Finite Group Databasebeta

← #13168080

Subgroups — #13168080

Order 1728.

1742 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89015C211yesmaximal, characteristic, complemented
2C2×C3×D3×D12C211yesmaximal, characteristic, complemented
3#11723677C211yesmaximal, characteristic, complemented
4#11723532C211yesmaximal, characteristic, complemented
5C4×#6291C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63857C211yesmaximal, characteristic, complemented
8#11722990C212yesmaximal, complemented
9#11722959C212yesmaximal, complemented
10#11722948C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595246—31nomaximal
13#10594889—31nomaximal
14#10594629—31nomaximal
15C22×C3×D32C2212yes—
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×#634C2211yescharacteristic, complemented
19C2×C32×D12C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6292C2212yescomplemented
22C2×#6291C2211yescharacteristic
23C2×#6291C2212yescomplemented
24C2×D3×C3⋊Dic3C2212yescomplemented
25#89015—24no—
26C2×C3×#626C2212yes—
27C2×C3×D3×Dic3C2212yescomplemented
28C3×D3×D12—24no—
29C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C32×C4⋊Dic3C2211yescharacteristic, complemented
31#88814C2212yescomplemented
32#88814C2212yescomplemented
33#88807C2211yescharacteristic, complemented
34#88804C2211yescharacteristic, complemented
35#88803C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
37C3×Dic3⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yes—
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×#3830—31no—
41C2×C3×D3×D4—31no—
42C22×C3×D12—31no—
43C2×D3×D12D311yescharacteristic, complemented
44C2×#3796—31no—
45C2×#3796—31no—
46C2×#3796—61no—
47C4×#638—31no—
48#64104—31no—
49C3×D4×Dic3—31no—
50C3×#924—31no—
51C3×#897—31no—
52C3×#893—31no—
53#63978—32no—
54#63977—32no—
55#63977—32no—
56D3×#217—32no—
57#63962—32no—
58C2×(C2×D3)⋊Dic3—32no—
59#63923—32no—
60D3×(C2×D3)⋊C4—32no—
61#63916—31no—
62#63916—31no—
63#63916—61no—
64#63909—32no—
65C4×#626—31no—
66C4×#626—31no—
67C4×#626—61no—
68#63898D311yescharacteristic, complemented
69#63890—32no—
70#63886—32no—
71#63884—32no—
72#63864—31no—
73#63863—31no—
74#63860—31no—
75#63857D311yescharacteristic, complemented
76C22×C3⋊(C3⋊D3)C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
85C4×C3⋊(C3⋊D3)—22no—
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2312yes—
89C3×C4⋊(C3⋊D3)—22no—
90C3×#634—22no—
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2311yescharacteristic
93C32×D12D414yescomplemented
94C32×C4×D3—22no—
95#6292—42no—
96#6291—24no—
97#6291—22no—
98D3×C3⋊Dic3—24no—
99C3×#626—24no—
100C3×D3×Dic3—42no—
101#5806—91no—
102#5630—91no—
103#5554—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×D4—31no—
108C22×C32×C4—31no—
109C2×#638—32no—
110C2×#638—31no—
111C22×C3⋊Dic3—32no—
112#3830—64no—
113C2×C4⋊(C3⋊D3)—32no—
