Finite Group Databasebeta

← #11824575

Subgroups — #11824575

Order 1152.

1523 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63885C211yesmaximal, characteristic, complemented
4C2×#63885C211yesmaximal, characteristic, complemented
5#10592681C211yesmaximal, characteristic, complemented
6C3×#4990C211yesmaximal, characteristic, complemented
7#10591394C211yesmaximal, characteristic, complemented
8#10591389C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591376C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13D3×C3⋊#95C211yesmaximal, characteristic, complemented
14#10591298C211yesmaximal, characteristic, complemented
15#10591280C211yesmaximal, characteristic, complemented
16#82670—31nomaximal
17#75882—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×#895—24no—
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46Dic3×D12—24no—
47#63885—24no—
48#63885—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
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×#895D311yescharacteristic, complemented
62C2×#884—31no—
63C2×#884—31no—
64C2×C4×D12—31no—
65C3×#388—31no—
66#5223—31no—
67#5220—31no—
68#5220—31no—
69#5213—31no—
70C2×C3⋊#95—31no—
71#4990D311yescharacteristic, complemented
72#4982—31no—
73#4982—31no—
74#4982—61no—
75#4961—31no—
76#4961—31no—
77#4960—31no—
78#4958—31no—
79#4956—31no—
80#4956—31no—
81#4952—31no—
82#4945—31no—
83#4940—31no—
84#4675—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×#625—22no—
116C2×#625—22no—
117C2×#625—22no—
118C2×#625—22no—
119C2×#625—22no—
120C2×#625—22no—
121C2×#625—41no—
122C2×#625—41no—
123C2×#625—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—
134C4⋊(C3⋊Dic3)—22no—
135#3750—22no—
136#3750—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—22no—
139C3×(C2×D3)⋊C4—22no—
140C3×(C2×D3)⋊C4—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×C4×Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3—22no—
147(C2×D3)⋊Dic3—22no—
148(C2×D3)⋊Dic3—41no—
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—
158C22×#67—31no—
159C22×#67—31no—
160C22×#67—31no—
161C23×Dic3—31no—
162C23×Dic3—31no—
163C23×Dic3—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⋊C4C2×D311yescharacteristic
174C2×C3×C4⋊C4C2×D311yescharacteristic
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—31no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C42—31no—
181C2×#217—31no—
182C2×#217—31no—
183C2×#217—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188#939—64no—
189#939—64no—
190D4×Dic3—64no—
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)⋊C4C2×D311yescharacteristic
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—61no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—61no—
211C2×Dic3⋊C4—61no—
212C2×C4×Dic3C2×D311yescharacteristic
213#895—24no—
214#884—64no—
215#884—64no—
216C4×D12—64no—
217C3×#95—31no—
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⋊#95—61no—
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⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3C2×D412yes—
285C2×C3⋊Dic3#4112yes—
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×Dic3—21no—
297C2×C3×Dic3C2×D412yes—
298C3×D12—28no—
299C3×D12—44no—
300C3×D12—44no—
301C3×C4×D3—44no—
302#625—44no—
303#625—44no—
304#625—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—91no—
313#397—91no—
314#394—91no—
315#392—91no—
316#388—31no—
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—
326C24×C3—31no—
327C23×D3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C23×D3C22×D311yescharacteristic
330C23×D3C22×D311yescharacteristic
331C2×C3×D4—34no—
332C2×C3×D4—62no—
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—121no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—62no—
348C22×C3×C4—62no—
349C22×C3×C4—121no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—121no—
369C2×#67—121no—
370C2×#67—121no—
371C2×#67—121no—
372C2×#67—121no—
373C2×#67—121no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—34no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—62no—
388C22×Dic3—62no—
389C22×Dic3—62no—
390C22×Dic3—121no—
391C22×Dic3—121no—
392C22×Dic3—121no—
393C22×Dic3—121no—
394C22×Dic3—121no—
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—22no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—22no—
403C2×D12—22no—
404C2×D12—22no—
405C2×D12—22no—
406C2×D12—41no—
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×C22⋊C4—62no—
