4—124no—
576C3×D4—182no—
577C3×D4—182no—
578C3×D4—184no—
579C3×D4—182no—
580C3×D4—362no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—31no—
588C2×C3×C4—32no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—32no—
592C2×C3×C4—31no—
593C2×C3×C4—41no—
594C2×C3×C4—42no—
595C2×C3×C4—61no—
596C2×C3×C4—62no—
597C2×C3×C4—61no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—62no—
601C2×C3×C4—62no—
602C2×C3×C4—91no—
603C2×C3×C4—94no—
604C2×C3×C4—92no—
605C2×C3×C4—122no—
606C2×C3×C4—122no—
607C2×C3×C4—184no—
608C2×C3×C4—362no—
609C2×C3×C4C2×D3212yes—
610C2×C3×C4C2×D3211yescharacteristic
611C2×C3×C4C22×C3×D312yes—
612C2×C3×C4C22×C3×D312yes—
613C2×C3×C4C22×C3×D311yescharacteristic
614C2×C3×C4C22×C3×D311yescharacteristic
615#67—62no—
616#67—62no—
617#67—64no—
618#67—62no—
619#67—62no—
620#67—122no—
621#67—122no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—61no—
627C2×Dic3—62no—
628C2×Dic3—64no—
629C2×Dic3C22×C3×D311yescharacteristic
630C2×Dic3C22×C3×D312yes—
631C2×Dic3C22×C3×D311yescharacteristic
632D12—22no—
633D12—42no—
634D12—62no—
635D12—62no—
636D12—64no—
637C4×D3—22no—
638C4×D3—22no—
639C4×D3—34no—
640C4×D3—34no—
641C4×D3—64no—
642C4×D3—64no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—124no—
646Dic6—22no—
647Dic6—62no—
648Dic6—62no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—21no—
652C2×C32—21no—
653C2×C32—21no—
654C2×C32—21no—
655C2×C32—21no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—41no—
659C2×C32—41no—
660C2×C32—41no—
661C2×C32—121no—
662C2×C32—121no—
663C2×C32—122no—
664C2×C32C2×D3×D411yescharacteristic
665C2×C32C2×D3×D411yescharacteristic
666C2×C32#100411yescharacteristic
667C2×C32#100711yescharacteristic
668C2×C32#100911yescharacteristic
669C2×C32#101011yescharacteristic
670C2×C32C22×C3×D411yescharacteristic
671C2×C32C3×H(5,𝔽2)11yescharacteristic
672C2×C32C3×2−1+411yescharacteristic
673C3⋊D3—22no—
674C3×D3—42no—
675C3×D3—42no—
676C3×D3—41no—
677C3×D3—42no—
678C3×D3—41no—
679C3×D3—42no—
680C3×D3—41no—
681C3×D3—41no—
682C3×D3—64no—
683C3×D3—62no—
684C3×D3—62no—
685C3×D3—82no—
686#41—184no—
687#41—184no—
688C2×Q8—31no—
689C2×Q8—91no—
690C2×D4—31no—
691C2×D4—32no—
692C2×D4—91no—
693C2×D4—92no—
694C2×D4—91no—
695C2×D4—91no—
696C2×D4—92no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—92no—
700C22×C4—91no—
701C22×C4—92no—
702C4⋊C4—32no—
703C4⋊C4—92no—
704C4⋊C4—92no—
705C4⋊C4—91no—
706C4⋊C4C3×D3211yescharacteristic
707C22⋊C4—32no—
708C22⋊C4—32no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—41no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—62no—
720C22×C3—61no—
721C22×C3—62no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—61no—
726C22×C3—62no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—61no—
734C22×C3—61no—
735C22×C3—92no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—122no—
741C22×C3—122no—
742C22×C3—122no—
743C22×C3—181no—
744C22×C3—181no—
745C22×C3C22×D3211yescharacteristic
746C22×C3C23×C3×D311yescharacteristic
747C22×C3C23×C3×D311yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—22no—
751C2×D3—21no—
752C2×D3—22no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—22no—
757C2×D3—32no—
758C2×D3—32no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—42no—
775C3×C4—42no—
776C3×C4—61no—
777C3×C4—61no—
778C3×C4—62no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—62no—
