Finite Group Databasebeta

← #11812904

Subgroups — #11812904

Order 1152.

1425 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic, complemented
2C2×#63905C211yesmaximal, characteristic, complemented
3C2×#63885C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10592632C211yesmaximal, characteristic, complemented
6C3×#4940C211yesmaximal, characteristic, complemented
7#10591390C211yesmaximal, characteristic, complemented
8#10591381C211yesmaximal, characteristic, complemented
9#10591376C211yesmaximal, characteristic, complemented
10#10591373C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591358C211yesmaximal, characteristic, complemented
13#10591324C211yesmaximal, characteristic, complemented
14#10591299C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#82356—31nomaximal
17#75848—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C3×C4×D12—24no—
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊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
46#63905—24no—
47#63885—24no—
48D3×Dic3⋊C4—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×#939—31no—
59C2×#929—31no—
60C22×Dic3⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×#884—31no—
63C2×#883—31no—
64C2×C4×D12D311yescharacteristic, complemented
65C3×#388—31no—
66#5220—31no—
67#5213—31no—
68#5210—31no—
69#4993—31no—
70#4989—31no—
71#4983—31no—
72#4961—31no—
73#4959—31no—
74#4958—31no—
75#4956—31no—
76#4956—31no—
77#4952—31no—
78#4949—31no—
79#4946—31no—
80#4940D311yescharacteristic, complemented
81#4933—31no—
82#4933—31no—
83#4933—61no—
84#4675—31no—
85#4668—31no—
86#4665—31no—
87#4661—31no—
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×D12D414yes—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×#625—22no—
113C2×#625—22no—
114C2×#625—22no—
115C2×#625—22no—
116C2×#625—22no—
117C2×#625—41no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C32×C42—22no—
125#3750—22no—
126#3750D414yescomplemented
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×C4⋊Dic3—22no—
133C3×Dic3⋊C4—22no—
134#3724—22no—
135#3724—41no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—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—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—31no—
152C23×Dic3—31no—
153C23×Dic3—31no—
154C22×D12C2×D311yescharacteristic
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C3×C4×D4—64no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C42—21no—
168C2×C3×C42C2×D311yescharacteristic
169C2×C3×C42C2×D311yescharacteristic
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176#939—64no—
177#929—64no—
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)⋊C4C2×D311yescharacteristic
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D311yescharacteristic
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×C4⋊Dic3—31no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—61no—
203C2×Dic3⋊C4—61no—
204C2×Dic3⋊C4—64no—
205C2×Dic3⋊C4C2×D311yescharacteristic
206D3×C4⋊C4—64no—
207#884—64no—
208#883—64no—
209C4×D12—24no—
210C3×#95—31no—
211C3×#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
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⋊#95—61no—
227C3⋊#95—61no—
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×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×D3C2×D412yes—
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×C4C2×D412yes—
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⋊Dic3C2×D412yes—
272C2×C3⋊Dic3C2×D412yes—
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×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3#4112yes—
288C3×D12—28no—
289C3×C4×D3—44no—
290C3×C4×D3—44no—
291#625—44no—
292#625—44no—
293D3×Dic3—28no—
294D3×Dic3—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—31no—
298C22×C4⋊C4—91no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—31no—
304#387—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3—31no—
313C23×D3C22×D311yescharacteristic
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C2×C3×D4—34no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—121no—
332C22×C3×C4—121no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—121no—
350C2×#67—121no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—62no—
