Finite Group Databasebeta

← C3×#10595229 #13174714

Subgroups — C3×#10595229 #13174714

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C32×#936C211yesmaximal, characteristic, complemented
5C3×#63977C212yesmaximal, complemented
6C3×#63971C212yesmaximal, complemented
7C3×#63969C212yesmaximal, complemented
8C3×D3×#217C212yesmaximal, complemented
9C3×C4×#626C211yesmaximal, characteristic, complemented
10C3×Dic3×D12C211yesmaximal, characteristic, complemented
11C3×#63856C211yesmaximal, characteristic, complemented
12C3×#5806—31nomaximal
13C3×#5676—31nomaximal
14#10595229C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2212yes—
16C2×C33×D4C2211yescharacteristic
17C2×C3×#638C2212yescomplemented
18C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
19C2×C32×#67C2212yes—
20C32×D3×D4—24no—
21C2×C32×D12C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic, complemented
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2212yescomplemented
26C2×C3×D3×Dic3C2212yescomplemented
27C2×C3×D3×Dic3C2212yescomplemented
28C3×#3796—24no—
29C3×#3757C2212yescomplemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C32×#217C2212yescomplemented
32C32×#217C2212yescomplemented
33C32×C4×Dic3C2211yescharacteristic, complemented
34C3×#3724C2212yescomplemented
35C3×Dic3⋊Dic3C2211yescharacteristic, complemented
36C3×#3722C2211yescharacteristic, complemented
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C32×D4—31no—
41C2×C3×#239—31no—
42C2×C3×#237—31no—
43C2×C3×D3×D4—21no—
44C2×C3×D3×D4D311yescharacteristic, complemented
45C2×C3×D3×D4C2×C311yescharacteristic, complemented
46C2×#3796C2×C311yescharacteristic, complemented
47C32×#124—31no—
48#64147C2×C311yescharacteristic, complemented
49C3×#953—32no—
50C2×C3×#217—32no—
51C3×#946—31no—
52C3×#939—32no—
53C3×#938—31no—
54C3×#938—31no—
55C3×#938—61no—
56C3×#936—21no—
57C3×#936D311yescharacteristic, complemented
58C3×#936C2×C311yescharacteristic, complemented
59C3×#935—32no—
60C3×D4×Dic3—31no—
61C3×C4×#67—31no—
62C3×#924—31no—
63C3×#884—32no—
64C3×#883—32no—
65C3×#882—32no—
66C3×D3×C22⋊C4—32no—
67C3×C4×D12—31no—
68C3×C4×D12—31no—
69#63977C2×C312yescomplemented
70#63971C2×C312yescomplemented
71#63969C2×C312yescomplemented
72D3×#217C2×C312yescomplemented
73C4×#626C2×C311yescharacteristic, complemented
74Dic3×D12C2×C311yescharacteristic, complemented
75#63856C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—24no—
79C22×C32×D3—24no—
80C22×C32×D3—42no—
81C22×C32×D3C2312yes—
82C22×C32×D3C2311yescharacteristic
83C33×D4—22no—
84C2×C33×C4C2311yescharacteristic
85C3×#638—42no—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4×C3⋊D3—22no—
89C32×#67—24no—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2311yescharacteristic
94C32×D12D414yescomplemented
95C32×C4×D3—22no—
96C32×Dic6—22no—
97C3×#626—24no—
98C3×#626—22no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—42no—
101C3×#546—91no—
102#5806—31no—
103#5676—31no—
104C24×C32—32no—
105C23×C3×D3—22no—
106C23×C3×D3C2×D312yes—
