Finite Group Databasebeta

← #11802102

Subgroups — #11802102

Order 1152.

1745 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic, complemented
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4C2×#63885C211yesmaximal, characteristic
5C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
6#10592348C211yesmaximal, characteristic, complemented
7C3×#4670C211yesmaximal, characteristic, complemented
8C3×#4665C211yesmaximal, characteristic, complemented
9#10591386C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591369C211yesmaximal, characteristic, complemented
12#10591368C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591279C211yesmaximal, characteristic, complemented
15#10591264C211yesmaximal, characteristic, complemented
16#75452—31nomaximal
17#74660—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×#3724C2211yescharacteristic
40C2×#3724C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47#63902—24no—
48#63902—24no—
49#63898—24no—
50#63885C418yescomplemented
51C4×D3×Dic3—24no—
52C32×#95C2211yescharacteristic
53#63658C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C2×#939—31no—
59C2×D4×Dic3—31no—
60C22×C4×Dic3—31no—
61C2×#893—31no—
62C2×#884—31no—
63C2×#67⋊C4—31no—
64C2×#67⋊C4—31no—
65C2×#67⋊C4—31no—
66C2×#67⋊C4—31no—
67C2×C42×D3—31no—
68C3×#388—31no—
69C3×#386—31no—
70#5213—31no—
71#4976—31no—
72#4957—31no—
73#4957—31no—
74#4956—31no—
75#4944—31no—
76#4942—31no—
77Dic3×C22⋊C4—31no—
78Dic3×C22⋊C4—31no—
79#4940—31no—
80#4670D311yescharacteristic, complemented
81#4667—31no—
82#4666—31no—
83#4666—31no—
84#4665D311yescharacteristic, complemented
85#4649—31no—
86#4649—31no—
87#4649—61no—
88#4647—31no—
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
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×D12—22no—
105C2×C3×D12—22no—
106C2×C3×D12C2×C414yescomplemented
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×#625—22no—
111C2×#625—22no—
112C2×#625—22no—
113C2×#625—22no—
114C2×#625C2×C414yescomplemented
115C2×#625C2×C414yescomplemented
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3C2×C414yescomplemented
127C2×D3×Dic3D414yescomplemented
128#3750—22no—
129#3750C2×C414yescomplemented
130C4×C3⋊Dic3—22no—
131C4×C3⋊Dic3—22no—
132C4×C3⋊Dic3D414yescomplemented
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4C2×C414yescomplemented
139C3×C4⋊Dic3—22no—
140C3×C4×Dic3—22no—
141#3724—22no—
142#3724—22no—
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146(C2×D3)⋊Dic3C2×C414yescomplemented
147Dic32—22no—
148Dic32—22no—
149C4×#121—91noSylow
150C22×C3×D4—31no—
151C23×C3×C4—31no—
152C22×#67—31no—
153C22×#67—31no—
154C22×#67—31no—
155C22×#67—31no—
156C23×Dic3—31no—
157C23×Dic3—31no—
158C23×Dic3—31no—
159C23×Dic3—31no—
160C22×D12C2×D311yescharacteristic
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3C2×D311yescharacteristic
166C2×C3×C4⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C42—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178#939—38no—
179D4×Dic3—64no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4C2×D311yescharacteristic
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×C4⋊Dic3C2×D311yescharacteristic
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—61no—
200C2×Dic3⋊C4—61no—
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—61no—
212C2×C4×Dic3—61no—
213C2×C4×Dic3—61no—
214C2×C4×Dic3—64no—
215C2×C4×Dic3C2×D311yescharacteristic
216#893—64no—
217#884—38no—
218#67⋊C4—64no—
219#67⋊C4—64no—
220#67⋊C4—64no—
221#67⋊C4—64no—
222C42×D3—64no—
223C3×#95—21no—
224C3×#95—31no—
225C3×#95—31no—
226C3×#95C2×D311yescharacteristic