364C22×Dic3—62no—
365C22×Dic3—62no—
366C22×Dic3—62no—
367C22×Dic3—62no—
368C22×Dic3—121no—
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C2×D12—22no—
375C2×D12—22no—
376C2×D12#6714yes—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—41no—
382C2×C4×D3—41no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—121no—
389C3×C4⋊C4—62no—
390C3×C4⋊C4—62no—
391C3×C22⋊C4—62no—
392C3×C22⋊C4—62no—
393C3×C22⋊C4—62no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C42—22no—
397C3×C42—22no—
398C3×C42—42no—
399#217—62no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—62no—
404#217—121no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—121no—
416C4⋊Dic3—22no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419Dic3⋊C4—22no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—64no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—122no—
430Dic3⋊C4—121no—
431Dic3⋊C4—121no—
432C22×C32C22×D411yescharacteristic
433C22×C32C22×D411yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C22×C32C2×#4111yescharacteristic
437C22×C32H(5,𝔽2)11yescharacteristic
438C22×C322−1+411yescharacteristic
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
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#12314yescomplemented
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—41no—
463C3⋊Dic3—22no—
464C3⋊Dic3—22no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3—41no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C22×D4—31no—
473C22×D4—91no—
474C22×D4—91no—
475C23×C4—31no—
476C23×C4—31no—
477C23×C4—91no—
478C23×C4—91no—
479#123—184no—
480#121—184no—
481C4×D4—64no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—91no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—184no—
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
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×C42D3211yescharacteristic
503#95—31no—
504#95—31no—
505#95—91no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95—91no—
510#95—91no—
511C23×C3—21no—
512C23×C3—32no—
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×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3C23×D311yescharacteristic
534C23×C3C23×D311yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
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#23512yes—
553C22×D3#23512yes—
554C22×D3C2×#6712yes—
555C22×D3C2×#6712yes—
556C3×D4—68no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—22no—
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—22no—
573C2×C3×C4—22no—
574C2×C3×C4—32no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—124no—
596C2×C3×C4—124no—
597C2×C3×C4D3×D412yes—
598C2×C3×C4D3×D412yes—
599C2×C3×C4D3×D412yes—
600C2×C3×C4C2×#6712yes—
601#67—124no—
602#67—124no—
603#67—124no—
604#67—124no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—68no—
626C2×Dic3—61no—
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—61no—
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—121no—
655C2×Dic3—121no—
656C2×Dic3—124no—
657C2×Dic3#23512yes—
658D12—28no—
659C4×D3—44no—
660C4×D3—44no—
661C4×D3—68no—
662C4×D3—124no—
663C2×C32C2×#12311yescharacteristic
664C2×C32#52511yescharacteristic
665C2×C32#53911yescharacteristic
666C2×C32D4211yescharacteristic
667C2×C32#54711yescharacteristic
668C2×C32#54811yescharacteristic
669C2×C32#55311yescharacteristic
670C3×D3—24no—
671C3×D3—42no—
672C3×D3—81no—
673C24—31no—
674C24—31no—
675C24—31no—
676C2×D4—34no—
677C2×D4—62no—
678C2×D4—62no—
679C2×D4—182no—
680C2×D4—182no—
681C2×D4—182no—
682C2×D4—182no—
683C2×D4—182no—
684C2×D4—361no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—91no—
697C22×C4—91no—
698C22×C4—121no—
699C22×C4—121no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—182no—
705C22×C4—361no—
706C22×C4C2×D3211yescharacteristic
707C22×C4C2×D3211yescharacteristic
708C22×C4C2×D3211yescharacteristic
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—94no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—361no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—62no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—361no—
728C42—22no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—34no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3C2×#23511yescharacteristic
