Finite Group Databasebeta

← #11812939

Subgroups — #11812939

Order 1152.

1433 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#63886C211yesmaximal, characteristic
3C2×#63880C211yesmaximal, characteristic, complemented
4C2×#63854C211yesmaximal, characteristic, complemented
5#10592373C211yesmaximal, characteristic, complemented
6C3×#4665C211yesmaximal, characteristic, complemented
7C3×#4654C211yesmaximal, characteristic, complemented
8#10591382C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591375C211yesmaximal, characteristic, complemented
11#10591373C211yesmaximal, characteristic, complemented
12#10591339C211yesmaximal, characteristic, complemented
13#10591317C211yesmaximal, characteristic, complemented
14#10591312C211yesmaximal, characteristic, complemented
15#10591305C211yesmaximal, characteristic, complemented
16#75319—31nomaximal
17#74704—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45D3×C4⋊Dic3—24no—
46#63886—24no—
47#63880—24no—
48#63854—24no—
49C32×#95C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#939—31no—
58C22×C4⋊Dic3—31no—
59C2×#895—31no—
60C2×#894—31no—
61C2×D3×C4⋊C4—31no—
62C2×#883—31no—
63C2×#67⋊C4—31no—
64C2×C4×D12—31no—
65C3×#387—31no—
66C3×#386—31no—
67#5220—31no—
68#5213—31no—
69#4981—31no—
70#4961—31no—
71#4951—31no—
72#4949—31no—
73#4946—31no—
74#4940—31no—
75#4677—31no—
76#4674—31no—
77#4674—31no—
78#4674—61no—
79#4672—31no—
80#4668—31no—
81#4668—31no—
82#4668—31no—
83#4665—31no—
84#4665—31no—
85#4665D311yescharacteristic, complemented
86#4657—31no—
87#4654D311yescharacteristic, complemented
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
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×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—41no—
114C2×#626D414yes—
115C2×#624—22no—
116C2×#624—22no—
117C2×#624—41no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124#3752—22no—
125#3752—22no—
126#3752—22no—
127C4⋊(C3⋊Dic3)—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×C4⋊Dic3D414yescomplemented
132C3×Dic3⋊C4—22no—
133C3×C4×Dic3—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—41no—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—41no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C22×#67—31no—
148C22×#67—31no—
149C23×Dic3—31no—
150C23×Dic3—31no—
151C22×D12—31no—
152C22×D12—31no—
153C22×D12C2×D311yescharacteristic
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3C2×D311yescharacteristic
159C2×C3×C4⋊C4—31no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169#939—64no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—61no—
183C2×(C2×D3)⋊C4—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×C4⋊Dic3—31no—
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—61no—
195C2×C4⋊Dic3—64no—
196C2×C4⋊Dic3C2×D311yescharacteristic
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3C2×D311yescharacteristic
205#895—64no—
206#894—64no—
207D3×C4⋊C4—64no—
208#883—64no—
209#67⋊C4—64no—
210C4×D12—64no—
211C3×#95—21no—
212C3×#95—31no—
213C3×#95—31no—
214C3×#95—31no—
215C3×#95—31no—
216C3×#95C2×D311yescharacteristic
217C3×#95C2×D311yescharacteristic
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—61no—
225C3⋊#95—61no—
226C3⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3—21no—
237C22×C3⋊D3C2×D412yes—
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×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2×D412yes—
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3#4112yes—
288C3×D12—44no—
289C3×C4×D3—28no—
290#626—28no—
291#626—44no—
292#624—44no—
293D3×Dic3—44no—
294D3×Dic3—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—91no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—31no—
305#386—31no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—31no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—61no—
315C23×D3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—34no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—121no—
344C22×Dic3—31no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—121no—