227C3×#95C2×D311yescharacteristic
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—61no—
235C3⋊#95C2×D311yescharacteristic
236C3⋊#95C2×D311yescharacteristic
237C23×C32C2411yescharacteristic
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×D3C22×C412yes—
255C22×C3×D3C22×C412yes—
256C22×C3×D3C22×C412yes—
257C22×C3×D3C2×D412yes—
258C22×C3×D3#4112yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C22×C412yes—
267C2×C32×C4C2×D412yes—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C22×C412yes—
274C2×C3⋊Dic3C22×C412yes—
275C2×C3⋊Dic3C2×D412yes—
276C2×C3⋊Dic3C2×D412yes—
277C2×C3⋊Dic3C2×D412yes—
278C2×C3⋊Dic3#4112yes—
279C2×C3⋊Dic3#4112yes—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
293C2×C3×Dic3C2×D412yes—
294C2×C3×Dic3#4112yes—
295C3×D12—28no—
296C3×C4×D3—28no—
297#625—28no—
298#625—28no—
299D3×Dic3—28no—
300D3×Dic3—28no—
301D3×Dic3—44no—
302D3×Dic3—44no—
303C2×#121—91no—
304C2×C4×D4—91no—
305C2×C4×D4—91no—
306C2×C4×D4—91no—
307C22×C42—91no—
308#390—91no—
309#389—91no—
310#388—31no—
311#388—91no—
312#386—31no—
313#386—91no—
314#380—91no—
315C4×C4⋊C4—91no—
316C4×C22⋊C4—91no—
317C4×C22⋊C4—91no—
318C24×C3—31no—
319C24×C3—31no—
320C24×C3—31no—
321C23×D3C22×D311yescharacteristic
322C23×D3C22×D311yescharacteristic
323C23×D3C22×D311yescharacteristic
324C2×C3×D4—34no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—62no—
336C22×C3×C4—62no—
337C22×C3×C4—62no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—34no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—62no—
354C2×#67—62no—
355C2×#67—62no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—34no—
363C22×Dic3—34no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—62no—
378C22×Dic3—62no—
379C22×Dic3—62no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C2×D12—22no—
386C2×D12—22no—
387C2×D12C4×D314yescomplemented
388C2×C4×D3—22no—
389C2×C4×D3—22no—
390C2×C4×D3—22no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C3×C4⋊C4—62no—
404C3×C22⋊C4—34no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—62no—
409C3×C22⋊C4—62no—
410C3×C42—62no—
411#217—34no—
412#217—62no—
413#217—62no—
414#217—62no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—62no—
422(C2×D3)⋊C4—62no—
423(C2×D3)⋊C4—62no—
424(C2×D3)⋊C4C4×D314yescomplemented
425C4⋊Dic3—22no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—64no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—64no—
435Dic3⋊C4—62no—
436C4×Dic3—22no—
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—64no—
440C4×Dic3—62no—
441C4×Dic3—62no—
442C4×Dic3—62no—
443C4×Dic3—62no—
444C4×Dic3—62no—
445C4×Dic3—62no—
446C4×Dic3—62no—
447C4×Dic3—62no—
448C4×Dic3—122no—
449C4×Dic3—122no—
450C22×C32C23×C411yescharacteristic
451C22×C32C22×D411yescharacteristic
452C22×C32C22×D411yescharacteristic
453C22×C32C2×#4111yescharacteristic
454C22×C32C2×#4111yescharacteristic
455C22×C32C2×#4111yescharacteristic
456C22×C32C2×#4111yescharacteristic
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3C4×D414yescomplemented
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—41no—
481C3⋊Dic3—22no—
482C3⋊Dic3—41no—
483C3⋊Dic3C4×D414yescomplemented
484C3⋊Dic3#12114yescomplemented
485C3×Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C22×D4—31no—
491C22×D4—91no—
492C22×D4—91no—
493C23×C4—31no—
494C23×C4—91no—
495C23×C4—91no—
496C23×C4—91no—
497C23×C4—91no—
498#121—98no—
499C4×D4—184no—
500C4×D4—184no—
501C4×D4—184no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—31no—
511C2×C22⋊C4—31no—
512C2×C22⋊C4—31no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C42—31no—
518C2×C42—91no—
519C2×C42—91no—
520C2×C42—91no—