114C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—61no—
119C2×C4×C3⋊D3—61no—
120C2×C4×C3⋊D3—61no—
121C2×C4×C3⋊D3—121no—
122C2×#634C2×D311yescharacteristic, complemented
123C2×C3×#67—32no—
124C22×C3×Dic3—32no—
125C3×D3×D4—64no—
126C2×C3×D12—21no—
127C2×C3×D12—32no—
128C2×C3×D12—31no—
129C2×C3×D12—31no—
130C2×C3×D12—64no—
131C2×C3×D12—61no—
132C2×C3×D12C2×D311yescharacteristic
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×C3×C4×D3C2×D311yescharacteristic
138C2×C3×Dic6—31no—
139C2×C3×Dic6—31no—
140C2×C3×Dic6—61no—
141C2×#626—32no—
142C2×#626—32no—
143C2×#626—31no—
144C2×#626—31no—
145C2×#626—32no—
146C2×#626—32no—
147C2×#626—62no—
148C2×#626—61no—
149C2×#626—62no—
150C2×#626C2×D312yes—
151C2×D3×Dic3—32no—
152C2×D3×Dic3—32no—
153C2×D3×Dic3—62no—
154C2×D3×Dic3C2×D312yescomplemented
155D3×D12—24no—
156#3796—68no—
157#3796—64no—
158#3796—64no—
159C32×C4⋊C4—31no—
160#3757—31no—
161#3752—32no—
162#3752—31no—
163#3750—31no—
164C4×C3⋊Dic3C2×D311yescharacteristic, complemented
165C3×#217—32no—
166C3×#217—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4⋊Dic3—21no—
170C3×C4⋊Dic3—32no—
171C3×C4⋊Dic3C2×D311yescharacteristic, complemented
172C3×C4⋊Dic3C2×D311yescharacteristic, complemented
173C3×Dic3⋊C4—32no—
174C3×C4×Dic3—31no—
175C3×C4×Dic3—31no—
176C3×C4×Dic3—61no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179Dic3⋊Dic3—61no—
180Dic3⋊Dic3C2×D312yescomplemented
181#3722—32no—
182#3722—32no—
183#3722—31no—
184#3722—31no—
185#3722—61no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3—62no—
195(C2×D3)⋊Dic3—61no—
196(C2×D3)⋊Dic3C2×D312yes—
197(C2×D3)⋊Dic3C2×D312yescomplemented
198C22×C33C2411yescharacteristic
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3—22no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—22no—
208C2×C32×D3—21no—
209C2×C32×D3C2×D414yes—
210C2×C32×D3#4112yescomplemented
211C3×D32—48no—
212C33×C4C2×D412yes—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—22no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C32×Dic3—21no—
218C32×Dic3—22no—
219C22×C3×D4—91no—
220C2×#239—91no—
221C2×#237—91no—
222C2×#237—91no—
223C2×#237—181no—
224C2×D3×D4—31no—
225C22×D12—31no—
226C3×C22⋊Q8—91no—
227C3×C4×D4—91no—
228#953—92no—
229C2×#217—92no—
230#947—91no—
231#939—92no—
232#938—91no—
233#936—91no—
234#935—92no—
235D4×Dic3—31no—
236#930—92no—
237C4×#67—91no—
238C4×#67—91no—
239C4×#67—181no—
240C2×(C2×D3)⋊C4—92no—
241#924—31no—
242#897—31no—
243#895—91no—
244#895—91no—
245#895—92no—
246#895—181no—
247#894—92no—
248#893—31no—
249#886—92no—
250#882—92no—
251#882—92no—
252D3×C22⋊C4—92no—
253#875—91no—
254C4×D12—91no—
255C23×C32—31no—
256C23×C32—32no—
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—61no—
261C22×C3⋊D3—61no—
262C22×C3⋊D3—61no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D312yes—
265C22×C3×D3—21no—
266C22×C3×D3—22no—
