Finite Group Databasebeta

← #11807614

Subgroups — #11807614

Order 1152.

1519 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63923C211yesmaximal, characteristic
2#10592364C211yesmaximal, characteristic, complemented
3C3×#4670C211yesmaximal, characteristic, complemented
4C3×#4669C211yesmaximal, characteristic, complemented
5#10591399C211yesmaximal, characteristic, complemented
6#10591399C211yesmaximal, characteristic, complemented
7#10591387C211yesmaximal, characteristic, complemented
8#10591387C211yesmaximal, characteristic, complemented
9#10591384C211yesmaximal, characteristic, complemented
10#10591383C211yesmaximal, characteristic, complemented
11#10591320C211yesmaximal, characteristic, complemented
12#10591307C211yesmaximal, characteristic, complemented
13#10591305C211yesmaximal, characteristic, complemented
14#10591289C211yesmaximal, characteristic, complemented
15#10591259C211yesmaximal, characteristic, complemented
16#75840—31nomaximal
17#75840—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic, complemented
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
34C2×C3×C4×Dic3C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36C2×Dic3⋊Dic3C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×#3722C2211yescharacteristic, complemented
41C2×#3722C2211yescharacteristic, complemented
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×Dic32C2211yescharacteristic, complemented
47#63923C418yescomplemented
48C32×#95C2211yescharacteristic, complemented
49#63658C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C2×#882—31no—
55C2×#882—31no—
56C3×#388—31no—
57C3×#388—31no—
58#4990—31no—
59#4990—31no—
60#4988—31no—
61#4988—31no—
62#4957—31no—
63#4957—31no—
64#4956—31no—
65#4956—31no—
66#4955—31no—
67#4955—31no—
68#4955—31no—
69#4955—31no—
70#4951—31no—
71#4951—31no—
72#4940—31no—
73#4940—31no—
74#4939—31no—
75#4939—31no—
76#4670—31no—
77#4670D311yescharacteristic, complemented
78#4669—31no—
79#4669D311yescharacteristic, complemented
80#4665—31no—
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4665—61no—
85C23×C3⋊D3C2311yescharacteristic
86C23×C3⋊D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×D32—41no—
90C22×D32—41no—
91C22×D32—41no—
92C22×D32—41no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32C2×C414yescomplemented
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4⋊(C3⋊D3)—41no—
102C2×C4⋊(C3⋊D3)—41no—
103C2×C4⋊(C3⋊D3)C2×C414yes—
104C2×C4×C3⋊D3—41no—
105C2×C4×C3⋊D3—41no—
106C2×C4×C3⋊D3—41no—
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C2×#626—41no—
114C2×#626—41no—
115C2×#626—41no—
116C2×#626—41no—
117C2×#626C2×C414yes—
118C2×#626C2×C414yes—
119#3752—41no—
120#3752—41no—
121#3752—41no—
122C3×(C2×D3)⋊C4—41no—
123C3×(C2×D3)⋊C4—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4C2×C414yescomplemented
127C3×(C2×D3)⋊C4C2×C414yescomplemented
128C3×C4⋊Dic3—41no—
129C3×Dic3⋊C4—41no—
130C3×C4×Dic3—41no—
131C3×C4×Dic3—41no—
132Dic3⋊Dic3—41no—
133#3722—41no—
134#3722—41no—
135#3722—41no—
136#3722—41no—
137#3722C2×C414yescomplemented
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3—41no—
142Dic32—41no—
143#2375—91noSylow
144C24×D3—31no—
145C24×D3—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×D12—31no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C42—31no—
165C2×C3×C42—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
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—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3C2×D311yescharacteristic, complemented
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4C2×D311yescharacteristic, complemented
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3C2×D311yescharacteristic, complemented
206C2×C4×Dic3C2×D311yescharacteristic, complemented
207#882—38no—
208#882—38no—
209C3×#95—21no—
210C3×#95—31no—
211C3×#95—31no—
212C3×#95C2×D311yescharacteristic, complemented
213C3×#95C2×D311yescharacteristic, complemented
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—61no—
221C3⋊#95C2×D311yescharacteristic, complemented