758C22×C3C2×#23511yescharacteristic
759C22×C3C2×#23511yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C22×C3#100411yescharacteristic
764C22×C3D3×#4111yescharacteristic
765C22×C3D3×#4111yescharacteristic
766C22×C3D3×#4111yescharacteristic
767C22×C3#100911yescharacteristic
768C22×C3#101011yescharacteristic
769C22×C3#101011yescharacteristic
770C22×C3C22×#6711yescharacteristic
771C2×D3—22no—
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3#92914yescomplemented
792C3×C4—22no—
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—42no—
797C3×C4—42no—
798C3×C4—42no—
799C3×C4—41no—
800C3×C4—41no—
801C3×C4—62no—
802C3×C4—121no—
803C3×C4—121no—
804C3×C4—121no—
805C3×C4—121no—
806Dic3—22no—
807Dic3—41no—
808Dic3—41no—
809Dic3—41no—
810Dic3—41no—
811Dic3—62no—
812Dic3—62no—
813Dic3—62no—
814Dic3—62no—
815Dic3—122no—
816Dic3—122no—
817Dic3—121no—
818Dic3—121no—
819Dic3—121no—
820Dic3—121no—
821Dic3—241no—
822Dic3—241no—
823C32#244311yescharacteristic, complemented, Sylow
824C23—32no—
825C23—32no—
826C23—32no—
827C23—32no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—61no—
839C23—61no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23C22×D3211yescharacteristic
846D4—68no—
847D4—364no—
848D4—364no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—32no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—61no—
861C2×C4—61no—
862C2×C4—61no—
863C2×C4—61no—
864C2×C4—61no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—92no—
872C2×C4—92no—
873C2×C4—124no—
874C2×C4—124no—
875C2×C4—188no—
876C2×C4—181no—
877C2×C4—181no—
878C2×C4—181no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—181no—
885C2×C4—181no—
886C2×C4—364no—
887C2×C4#380212yes—
888C2×C4D3×#6712yes—
889C2×C3—21no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—64no—
897C2×C3—122no—
898C2×C3—241no—
899C2×C3#553011yescharacteristic
900C2×C3#554011yescharacteristic
901C2×C3#554711yescharacteristic
902C2×C3#554711yescharacteristic
903C2×C3#555111yescharacteristic
904C2×C3#555211yescharacteristic
905C2×C3#556411yescharacteristic
906C2×C3#560911yescharacteristic
907C2×C3D3×#12311yescharacteristic
908C2×C3#567711yescharacteristic
909C2×C3#570711yescharacteristic
910C2×C3C2×#92911yescharacteristic
911C2×C3D4×#6711yescharacteristic
912C2×C3#582411yescharacteristic
913D3—24no—
914D3—42no—
915D3—81no—
916C22—34no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—121no—
930C22—121no—
931C22—121no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22#6429811yescharacteristic
938C22C2×#380211yescharacteristic
939C22D3×#23511yescharacteristic
940C22D3×#23511yescharacteristic
941C22D3×#23511yescharacteristic
942C22#6430711yescharacteristic
943C22C2×D3×#6711yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—62no—
948C4—121no—
949C4—121no—
950C4—121no—
951C4—121no—
952C4—182no—
953C4—182no—
954C4—361no—
955C4—361no—
956C3—21no—
957C3#7584811yescharacteristic, complemented
958C3#8235611yescharacteristic, complemented
959C2—64no—
960C2—122no—
961C2—241no—
962C2#1059390511yescharacteristic
963C2#1059391411yescharacteristic
964C2#1059392211yescharacteristic
965C2#1059400611yescharacteristic
966C2#1059488711yescharacteristic
967C2D3×#92911yescharacteristic
968C2#1059506911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC2×#63885C2
hypercenterC2×C42D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×D12C2semidirect
2. C2×#63905C2semidirect
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592632C2semidirect
6. C3×#4940C2semidirect
7. #10591390C2semidirect
8. #10591381C2semidirect
9. #10591376C2semidirect
10. #10591373C2semidirect
11. #10591363C2semidirect
12. #10591358C2semidirect
13. #10591324C2semidirect
14. #10591299C2semidirect
15. #10591277C2semidirect
64. C2×C4×D12D3semidirect
80. #4940D3semidirect
126. #3750D4semidirect
459. C2×C3×D3#123semidirect
791. C2×D3#929semidirect
823. C32#2443semidirect
957. C3#75848semidirect
958. C3#82356semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×#639052
C2×#638852
C2×D3×Dic3⋊C42
#105926322
C3×#49402
#105913902
#105913812
#105913762
#105913732
#105913632
#105913582
#105913242
#105912992
#105912772
#823563
#758483