267C22×C3×D3—32no—
268C22×C3×D3—32no—
269C22×C3×D3—62no—
270C22×C3×D3—64no—
271C22×C3×D3—64no—
272C22×C3×D3—64no—
273C22×C3×D3—64no—
274C22×C3×D3—122no—
275C22×C3×D3—122no—
276C22×C3×D3C22×D312yes—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
279C22×C3×D3C22×D312yes—
280C2×D32—24no—
281C2×D32—24no—
282C2×D32—42no—
283C32×D4—34no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—31no—
288C2×C32×C4—32no—
289C2×C32×C4—41no—
290C2×C32×C4—62no—
291C2×C32×C4C22×D311yescharacteristic
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294#638—64no—
295#638—62no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—31no—
299C2×C3⋊Dic3—61no—
300C2×C3⋊Dic3—61no—
301C2×C3⋊Dic3—61no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3—121no—
304C2×C3⋊Dic3C22×D312yes—
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C4⋊(C3⋊D3)—22no—
308C4⋊(C3⋊D3)—122no—
309C4×C3⋊D3—62no—
310C4×C3⋊D3—64no—
311C4×C3⋊D3—62no—
312C4×C3⋊D3—62no—
313C4×C3⋊D3—122no—
314C4×C3⋊D3—122no—
315C4×C3⋊D3—124no—
316#634—22no—
317C3×#67—64no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—32no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—32no—
326C2×C3×Dic3—61no—
327C2×C3×Dic3—62no—
328C2×C3×Dic3—61no—
329C2×C3×Dic3—122no—
330C2×C3×Dic3C22×D312yes—
331C2×C3×Dic3C22×D312yes—
332C2×C3×Dic3C22×D311yescharacteristic
333C2×C3×Dic3C22×D311yescharacteristic
334C3×D12—24no—
335C3×D12—64no—
336C3×D12—62no—
337C3×D12—62no—
338C3×D12—122no—
339C3×D12D1214yescomplemented
340C3×D12#6714yescomplemented
341C3×C4×D3—22no—
342C3×C4×D3—22no—
343C3×C4×D3—42no—
344C3×C4×D3—122no—
345C3×Dic6—64no—
346C3×Dic6—62no—
347C3×Dic6—62no—
348#626—24no—
349#626—68no—
350#626—64no—
351#626—64no—
352#626—62no—
353#626—62no—
354#626—64no—
355#626—122no—
356#626—122no—
357#626—124no—
358D3×Dic3—42no—
359D3×Dic3—68no—
360D3×Dic3—64no—
361D3×Dic3—64no—
362#546—271noSylow
363C2×C33C22×D411yescharacteristic
364C2×C33C2×#4111yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C3⋊(C3⋊D3)—41no—
367C3×C3⋊D3—42no—
368C32×D3—22no—
369C32×D3—24no—
370C24×C3—92no—
371C23×D3—32no—
372C23×D3—32no—
373C2×C3×Q8—91no—
374C2×C3×D4—31no—
375C2×C3×D4—31no—
376C2×C3×D4—61no—
377C2×C3×D4—92no—
378C2×C3×D4—91no—
379C2×C3×D4—184no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—61no—
383C22×C3×C4—92no—
384C2×#67—32no—
385C2×#67—91no—
386C2×#67—92no—
387C2×#67—91no—
388C2×#67—92no—
389C2×#67—92no—
390C2×#67—181no—
391C2×#67—182no—
392C22×Dic3—32no—
393C22×Dic3—92no—
394C22×Dic3—92no—
395C22×Dic3—182no—
396#239—184no—
397#237—184no—
398#237—184no—
399#237—188no—
400D3×D4—64no—
401C2×D12—32no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—61no—
405C2×D12—64no—
406C2×D12—91no—
407C2×D12—92no—
408C2×D12—92no—
409C2×D12—92no—
410C2×D12—182no—
411C2×D12D3211yescharacteristic
412C2×C4×D3—32no—
413C2×C4×D3—92no—
414C2×C4×D3—91no—