424C3×C22⋊C4—62no—
425C3×C22⋊C4—62no—
426C3×C22⋊C4—62no—
427C3×C22⋊C4—62no—
428C3×C42—62no—
429#217—62no—
430#217—62no—
431#217—62no—
432#217—62no—
433#217—62no—
434#217—121no—
435#217—121no—
436(C2×D3)⋊C4—22no—
437(C2×D3)⋊C4—22no—
438(C2×D3)⋊C4—22no—
439(C2×D3)⋊C4—22no—
440(C2×D3)⋊C4—22no—
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—121no—
447(C2×D3)⋊C4—121no—
448C4⋊Dic3—62no—
449C4⋊Dic3—62no—
450C4⋊Dic3—122no—
451Dic3⋊C4—62no—
452Dic3⋊C4—62no—
453Dic3⋊C4—62no—
454Dic3⋊C4—62no—
455Dic3⋊C4—122no—
456Dic3⋊C4—122no—
457C4×Dic3—22no—
458C22×C32C22×D411yescharacteristic
459C22×C32C22×D411yescharacteristic
460C22×C32C2×#4111yescharacteristic
461C22×C32C2×#4111yescharacteristic
462C22×C32C2×#4111yescharacteristic
463C22×C32H(5,𝔽2)11yescharacteristic
464C22×C32H(5,𝔽2)11yescharacteristic
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
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#12114yes—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—41no—
496C3⋊Dic3—22no—
497C3⋊Dic3—22no—
498C3⋊Dic3—41no—
499C3⋊Dic3—41no—
500C3×Dic3—22no—
501C3×Dic3—41no—
502C3×Dic3—41no—
503C3×Dic3—41no—
504C22×D4—31no—
505C22×D4—31no—
506C22×D4—31no—
507C22×D4—91no—
508C22×D4—91no—
509C22×D4—91no—
510C23×C4—31no—
511C23×C4—91no—
512C23×C4—91no—
513C23×C4—91no—
514#121—64no—
515#121—184no—
516#121—184no—
517C4×D4—184no—
518C2×C4⋊C4—91no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4D3211yescharacteristic
522C2×C22⋊C4—31no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—31no—
526C2×C22⋊C4—31no—
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×C42—31no—
535#95—31no—
536#95—31no—
537#95—91no—
538#95—91no—
539#95—91no—
540#95—91no—
541#95—91no—
542#95—91no—
543C23×C3—21no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—61no—
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×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
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—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3D3×D412yes—
599C22×D3#23712yes—
600C22×D3C2×#6712yes—
601C22×D3C2×#6712yes—
602C3×D4—68no—
603C3×D4—124no—
604C3×D4—124no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
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—22no—
620C2×C3×C4—22no—
621C2×C3×C4—32no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—124no—
641C2×C3×C4#23512yes—
642C2×C3×C4D3×D412yes—
643C2×C3×C4#23712yes—
644C2×C3×C4C2×#6712yes—
645#67—124no—
646#67—124no—
647#67—124no—
648#67—124no—
649#67—124no—
650#67—124no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—61no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
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—121no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3—121no—
696C2×Dic3—121no—
697C2×Dic3—121no—
698C2×Dic3—124no—
699C2×Dic3—124no—
700C2×Dic3—124no—
701C2×Dic3D3×D412yes—
702D12—28no—
703D12—44no—
704D12—44no—
705C4×D3—44no—
706C4×D3—124no—
707C4×D3—124no—
708C4×D3—124no—
709C2×C32C2×#12111yescharacteristic
710C2×C32#53211yescharacteristic
711C2×C32#53411yescharacteristic
712C2×C32#54611yescharacteristic
713C2×C32#54611yescharacteristic
714C2×C32#55311yescharacteristic
715C2×C32#55311yescharacteristic
716C3×D3—24no—
717C3×D3—42no—
718C3×D3—81no—
719C3×D3—81no—
720C24—31no—
721C24—31no—
722C24—31no—
723C24—31no—
724C2×D4—34no—
725C2×D4—62no—
726C2×D4—62no—
727C2×D4—62no—
728C2×D4—62no—
729C2×D4—62no—
730C2×D4—62no—
731C2×D4—62no—
732C2×D4—121no—
733C2×D4—182no—
734C2×D4—182no—
735C2×D4—182no—
736C2×D4—182no—
737C2×D4—182no—
738C2×D4—182no—
739C2×D4—361no—
740C2×D4—361no—
741C2×D4—361no—
742C22×C4—31no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—62no—
747C22×C4—62no—
748C22×C4—94no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4—91no—
753C22×C4—121no—
754C22×C4—182no—
755C22×C4—182no—
756C22×C4—182no—
757C22×C4—361no—
758C22×C4—361no—
759C22×C4—361no—
760C22×C4—361no—
761C22×C4—361no—
762C22×C4C2×D3211yescharacteristic
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—22no—
766C4⋊C4—182no—
767C4⋊C4—182no—
768C4⋊C4—182no—
769C22⋊C4—62no—
770C22⋊C4—62no—
771C22⋊C4—62no—
772C22⋊C4—62no—
773C22⋊C4—62no—
774C22⋊C4—182no—
775C22⋊C4—182no—
776C22⋊C4—182no—
777C22⋊C4—182no—
778C22⋊C4—182no—
779C22⋊C4—361no—
780C22⋊C4—361no—
781C42—62no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—34no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
