Finite Group Databasebeta

← #11824577

Subgroups — #11824577

Order 1152.

1543 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3C2×#63886C211yesmaximal, characteristic, complemented
4C2×#63886C211yesmaximal, characteristic, complemented
5#10592689C211yesmaximal, characteristic, complemented
6C3×#4982C211yesmaximal, characteristic, complemented
7#10591392C211yesmaximal, characteristic, complemented
8#10591391C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591364C211yesmaximal, characteristic, complemented
13D3×C3⋊#95C211yesmaximal, characteristic, complemented
14#10591301C211yesmaximal, characteristic, complemented
15#10591283C211yesmaximal, characteristic, complemented
16#82670—31nomaximal
17#77957—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C3×#895—24no—
39C2×#3722C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46#63898—24no—
47#63886—24no—
48#63886—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#121—31no—
58C2×#939—31no—
59C2×#939—31no—
60C2×D4×Dic3—31no—
61C2×#895—31no—
62C2×#895—31no—
63C2×#895D311yescharacteristic, complemented
64C2×#893—31no—
65C3×#398—31no—
66#5223—31no—
67#5220—31no—
68#5220—31no—
69#5213—31no—
70C2×C3⋊#95—31no—
71#4992—31no—
72#4991—31no—
73#4990—31no—
74#4990—31no—
75#4990—31no—
76#4990—61no—
77#4982D311yescharacteristic, complemented
78#4961—31no—
79#4958—31no—
80#4952—31no—
81#4945—31no—
82#4671—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87D3×#95—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×D12—22no—
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12—22no—
107C2×C3×D12—22no—
108C2×C3×D12—22no—
109C2×C3×D12—22no—
110C2×C3×D12—41no—
111C2×C3×D12D414yescomplemented
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—41no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×#626—22no—
119C2×#626—22no—
120C2×#626—22no—
121C2×#626—41no—
122C2×#626—41no—
123C2×#626—41no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—41no—
128C2×D3×Dic3—41no—
129C2×D3×Dic3—41no—
130C2×D3×Dic3—41no—
131C2×D3×Dic3—41no—
132C2×D3×Dic3D414yescomplemented
133C32×C4⋊C4—22no—
134#3752—22no—
135#3752—22no—
136#3752—22no—
137C4×C3⋊Dic3—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×C4⋊Dic3—22no—
141C3×Dic3⋊C4—22no—
142C3×Dic3⋊C4—22no—
143#3722—41no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—22no—
149(C2×D3)⋊Dic3—41no—
150#2543—91noSylow
151C22×C3×D4—31no—
152C22×C3×D4—31no—
153C22×C3×D4—31no—
154C23×C3×C4—31no—
155C22×#67—31no—
156C22×#67—31no—
157C22×#67—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C23×Dic3—31no—
161C22×D12—31no—
162C22×D12—31no—
163C22×D12—31no—
164C22×D12C2×D311yescharacteristic
165C22×D12C2×D311yescharacteristic
166C22×D12C2×D311yescharacteristic
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—31no—
170C22×C4×D3C2×D311yescharacteristic
171C3×#121—64no—
172C2×C3×C4⋊C4—21no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4C2×D311yescharacteristic
177C2×C3×C4⋊C4C2×D311yescharacteristic
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×#217—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186#939—64no—
187#939—64no—
188D4×Dic3—64no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4C2×D311yescharacteristic
207C2×(C2×D3)⋊C4C2×D311yescharacteristic
208C2×C4⋊Dic3C2×D311yescharacteristic
209C2×Dic3⋊C4C2×D311yescharacteristic
210C2×Dic3⋊C4C2×D311yescharacteristic
211C2×C4×Dic3—31no—
212C2×C4×Dic3—31no—
213C2×C4×Dic3—61no—
214#895—24no—
215#895—64no—
216#895—64no—
217#893—64no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—61no—
232C3⋊#95—61no—
233C3⋊#95C2×D311yescharacteristic
234C3⋊#95C2×D311yescharacteristic
235C3⋊#95C2×D311yescharacteristic
236C23×C32C2411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3C2×D412yes—