415C2×C4×D3—91no—
416C2×C4×D3—91no—
417C2×C4×D3—181no—
418C2×C4×D3—181no—
419C2×C4×D3—181no—
420C2×C4×D3—361no—
421C2×C4×D3D3211yescharacteristic
422C2×Dic6—31no—
423C2×Dic6—31no—
424C2×Dic6—61no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—61no—
428C3×C4⋊C4—92no—
429C3×C22⋊C4—92no—
430C3×C22⋊C4—92no—
431C3×C42—91no—
432#217—32no—
433#217—32no—
434#217—92no—
435#217—92no—
436#217—91no—
437#217—91no—
438#217—92no—
439#217—181no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4—32no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—92no—
445(C2×D3)⋊C4—92no—
446(C2×D3)⋊C4—92no—
447(C2×D3)⋊C4—92no—
448(C2×D3)⋊C4—92no—
449(C2×D3)⋊C4—92no—
450(C2×D3)⋊C4—91no—
451(C2×D3)⋊C4—91no—
452(C2×D3)⋊C4—181no—
453(C2×D3)⋊C4—182no—
454C4⋊Dic3—32no—
455C4⋊Dic3—91no—
456C4⋊Dic3D3211yescharacteristic, complemented
457Dic3⋊C4—32no—
458Dic3⋊C4—91no—
459Dic3⋊C4—91no—
460Dic3⋊C4—181no—
461C4×Dic3—31no—
462C4×Dic3—31no—
463C4×Dic3—61no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32—21no—
467C22×C32—34no—
468C22×C32—32no—
469C22×C32—41no—
470C22×C32—61no—
471C22×C32—61no—
472C22×C32—62no—
473C22×C32—62no—
474C22×C32C23×D311yescharacteristic
475C22×C32C23×D311yescharacteristic
476C22×C32C23×D311yescharacteristic
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—61no—
483C2×C3⋊D3—62no—
484C2×C3⋊D3—62no—
485C2×C3⋊D3—62no—
486C2×C3⋊D3—61no—
487C2×C3⋊D3—61no—
488C2×C3⋊D3—61no—
489C2×C3⋊D3—61no—
490C2×C3⋊D3—61no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—121no—
493C2×C3⋊D3—121no—
494C2×C3⋊D3—121no—
495C2×C3⋊D3—121no—
496C2×C3⋊D3—121no—
497C2×C3⋊D3—121no—
498C2×C3⋊D3—122no—
499C2×C3⋊D3—122no—
500C2×C3⋊D3—122no—
501C2×C3×D3—21no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—21no—
506C2×C3×D3—22no—
507C2×C3×D3—21no—
508C2×C3×D3—21no—
509C2×C3×D3—22no—
510C2×C3×D3—24no—
511C2×C3×D3—41no—
512C2×C3×D3—41no—
513C2×C3×D3—42no—
514C2×C3×D3—42no—
515C2×C3×D3—62no—
516C2×C3×D3—62no—
517C2×C3×D3—62no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—122no—
522C2×C3×D3—122no—
523C2×C3×D3—122no—
524C2×C3×D3—128no—
525C2×C3×D3—128no—
526C2×C3×D3C2×D1214yes—
527C2×C3×D3#23712yescomplemented
528C2×C3×D3#23912yescomplemented
529C2×C3×D3C2×#6714yes—
530D32—48no—
531C32×C4—22no—
532C32×C4—22no—
533C32×C4—22no—
534C32×C4—42no—
535C32×C4—61no—
536C32×C4—62no—
537C32×C4C2×D1212yes—
538C32×C4D3×D412yes—
539C32×C4C2×#6712yes—
540C3⋊Dic3—22no—
541C3⋊Dic3—21no—
542C3⋊Dic3—21no—
543C3⋊Dic3—61no—
544C3⋊Dic3—62no—
545C3⋊Dic3—61no—
546C3⋊Dic3—61no—
547C3⋊Dic3—121no—
548C3⋊Dic3—121no—
549C3⋊Dic3—122no—
550C3×Dic3—21no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—21no—
554C3×Dic3—42no—
555C3×Dic3—41no—
556C3×Dic3—64no—
557C3×Dic3—62no—
558C3×Dic3—62no—
559C3×Dic3—61no—
560C3×Dic3—61no—
561C3×Dic3—61no—
562C3×Dic3—61no—
563C3×Dic3—62no—
564C3×Dic3—121no—
565C2×#41—271no—