782C3×C4—82no—
783C3×C4—92no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4—122no—
787C3×C4—182no—
788C3×C4#380212yes—
789C3×C4C3×D3×D412yes—
790C3×C4C3×D3×D412yes—
791Dic3—22no—
792Dic3—21no—
793Dic3—21no—
794Dic3—32no—
795Dic3—32no—
796Dic3—62no—
797Dic3—62no—
798Dic3—62no—
799Dic3—122no—
800C32—21no—
801C32—21no—
802C32—21no—
803C32—41no—
804C32#560811yescharacteristic, complemented
805C32#562911yescharacteristic, complemented
806C32C3×#53711yescharacteristic, complemented
807C23—31no—
808C23—32no—
809C23—31no—
810C23—91no—
811Q8—62no—
812Q8—182no—
813D4—62no—
814D4—122no—
815D4—182no—
816D4—182no—
817D4—184no—
818D4—182no—
819D4—362no—
820C2×C4—31no—
821C2×C4—32no—
822C2×C4—31no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—91no—
826C2×C4—94no—
827C2×C4—92no—
828C2×C4—184no—
829C2×C4—362no—
830C2×C4C2×C3×D3212yes—
831C2×C4C2×C3×D3211yescharacteristic
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—41no—
844C2×C3—122no—
845C2×C3—122no—
846C2×C3—121no—
847C2×C3—121no—
848C2×C3—122no—
849C2×C3—121no—
850C2×C3—121no—
851C2×C3—122no—
852C2×C3—182no—
853C2×C3—242no—
854C2×C3C2×#380211yescharacteristic
855C2×C3#6431411yescharacteristic
856C2×C3#6431511yescharacteristic
857C2×C3C2×C3×D3×D411yescharacteristic
858C2×C3C2×C3×D3×D411yescharacteristic
859C2×C3C3×#100411yescharacteristic
860C2×C3C3×#100711yescharacteristic
861C2×C3C3×#100911yescharacteristic
862C2×C3C3×#101011yescharacteristic
863D3—41no—
864D3—42no—
865D3—41no—
866D3—64no—
867D3—62no—
868D3—62no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—61no—
873C22—62no—
874C22—61no—
875C22—61no—
876C22—61no—
877C22—62no—
878C22—92no—
879C22—181no—
880C22—181no—
881C22C22×C3×D3211yescharacteristic
882C4—22no—
883C4—61no—
884C4—61no—
885C4—62no—
886C4—92no—
887C4—182no—
888C4C3×#380212yes—
889C3—21no—
890C3—21no—
891C3—21no—
892C3—41no—
893C3#1059452811yescharacteristic, direct product factor
894C3C3×#560811yescharacteristic, complemented
895C3C3×#562911yescharacteristic, complemented
896C2—121no—
897C2—121no—
898C2—122no—
899C2—182no—
900C2C2×C3×#380211yescharacteristic
901C2C3×#6431411yescharacteristic
902C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3798C2semidirect
2. C2×C3×#3796C2semidirect
3. C3×C4⋊C4×C3⋊D3C2semidirect
4. C32×#897C2semidirect
5. C32×#895C2semidirect
6. C3×#63916C2semidirect
7. C3×#63912C2semidirect
8. C3×#63908C2semidirect
9. C3×#63899C2semidirect
10. C3×#63885C2semidirect
11. C3×#63856C2semidirect
14. #10594528C3direct (N × H)
44. C2×#3798C2×C3semidirect
45. C2×#3796C2×C3semidirect
48. C4⋊C4×C3⋊D3C2×C3semidirect
56. C3×#897D3semidirect
57. C3×#897C2×C3semidirect
61. C3×#895D3semidirect
62. C3×#895C2×C3semidirect
70. #63916C2×C3semidirect
71. #63912C2×C3semidirect
72. #63908C2×C3semidirect
73. #63899C2×C3semidirect
74. #63885C2×C3semidirect
75. #63856C2×C3semidirect
85. C3×C4×C3⋊D3D4semidirect
240. #897C3×D3semidirect
243. #895C3×D3semidirect
292. C4×C3⋊D3C3×D4semidirect
549. C33#537semidirect
804. C32#5608semidirect
805. C32#5629semidirect
806. C32C3×#537semidirect
893. C3#10594528direct (N × H)
894. C3C3×#5608semidirect
895. C3C3×#5629semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37982
C2×C3×#37962
C3×C4⋊C4×C3⋊D32
C32×#8972
C32×#8952
C3×#639162
C3×#639122
C3×#639082
C3×#638992
C3×#638852
C3×#638562
C3×#56293
C3×#56083
#105945283