222C3⋊#95C2×D311yescharacteristic, complemented
223C23×C32C2411yescharacteristic
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3—21no—
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C22×C412yes—
237C22×C3⋊D3C22×C412yes—
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×D3C22×C412yes—
251C22×C3×D3C22×C412yes—
252C2×D32—44no—
253C2×D32—44no—
254C2×D32—44no—
255C2×D32—44no—
256C2×D32—44no—
257C2×D32—44no—
258C2×D32—44no—
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×C4—21no—
267C2×C32×C4C22×C412yes—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C4⋊(C3⋊D3)—44no—
275C4×C3⋊D3—44no—
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×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×Dic3C22×C412yes—
294#626—44no—
295#626—44no—
296C2×#120—91no—
297#390—91no—
298#390—91no—
299#390—91no—
300#388—31no—
301#388—31no—
302#388—91no—
303#388—91no—
304#388—91no—
305#388—91no—
306#386—91no—
307#386—91no—
308#386—91no—
309#379—91no—
310#379—91no—
311C24×C3—31no—
312C24×C3—31no—
313C23×D3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—31no—
317C23×D3—34no—
318C23×D3—34no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C23×D3—121no—
323C23×D3—121no—
324C23×D3—121no—
325C23×D3—121no—
326C23×D3—121no—
327C23×D3—121no—
328C23×D3—121no—
329C23×D3—121no—
330C23×D3—121no—
331C23×D3—121no—
332C23×D3—121no—
333C23×D3C22×D311yescharacteristic
334C23×D3C22×D311yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—121no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—121no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C2×D12—34no—
369C2×D12—34no—
370C2×D12—34no—
371C2×D12—34no—
372C2×D12—64no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12—121no—
376C2×D12—121no—
377C2×D12—122no—
378C2×D12—122no—
379C2×D12—121no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12—121no—
383C2×C4×D3—121no—
384C2×C4×D3—121no—
385C2×C4×D3—121no—
386C2×C4×D3—121no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C2×C4×D3—122no—
390C2×C4×D3—122no—
391C2×C4×D3—122no—
392C3×C4⋊C4—121no—
393C3×C4⋊C4—121no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—121no—
397C3×C22⋊C4—121no—
398C3×C22⋊C4—121no—
399C3×C22⋊C4—121no—
400C3×C42—121no—
401C3×C42—121no—
402#217—121no—
403#217—121no—
404#217—121no—
405#217—121no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—41no—
409(C2×D3)⋊C4—41no—
410(C2×D3)⋊C4—41no—
411(C2×D3)⋊C4—41no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—121no—
426(C2×D3)⋊C4—122no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4—121no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4—122no—
432(C2×D3)⋊C4—122no—
433(C2×D3)⋊C4C4×D314yescomplemented
434(C2×D3)⋊C4C4×D314yescomplemented
435C4⋊Dic3—41no—
436C4⋊Dic3—121no—
437Dic3⋊C4—41no—
438Dic3⋊C4—121no—
439C4×Dic3—41no—
440C4×Dic3—41no—
441C4×Dic3—121no—
442C4×Dic3—121no—
443C22×C32C23×C411yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C22×C32H(5,𝔽2)11yescharacteristic
447C22×C32H(5,𝔽2)11yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C2×C3⋊D3—22no—
451C2×C3⋊D3—22no—
452C2×C3⋊D3—22no—
453C2×C3⋊D3—22no—
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
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×D3—41no—
478D32—416no—
479C32×C4—22no—
480C32×C4—41no—
481C32×C4—41no—
482C3⋊Dic3—41no—
483C3⋊Dic3—41no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C25—91no—
491C22×D4—91no—
492C22×D4—91no—
493C22×D4—91no—
494C23×C4—91no—
495#120—98no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—91no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—91no—
520#95—31no—
521#95—31no—
522#95—91no—
523#95—91no—
524#95—91no—
525#95D3211yescharacteristic, complemented
526C23×C3—21no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—32no—
556C22×D3—32no—
557C22×D3—32no—
558C22×D3—32no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—61no—
580C22×D3—61no—
581C22×D3—61no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—121no—
588C22×D3—121no—
589C22×D3—121no—
590C22×D3—121no—