566C22×D4—91no—
567#124—271no—
568#123—272no—
569C22⋊Q8—91no—
570#121—271no—
571#121—272no—
572#120—272no—
573C4×D4—91no—
574C4×D4—271no—
575C2×C22⋊C4—272no—
576C33#54611yescharacteristic, complemented, Sylow
577C23×C3—31no—
578C23×C3—32no—
579C23×C3—31no—
580C23×C3—32no—
581C23×C3—61no—
582C23×C3—62no—
583C23×C3—92no—
584C23×C3—184no—
585C23×C3—184no—
586C23×C3—362no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—62no—
590C22×D3—64no—
591C22×D3—64no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—91no—
595C22×D3—91no—
596C22×D3—91no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—181no—
600C22×D3—181no—
601C22×D3—181no—
602C22×D3—361no—
603C22×D3C2×D3211yescharacteristic
604C22×D3C2×D3212yes—
605C3×Q8—182no—
606C3×D4—34no—
607C3×D4—34no—
608C3×D4—64no—
609C3×D4—184no—
610C3×D4—182no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—31no—
615C2×C3×C4—31no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—41no—
619C2×C3×C4—61no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—91no—
624C2×C3×C4—91no—
625C2×C3×C4—92no—
626C2×C3×C4—122no—
627C2×C3×C4—362no—
628C2×C3×C4C2×D3211yescharacteristic
629C2×C3×C4C2×D3211yescharacteristic
630C2×C3×C4C2×D3211yescharacteristic
631#67—64no—
632#67—184no—
633#67—184no—
634#67—182no—
635#67—182no—
636#67—188no—
637#67—184no—
638#67—362no—
639C2×Dic3—31no—
640C2×Dic3—31no—
641C2×Dic3—31no—
642C2×Dic3—31no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—61no—
646C2×Dic3—62no—
647C2×Dic3—61no—
648C2×Dic3—91no—
649C2×Dic3—91no—
650C2×Dic3—91no—
651C2×Dic3—122no—
652C2×Dic3—181no—
653C2×Dic3—181no—
654C2×Dic3—181no—
655C2×Dic3—184no—
656C2×Dic3—184no—
657C2×Dic3—188no—
658C2×Dic3—361no—
659C2×Dic3C2×D3212yes—
660C2×Dic3C2×D3211yescharacteristic
661D12—64no—
662D12—62no—
663D12—62no—
664D12—122no—
665D12—182no—
666D12—184no—
667D12—362no—
668D12—362no—
669D12—364no—
670D12#62614yescomplemented
671C4×D3—22no—
672C4×D3—122no—
673C4×D3—184no—
674C4×D3—184no—
675C4×D3—182no—
676C4×D3—182no—
677C4×D3—182no—
678C4×D3—362no—
679C4×D3—362no—
680C4×D3—364no—
681Dic6—64no—
682Dic6—62no—
683Dic6—62no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—41no—
694C2×C32—41no—
695C2×C32—41no—
696C2×C32—62no—
697C2×C32—64no—
698C2×C32C22×D1211yescharacteristic
699C2×C32C2×D3×D411yescharacteristic
700C2×C32C2×#23711yescharacteristic
701C2×C32#100411yescharacteristic
702C2×C32#100411yescharacteristic
703C2×C32C2×#23911yescharacteristic
704C2×C32D3×#4111yescharacteristic
705C2×C32#100911yescharacteristic
706C2×C32C22×#6711yescharacteristic
707C3⋊D3—42no—
708C3⋊D3—122no—
709C3⋊D3—122no—
710C3⋊D3—122no—
711C3⋊D3—124no—
712C3⋊D3—121no—
713C3⋊D3—121no—
714C3⋊D3—121no—
715C3×D3—22no—
716C3×D3—24no—
717C3×D3—24no—
718C3×D3—22no—
719C3×D3—42no—
720C3×D3—44no—
721C3×D3—122no—
722C3×D3—122no—
723C3×D3—242no—
724C24—92no—
