Finite Group Databasebeta

← #11812884

Subgroups — #11812884

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63980C211yesmaximal, characteristic
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63891C211yesmaximal, characteristic, complemented
5#10592649C211yesmaximal, characteristic, complemented
6C3×#4958C211yesmaximal, characteristic, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8#10591710C211yesmaximal, characteristic, complemented
9#10591390C211yesmaximal, characteristic, complemented
10#10591379C211yesmaximal, characteristic, complemented
11#10591351C211yesmaximal, characteristic, complemented
12#10591317C211yesmaximal, characteristic, complemented
13#10591297C211yesmaximal, characteristic, complemented
14#10591284C211yesmaximal, characteristic, complemented
15#10591250C211yesmaximal, characteristic, complemented
16#74703—31nomaximal
17#74702—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33#63980—24no—
34Dic3×#67—24no—
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3—24no—
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48#63891—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#939—31no—
58C2×#939—31no—
59C2×D4×Dic3—31no—
60C2×C4×#67—31no—
61C22×C4⋊Dic3—31no—
62C22×Dic3⋊C4—31no—
63C2×#886—31no—
64C2×#883—31no—
65C3×#386—31no—
66C3×#386—31no—
67#5220—31no—
68#5213—31no—
69#4961—31no—
70#4959—31no—
71#4958D311yescharacteristic, complemented
72#4958D311yescharacteristic, complemented
73#4953—31no—
74#4950—31no—
75#4950—31no—
76#4950—31no—
77#4950—61no—
78#4949—31no—
79#4945—31no—
80#4677—31no—
81#4675—31no—
82#4670—31no—
83#4668—31no—
84#4661—31no—
85#4657—31no—
86#4653—31no—
87#4652—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—22no—
94C22×C3⋊Dic3—22no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67D414yes—
106C22×C3×Dic3—22no—
107C22×C3×Dic3—22no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3—22no—
110C22×C3×Dic3—22no—
111C22×C3×Dic3—41no—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C2×#625—22no—
119C2×#625—22no—
120C2×#625—41no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—41no—
124C32×C22⋊C4—22no—
125#3757—22no—
126C4⋊(C3⋊Dic3)—22no—
127C4⋊(C3⋊Dic3)—41no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—41no—
132#3724—22no—
133Dic3⋊Dic3—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3D414yescomplemented
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—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—31no—
148C23×C3×C4—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67C2×D311yescharacteristic
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3—31no—
156C23×Dic3—61no—
157C23×Dic3C2×D311yescharacteristic
158C23×Dic3C2×D311yescharacteristic
159C22×C4×D3—31no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4C2×D311yescharacteristic
167C2×#217—31no—
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—61no—
175#939—64no—
176#939—64no—
177D4×Dic3—64no—
178C4×#67—64no—
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×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—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—61no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3—64no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—64no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210#886—64no—
211#883—64no—
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⋊#95C2×D311yescharacteristic
227C3⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32C2×D412yes—
235C23×C32#4112yes—
236C23×C32#4112yes—
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×D3C2×D412yes—
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×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
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—44no—
270C2×C3⋊Dic3C2×D412yes—
271C3×#67—28no—
272C3×#67—44no—
273C2×C3×Dic3—28no—
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—21no—
288C2×C3×Dic3—44no—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3#4112yes—
293#625—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—91no—
305#386—31no—
306#386—31no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C2×C3×D4—34no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—62no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—22no—
342C2×#67—22no—
343C2×#67—22no—
344C2×#67—22no—
345C2×#67—22no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—121no—
351C2×#67—121no—
352C2×#67D1214yes—
353C22×Dic3—22no—
354C22×Dic3—22no—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3—22no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—41no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—122no—
378C22×Dic3—122no—
379C22×Dic3—121no—
380C22×Dic3—121no—
381C22×Dic3—121no—
382C22×Dic3—122no—
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—121no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—121no—
399#217—62no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—122no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—41no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416C4⋊Dic3—34no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—62no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—62no—
423C4⋊Dic3—122no—
424C4⋊Dic3—121no—
425C4⋊Dic3—121no—
426C4⋊Dic3—122no—
427Dic3⋊C4—34no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32#12314yescomplemented
443C22×C32C22×D411yescharacteristic
444C22×C32C22×D411yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32H(5,𝔽2)11yescharacteristic
449C22×C322−1+411yescharacteristic
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—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C32×C4—41no—
465C32×C4—41no—
466C3⋊Dic3—22no—
467C3⋊Dic3—41no—
468C3⋊Dic3—41no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C22×D4—31no—
477C22×D4—31no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—91no—
482C23×C4—91no—
483#123—184no—
484#121—184no—
485C4×D4—184no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—184no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4D3211yescharacteristic
506C2×C42—91no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—32no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
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×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3C2×D1212yes—
546C23×C3#23512yes—