262C22×C3×D3C2×D412yes—
263C22×C3×D3C2×D412yes—
264C22×C3×D3#4112yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C2×D412yes—
273C2×C32×C4#4112yes—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3—21no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—21no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3C2×D412yes—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3C2×D412yes—
297C2×C3×Dic3#4112yes—
298C3×D12—28no—
299C3×D12—44no—
300C3×D12—44no—
301C3×C4×D3—44no—
302#626—44no—
303#626—44no—
304#626—44no—
305D3×Dic3—44no—
306D3×Dic3—44no—
307D3×Dic3—44no—
308C2×#121—31no—
309C2×#121—91no—
310C2×#121—91no—
311C2×C4×D4—91no—
312#398—31no—
313#397—91no—
314#394—91no—
315#392—91no—
316#388—91no—
317#388—91no—
318#386—91no—
319#386—91no—
320#386—91no—
321#386—91no—
322C2×#95—91no—
323C24×C3—31no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—61no—
329C23×D3C22×D311yescharacteristic
330C23×D3C22×D311yescharacteristic
331C23×D3C22×D311yescharacteristic
332C2×C3×D4—34no—
333C2×C3×D4—62no—
334C2×C3×D4—62no—
335C2×C3×D4—62no—
336C2×C3×D4—62no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—62no—
340C2×C3×D4—121no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—62no—
350C22×C3×C4—62no—
351C22×C3×C4—121no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—121no—
365C2×#67—121no—
366C2×#67—121no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—34no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—62no—
378C22×Dic3—62no—
379C22×Dic3—62no—
380C22×Dic3—121no—
381C22×Dic3—121no—
382C22×Dic3—121no—
383C22×Dic3—121no—
384C22×Dic3—121no—
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C2×D12—22no—
391C2×D12—22no—
392C2×D12—22no—
393C2×D12—22no—
394C2×D12—22no—
395C2×D12—22no—
396C2×D12—22no—
397C2×D12—41no—
398C2×D12—62no—
399C2×D12—62no—
400C2×D12—62no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—121no—
405C2×D12—121no—
406C2×D12—121no—
407C2×D12#6714yescomplemented
408C2×C4×D3—22no—
409C2×C4×D3—22no—
410C2×C4×D3—34no—
411C2×C4×D3—41no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—121no—
416C2×C4×D3—121no—
417C2×C4×D3—121no—
418C2×C4×D3—121no—
419C2×C4×D3—121no—
420C3×C4⋊C4—22no—
421C3×C4⋊C4—22no—
422C3×C4⋊C4—42no—
423C3×C4⋊C4—62no—
424C3×C4⋊C4—62no—
425C3×C4⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428#217—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—121no—
434(C2×D3)⋊C4—22no—
435(C2×D3)⋊C4—22no—
436(C2×D3)⋊C4—62no—
437(C2×D3)⋊C4—62no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—64no—
440(C2×D3)⋊C4—62no—
441(C2×D3)⋊C4—62no—
442(C2×D3)⋊C4—62no—
443(C2×D3)⋊C4—62no—
444(C2×D3)⋊C4—62no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—122no—
449(C2×D3)⋊C4—122no—
450(C2×D3)⋊C4—121no—
451(C2×D3)⋊C4—121no—
452(C2×D3)⋊C4—121no—
453C4⋊Dic3—22no—
454Dic3⋊C4—22no—
455Dic3⋊C4—22no—
456C4×Dic3—62no—
457C4×Dic3—62no—
458C4×Dic3—122no—
459C22×C32C22×D411yescharacteristic
460C22×C32C22×D411yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32C2×#4111yescharacteristic
463C22×C32C2×#4111yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C22×C32H(5,𝔽2)11yescharacteristic
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3#12114yes—
494C32×C4—22no—
495C32×C4—22no—
496C32×C4—41no—
497C3⋊Dic3—22no—
498C3⋊Dic3—41no—
499C3⋊Dic3—41no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C3×Dic3—41no—
505C22×D4—31no—
506C22×D4—31no—
507C22×D4—31no—
508C22×D4—91no—
509C22×D4—91no—
510C22×D4—91no—
511C23×C4—31no—
512C23×C4—91no—
513C23×C4—91no—
514C23×C4—91no—
515#121—64no—
516#121—184no—
517#121—184no—
518C4×D4—184no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4D3211yescharacteristic
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—91no—
