Finite Group Databasebeta

← #13178762

Subgroups — #13178762

Order 1728.

1688 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3832C211yesmaximal, characteristic, complemented
2C2×C4⋊#1113C211yesmaximal, characteristic, complemented
3C3×#64156C211yesmaximal, characteristic, complemented
4C3×#64155C211yesmaximal, characteristic, complemented
5#11723701C212yesmaximal, complemented
6#11723700C212yesmaximal, complemented
7#11723696C211yesmaximal, characteristic, complemented
8#11723694C212yesmaximal, complemented
9C4×#6295C211yesmaximal, characteristic, complemented
10#11723691C211yesmaximal, characteristic, complemented
11#11723687C212yesmaximal, complemented
12#10595431—31nomaximal
13#10595428—31nomaximal
14#10595427—31nomaximal
15C22×#1113C2212yes—
16C2×C33×Q8C2211yescharacteristic, complemented
17C3×#3832—24no—
18C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×C4×C3⋊D3C2212yescomplemented
24C2×#6295C2212yes—
25C2×#6295C2211yescharacteristic
26C2×#6295C2212yescomplemented
27C2×#6294C2212yescomplemented
28C4⋊#1113—24no—
29C3×#3752C2212yes—
30C3×#3752C2212yescomplemented
31C3×#3752C2212yescomplemented
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C3×#3750C2212yescomplemented
34C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic, complemented
38#88814C2212yescomplemented
39#88814C2212yescomplemented
40C2×#3832D311yescharacteristic, complemented
41C2×C3×#239—31no—
42C2×C3×#239—31no—
43C2×C3×#239—61no—
44C2×#3802—31no—
45C2×D3×D12—31no—
46C2×D3×D12—31no—
47#64156D311yescharacteristic, complemented
48#64155D311yescharacteristic, complemented
49C3×#947—31no—
50C3×#947—31no—
51C3×#947—61no—
52C3×#946—31no—
53C3×#946—31no—
54C3×#946—61no—
55#63923—32no—
56#63922—32no—
57#63922—32no—
58#63921—32no—
59D3×(C2×D3)⋊C4—32no—
60D3×(C2×D3)⋊C4—32no—
61#63916—31no—
62#63910—32no—
63#63909—31no—
64#63908—31no—
65#63905—32no—
66C4×#626—31no—
67C4×#626—31no—
68C4×#625—31no—
69#63898—31no—
70#63894—31no—
71Dic3×D12—31no—
72#63886—32no—
73#63885—32no—
74#63853—32no—
75#63850—32no—
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2312yes—
79C22×C3×C3⋊D3C2311yescharacteristic
80C2×#1113—24no—
81C2×#1113—24no—
82C2×#1113—42no—
83C33×Q8—22no—
84C2×C33×C4C2312yes—
85C2×C33×C4C2311yescharacteristic
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2312yes—
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C3×C4⋊(C3⋊D3)—24no—
92C3×C4⋊(C3⋊D3)—22no—
93C3×C4⋊(C3⋊D3)D414yescomplemented
94C3×C4×C3⋊D3—24no—
95C3×C4×C3⋊D3—22no—
96C3×C4×C3⋊D3—22no—
97#6295—24no—
98#6295—22no—
99#6295—42no—
100#6294—42no—
101#5829—91no—
102#5676—91no—
103#5630—91no—
104C22×D32—32no—
105C22×D32—32no—
106C22×D32—32no—
107C2×C32×Q8—21no—
108C2×C32×Q8—21no—
109C2×C32×Q8—21no—
110C2×C32×Q8—41no—
111C2×C32×Q8C2×D311yescharacteristic, complemented
112C2×C32×Q8C2×D311yescharacteristic, complemented
113C2×C32×Q8C2×D311yescharacteristic, complemented
114#3832—24no—
115C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
116C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
117C2×C4⋊(C3⋊D3)C2×D312yescomplemented