358C22×Dic3—121no—
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C2×D12—22no—
366C2×D12—22no—
367C2×D12—22no—
368C2×D12—34no—
369C2×D12—62no—
370C2×D12—62no—
371C2×D12—62no—
372C2×D12—62no—
373C2×D12—121no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—62no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C42—62no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—121no—
399(C2×D3)⋊C4—22no—
400(C2×D3)⋊C4—22no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—122no—
414(C2×D3)⋊C4—122no—
415(C2×D3)⋊C4—122no—
416(C2×D3)⋊C4—121no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—62no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—122no—
423C4⋊Dic3—121no—
424C4⋊Dic3D1214yescomplemented
425Dic3⋊C4—22no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—121no—
432C4×Dic3—22no—
433C22×C32C22×D411yescharacteristic
434C22×C32C22×D411yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32C2×#4111yescharacteristic
438C22×C32H(5,𝔽2)11yescharacteristic
439C22×C322−1+411yescharacteristic
440C2×C3⋊D3—22no—
441C2×C3⋊D3—22no—
442C2×C3⋊D3—22no—
443C2×C3⋊D3—41no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3⋊D3—41no—
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3#12314yescomplemented
461C32×C4—22no—
462C32×C4—41no—
463C32×C4—41no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C22×D4—31no—
474C22×D4—91no—
475C22×D4—91no—
476C23×C4—31no—
477C23×C4—91no—
478C23×C4—91no—
479C23×C4—91no—
480#123—184no—
481#121—184no—
482C4×D4—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—184no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—91no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C42—31no—
504#95—31no—
505#95—31no—
506#95—31no—
507#95—31no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95D3211yescharacteristic
512C23×C3—21no—
513C23×C3—32no—
514C23×C3—32no—
515C23×C3—32no—
516C23×C3—61no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3C23×D311yescharacteristic
528C23×C3C23×D311yescharacteristic
529C22×D3—21no—
530C22×D3—21no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—62no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—121no—
556C22×D3—121no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—121no—
560C22×D3—121no—
561C22×D3#23512yes—
562C22×D3D3×D412yes—
563C22×D3#23712yes—
564C3×D4—124no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—22no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—68no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4C2×D1212yes—
610C2×C3×C4D3×D412yes—
611#67—68no—
612#67—124no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—124no—
655C2×Dic3—124no—
656C2×Dic3C2×D1212yes—
657C2×Dic3C2×D1212yes—
658C2×Dic3D3×D412yes—
659C2×Dic3#23712yes—
660D12—44no—
661D12—68no—
662D12—124no—
663C4×D3—28no—
664C4×D3—124no—
665C4×D3—124no—
666C4×D3—124no—
667C4×D3—124no—
668C2×C32C2×#12311yescharacteristic
669C2×C32#52511yescharacteristic
670C2×C32#53911yescharacteristic
671C2×C32D4211yescharacteristic
672C2×C32#54711yescharacteristic
673C2×C32#54811yescharacteristic
674C2×C32#55311yescharacteristic
675C3⋊D3—42no—
676C3×D3—24no—
677C3×D3—81no—
678C24—31no—
679C24—31no—
680C24—91no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—94no—
685C2×D4—182no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—361no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—91no—
700C22×C4—91no—
701C22×C4—91no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—182no—
706C22×C4—182no—
707C22×C4—182no—
708C22×C4—361no—
709C22×C4—361no—
710C22×C4—361no—
711C22×C4C2×D3211yescharacteristic
712C22×C4C2×D3211yescharacteristic
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—34no—
715C4⋊C4—62no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—62no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C22⋊C4—361no—
733C42—62no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—34no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3C22×D1211yescharacteristic