107C23×C3×D3C22×C312yes—
108C2×C32×Q8—31no—
109C2×C32×D4—21no—
110C2×C32×D4—21no—
111C2×C32×D4—21no—
112C2×C32×D4—32no—
113C2×C32×D4—31no—
114C2×C32×D4—41no—
115C2×C32×D4—64no—
116C2×C32×D4C2×D311yescharacteristic
117C2×C32×D4C2×D311yescharacteristic
118C2×C32×D4C22×C311yescharacteristic
119C22×C32×C4—31no—
120C2×#638C22×C312yescomplemented
121C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
122C2×C3×#67—22no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—31no—
126C2×C3×#67—32no—
127C2×C3×#67—62no—
128C2×C3×#67C2×D312yes—
129C2×C3×#67C22×C312yes—
130C22×C3×Dic3—32no—
131C22×C3×Dic3—32no—
132C3×#239—64no—
133C3×#237—64no—
134C3×D3×D4—28no—
135C3×D3×D4—24no—
136C3×D3×D4—24no—
137C2×C3×D12—21no—
138C2×C3×D12—31no—
139C2×C3×D12—32no—
140C2×C3×D12C2×D311yescharacteristic
141C2×C3×D12C22×C311yescharacteristic
142C2×C3×C4×D3—21no—
143C2×C3×C4×D3—32no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—32no—
147C2×C3×C4×D3—61no—
148C2×C3×C4×D3C2×D311yescharacteristic
149C2×C3×C4×D3C22×C311yescharacteristic
150C2×C3×Dic6—21no—
151C2×C3×Dic6C2×D311yescharacteristic, complemented
152C2×C3×Dic6C22×C311yescharacteristic, complemented
153C2×#626C22×C311yescharacteristic
154C2×#626C22×C312yescomplemented
155C2×D3×Dic3C22×C312yescomplemented
156C2×D3×Dic3C22×C312yescomplemented
157#3796—24no—
158C32×C22⋊C4—32no—
159C32×C22⋊C4—32no—
160C32×C42—31no—
161#3757C22×C312yescomplemented
162C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
163C3×#217—22no—
164C3×#217—22no—
165C3×#217—32no—
166C3×#217—32no—
167C3×#217—32no—
168C3×#217—31no—
169C3×#217—32no—
170C3×#217—62no—
171C3×#217C2×D312yescomplemented
172C3×#217C2×D312yescomplemented
173C3×#217C22×C312yescomplemented
174C3×#217C22×C312yescomplemented
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—61no—
184C3×Dic3⋊C4—32no—
185C3×Dic3⋊C4—32no—
186C3×Dic3⋊C4—31no—
187C3×C4×Dic3—21no—
188C3×C4×Dic3C2×D311yescharacteristic, complemented
189C3×C4×Dic3C22×C311yescharacteristic, complemented
190#3724C22×C312yescomplemented
191Dic3⋊Dic3C22×C311yescharacteristic, complemented
192#3722C22×C311yescharacteristic, complemented
193(C2×D3)⋊Dic3C22×C312yes—
194(C2×D3)⋊Dic3C22×C311yescharacteristic
195(C2×D3)⋊Dic3C22×C312yescomplemented
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—48no—
208C2×C32×D3C2×D414yes—
209C2×C32×D3#4112yescomplemented
210C33×C4C2×D412yes—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—22no—
213C32×Dic3—21no—
214C32×Dic3—22no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C2×C3×#41—91no—
218C22×C3×D4—31no—
219C22×C3×D4—31no—
220C22×C3×D4—61no—
221C2×#239—31no—
222C2×#237—31no—
223C2×D3×D4C3×D311yescharacteristic, complemented
224C3×#124—31no—
225C3×#124—31no—
226C3×#124—61no—
227C3×#123—92no—
228C3×C22⋊Q8—91no—
229C3×#121—92no—
230C3×#121—91no—
231C3×#120—92no—
232C3×C4×D4—91no—
233C3×C4×D4—91no—
234C2×C3×C22⋊C4—92no—
235#953—32no—
236C2×#217—32no—
237#946—31no—
238#939—32no—
239#938—31no—
240#938—31no—
241#938—61no—
242#936C3×D311yescharacteristic, complemented