118C2×C4×C3⋊D3C2×D311yescharacteristic
119C2×C4×C3⋊D3C2×D312yescomplemented
120C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
121C3×#239—64no—
122C3×#239—64no—
123C3×#239—68no—
124C2×C3×D12—31no—
125C2×C3×D12—31no—
126C2×C3×D12—31no—
127C2×C3×D12—31no—
128C2×C3×D12—32no—
129C2×C3×D12—32no—
130C2×C3×D12—61no—
131C2×C3×D12—62no—
132C2×C3×D12—61no—
133C2×C3×C4×D3—31no—
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—32no—
136C2×C3×C4×D3—31no—
137C2×C3×C4×D3—31no—
138C2×C3×C4×D3—32no—
139C2×C3×C4×D3—62no—
140C2×C3×C4×D3—61no—
141C2×C3×C4×D3—61no—
142C2×#626—32no—
143C2×#626—32no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—32no—
147C2×#626—32no—
148C2×#625—32no—
149C2×#625—31no—
150C2×#625—32no—
151C2×#624—32no—
152C2×D3×Dic3—32no—
153C2×D3×Dic3—32no—
154#3802—64no—
155D3×D12—64no—
156D3×D12—64no—
157#3752C2×D312yes—
158#3752C2×D312yescomplemented
159#3752C2×D312yescomplemented
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
161#3750C2×D312yescomplemented
162C4×C3⋊Dic3C2×D311yescharacteristic, complemented
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×(C2×D3)⋊C4—62no—
170C3×(C2×D3)⋊C4—62no—
171C3×(C2×D3)⋊C4—62no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—61no—
175C3×Dic3⋊C4—32no—
176C3×Dic3⋊C4—32no—
177C3×Dic3⋊C4—62no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—61no—
181#3724—31no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184#3722—32no—
185#3722—32no—
186#3722—31no—
187#3722—31no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—32no—
196C22×C33C2411yescharacteristic
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—22no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3C2×D414yes—
208C2×C3×C3⋊D3#4112yescomplemented
209#1113—48no—
210C33×C4—22no—
211C33×C4C2×D412yes—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—22no—
217C2×C3×#41—91no—
218C2×#239—31no—
219C2×#239—31no—
220C2×#239—61no—
221C2×D3×D4—91no—
222C2×D3×D4—91no—
223C22×D12—91no—
224C3×#124—91no—
225C3×C22⋊Q8—91no—
226#947—31no—
227#947—31no—
228#947—61no—
229#946—31no—
230#946—31no—
231#946—61no—
232#939—92no—
233#938—91no—
234#937—92no—
235D4×Dic3—91no—
236#930—91no—
237#929—92no—
238C4×#67—91no—
239C4×#67—91no—
240C2×(C2×D3)⋊C4—92no—
241#895—92no—
242#895—91no—
243#894—92no—
244#893—91no—
245#884—92no—
246#883—92no—
247#882—92no—
248#882—92no—
249D3×C22⋊C4—92no—
250D3×C22⋊C4—92no—
251C4×D12—91no—
252C4×D12—91no—
253C22×C3⋊D3C22×D312yes—
254C22×C3⋊D3C22×D311yescharacteristic
255C22×C3⋊D3C22×D311yescharacteristic
256C22×C3⋊D3C22×D312yes—
257C22×C3×D3—31no—
258C22×C3×D3—31no—
259C22×C3×D3—32no—
260C22×C3×D3—32no—
261C22×C3×D3—32no—
262C22×C3×D3—32no—
263C22×C3×D3—31no—
264C22×C3×D3—31no—
265C22×C3×D3—61no—
266C22×C3×D3—62no—
267C22×C3×D3—61no—
268C22×C3×D3—62no—
269C2×D32—64no—
270C2×D32—64no—
271C2×D32—64no—
272C2×D32—64no—
273C2×D32—64no—
274C2×D32—64no—
275C2×D32—122no—
276C2×D32—122no—
277C2×D32—122no—
278C32×Q8—22no—
279C32×Q8—24no—
280C32×Q8—22no—
281C32×Q8—22no—
282C32×Q8—42no—
283C32×Q8—42no—
284C32×Q8—44no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—22no—