756C22×C3C2×#23511yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×#23711yescharacteristic
761C22×C3C2×#23711yescharacteristic
762C22×C3#100711yescharacteristic
763C22×C3D3×#4111yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3#100911yescharacteristic
767C22×C3#100911yescharacteristic
768C22×C3#101011yescharacteristic
769C2×D3—22no—
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—41no—
776C2×D3—41no—
777C2×D3—41no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
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—121no—
792C2×D3—121no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—241no—
800C2×D3—241no—
801C2×D3—241no—
802C2×D3—241no—
803C2×D3#88314yescomplemented
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—41no—
810C3×C4—41no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—81no—
816C3×C4—81no—
817C3×C4—121no—
818C3×C4—121no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—41no—
824Dic3—41no—
825Dic3—121no—
826Dic3—121no—
827Dic3—121no—
828Dic3—121no—
829Dic3—121no—
830Dic3—121no—
831Dic3—241no—
832Dic3—241no—
833Dic3—241no—
834C32#244311yescharacteristic, complemented, Sylow
835C23—32no—
836C23—32no—
837C23—32no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—92no—
850C23—181no—
851C23—181no—
852C23—181no—
853C23—181no—
854C23—181no—
855C23—181no—
856C23C22×D3211yescharacteristic
857D4—124no—
858D4—188no—
859D4—364no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—68no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—364no—
897C2×C4—364no—
898C2×C4—364no—
899C2×C4D3×D1212yes—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—64no—
908C2×C3—241no—
909C2×C3C2×#88311yescharacteristic
910C2×C3#552411yescharacteristic
911C2×C3D4×D1211yescharacteristic
912C2×C3#555211yescharacteristic
913C2×C3#556511yescharacteristic
914C2×C3#557611yescharacteristic
915C2×C3#558611yescharacteristic
916C2×C3#560911yescharacteristic
917C2×C3#561111yescharacteristic
918C2×C3#563111yescharacteristic
919C2×C3D3×#12311yescharacteristic
920C2×C3#566511yescharacteristic
921C2×C3#569211yescharacteristic
922C2×C3#570911yescharacteristic
923D3—24no—
924D3—81no—
925D3—122no—
926D3—122no—
927D3—242no—
928C22—34no—
929C22—62no—
930C22—62no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—182no—
943C22—182no—
944C22—182no—
945C22—361no—
946C22—361no—
947C22—361no—
948C22—361no—
949C22#6429711yescharacteristic
950C22C2×D3×D1211yescharacteristic
951C22D3×#23511yescharacteristic
952C22D32×D411yescharacteristic
953C22D3×#23711yescharacteristic
954C22D3×#23711yescharacteristic
955C22#6432011yescharacteristic
956C4—22no—
957C4—41no—
958C4—41no—
959C4—62no—
960C4—62no—
961C4—62no—
962C4—62no—
963C4—121no—
964C4—121no—
965C4—361no—
966C4—361no—
967C4—361no—
968C3—21no—
969C3#7470411yescharacteristic, complemented
970C3#7531911yescharacteristic, complemented
971C2—64no—
972C2—241no—
973C2—362no—
974C2#1059389911yescharacteristic
975C2#1059406511yescharacteristic
976C2#1059407811yescharacteristic
977C2D3×#88311yescharacteristic
978C2#1059441411yescharacteristic
979C2#1059444011yescharacteristic
980C2#1059462111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC2×#63886C2
hypercenter#95D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×D3×C4⋊Dic3C2semidirect
3. C2×#63880C2semidirect
4. C2×#63854C2semidirect
5. #10592373C2semidirect
6. C3×#4665C2semidirect
7. C3×#4654C2semidirect
8. #10591382C2semidirect
9. #10591376C2semidirect
10. #10591375C2semidirect
11. #10591373C2semidirect
12. #10591339C2semidirect
13. #10591317C2semidirect
14. #10591312C2semidirect
15. #10591305C2semidirect
85. #4665D3semidirect
87. #4654D3semidirect
131. C3×C4⋊Dic3D4semidirect
424. C4⋊Dic3D12semidirect
460. C2×C3×D3#123semidirect
803. C2×D3#883semidirect
834. C32#2443semidirect
969. C3#74704semidirect
970. C3#75319semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×#638862
C2×#638802
C2×#638542
#105923732
C3×#46652
C3×#46542
#105913822
#105913762
#105913752
#105913732
#105913392
#105913172
#105913122
#105913052
#753193
#747043