243#935—32no—
244D4×Dic3—31no—
245C4×#67—31no—
246#924—31no—
247#884—32no—
248#883—32no—
249#882—32no—
250D3×C22⋊C4—32no—
251C4×D12—31no—
252C4×D12—31no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—22no—
256C23×C32—31no—
257C23×C32—32no—
258C23×C32—42no—
259C23×C32—64no—
260C23×C32—64no—
261C23×C32—122no—
262C23×C32C22×D312yes—
263C23×C32C22×D312yes—
264C23×C32C23×C312yes—
265C22×C3⋊D3C23×C311yescharacteristic
266C22×C3×D3—28no—
267C22×C3×D3—24no—
268C22×C3×D3—24no—
269C22×C3×D3—24no—
270C22×C3×D3—24no—
271C22×C3×D3—21no—
272C22×C3×D3—22no—
273C22×C3×D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—44no—
276C22×C3×D3—42no—
277C22×C3×D3—42no—
278C22×C3×D3—44no—
279C22×C3×D3—61no—
280C22×C3×D3C22×D311yescharacteristic
281C22×C3×D3C22×D312yes—
282C22×C3×D3C23×C312yes—
283C22×C3×D3C23×C311yescharacteristic
284C32×Q8—62no—
285C32×D4—22no—
286C32×D4—24no—
287C32×D4—22no—
288C32×D4—22no—
289C32×D4—34no—
290C32×D4—42no—
291C32×D4—42no—
292C32×D4—44no—
293C32×D4—64no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4—31no—
298C2×C32×C4—32no—
299C2×C32×C4—31no—
300C2×C32×C4—31no—
301C2×C32×C4—41no—
302C2×C32×C4—62no—
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305C2×C32×C4C23×C311yescharacteristic
306#638—42no—
307C2×C3⋊Dic3C23×C312yes—
308C2×C3⋊Dic3C23×C311yescharacteristic
309C4×C3⋊D3—22no—
310C3×#67—28no—
311C3×#67—24no—
312C3×#67—24no—
313C3×#67—64no—
314C3×#67—62no—
315C3×#67—122no—
316C3×#67—122no—
317C3×#67—124no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3—21no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—32no—
323C2×C3×Dic3—32no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—62no—
327C2×C3×Dic3—61no—
328C2×C3×Dic3—64no—
329C2×C3×Dic3—122no—
330C2×C3×Dic3C22×D311yescharacteristic
331C2×C3×Dic3C22×D311yescharacteristic
332C2×C3×Dic3C22×D311yescharacteristic
333C2×C3×Dic3C22×D312yes—
334C2×C3×Dic3C23×C311yescharacteristic
335C2×C3×Dic3C23×C312yes—
336C2×C3×Dic3C23×C311yescharacteristic
337C2×C3×Dic3C23×C311yescharacteristic
338C3×D12—24no—
339C3×D12—62no—
340C3×D12—64no—
341C3×D12#6714yescomplemented
342C3×D12C3×D414yescomplemented
343C3×C4×D3—24no—
344C3×C4×D3—22no—
345C3×C4×D3—22no—
346C3×C4×D3—64no—
347C3×C4×D3—62no—
348C3×C4×D3—62no—
349C3×C4×D3—122no—
350C3×C4×D3—122no—
351C3×Dic6—22no—
352C3×Dic6—22no—
353C3×Dic6—42no—
354#626—24no—
355#626—22no—
356D3×Dic3—24no—
357D3×Dic3—42no—
358#546—91noSylow
359C2×C33—42no—
360C2×C33C22×D411yescharacteristic
361C2×C33C2×#4111yescharacteristic
362C2×C33H(5,𝔽2)11yescharacteristic
363C3×C3⋊D3—41no—
364C32×D3—22no—
365C32×D3—24no—
366C24×C3—32no—
367C24×C3—32no—
368C24×C3—62no—
369C23×D3C2×C3×D312yes—
370C3×#41—184no—
371C2×C3×Q8—31no—
372C2×C3×Q8—31no—
373C2×C3×Q8—61no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—32no—
378C2×C3×D4—32no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—41no—
382C2×C3×D4—61no—
383C2×C3×D4—62no—
384C2×C3×D4—64no—
385C2×C3×D4—64no—
386C2×C3×D4—68no—
387C2×C3×D4—91no—
388C2×C3×D4—92no—