547C23×C3D3×D412yes—
548C23×C3#23712yes—
549C23×C3#23712yes—
550C23×C3#23712yes—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—21no—
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×D3C2×D1212yes—
567C3×D4—68no—
568C3×D4—124no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
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—21no—
582C2×C3×C4—21no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—68no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
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—124no—
607#67—28no—
608#67—44no—
609#67—124no—
610#67—124no—
611C2×Dic3—28no—
612C2×Dic3—21no—
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—32no—
627C2×Dic3—32no—
628C2×Dic3—44no—
629C2×Dic3—62no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—62no—
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—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—124no—
664C2×Dic3—124no—
665C2×Dic3—124no—
666C2×Dic3—128no—
667C2×Dic3C2×D1212yes—
668C2×Dic3D3×D412yes—
669C2×Dic3D3×D412yes—
670C2×Dic3#23712yes—
671C4×D3—124no—
672C2×C32—24no—
673C2×C32C2×#12311yescharacteristic
674C2×C32#52511yescharacteristic
675C2×C32#53911yescharacteristic
676C2×C32D4211yescharacteristic
677C2×C32#54711yescharacteristic
678C2×C32#54811yescharacteristic
679C2×C32#55311yescharacteristic
680C3×D3—42no—
681C3×D3—81no—
682C24—31no—
683C24—31no—
684C24C2×D3211yescharacteristic
685C2×D4—34no—
686C2×D4—62no—
687C2×D4—62no—
688C2×D4—62no—
689C2×D4—62no—
690C2×D4—62no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—361no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—121no—
710C22×C4—182no—
711C22×C4—182no—
712C22×C4—182no—
713C22×C4—182no—
714C22×C4—361no—
715C22×C4—361no—
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3211yescharacteristic
718C4⋊C4—94no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—182no—
722C4⋊C4—182no—
723C4⋊C4—182no—
724C4⋊C4—182no—
725C4⋊C4—361no—
726C22⋊C4—22no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C22⋊C4—62no—
730C22⋊C4—121no—
731C22⋊C4—182no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C42—182no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—24no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—42no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3#88314yescomplemented
779C22×C3#88614yescomplemented
780C22×C3C22×D1211yescharacteristic
781C22×C3C2×#23511yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×D3×D411yescharacteristic
784C22×C3C2×D3×D411yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3C2×#23711yescharacteristic
787C22×C3C2×#23711yescharacteristic
788C22×C3C2×#23711yescharacteristic
789C22×C3#100411yescharacteristic
790C22×C3D3×#4111yescharacteristic
791C22×C3#100911yescharacteristic
792C22×C3#101011yescharacteristic
793C22×C3#101011yescharacteristic
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—41no—
805C2×D3—41no—
806C2×D3—41no—
807C2×D3—41no—
808C3×C4—42no—
809C3×C4—42no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—121no—
819C3×C4—121no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—41no—
825Dic3—41no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830Dic3—121no—
831Dic3—121no—
832Dic3—121no—
833Dic3—121no—
834Dic3—121no—
835Dic3—121no—
836Dic3—241no—
837Dic3—241no—
838C32#244311yescharacteristic, complemented, Sylow
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—32no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23—61no—
857C23#379512yes—
858C23D3×D1212yes—
859C23#380512yes—
860C23C22×D3211yescharacteristic
861D4—68no—
862D4—124no—
863D4—364no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—68no—
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—61no—
888C2×C4—61no—
889C2×C4—92no—
890C2×C4—124no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—364no—
903C2×C4—364no—
904C2×C3—24no—
905C2×C3—24no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—44no—
914C2×C3—122no—
915C2×C3—241no—
916C2×C3C2×#88311yescharacteristic
917C2×C3C2×#88611yescharacteristic
918C2×C3#554711yescharacteristic
919C2×C3D4×D1211yescharacteristic
920C2×C3#555511yescharacteristic
921C2×C3#556411yescharacteristic
922C2×C3#558611yescharacteristic
923C2×C3#559011yescharacteristic
924C2×C3#559811yescharacteristic
925C2×C3#559811yescharacteristic
926C2×C3#560111yescharacteristic
927C2×C3#561811yescharacteristic
928C2×C3#565511yescharacteristic
929C2×C3#566511yescharacteristic
930D3—42no—
931D3—81no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22—121no—
950C22—121no—
951C22—121no—
952C22#6389114yescomplemented
953C22C2×#379511yescharacteristic
954C22C2×D3×D1211yescharacteristic
955C22#6430911yescharacteristic
956C22D32×D411yescharacteristic
957C22D3×#23711yescharacteristic
958C22#6431411yescharacteristic
959C22C2×#380511yescharacteristic
960C4—41no—
961C4—41no—
962C4—62no—
963C4—62no—
964C4—62no—
965C4—62no—
966C4—121no—
967C4—121no—
968C4—182no—
969C4—361no—
970C4—361no—
971C4—361no—
972C3—21no—
973C3#7470211yescharacteristic, complemented
974C3#7470311yescharacteristic, complemented
975C2—24no—
976C2—122no—
977C2—241no—
978C2#1059405411yescharacteristic
979C2#1059407711yescharacteristic
980C2#1059417711yescharacteristic
981C2#1059427711yescharacteristic
982C2C2×#6389111yescharacteristic
983C2#1059514211yescharacteristic
984C2#1059518911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63980C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×#67C2semidirect
3. C22×Dic3⋊Dic3C2semidirect
4. C2×#63891C2semidirect
5. #10592649C2semidirect
6. C3×#4958C2semidirect
7. C3×#4958C2semidirect
8. #10591710C2semidirect
9. #10591390C2semidirect
10. #10591379C2semidirect
11. #10591351C2semidirect
12. #10591317C2semidirect
13. #10591297C2semidirect
14. #10591284C2semidirect
15. #10591250C2semidirect
71. #4958D3semidirect
72. #4958D3semidirect
137. Dic3⋊Dic3D4semidirect
442. C22×C32#123semidirect
778. C22×C3#883semidirect
779. C22×C3#886semidirect
838. C32#2443semidirect
952. C22#63891semidirect
973. C3#74702semidirect
974. C3#74703semidirect

Maximal subgroups

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

subgroupindex
C2×#639802
C2×Dic3×#672
C22×Dic3⋊Dic32
C2×#638912
#105926492
C3×#49582
#105917102
#105913902
#105913792
#105913512
#105913172
#105912972
#105912842
#105912502
#747033
#747023