725#41—544no—
726C2×Q8—91no—
727C2×D4—31no—
728C2×D4—92no—
729C2×D4—91no—
730C2×D4—184no—
731C2×D4—272no—
732C2×D4—271no—
733C2×D4—272no—
734C22×C4—31no—
735C22×C4—92no—
736C22×C4—272no—
737C22×C4—271no—
738C4⋊C4—31no—
739C4⋊C4—92no—
740C4⋊C4—271no—
741C22⋊C4—92no—
742C22⋊C4—92no—
743C22⋊C4—271no—
744C22⋊C4—272no—
745C22⋊C4—272no—
746C22⋊C4—272no—
747C22⋊C4—271no—
748C42—91no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—34no—
753C22×C3—32no—
754C22×C3—32no—
755C22×C3—34no—
756C22×C3—41no—
757C22×C3—64no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—61no—
761C22×C3—62no—
762C22×C3—61no—
763C22×C3—62no—
764C22×C3—61no—
765C22×C3—62no—
766C22×C3—61no—
767C22×C3—121no—
768C22×C3—122no—
769C22×C3—122no—
770C22×C3—121no—
771C22×C3—182no—
772C22×C3—182no—
773C22×C3—182no—
774C22×C3—368no—
775C22×C3C22×D3211yescharacteristic
776C22×C3C22×D3211yescharacteristic
777C22×C3C22×D3211yescharacteristic
778C2×D3—21no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—21no—
782C2×D3—62no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—122no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—128no—
792C2×D3—128no—
793C2×D3—182no—
794C2×D3—182no—
795C2×D3—182no—
796C2×D3—181no—
797C2×D3—181no—
798C2×D3—181no—
799C2×D3—181no—
800C2×D3—181no—
801C2×D3—181no—
802C2×D3—181no—
803C2×D3—181no—
804C2×D3—181no—
805C2×D3—361no—
806C2×D3—361no—
807C2×D3—361no—
808C2×D3—361no—
809C2×D3—361no—
810C2×D3—361no—
811C2×D3—362no—
812C2×D3—362no—
813C2×D3—362no—
814C2×D3#379612yescomplemented
815C2×D3C2×#62614yes—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—42no—
820C3×C4—61no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—61no—
824C3×C4—122no—
825C3×C4—121no—
826C3×C4—181no—
827C3×C4—181no—
828C3×C4—182no—
829C3×C4D3×D1212yes—
830C3×C4C2×#62612yes—
831C3×C4D3×#6712yes—
832Dic3—22no—
833Dic3—21no—
834Dic3—64no—
835Dic3—62no—
836Dic3—62no—
837Dic3—61no—
838Dic3—61no—
839Dic3—61no—
840Dic3—61no—
841Dic3—62no—
842Dic3—121no—
843Dic3—182no—
844Dic3—181no—
845Dic3—181no—
846Dic3—181no—
847Dic3—361no—
848Dic3—361no—
849Dic3—362no—
850C32—21no—
851C32—21no—
852C32—21no—
853C32—41no—
854C32#555411yescharacteristic, complemented
855C32#563011yescharacteristic, complemented
856C32#580611yescharacteristic, complemented
857C23—31no—
858C23—32no—
859C23—92no—
860C23—184no—
861C23—184no—
862C23—271no—
863C23—362no—
864Q8—182no—
865D4—34no—
866D4—184no—
867D4—182no—
868D4—544no—
869D4—542no—
870D4—1082no—
871C2×C4—32no—
872C2×C4—31no—
873C2×C4—62no—
874C2×C4—91no—
875C2×C4—91no—
876C2×C4—92no—
877C2×C4—271no—
878C2×C4—362no—
879C2×C4—544no—
880C2×C4—542no—
881C2×C4D3311yescharacteristic
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—41no—
892C2×C3—41no—
893C2×C3—41no—
894C2×C3—62no—
895C2×C3—64no—
896C2×C3—64no—
897C2×C3—62no—
898C2×C3—122no—
899C2×C3—124no—
900C2×C3—362no—