389C2×C3×D4—92no—
390C2×C3×D4D3211yescharacteristic
391C2×C3×D4C2×C3×D311yescharacteristic
392C2×C3×D4C2×C3×D311yescharacteristic
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—61no—
396C22×C3×C4—92no—
397C22×C3×C4—92no—
398C22×C3×C4—91no—
399C2×#67—32no—
400C2×#67—32no—
401C2×#67—31no—
402C2×#67—32no—
403C2×#67—62no—
404C2×#67C2×C3×D312yes—
405C22×Dic3—32no—
406C22×Dic3—32no—
407#239—64no—
408#237—64no—
409D3×D4—24no—
410C2×D12—31no—
411C2×D12—32no—
412C2×D12C2×C3×D311yescharacteristic
413C2×C4×D3—32no—
414C2×C4×D3—31no—
415C2×C4×D3—31no—
416C2×C4×D3—32no—
417C2×C4×D3—61no—
418C2×C4×D3C2×C3×D311yescharacteristic
419C2×Dic6C2×C3×D311yescharacteristic, complemented
420C3×C4⋊C4—92no—
421C3×C4⋊C4—91no—
422C3×C4⋊C4—91no—
423C3×C22⋊C4—32no—
424C3×C22⋊C4—32no—
425C3×C22⋊C4—32no—
426C3×C22⋊C4—32no—
427C3×C22⋊C4—62no—
428C3×C22⋊C4—62no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4—91no—
431C3×C22⋊C4—92no—
432C3×C22⋊C4—92no—
433C3×C22⋊C4—92no—
434C3×C42—31no—
435C3×C42—31no—
436C3×C42—61no—
437#217—32no—
438#217—32no—
439#217—32no—
440#217—31no—
441#217—32no—
442#217—62no—
443#217C2×C3×D312yescomplemented
444#217C2×C3×D312yescomplemented
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—32no—
447(C2×D3)⋊C4—32no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—31no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—61no—
454Dic3⋊C4—32no—
455Dic3⋊C4—31no—
456Dic3⋊C4—32no—
457C4×Dic3C2×C3×D311yescharacteristic, complemented
458C22×C32—22no—
459C22×C32—24no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—34no—
472C22×C32—32no—
473C22×C32—41no—
474C22×C32—42no—
475C22×C32—42no—
476C22×C32—44no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—42no—
481C22×C32—42no—
482C22×C32—42no—
483C22×C32—61no—
484C22×C32—61no—
485C22×C32—62no—
486C22×C32—62no—
487C22×C32—82no—
488C22×C32—82no—
489C22×C32—128no—
490C22×C32C23×D311yescharacteristic
491C22×C32C23×D311yescharacteristic
492C22×C32C24×C311yescharacteristic
493C2×C3⋊D3—21no—
494C2×C3⋊D3—21no—
495C2×C3⋊D3—21no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—21no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—21no—
506C2×C3×D3—22no—
507C2×C3×D3—24no—
508C2×C3×D3—42no—
509C2×C3×D3—42no—
510C2×C3×D3—48no—
511C2×C3×D3—48no—
512C2×C3×D3—416no—
513C2×C3×D3—62no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—61no—
519C2×C3×D3—61no—
520C2×C3×D3—121no—
521C2×C3×D3—121no—
522C2×C3×D3#23712yescomplemented
523C2×C3×D3C2×#6714yes—
524C2×C3×D3C2×C3×D414yes—
525C2×C3×D3C3×#4112yescomplemented
526C32×C4—22no—
527C32×C4—22no—
528C32×C4—22no—
529C32×C4—42no—
530C32×C4—61no—
531C32×C4—61no—
532C32×C4—61no—
533C32×C4—62no—
534C32×C4D3×D412yes—
535C32×C4C2×#6712yes—
536C32×C4C2×C3×D412yes—
537C3⋊Dic3—21no—
538C3⋊Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—22no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C3×Dic3—42no—
549C3×Dic3—41no—
550C3×Dic3—41no—
551C3×Dic3—61no—
552C3×Dic3—62no—
553C3×Dic3—62no—
554C3×Dic3—61no—
555C3×Dic3—121no—
556C3×Dic3—122no—