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×C3—121no—
816C22×C3—121no—
817C22×C3C2×#23511yescharacteristic
818C22×C3C2×D3×D411yescharacteristic
819C22×C3C2×D3×D411yescharacteristic
820C22×C3C2×D3×D411yescharacteristic
821C22×C3C2×#23711yescharacteristic
822C22×C3C2×#23711yescharacteristic
823C22×C3#100411yescharacteristic
824C22×C3D3×#4111yescharacteristic
825C22×C3D3×#4111yescharacteristic
826C22×C3D3×#4111yescharacteristic
827C22×C3#100911yescharacteristic
828C22×C3#100911yescharacteristic
829C22×C3#100911yescharacteristic
830C22×C3C22×#6711yescharacteristic
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
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—41no—
850C2×D3—41no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3#93914yes—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—62no—
868C3×C4—81no—
869C3×C4—121no—
870C3×C4—121no—
871C3×C4—121no—
872Dic3—22no—
873Dic3—41no—
874Dic3—41no—
875Dic3—41no—
876Dic3—62no—
877Dic3—62no—
878Dic3—62no—
879Dic3—62no—
880Dic3—122no—
881Dic3—122no—
882Dic3—121no—
883Dic3—121no—
884Dic3—121no—
885Dic3—121no—
886Dic3—241no—
887Dic3—241no—
888C32#254311yescharacteristic, complemented, Sylow
889C23—32no—
890C23—32no—
891C23—32no—
892C23—32no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23—61no—
901C23—61no—
902C23—61no—
903C23—61no—
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—
917C23C22×D3211yescharacteristic
918D4—68no—
919D4—124no—
920D4—124no—
921D4—364no—
922D4—364no—
923D4—364no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—32no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—61no—
941C2×C4—61no—
942C2×C4—61no—
943C2×C4—92no—
944C2×C4—92no—
945C2×C4—124no—
946C2×C4—181no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4—181no—
951C2×C4—181no—
952C2×C4—181no—
953C2×C4—181no—
954C2×C4—181no—
955C2×C4—181no—
956C2×C4—364no—
957C2×C4—364no—
958C2×C4—364no—
959C2×C4#379512yes—
960C2×C4D3×#6712yes—
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—64no—
969C2×C3—122no—
970C2×C3—241no—
971C2×C3—241no—
972C2×C3#553011yescharacteristic
973C2×C3#554811yescharacteristic
974C2×C3#555011yescharacteristic
975C2×C3#559611yescharacteristic
976C2×C3#560111yescharacteristic
977C2×C3D3×#12111yescharacteristic
978C2×C3#560511yescharacteristic
979C2×C3#561811yescharacteristic
980C2×C3#565311yescharacteristic
981C2×C3#567611yescharacteristic
982C2×C3#570911yescharacteristic
983C2×C3C2×#93911yescharacteristic
984C2×C3#580611yescharacteristic
985C2×C3#582911yescharacteristic
986D3—24no—
987D3—42no—
988D3—81no—
989D3—81no—
990C22—34no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—62no—
999C22—62no—
1000C22—121no—
1001C22—121no—
1002C22—121no—
1003C22—121no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22C2×#379511yescharacteristic
1019C22#6430711yescharacteristic
1020C22D32×D411yescharacteristic
1021C22D3×#23711yescharacteristic
1022C22#6431911yescharacteristic
1023C22#6432011yescharacteristic
1024C22C2×D3×#6711yescharacteristic
1025C4—22no—
1026C4—22no—
1027C4—41no—
1028C4—62no—
1029C4—121no—
1030C4—121no—
1031C4—121no—
1032C4—182no—
1033C4—182no—
1034C4—361no—
1035C4—361no—
1036C3—21no—
1037C3#7588211yescharacteristic, complemented
1038C3#8267011yescharacteristic, complemented
1039C2—64no—
1040C2—122no—
1041C2—241no—
1042C2—241no—
1043C2#1059436711yescharacteristic
1044C2#1059443311yescharacteristic
1045C2#1059443411yescharacteristic
1046C2#1059461111yescharacteristic
1047C2#1059488611yescharacteristic
1048C2D3×#93911yescharacteristic
1049C2#1059542811yescharacteristic
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×Dic3×D12C2semidirect
3. C2×#63885C2semidirect
4. C2×#63885C2semidirect
5. #10592681C2semidirect
6. C3×#4990C2semidirect
7. #10591394C2semidirect
8. #10591389C2semidirect
9. #10591381C2semidirect
10. #10591376C2semidirect
11. #10591376C2semidirect
12. #10591363C2semidirect
13. D3×C3⋊#95C2semidirect
14. #10591298C2semidirect
15. #10591280C2semidirect
61. C2×#895D3semidirect
71. #4990D3semidirect
111. C2×C3×D12D4semidirect
132. C2×D3×Dic3D4semidirect
407. C2×D12#67semidirect
888. C32#2543semidirect
1037. C3#75882semidirect
1038. 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×Dic3×D122
C2×#638852
#105926812
C3×#49902
#105913942
#105913892
#105913812
#105913762
#105913632
D3×C3⋊#952
#105912982
#105912802
#826703
#758823