901C2×C3C2×#379611yescharacteristic
902C2×C3C2×D3×D1211yescharacteristic
903C2×C3#6430711yescharacteristic
904C2×C3D3×#23711yescharacteristic
905C2×C3#6431311yescharacteristic
906C2×C3#6431411yescharacteristic
907C2×C3D3×#23911yescharacteristic
908C2×C3C22×#62611yescharacteristic
909C2×C3C2×D3×#6711yescharacteristic
910D3—22no—
911D3—24no—
912D3—122no—
913D3—122no—
914D3—242no—
915D3—362no—
916D3—362no—
917D3—362no—
918D3—364no—
919D3—361no—
920D3—361no—
921D3—361no—
922C22—32no—
923C22—34no—
924C22—62no—
925C22—62no—
926C22—61no—
927C22—61no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—368no—
932C22—541no—
933C22—541no—
934C22—541no—
935C22C2×D3311yescharacteristic
936C4—62no—
937C4—61no—
938C4—181no—
939C4—181no—
940C4—182no—
941C4—541no—
942C4D3×#62612yes—
943C3—21no—
944C3—21no—
945C3—21no—
946C3—41no—
947C3#1059462911yescharacteristic, complemented
948C3#1059488911yescharacteristic, complemented
949C3#1059524611yescharacteristic, complemented
950C2—62no—
951C2—64no—
952C2—362no—
953C2—1081no—
954C2D3×#379611yescharacteristic
955C2#1172438111yescharacteristic
956C2C2×D3×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#89015C2semidirect
2. C2×C3×D3×D12C2semidirect
3. #11723677C2semidirect
4. #11723532C2semidirect
5. C4×#6291C2semidirect
6. C3×#63898C2semidirect
7. C3×#63857C2semidirect
8. #11722990C2semidirect
9. #11722959C2semidirect
10. #11722948C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
16. C2×C4×C3⋊(C3⋊D3)C22semidirect
18. C2×C3×#634C22semidirect
21. C2×#6292C22semidirect
23. C2×#6291C22semidirect
24. C2×D3×C3⋊Dic3C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×C4×C3⋊Dic3C22semidirect
30. C32×C4⋊Dic3C22semidirect
31. #88814C22semidirect
32. #88814C22semidirect
33. #88807C22semidirect
34. #88804C22semidirect
35. #88803C22semidirect
37. C3×Dic3⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
43. C2×D3×D12D3semidirect
68. #63898D3semidirect
75. #63857D3semidirect
93. C32×D12D4semidirect
122. C2×#634C2×D3semidirect
154. C2×D3×Dic3C2×D3semidirect
164. C4×C3⋊Dic3C2×D3semidirect
171. C3×C4⋊Dic3C2×D3semidirect
172. C3×C4⋊Dic3C2×D3semidirect
180. Dic3⋊Dic3C2×D3semidirect
197. (C2×D3)⋊Dic3C2×D3semidirect
210. C2×C32×D3#41semidirect
339. C3×D12D12semidirect
340. C3×D12#67semidirect
456. C4⋊Dic3D32semidirect
527. C2×C3×D3#237semidirect
528. C2×C3×D3#239semidirect
576. C33#546semidirect
670. D12#626semidirect
814. C2×D3#3796semidirect
854. C32#5554semidirect
855. C32#5630semidirect
856. C32#5806semidirect
947. C3#10594629semidirect
948. C3#10594889semidirect
949. C3#10595246semidirect

Maximal subgroups

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

subgroupindex
C2×#890152
C2×C3×D3×D122
#117236772
#117235322
C4×#62912
C3×#638982
C3×#638572
#117229902
#117229592
#117229482
D3×(C2×D3)⋊Dic32
#105952463
#105948893
#105946293