557C2×#41—91no—
558C22×D4—31no—
559#124—31no—
560#123—92no—
561C22⋊Q8—91no—
562#121—92no—
563#121—91no—
564#120—92no—
565C4×D4—91no—
566C4×D4—91no—
567C2×C22⋊C4—92no—
568C33#54611yescharacteristic, complemented, Sylow
569C23×C3—22no—
570C23×C3—22no—
571C23×C3—22no—
572C23×C3—31no—
573C23×C3—32no—
574C23×C3—31no—
575C23×C3—32no—
576C23×C3—42no—
577C23×C3—61no—
578C23×C3—62no—
579C23×C3—64no—
580C23×C3—64no—
581C23×C3—64no—
582C23×C3—64no—
583C23×C3—68no—
584C23×C3—91no—
585C23×C3—124no—
586C23×C3—122no—
587C23×C3—122no—
588C23×C3—124no—
589C23×C3C2×D3212yes—
590C23×C3C22×C3×D312yes—
591C23×C3C22×C3×D312yes—
592C22×D3—24no—
593C22×D3—24no—
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—42no—
597C22×D3—61no—
598C22×D3C22×C3×D311yescharacteristic
599C22×D3C22×C3×D312yes—
600C3×Q8—62no—
601C3×Q8—62no—
602C3×Q8—122no—
603C3×D4—24no—
604C3×D4—22no—
605C3×D4—22no—
606C3×D4—22no—
607C3×D4—34no—
608C3×D4—34no—
609C3×D4—42no—
610C3×D4—42no—
611C3×D4—44no—
612C3×D4—64no—
613C3×D4—64no—
614C3×D4—64no—
615C3×D4—68no—
616C3×D4—182no—
617C3×D4—184no—
618C3×D4—362no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—31no—
623C2×C3×C4—31no—
624C2×C3×C4—32no—
625C2×C3×C4—31no—
626C2×C3×C4—31no—
627C2×C3×C4—32no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—41no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—62no—
635C2×C3×C4—64no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—92no—
639C2×C3×C4—91no—
640C2×C3×C4—184no—
641C2×C3×C4—182no—
642C2×C3×C4—362no—
643C2×C3×C4C2×D3211yescharacteristic
644C2×C3×C4C22×C3×D311yescharacteristic
645C2×C3×C4C22×C3×D311yescharacteristic
646#67—24no—
647#67—64no—
648#67—62no—
649#67—122no—
650#67—122no—
651#67—124no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—62no—
657C2×Dic3—61no—
658C2×Dic3—64no—
659C2×Dic3—122no—
660C2×Dic3C22×C3×D311yescharacteristic
661C2×Dic3C22×C3×D311yescharacteristic
662C2×Dic3C22×C3×D311yescharacteristic
663C2×Dic3C22×C3×D312yes—
664D12—62no—
665D12—64no—
666D12C3×#6714yescomplemented
667C4×D3—22no—
668C4×D3—64no—
669C4×D3—62no—
670C4×D3—62no—
671C4×D3—122no—
672C4×D3—122no—
673Dic6—22no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—41no—
684C2×C32—41no—
685C2×C32—41no—
686C2×C32—42no—
687C2×C32—44no—
688C2×C32—42no—
689C2×C32—42no—
690C2×C32—62no—
691C2×C32—64no—
692C2×C32—82no—
693C2×C32—82no—
694C2×C32—84no—
695C2×C32C2×D3×D411yescharacteristic
696C2×C32C2×#23711yescharacteristic
697C2×C32#100411yescharacteristic
698C2×C32D3×#4111yescharacteristic
699C2×C32#100911yescharacteristic
700C2×C32C22×#6711yescharacteristic
701C2×C32C22×C3×D411yescharacteristic
702C2×C32C2×C3×#4111yescharacteristic
703C2×C32C3×H(5,𝔽2)11yescharacteristic
704C3⋊D3—41no—
705C3×D3—24no—
706C3×D3—22no—
707C3×D3—24no—
708C3×D3—22no—
709C3×D3—24no—
710C3×D3—44no—
711C3×D3—122no—
712C3×D3—121no—
713C3×D3—121no—
714C24—32no—
715#41—184no—
716C2×Q8—31no—
717C2×D4—32no—
718C2×D4—31no—
719C2×D4—64no—
720C2×D4—91no—
721C2×D4—92no—
722C2×D4—92no—
723C2×D4C3×D3211yescharacteristic