288C2×C32×C4—21no—
289C2×C32×C4—22no—
290C2×C32×C4—22no—
291C2×C32×C4—41no—
292C2×C32×C4—42no—
293C2×C32×C4C22×D312yes—
294C2×C32×C4C22×D312yes—
295C2×C32×C4C22×D312yes—
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D311yescharacteristic
301C2×C3⋊Dic3C22×D311yescharacteristic
302C2×C3⋊Dic3C22×D312yes—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)—24no—
305C4⋊(C3⋊D3)—22no—
306C4⋊(C3⋊D3)#6714yescomplemented
307C4×C3⋊D3—24no—
308C4×C3⋊D3—22no—
309C4×C3⋊D3—22no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—32no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—62no—
325C3×D12—34no—
326C3×D12—34no—
327C3×D12—64no—
328C3×D12—64no—
329C3×D12—64no—
330C3×D12—68no—
331C3×D12—62no—
332C3×D12—62no—
333C3×D12—122no—
334C3×C4×D3—64no—
335C3×C4×D3—64no—
336C3×C4×D3—68no—
337C3×C4×D3—64no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3—122no—
343#626—64no—
344#626—62no—
345#626—62no—
346#626—64no—
347#626—122no—
348#626—122no—
349#625—64no—
350#625—62no—
351#625—122no—
352#624—122no—
353D3×Dic3—122no—
354D3×Dic3—122no—
355#546—271noSylow
356C2×C33C22×D411yescharacteristic
357C2×C33C2×#4111yescharacteristic
358C2×C33H(5,𝔽2)11yescharacteristic
359C3×C3⋊D3—22no—
360C3×C3⋊D3—24no—
361C3×C3⋊D3—41no—
362C3×C3⋊D3—42no—
363C23×D3—92no—
364C23×D3—92no—
365C23×D3—92no—
366C3×#41—184no—
367C2×C3×Q8—21no—
368C2×C3×Q8—21no—
369C2×C3×Q8—21no—
370C2×C3×Q8—41no—
371C2×C3×Q8D3211yescharacteristic, complemented
372C2×C3×Q8D3211yescharacteristic, complemented
373C2×C3×Q8D3211yescharacteristic, complemented
374C2×C3×D4—91no—
375C2×C3×D4—92no—
376C2×C3×D4—91no—
377C22×C3×C4—92no—
378C22×C3×C4—91no—
379C22×C3×C4—91no—
380C2×#67—91no—
381C2×#67—92no—
382C2×#67—91no—
383C2×#67—92no—
384C2×#67—92no—
385C2×#67—92no—
386C22×Dic3—92no—
387#239—64no—
388#239—64no—
389#239—68no—
390D3×D4—184no—
391D3×D4—184no—
392C2×D12—31no—
393C2×D12—31no—
394C2×D12—32no—
395C2×D12—32no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—61no—
399C2×D12—62no—
400C2×D12—61no—
401C2×D12—91no—
402C2×D12—92no—
403C2×D12—92no—
404C2×D12—184no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—31no—
410C2×C4×D3—31no—
411C2×C4×D3—62no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—92no—
415C2×C4×D3—92no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—92no—
418C3×C22⋊C4—92no—
419C3×C22⋊C4—92no—
420C3×C22⋊C4—92no—
421C3×C42—91no—
422#217—91no—
423#217—92no—
424#217—91no—
425#217—92no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—32no—
431(C2×D3)⋊C4—32no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—91no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—92no—
439(C2×D3)⋊C4—92no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—92no—
443C4⋊Dic3—31no—
444C4⋊Dic3—31no—
445C4⋊Dic3—61no—
446C4⋊Dic3—91no—
447Dic3⋊C4—32no—
448Dic3⋊C4—32no—
449Dic3⋊C4—62no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452C4×Dic3—31no—
453C4×Dic3—31no—
454C4×Dic3—61no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—41no—
459C22×C32C23×D311yescharacteristic