591C22×D3—121no—
592C22×D3—121no—
593C22×D3—121no—
594C22×D3—121no—
595C22×D3—121no—
596C22×D3—121no—
597C22×D3—124no—
598C22×D3—124no—
599C22×D3—124no—
600C22×D3—124no—
601C22×D3—124no—
602C22×D3—124no—
603C22×D3—124no—
604C22×D3—124no—
605C22×D3—124no—
606C22×D3—124no—
607C22×D3—124no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—124no—
611C22×D3C2×C4×D312yes—
612C22×D3C2×C4×D312yes—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—22no—
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—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—22no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—41no—
634C2×C3×C4—41no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
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—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4C2×C4×D312yes—
657C2×C3×C4C2×C4×D312yes—
658#67—124no—
659#67—124no—
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—21no—
673C2×Dic3—21no—
674C2×Dic3—21no—
675C2×Dic3—21no—
676C2×Dic3—62no—
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—61no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—121no—
692C2×Dic3—121no—
693C2×Dic3—121no—
694C2×Dic3C2×C4×D312yes—
695C2×Dic3C2×C4×D312yes—
696D12—124no—
697D12—124no—
698D12—128no—
699D12—124no—
700D12—124no—
701C4×D3—128no—
702C4×D3—124no—
703C4×D3—124no—
704C2×C32#51811yescharacteristic
705C2×C32#51811yescharacteristic
706C2×C32#51811yescharacteristic
707C2×C32#56011yescharacteristic
708C2×C32#56011yescharacteristic
709C2×C32#56011yescharacteristic
710C2×C32H(3,𝔽4)11yescharacteristic
711C3⋊D3—42no—
712C3⋊D3—42no—
713C3×D3—42no—
714C3×D3—42no—
715C24—31no—
716C24—31no—
717C24—94no—
718C24—91no—
719C24—91no—
720C24—361no—
721C24—361no—
722C24—361no—
723C24—361no—
724C24—361no—
725C24—361no—
726C2×D4—94no—
727C2×D4—94no—
728C2×D4—94no—
729C2×D4—361no—
730C2×D4—361no—
731C2×D4—361no—
732C2×D4—361no—
733C2×D4—361no—
734C2×D4—361no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—361no—
744C22×C4—361no—
745C22×C4—361no—
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C22×C4C2×D3211yescharacteristic
749C4⋊C4—121no—
750C4⋊C4—121no—
751C4⋊C4—361no—
752C22⋊C4—34no—
753C22⋊C4—34no—
754C22⋊C4—94no—
755C22⋊C4—121no—
756C22⋊C4—121no—
757C22⋊C4—121no—
758C22⋊C4—121no—
759C22⋊C4—361no—
760C22⋊C4—361no—
761C22⋊C4—361no—
762C22⋊C4—361no—
763C22⋊C4—361no—
764C22⋊C4—361no—
765C22⋊C4—361no—
766C22⋊C4—361no—
767C22⋊C4—361no—
768C22⋊C4—361no—
769C22⋊C4—361no—
770C42—121no—
771C42—121no—
772C42—361no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3C22×C4×D311yescharacteristic
795C22×C3C22×C4×D311yescharacteristic
796C22×C3#100411yescharacteristic
797C22×C3#100411yescharacteristic
798C22×C3#100411yescharacteristic
799C22×C3#100411yescharacteristic
800C22×C3#100911yescharacteristic
801C22×C3#100911yescharacteristic
802C22×C3#100911yescharacteristic
803C22×C3#100911yescharacteristic
804C22×C3#100911yescharacteristic
805C22×C3#100911yescharacteristic
806C22×C3#100911yescharacteristic
807C22×C3#100911yescharacteristic
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—64no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—122no—
836C2×D3—122no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—1216no—
841C2×D3—1216no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
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—241no—
863C2×D3—241no—
864C2×D3—241no—
865C2×D3—241no—
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—42no—
869C3×C4—42no—
870C3×C4—41no—
871C3×C4—41no—
872C3×C4—41no—
873C3×C4—41no—
874C3×C4—62no—
875C3×C4—62no—
876C3×C4—81no—
877C3×C4—121no—
878C3×C4—121no—
879C3×C4—121no—
880C3×C4—121no—
881Dic3—22no—
882Dic3—22no—
883Dic3—41no—
884Dic3—41no—
885Dic3—41no—
886Dic3—41no—
887Dic3—122no—
888Dic3—121no—
889Dic3—121no—
890Dic3—121no—
891Dic3—121no—
892Dic3—241no—
893C32#237511yescharacteristic, complemented, Sylow
894C23—32no—
895C23—32no—
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—92no—
909C23—92no—
910C23—181no—
911C23—181no—
912C23—181no—