521C2×C42—91no—
522C2×C42—91no—
523C2×C42—184no—
524#95—31no—
525#95—31no—
526#95—91no—
527#95—91no—
528#95—91no—
529#95D3211yescharacteristic
530C23×C3—21no—
531C23×C3—32no—
532C23×C3—32no—
533C23×C3—32no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3C23×D311yescharacteristic
553C23×C3C23×D311yescharacteristic
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3C2×C4×D312yes—
571C22×D3C2×C4×D312yes—
572C22×D3C2×C4×D312yes—
573C22×D3D3×D412yes—
574C22×D3#23712yes—
575C3×D4—68no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—68no—
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×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4C2×C4×D312yes—
616C2×C3×C4C2×C4×D312yes—
617C2×C3×C4D3×D412yes—
618C2×C3×C4D3×D412yes—
619#67—68no—
620#67—68no—
621#67—68no—
622#67—68no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—32no—
638C2×Dic3—32no—
639C2×Dic3—32no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—68no—
657C2×Dic3—68no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—62no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—124no—
674C2×Dic3—124no—
675C2×Dic3C2×C4×D312yes—
676C2×Dic3D3×D412yes—
677C2×Dic3#23712yes—
678D12—28no—
679C4×D3—28no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3—124no—
683C4×D3—124no—
684C2×C32C2×C4×D411yescharacteristic
685C2×C32C2×C4×D411yescharacteristic
686C2×C32C4×#4111yescharacteristic
687C2×C32C2×#12111yescharacteristic
688C2×C32#52511yescharacteristic
689C2×C32#52911yescharacteristic
690C2×C32#53211yescharacteristic
691C3×D3—24no—
692C3×D3—42no—
693C3×D3—42no—
694C24—31no—
695C24—31no—
696C24—31no—
697C2×D4—34no—
698C2×D4—62no—
699C2×D4—62no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—182no—
703C2×D4—182no—
704C2×D4—182no—
705C2×D4—182no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—62no—
712C22×C4—62no—
713C22×C4—62no—
714C22×C4—94no—
715C22×C4—94no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—182no—
728C22×C4—182no—
729C22×C4—182no—
730C22×C4C2×D3211yescharacteristic
731C22×C4C2×D3211yescharacteristic
732C22×C4C2×D3211yescharacteristic
733C4⋊C4—62no—
734C4⋊C4—94no—
735C4⋊C4—182no—
736C4⋊C4—182no—
737C4⋊C4—182no—
738C22⋊C4—34no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—94no—
745C22⋊C4—182no—
746C22⋊C4—182no—
747C22⋊C4—182no—
748C42—62no—
749C42—94no—
750C42—182no—
751C42—182no—
752C42—182no—
753C42—182no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—34no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—121no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3C22×C4×D311yescharacteristic
783C22×C3C22×C4×D311yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×D3×D411yescharacteristic
786C22×C3C2×D3×D411yescharacteristic
787C22×C3C2×D3×D411yescharacteristic
788C22×C3C2×#23711yescharacteristic
789C22×C3C2×#23711yescharacteristic
790C22×C3D3×#4111yescharacteristic
791C22×C3D3×#4111yescharacteristic
792C22×C3D3×#4111yescharacteristic
793C22×C3D3×#4111yescharacteristic
794C22×C3D3×#4111yescharacteristic
795C22×C3D3×#4111yescharacteristic
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—22no—
799C2×D3—22no—
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—41no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3#67⋊C414yescomplemented
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—42no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—121no—
830C3×C4—121no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—34no—
835Dic3—34no—
836Dic3—34no—
837Dic3—34no—
838Dic3—41no—
839Dic3—41no—
840Dic3—64no—
841Dic3—64no—
842Dic3—62no—
843Dic3—62no—
844Dic3—122no—
845Dic3—122no—