460C22×C32C23×D311yescharacteristic
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3#23912yescomplemented
473C2×C3⋊D3C2×#6714yes—
474C2×C3×D3—34no—
475C2×C3×D3—34no—
476C2×C3×D3—32no—
477C2×C3×D3—32no—
478C2×C3×D3—64no—
479C2×C3×D3—62no—
480C2×C3×D3—61no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—61no—
486C2×C3×D3—61no—
487C2×C3×D3—61no—
488C2×C3×D3—62no—
489C2×C3×D3—62no—
490C2×C3×D3—61no—
491C2×C3×D3—61no—
492C2×C3×D3—61no—
493C2×C3×D3—62no—
494C2×C3×D3—61no—
495C2×C3×D3—62no—
496C2×C3×D3—61no—
497C2×C3×D3—62no—
498C2×C3×D3—61no—
499C2×C3×D3—62no—
500C2×C3×D3—62no—
501C2×C3×D3—121no—
502C2×C3×D3—122no—
503C2×C3×D3—122no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—121no—
507C2×C3×D3—122no—
508C2×C3×D3—122no—
509C2×C3×D3—122no—
510D32—128no—
511D32—128no—
512D32—128no—
513C32×C4—22no—
514C32×C4—24no—
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—42no—
521C32×C4—42no—
522C32×C4—42no—
523C32×C4—44no—
524C32×C4D3×D412yes—
525C32×C4D3×D412yes—
526C32×C4C2×#6712yes—
527C3⋊Dic3—21no—
528C3⋊Dic3—21no—
529C3⋊Dic3—21no—
530C3⋊Dic3—21no—
531C3⋊Dic3—22no—
532C3×Dic3—62no—
533C3×Dic3—61no—
534C3×Dic3—61no—
535C3×Dic3—61no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—61no—
539C3×Dic3—62no—
540C3×Dic3—61no—
541C3×Dic3—62no—
542C3×Dic3—61no—
543C3×Dic3—121no—
544C3×Dic3—121no—
545C3×Dic3—121no—
546C3×Dic3—122no—
547C2×#41—91no—
548C22×D4—271no—
549#124—91no—
550#123—272no—
551C22⋊Q8—91no—
552#121—272no—
553#121—271no—
554#120—272no—
555C4×D4—271no—
556C4×D4—271no—
557C2×C22⋊C4—272no—
558C33#54611yescharacteristic, complemented, Sylow
559C23×C3—91no—
560C23×C3—92no—
561C23×C3—92no—
562C23×C3—91no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—32no—
566C22×D3—32no—
567C22×D3—32no—
568C22×D3—32no—
569C22×D3—31no—
570C22×D3—31no—
571C22×D3—61no—
572C22×D3—62no—
573C22×D3—61no—
574C22×D3—62no—
575C22×D3—184no—
576C22×D3—184no—
577C22×D3—184no—
578C22×D3—184no—
579C22×D3—184no—
580C22×D3—184no—
581C22×D3—362no—
582C22×D3—362no—
583C22×D3—362no—
584C3×Q8—24no—
585C3×Q8—22no—
586C3×Q8—22no—
587C3×Q8—22no—
588C3×Q8—42no—
589C3×Q8—42no—
590C3×Q8—44no—
591C3×D4—94no—
592C3×D4—184no—
593C3×D4—182no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—22no—
597C2×C3×C4—21no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—42no—
601C2×C3×C4—41no—
602C2×C3×C4—91no—
603C2×C3×C4—91no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—92no—
607C2×C3×C4—184no—
608C2×C3×C4—182no—
609C2×C3×C4—182no—
610C2×C3×C4C2×D3212yes—
611C2×C3×C4C2×D3212yes—
612C2×C3×C4C2×D3212yes—
613C2×C3×C4C2×D3211yescharacteristic
614C2×C3×C4C2×D3211yescharacteristic
615C2×C3×C4C2×D3211yescharacteristic
616#67—184no—
617#67—182no—
618#67—184no—
619#67—182no—
620#67—362no—
621#67—362no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—62no—
637C2×Dic3—362no—
638D12—34no—
639D12—34no—
640D12—64no—
641D12—64no—
642D12—64no—
643D12—68no—
644D12—62no—
645D12—62no—
646D12—122no—
647D12—182no—
648D12—184no—
649D12—362no—
650C4×D3—64no—
651C4×D3—64no—
652C4×D3—68no—
653C4×D3—64no—
654C4×D3—62no—
655C4×D3—62no—