724C22×C4—31no—
725C22×C4—92no—
726C22×C4—92no—
727C22×C4—91no—
728C4⋊C4—91no—
729C4⋊C4—92no—
730C4⋊C4—91no—
731C22⋊C4—32no—
732C22⋊C4—32no—
733C22⋊C4—91no—
734C22⋊C4—91no—
735C22⋊C4—92no—
736C22⋊C4—92no—
737C22⋊C4—92no—
738C42—31no—
739C22×C3—24no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—32no—
753C22×C3—34no—
754C22×C3—34no—
755C22×C3—32no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—44no—
765C22×C3—41no—
766C22×C3—62no—
767C22×C3—64no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—61no—
773C22×C3—61no—
774C22×C3—61no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—61no—
778C22×C3—82no—
779C22×C3—82no—
780C22×C3—122no—
781C22×C3—122no—
782C22×C3—128no—
783C22×C3—128no—
784C22×C3—1216no—
785C22×C3—181no—
786C22×C3—181no—
787C22×C3—181no—
788C22×C3C22×D3211yescharacteristic
789C22×C3C23×C3×D311yescharacteristic
790C22×C3C23×C3×D311yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—21no—
794C2×D3—21no—
795C2×D3—48no—
796C2×D3—62no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—61no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3C3×#23712yescomplemented
806C2×D3C2×C3×#6714yes—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—42no—
811C3×C4—62no—
812C3×C4—61no—
813C3×C4—61no—
814C3×C4—61no—
815C3×C4—62no—
816C3×C4—61no—
817C3×C4—61no—
818C3×C4—61no—
819C3×C4—62no—
820C3×C4—122no—
821C3×C4—121no—
822C3×C4—121no—
823C3×C4—182no—
824C3×C4—181no—
825C3×C4D3×#6712yes—
826C3×C4C3×D3×D412yes—
827C3×C4C2×C3×#6712yes—
828Dic3—22no—
829Dic3—21no—
830Dic3—21no—
831Dic3—21no—
832Dic3—61no—
833Dic3—62no—
834Dic3—62no—
835Dic3—61no—
836Dic3—121no—
837Dic3—122no—
838C32—21no—
839C32—21no—
840C32—21no—
841C32—41no—
842C32#567611yescharacteristic, complemented
843C32#580611yescharacteristic, complemented
844C32C3×#54611yescharacteristic, complemented
845C23—31no—
846C23—32no—
847C23—64no—
848C23—64no—
849C23—91no—
850C23—122no—
851C23C2×C3×D3212yes—
852Q8—62no—
853D4—22no—
854D4—34no—
855D4—64no—
856D4—184no—
857D4—182no—
858D4—362no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—32no—
862C2×C4—31no—
863C2×C4—62no—
864C2×C4—92no—
865C2×C4—91no—
866C2×C4—184no—
867C2×C4—182no—
868C2×C4—362no—
869C2×C4C2×C3×D3211yescharacteristic
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—44no—
880C2×C3—42no—
881C2×C3—42no—
882C2×C3—42no—
883C2×C3—41no—
884C2×C3—41no—
885C2×C3—41no—
886C2×C3—64no—
887C2×C3—62no—
888C2×C3—64no—
889C2×C3—62no—
890C2×C3—64no—
891C2×C3—82no—
892C2×C3—82no—
893C2×C3—84no—
894C2×C3—124no—
895C2×C3—361no—
896C2×C3D3×#23711yescharacteristic
897C2×C3#6431411yescharacteristic
898C2×C3C2×D3×#6711yescharacteristic
899C2×C3C2×C3×D3×D411yescharacteristic
900C2×C3C2×C3×#23711yescharacteristic
901C2×C3C3×#100411yescharacteristic
902C2×C3C3×D3×#4111yescharacteristic
903C2×C3C3×#100911yescharacteristic
904C2×C3C22×C3×#6711yescharacteristic
905D3—22no—
906D3—24no—
907D3—122no—
908D3—121no—
909D3—121no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—34no—
914C22—32no—