846Dic3—121no—
847Dic3—121no—
848C32C4×#12111yescharacteristic, complemented, Sylow
849C23—32no—
850C23—32no—
851C23—32no—
852C23—32no—
853C23—32no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23—61no—
858C23—61no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—61no—
864C23—61no—
865C23—61no—
866C23—61no—
867C23—61no—
868C23—61no—
869C23—61no—
870C23C22×D3211yescharacteristic
871D4—68no—
872D4—188no—
873D4—188no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—32no—
884C2×C4—68no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—92no—
898C2×C4—92no—
899C2×C4—92no—
900C2×C4—92no—
901C2×C4—92no—
902C2×C4—92no—
903C2×C4—92no—
904C2×C4—188no—
905C2×C4—188no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—364no—
912C2×C4—364no—
913C2×C4C4×D3212yes—
914C2×C4#380212yes—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—64no—
923C2×C3—122no—
924C2×C3—122no—
925C2×C3C2×#67⋊C411yescharacteristic
926C2×C3#552211yescharacteristic
927C2×C3C4×#23711yescharacteristic
928C2×C3C4×D3×D411yescharacteristic
929C2×C3C4×D3×D411yescharacteristic
930C2×C3C4×D3×D411yescharacteristic
931C2×C3#558611yescharacteristic
932C2×C3#559611yescharacteristic
933C2×C3D3×#12111yescharacteristic
934C2×C3D3×#12111yescharacteristic
935C2×C3#564911yescharacteristic
936C2×C3#565611yescharacteristic
937C2×C3#566811yescharacteristic
938C2×C3#570611yescharacteristic
939D3—24no—
940D3—42no—
941D3—42no—
942C22—34no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—121no—
956C22—121no—
957C22—121no—
958C22—121no—
959C22—121no—
960C22—121no—
961C22—121no—
962C22—121no—
963C22C2×C4×D3211yescharacteristic
964C22C2×#380211yescharacteristic
965C22#6430611yescharacteristic
966C22D32×D411yescharacteristic
967C22D3×#23711yescharacteristic
968C22D3×#23711yescharacteristic
969C22#6431911yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—62no—
974C4—62no—
975C4—62no—
976C4—94no—
977C4—94no—
978C4—121no—
979C4—121no—
980C4—182no—
981C4—361no—
982C3—21no—
983C3#7466011yescharacteristic, complemented
984C3#7545211yescharacteristic, complemented
985C2—64no—
986C2—122no—
987C2—122no—
988C2C4×#380211yescharacteristic
989C2#1059406111yescharacteristic
990C2#1059408211yescharacteristic
991C2D3×#67⋊C411yescharacteristic
992C2#1059435811yescharacteristic
993C2#1059443511yescharacteristic
994C2#1059461211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63885C2
hypercenter#95D32
hypocenterC32C4×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63902C2semidirect
2. C2×#63902C2semidirect
3. C2×#63898C2semidirect
5. C2×C4×D3×Dic3C2semidirect
6. #10592348C2semidirect
7. C3×#4670C2semidirect
8. C3×#4665C2semidirect
9. #10591386C2semidirect
10. #10591381C2semidirect
11. #10591369C2semidirect
12. #10591368C2semidirect
13. #10591368C2semidirect
14. #10591279C2semidirect
15. #10591264C2semidirect
50. #63885C4semidirect
80. #4670D3semidirect
84. #4665D3semidirect
106. C2×C3×D12C2×C4semidirect
114. C2×#625C2×C4semidirect
115. C2×#625C2×C4semidirect
126. C2×D3×Dic3C2×C4semidirect
127. C2×D3×Dic3D4semidirect
129. #3750C2×C4semidirect
132. C4×C3⋊Dic3D4semidirect
138. C3×(C2×D3)⋊C4C2×C4semidirect
146. (C2×D3)⋊Dic3C2×C4semidirect
387. C2×D12C4×D3semidirect
424. (C2×D3)⋊C4C4×D3semidirect
477. C2×C3×D3C4×D4semidirect
483. C3⋊Dic3C4×D4semidirect
484. C3⋊Dic3#121semidirect
816. C2×D3#67⋊C4semidirect
848. C32C4×#121semidirect
983. C3#74660semidirect
984. C3#75452semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C2×#638982
C2×#638852
C2×C4×D3×Dic32
#105923482
C3×#46702
C3×#46652
#105913862
#105913812
#105913692
#105913682
#105912792
#105912642
#754523
#746603