529C2×C22⋊C4—91no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C42—91no—
536#95—31no—
537#95—31no—
538#95—31no—
539#95—91no—
540#95—91no—
541#95—91no—
542#95—91no—
543#95—91no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3C23×D311yescharacteristic
567C23×C3C23×D311yescharacteristic
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—21no—
571C22×D3—21no—
572C22×D3—21no—
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—62no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—121no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C22×D3D3×D412yes—
607C22×D3#23712yes—
608C22×D3C2×#6712yes—
609C22×D3C2×#6712yes—
610C3×D4—68no—
611C3×D4—124no—
612C3×D4—124no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—61no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—124no—
652C2×C3×C4D3×D412yes—
653C2×C3×C4#23712yes—
654C2×C3×C4#23912yes—
655C2×C3×C4C2×#6712yes—
656#67—124no—
657#67—124no—
658#67—124no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—21no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—62no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—62no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—121no—
699C2×Dic3—124no—
700C2×Dic3—124no—
701C2×Dic3—124no—
702C2×Dic3D3×D412yes—
703C2×Dic3#23912yes—
704D12—28no—
705D12—44no—
706D12—44no—
707D12—124no—
708D12—124no—
709D12—124no—
710C4×D3—44no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C2×C32C2×#12111yescharacteristic
715C2×C32#53211yescharacteristic
716C2×C32#53411yescharacteristic
717C2×C32#54611yescharacteristic
718C2×C32#54611yescharacteristic
719C2×C32#55311yescharacteristic
720C2×C32#55311yescharacteristic
721C3⋊D3—81no—
722C3×D3—24no—
723C3×D3—42no—
724C3×D3—81no—
725C24—31no—
726C24—31no—
727C24—31no—
728C24—91no—
729C2×D4—34no—
730C2×D4—62no—
731C2×D4—62no—
732C2×D4—62no—
733C2×D4—62no—
734C2×D4—62no—
735C2×D4—62no—
736C2×D4—62no—
737C2×D4—121no—
738C2×D4—182no—
739C2×D4—182no—
740C2×D4—182no—
741C2×D4—182no—
742C2×D4—182no—
743C2×D4—182no—
744C2×D4—361no—
745C2×D4—361no—
746C2×D4—361no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—31no—
752C22×C4—62no—
753C22×C4—62no—
754C22×C4—94no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—91no—
758C22×C4—121no—
759C22×C4—182no—
760C22×C4—182no—
761C22×C4—182no—
762C22×C4—361no—
763C22×C4—361no—
764C22×C4—361no—
765C22×C4—361no—
766C22×C4—361no—
767C22×C4C2×D3211yescharacteristic
768C22×C4C2×D3211yescharacteristic
769C22×C4C2×D3211yescharacteristic
770C4⋊C4—22no—
771C4⋊C4—62no—
772C4⋊C4—62no—
773C4⋊C4—62no—
774C22⋊C4—62no—
775C22⋊C4—62no—
776C22⋊C4—182no—
777C22⋊C4—182no—
778C22⋊C4—182no—
779C22⋊C4—182no—
780C22⋊C4—182no—
781C22⋊C4—182no—
782C22⋊C4—182no—
783C22⋊C4—182no—
784C22⋊C4—361no—
785C22⋊C4—361no—
786C42—182no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—34no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—121no—
809C22×C3—121no—
810C22×C3—121no—
811C22×C3—121no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3C2×D3×D411yescharacteristic
816C22×C3C2×D3×D411yescharacteristic
817C22×C3C2×D3×D411yescharacteristic
818C22×C3C2×#23711yescharacteristic
819C22×C3C2×#23711yescharacteristic
820C22×C3#100411yescharacteristic
821C22×C3C2×#23911yescharacteristic
822C22×C3C2×#23911yescharacteristic
823C22×C3D3×#4111yescharacteristic
824C22×C3D3×#4111yescharacteristic
825C22×C3#100911yescharacteristic
826C22×C3#100911yescharacteristic
827C22×C3#100911yescharacteristic
828C22×C3C22×#6711yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—121no—
863C2×D3—121no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—241no—
867C2×D3—241no—
868C2×D3—241no—
869C2×D3—241no—
870C2×D3#93914yes—
871C3×C4—22no—
872C3×C4—22no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—42no—