656C4×D3—62no—
657C4×D3—62no—
658C4×D3—122no—
659C4×D3—362no—
660C4×D3—362no—
661C2×C32—21no—
662C2×C32—21no—
663C2×C32—21no—
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—41no—
671C2×C32—41no—
672C2×C32—41no—
673C2×C32C2×D3×D411yescharacteristic
674C2×C32C2×D3×D411yescharacteristic
675C2×C32C2×#23911yescharacteristic
676C2×C32D3×#4111yescharacteristic
677C2×C32D3×#4111yescharacteristic
678C2×C32#100911yescharacteristic
679C2×C32#100911yescharacteristic
680C2×C32#100911yescharacteristic
681C2×C32C22×#6711yescharacteristic
682C3⋊D3—24no—
683C3⋊D3—22no—
684C3⋊D3—41no—
685C3⋊D3—42no—
686C3×D3—62no—
687C3×D3—64no—
688C3×D3—62no—
689C3×D3—64no—
690C3×D3—122no—
691C3×D3—124no—
692C3×D3—122no—
693C3×D3—121no—
694C3×D3—122no—
695C3×D3—122no—
696C3×D3—121no—
697C3×D3—242no—
698C24—272no—
699#41—184no—
700C2×Q8#111311yescharacteristic, complemented
701C2×D4—91no—
702C2×D4—92no—
703C2×D4—91no—
704C2×D4—271no—
705C2×D4—272no—
706C2×D4—272no—
707C2×D4—544no—
708C22×C4—92no—
709C22×C4—91no—
710C22×C4—91no—
711C22×C4—272no—
712C4⋊C4—91no—
713C4⋊C4—92no—
714C4⋊C4—271no—
715C22⋊C4—92no—
716C22⋊C4—92no—
717C22⋊C4—92no—
718C22⋊C4—271no—
719C22⋊C4—272no—
720C22⋊C4—272no—
721C22⋊C4—271no—
722C42—91no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—41no—
727C22×C3—92no—
728C22×C3—94no—
729C22×C3—182no—
730C22×C3—182no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—182no—
735C22×C3—181no—
736C22×C3—182no—
737C22×C3—182no—
738C22×C3—181no—
739C22×C3C22×D3211yescharacteristic
740C22×C3C22×D3211yescharacteristic
741C22×C3C22×D3211yescharacteristic
742C2×D3—32no—
743C2×D3—32no—
744C2×D3—34no—
745C2×D3—34no—
746C2×D3—64no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—62no—
757C2×D3—61no—
758C2×D3—62no—
759C2×D3—61no—
760C2×D3—62no—
761C2×D3—61no—
762C2×D3—62no—
763C2×D3—61no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—121no—
770C2×D3—122no—
771C2×D3—122no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—122no—
776C2×D3—122no—
777C2×D3—122no—
778C2×D3—368no—
779C2×D3—368no—
780C2×D3—368no—
781C3×C4—24no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—42no—
789C3×C4—42no—
790C3×C4—44no—
791C3×C4—42no—
792C3×C4—181no—
793C3×C4—181no—
794C3×C4—182no—
795C3×C4—181no—
796C3×C4—181no—
797C3×C4D3×#6712yes—
798C3×C4D3×#6712yes—
799C3×C4#381112yes—
800Dic3—62no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—62no—
805Dic3—61no—
806Dic3—62no—
807Dic3—61no—
808Dic3—61no—
809Dic3—61no—
810Dic3—61no—
811Dic3—121no—
812Dic3—121no—
813Dic3—121no—
814Dic3—122no—
815C32—21no—
816C32—21no—
817C32—21no—
818C32—41no—
819C32#563011yescharacteristic, complemented
820C32#567611yescharacteristic, complemented
821C32#582911yescharacteristic, complemented
822C23—91no—
823C23—92no—
824C23—92no—
825C23—91no—
826C23—544no—
827C23—544no—
828C23—1082no—
829Q8—22no—
830D4—94no—
831D4—184no—
832D4—182no—
833D4—544no—
834D4—542no—
835D4—1082no—
836C2×C4—91no—
837C2×C4—91no—
838C2×C4—92no—
839C2×C4—91no—
840C2×C4—91no—
841C2×C4—184no—
842C2×C4—182no—
843C2×C4—182no—
844C2×C4—1082no—