913C23—181no—
914C23—181no—
915C23—181no—
916C23—181no—
917C23—181no—
918C23—181no—
919C23—181no—
920C23—181no—
921C23—181no—
922C23—364no—
923C23—364no—
924C23—364no—
925C23—364no—
926C23—364no—
927C23—364no—
928C23—364no—
929C23C22×D3211yescharacteristic
930D4—364no—
931D4—364no—
932D4—364no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—32no—
942C2×C4—32no—
943C2×C4—61no—
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—61no—
958C2×C4—61no—
959C2×C4—181no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—364no—
966C2×C4C4×D3212yes—
967C2×C3—21no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—122no—
975C2×C3—122no—
976C2×C3#552111yescharacteristic
977C2×C3#552111yescharacteristic
978C2×C3#554511yescharacteristic
979C2×C3#554511yescharacteristic
980C2×C3#554511yescharacteristic
981C2×C3#554511yescharacteristic
982C2×C3#562011yescharacteristic
983C2×C3#562011yescharacteristic
984C2×C3#566611yescharacteristic
985C2×C3#566611yescharacteristic
986C2×C3#568311yescharacteristic
987C2×C3#568311yescharacteristic
988C2×C3#571111yescharacteristic
989C2×C3#571111yescharacteristic
990D3—42no—
991D3—42no—
992D3—124no—
993D3—122no—
994D3—122no—
995D3—122no—
996D3—122no—
997D3—242no—
998C22—62no—
999C22—62no—
1000C22—62no—
1001C22—62no—
1002C22—62no—
1003C22—62no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—182no—
1013C22—182no—
1014C22—182no—
1015C22—182no—
1016C22—182no—
1017C22—182no—
1018C22—3616no—
1019C22—361no—
1020C22—361no—
1021C22—361no—
1022C22—361no—
1023C22—361no—
1024C22—361no—
1025C22—361no—
1026C22—361no—
1027C22C2×C4×D3211yescharacteristic
1028C22#6430711yescharacteristic
1029C22#6430811yescharacteristic
1030C22#6431411yescharacteristic
1031C22#6431411yescharacteristic
1032C22#6431411yescharacteristic
1033C22#6432011yescharacteristic
1034C4—22no—
1035C4—41no—
1036C4—41no—
1037C4—62no—
1038C4—62no—
1039C4—121no—
1040C4—121no—
1041C4—121no—
1042C4—121no—
1043C4—361no—
1044C4—361no—
1045C3—21no—
1046C3#7584011yescharacteristic, complemented
1047C3#7584011yescharacteristic, complemented
1048C2—122no—
1049C2—122no—
1050C2—362no—
1051C2—362no—
1052C2#1059399411yescharacteristic
1053C2#1059425611yescharacteristic
1054C2#1059430811yescharacteristic
1055C2#1059431111yescharacteristic
1056C2#1059460411yescharacteristic
1057C2#1059466111yescharacteristic
1058C2#1059466311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
hypercenter#95D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. #10592364C2semidirect
3. C3×#4670C2semidirect
4. C3×#4669C2semidirect
5. #10591399C2semidirect
6. #10591399C2semidirect
7. #10591387C2semidirect
8. #10591387C2semidirect
9. #10591384C2semidirect
10. #10591383C2semidirect
11. #10591320C2semidirect
12. #10591307C2semidirect
13. #10591305C2semidirect
14. #10591289C2semidirect
15. #10591259C2semidirect
20. C22×C4×C3⋊D3C22semidirect
25. C2×#3752C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C2×C3×Dic3⋊C4C22semidirect
34. C2×C3×C4×Dic3C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
40. C2×#3722C22semidirect
41. C2×#3722C22semidirect
46. C2×Dic32C22semidirect
47. #63923C4semidirect
48. C32×#95C22semidirect
49. #63658C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
77. #4670D3semidirect
79. #4669D3semidirect
95. C22×D32C2×C4semidirect
126. C3×(C2×D3)⋊C4C2×C4semidirect
127. C3×(C2×D3)⋊C4C2×C4semidirect
137. #3722C2×C4semidirect
200. C2×C4⋊Dic3C2×D3semidirect
202. C2×Dic3⋊C4C2×D3semidirect
205. C2×C4×Dic3C2×D3semidirect
206. C2×C4×Dic3C2×D3semidirect
212. C3×#95C2×D3semidirect
213. C3×#95C2×D3semidirect
221. C3⋊#95C2×D3semidirect
222. C3⋊#95C2×D3semidirect
433. (C2×D3)⋊C4C4×D3semidirect
434. (C2×D3)⋊C4C4×D3semidirect
525. #95D32semidirect
893. C32#2375semidirect
1046. C3#75840semidirect
1047. C3#75840semidirect

Maximal subgroups

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

subgroupindex
C2×#639232
#105923642
C3×#46702
C3×#46692
#105913992
#105913872
#105913842
#105913832
#105913202
#105913072
#105913052
#105912892
#105912592
#758403