876C3×C4—42no—
877C3×C4—41no—
878C3×C4—41no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—81no—
882C3×C4—121no—
883C3×C4—121no—
884C3×C4—121no—
885Dic3—22no—
886Dic3—22no—
887Dic3—41no—
888Dic3—41no—
889Dic3—41no—
890Dic3—62no—
891Dic3—62no—
892Dic3—122no—
893Dic3—122no—
894Dic3—121no—
895Dic3—121no—
896Dic3—121no—
897Dic3—121no—
898Dic3—241no—
899C32#254311yescharacteristic, complemented, Sylow
900C23—32no—
901C23—32no—
902C23—32no—
903C23—32no—
904C23—61no—
905C23—61no—
906C23—61no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—61no—
920C23—61no—
921C23—181no—
922C23—181no—
923C23—181no—
924C23—181no—
925C23—181no—
926C23—181no—
927C23—181no—
928C23C22×D3211yescharacteristic
929D4—68no—
930D4—124no—
931D4—124no—
932D4—364no—
933D4—364no—
934D4—364no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—32no—
943C2×C4—32no—
944C2×C4—61no—
945C2×C4—61no—
946C2×C4—61no—
947C2×C4—61no—
948C2×C4—61no—
949C2×C4—61no—
950C2×C4—61no—
951C2×C4—61no—
952C2×C4—61no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—92no—
958C2×C4—124no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—181no—
966C2×C4—181no—
967C2×C4—364no—
968C2×C4—364no—
969C2×C4—364no—
970C2×C4#379612yes—
971C2×C4D3×#6712yes—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—64no—
980C2×C3—122no—
981C2×C3—241no—
982C2×C3#559611yescharacteristic
983C2×C3#560111yescharacteristic
984C2×C3D3×#12111yescharacteristic
985C2×C3#560511yescharacteristic
986C2×C3#561811yescharacteristic
987C2×C3#563011yescharacteristic
988C2×C3#563011yescharacteristic
989C2×C3#565311yescharacteristic
990C2×C3#569511yescharacteristic
991C2×C3#569511yescharacteristic
992C2×C3#572511yescharacteristic
993C2×C3C2×#93911yescharacteristic
994C2×C3#580611yescharacteristic
995C2×C3#582911yescharacteristic
996D3—24no—
997D3—42no—
998D3—81no—
999D3—242no—
1000D3—241no—
1001D3—241no—
1002C22—34no—
1003C22—62no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—62no—
1011C22—62no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—361no—
1024C22—361no—
1025C22—361no—
1026C22—361no—
1027C22—361no—
1028C22—361no—
1029C22—361no—
1030C22C2×#379611yescharacteristic
1031C22#6430711yescharacteristic
1032C22D32×D411yescharacteristic
1033C22D3×#23711yescharacteristic
1034C22D3×#23911yescharacteristic
1035C22#6432011yescharacteristic
1036C22C2×D3×#6711yescharacteristic
1037C4—22no—
1038C4—22no—
1039C4—41no—
1040C4—62no—
1041C4—62no—
1042C4—121no—
1043C4—121no—
1044C4—121no—
1045C4—182no—
1046C4—361no—
1047C4—361no—
1048C3—21no—
1049C3#7795711yescharacteristic, complemented
1050C3#8267011yescharacteristic, complemented
1051C2—64no—
1052C2—122no—
1053C2—241no—
1054C2—721no—
1055C2#1059436911yescharacteristic
1056C2#1059443711yescharacteristic
1057C2#1059443811yescharacteristic
1058C2#1059461111yescharacteristic
1059C2#1059488911yescharacteristic
1060C2D3×#93911yescharacteristic
1061C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#895C2semidirect
2. C2×#63898C2semidirect
3. C2×#63886C2semidirect
4. C2×#63886C2semidirect
5. #10592689C2semidirect
6. C3×#4982C2semidirect
7. #10591392C2semidirect
8. #10591391C2semidirect
9. #10591382C2semidirect
10. #10591376C2semidirect
11. #10591376C2semidirect
12. #10591364C2semidirect
13. D3×C3⋊#95C2semidirect
14. #10591301C2semidirect
15. #10591283C2semidirect
63. C2×#895D3semidirect
77. #4982D3semidirect
111. C2×C3×D12D4semidirect
132. C2×D3×Dic3D4semidirect
407. C2×D12#67semidirect
899. C32#2543semidirect
1049. C3#77957semidirect
1050. C3#82670semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#638982
C2×#638862
#105926892
C3×#49822
#105913922
#105913912
#105913822
#105913762
#105913642
D3×C3⋊#952
#105913012
#105912832
#826703
#779573