915C22—61no—
916C22—62no—
917C22—62no—
918C22—61no—
919C22—128no—
920C22—181no—
921C22—181no—
922C22—181no—
923C22C22×C3×D3211yescharacteristic
924C4—61no—
925C4—62no—
926C4—61no—
927C4—61no—
928C4—181no—
929C4—182no—
930C4C3×D3×#6712yes—
931C3—21no—
932C3—21no—
933C3—21no—
934C3—41no—
935C3#1059522911yescharacteristic, direct product factor
936C3C3×#567611yescharacteristic, complemented
937C3C3×#580611yescharacteristic, complemented
938C2—42no—
939C2—62no—
940C2—64no—
941C2—361no—
942C2C3×D3×#23711yescharacteristic
943C2C3×#6431411yescharacteristic
944C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C2×C3×#3796C2semidirect
3. C3×#64147C2semidirect
4. C32×#936C2semidirect
5. C3×#63977C2semidirect
6. C3×#63971C2semidirect
7. C3×#63969C2semidirect
8. C3×D3×#217C2semidirect
9. C3×C4×#626C2semidirect
10. C3×Dic3×D12C2semidirect
11. C3×#63856C2semidirect
14. #10595229C3direct (N × H)
17. C2×C3×#638C22semidirect
18. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C32×Dic6C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×#3757C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C32×#217C22semidirect
32. C32×#217C22semidirect
33. C32×C4×Dic3C22semidirect
34. C3×#3724C22semidirect
35. C3×Dic3⋊Dic3C22semidirect
36. C3×#3722C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×C3×D3×D4D3semidirect
45. C2×C3×D3×D4C2×C3semidirect
46. C2×#3796C2×C3semidirect
48. #64147C2×C3semidirect
57. C3×#936D3semidirect
58. C3×#936C2×C3semidirect
69. #63977C2×C3semidirect
70. #63971C2×C3semidirect
71. #63969C2×C3semidirect
72. D3×#217C2×C3semidirect
73. C4×#626C2×C3semidirect
74. Dic3×D12C2×C3semidirect
75. #63856C2×C3semidirect
94. C32×D12D4semidirect
120. C2×#638C22×C3semidirect
121. C2×C4×C3⋊D3C22×C3semidirect
151. C2×C3×Dic6C2×D3semidirect
152. C2×C3×Dic6C22×C3semidirect
154. C2×#626C22×C3semidirect
155. C2×D3×Dic3C22×C3semidirect
156. C2×D3×Dic3C22×C3semidirect
161. #3757C22×C3semidirect
162. C4⋊(C3⋊Dic3)C22×C3semidirect
171. C3×#217C2×D3semidirect
172. C3×#217C2×D3semidirect
173. C3×#217C22×C3semidirect
174. C3×#217C22×C3semidirect
188. C3×C4×Dic3C2×D3semidirect
189. C3×C4×Dic3C22×C3semidirect
190. #3724C22×C3semidirect
191. Dic3⋊Dic3C22×C3semidirect
192. #3722C22×C3semidirect
195. (C2×D3)⋊Dic3C22×C3semidirect
209. C2×C32×D3#41semidirect
223. C2×D3×D4C3×D3semidirect
242. #936C3×D3semidirect
341. C3×D12#67semidirect
342. C3×D12C3×D4semidirect
419. C2×Dic6C2×C3×D3semidirect
443. #217C2×C3×D3semidirect
444. #217C2×C3×D3semidirect
457. C4×Dic3C2×C3×D3semidirect
522. C2×C3×D3#237semidirect
525. C2×C3×D3C3×#41semidirect
568. C33#546semidirect
666. D12C3×#67semidirect
805. C2×D3C3×#237semidirect
842. C32#5676semidirect
843. C32#5806semidirect
844. C32C3×#546semidirect
935. C3#10595229direct (N × H)
936. C3C3×#5676semidirect
937. C3C3×#5806semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C2×C3×#37962
C3×#641472
C32×#9362
C3×#639772
C3×#639712
C3×#639692
C3×D3×#2172
C3×C4×#6262
C3×Dic3×D122
C3×#638562
C3×#58063
C3×#56763
#105952293