845C2×C4C2×#111312yes—
846C2×C4C2×#111311yescharacteristic
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—41no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—182no—
860C2×C3—184no—
861C2×C3—362no—
862C2×C3—361no—
863C2×C3D3×#23911yescharacteristic
864C2×C3D3×#23911yescharacteristic
865C2×C3#6431911yescharacteristic
866C2×C3#6432011yescharacteristic
867C2×C3#6432011yescharacteristic
868C2×C3#6432011yescharacteristic
869C2×C3C2×D3×#6711yescharacteristic
870C2×C3C2×D3×#6711yescharacteristic
871C2×C3C2×#381111yescharacteristic
872D3—62no—
873D3—64no—
874D3—64no—
875D3—62no—
876D3—122no—
877D3—124no—
878D3—122no—
879D3—121no—
880D3—122no—
881D3—121no—
882D3—122no—
883D3—242no—
884C22—92no—
885C22—94no—
886C22—182no—
887C22—182no—
888C22—181no—
889C22—181no—
890C22—181no—
891C22—182no—
892C22—181no—
893C22—182no—
894C22—181no—
895C22—182no—
896C22—1088no—
897C22C22×#111311yescharacteristic
898C4—22no—
899C4—181no—
900C4—181no—
901C4—182no—
902C4—181no—
903C4—181no—
904C4#8904912yes—
905C3—21no—
906C3—21no—
907C3—21no—
908C3—41no—
909C3#1059542711yescharacteristic, complemented
910C3#1059542811yescharacteristic, complemented
911C3#1059543111yescharacteristic, complemented
912C2—182no—
913C2—184no—
914C2—362no—
915C2—361no—
916C2#1172462611yescharacteristic
917C2#1172462711yescharacteristic
918C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
hypercenterC2×Q8#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3832C2semidirect
2. C2×C4⋊#1113C2semidirect
3. C3×#64156C2semidirect
4. C3×#64155C2semidirect
5. #11723701C2semidirect
6. #11723700C2semidirect
7. #11723696C2semidirect
8. #11723694C2semidirect
9. C4×#6295C2semidirect
10. #11723691C2semidirect
11. #11723687C2semidirect
16. C2×C33×Q8C22semidirect
20. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
26. C2×#6295C22semidirect
27. C2×#6294C22semidirect
30. C3×#3752C22semidirect
31. C3×#3752C22semidirect
32. C3×C4⋊(C3⋊Dic3)C22semidirect
33. C3×#3750C22semidirect
34. C3×C4×C3⋊Dic3C22semidirect
35. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
40. C2×#3832D3semidirect
47. #64156D3semidirect
48. #64155D3semidirect
93. C3×C4⋊(C3⋊D3)D4semidirect
111. C2×C32×Q8C2×D3semidirect
112. C2×C32×Q8C2×D3semidirect
113. C2×C32×Q8C2×D3semidirect
117. C2×C4⋊(C3⋊D3)C2×D3semidirect
119. C2×C4×C3⋊D3C2×D3semidirect
120. C2×C4×C3⋊D3C2×D3semidirect
158. #3752C2×D3semidirect
159. #3752C2×D3semidirect
160. C4⋊(C3⋊Dic3)C2×D3semidirect
161. #3750C2×D3semidirect
162. C4×C3⋊Dic3C2×D3semidirect
208. C2×C3×C3⋊D3#41semidirect
306. C4⋊(C3⋊D3)#67semidirect
371. C2×C3×Q8D32semidirect
372. C2×C3×Q8D32semidirect
373. C2×C3×Q8D32semidirect
472. C2×C3⋊D3#239semidirect
558. C33#546semidirect
700. C2×Q8#1113semidirect
819. C32#5630semidirect
820. C32#5676semidirect
821. C32#5829semidirect
909. C3#10595427semidirect
910. C3#10595428semidirect
911. C3#10595431semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38322
C2×C4⋊#11132
C3×#641562
C3×#641552
#117237012
#117237002
#117236962
#117236942
C4×#62952
#117236912
#117236872
#105954313
#105954283
#105954273