Finite Group Databasebeta

← #11803039

Subgroups — #11803039

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊Dic3C211yesmaximal, characteristic
2C2×#63658C211yesmaximal, characteristic, complemented
3C3×#5213C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5#10591719C211yesmaximal, characteristic, complemented
6#10591713C211yesmaximal, characteristic
7#10591705C211yesmaximal, characteristic, complemented
8#10591366C211yesmaximal, characteristic, complemented
9#10591362C211yesmaximal, characteristic, complemented
10#10591285C211yesmaximal, characteristic, complemented
11#10591284C211yesmaximal, characteristic, complemented
12#10591254C211yesmaximal, characteristic, complemented
13#10591253C211yesmaximal, characteristic, complemented
14#10591248C211yesmaximal, characteristic, complemented
15#10591245C211yesmaximal, characteristic, complemented
16#74663—31nomaximal
17#74383—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C23×C3⋊Dic3C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30#67⋊Dic3C418yescomplemented
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×D4×Dic3—31no—
55C2×#67⋊C4—31no—
56C3×#386—31no—
57C3×#385—31no—
58#5220—31no—
59#5213D311yescharacteristic
60#5210D311yescharacteristic, complemented
61C2×C3⋊#95—31no—
62C2×C3⋊#95—31no—
63C2×C3⋊#95—61no—
64#4990—31no—
65#4987—31no—
66#4978—31no—
67#4977—31no—
68#4958—31no—
69#4950—31no—
70#4946—31no—
71#4945—31no—
72#4944—31no—
73#4943—31no—
74#4942—31no—
75Dic3×C22⋊C4—31no—
76Dic3×C22⋊C4—31no—
77#4670—31no—
78#4664—31no—
79#4655—31no—
80#4654—31no—
81#4653—31no—
82#4651—31no—
83#4651—31no—
84#4650—31no—
85C24×C32C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4—22no—
88C22×C32×C4—41no—
89C22×C32×C4—41no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3—41no—
94C22×C3⋊Dic3—41no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3C2×C414yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67C2×C414yes—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×D3×Dic3—41no—
113C2×D3×Dic3—41no—
114C2×D3×Dic3C2×C414yescomplemented
115C3×#217—22no—
116C3×#217—22no—
117C3×#217C2×C414yes—
118C3×(C2×D3)⋊C4—41no—
119C3×(C2×D3)⋊C4—41no—
120C3×Dic3⋊C4—41no—
121C3×Dic3⋊C4—41no—
122Dic3⋊Dic3—41no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3C2×C414yescomplemented
125(C2×D3)⋊Dic3—41no—
126(C2×D3)⋊Dic3—41no—
127(C2×D3)⋊Dic3C2×C414yescomplemented
128Dic32—41no—
129Dic32—41no—
130Dic32C2×C414yescomplemented
131#2318—91noSylow
132C22×C3×D4—31no—
133C23×C3×C4—21no—
134C23×C3×C4C2×D311yescharacteristic
135C23×C3×C4C2×D311yescharacteristic
136C22×#67C2×D311yescharacteristic
137C23×Dic3—31no—
138C23×Dic3—31no—
139C23×Dic3—31no—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C23×Dic3—61no—
143C23×Dic3—61no—
144C22×C4×D3—31no—
145C2×C3×C4⋊C4—31no—
146C2×C3×C4⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217C2×D311yescharacteristic
156C2×#217C2×D311yescharacteristic
157C2×#217C2×D311yescharacteristic
158D4×Dic3—38no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4C2×D311yescharacteristic
163C2×(C2×D3)⋊C4C2×D311yescharacteristic
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178#67⋊C4—38no—
179C3×#95—31no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3⋊#95—31no—
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95—61no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C23×C32—21no—
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32C22×C412yes—
216C23×C32#4112yes—
217C23×C32#4112yes—
218C23×C32C2411yescharacteristic
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3C22×C412yes—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—44no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—44no—
244C2×C3⋊Dic3—44no—
245C2×C3⋊Dic3C22×C412yes—
246C2×C3⋊Dic3C22×C412yes—
247C3×#67—28no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—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×Dic3C22×C412yes—
267C2×C3×Dic3C22×C412yes—
268C2×C3×Dic3C22×C412yes—
269D3×Dic3—44no—
270C2×C4×D4—91no—
271#388—91no—
272#388—91no—
273#387—91no—
274#387—91no—
275#386—31no—
276#386—91no—
277#385—31no—
278#385—91no—
279#383—91no—
280#382—91no—
281#381—91no—
282#380—91no—
283C4×C22⋊C4—91no—
284C2×#95—91no—
285C24×C3—21no—
286C24×C3—31no—
287C24×C3C22×D311yescharacteristic
288C24×C3C22×D311yescharacteristic
289C23×D3C22×D311yescharacteristic
290C2×C3×D4—34no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C22×C3×C4—24no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—41no—
306C22×C3×C4—41no—
307C22×C3×C4—41no—
308C22×C3×C4—41no—
309C22×C3×C4—42no—
310C22×C3×C4—42no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—22no—
316C2×#67—22no—
317C2×#67C4×D314yes—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—34no—
323C22×Dic3—34no—
324C22×Dic3—34no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—64no—
334C22×Dic3—64no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—121no—
338C22×Dic3—121no—
339C22×Dic3—121no—
340C22×Dic3—121no—
341C22×Dic3—121no—
342C22×Dic3—121no—
343C22×Dic3—121no—
344C22×Dic3—121no—
345C22×Dic3—121no—
346C22×Dic3—121no—
347C22×Dic3—122no—
348C22×Dic3—122no—
349C22×Dic3—122no—
350C22×Dic3—122no—
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C2×C4×D3—34no—
359C2×C4×D3—121no—
360C2×C4×D3—121no—
361C3×C4⋊C4—121no—
362C3×C4⋊C4—121no—
363C3×C22⋊C4—34no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—62no—
366C3×C22⋊C4—121no—
367C3×C22⋊C4—121no—
368#217—22no—
369#217—22no—
370#217—34no—
371#217—121no—
372#217—121no—
373#217C4×D314yes—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—41no—
376(C2×D3)⋊C4—41no—
377(C2×D3)⋊C4—121no—
378(C2×D3)⋊C4—121no—
379C4⋊Dic3—34no—
380C4⋊Dic3—121no—
381C4⋊Dic3—121no—
382Dic3⋊C4—34no—
383Dic3⋊C4—41no—
384Dic3⋊C4—41no—
385Dic3⋊C4—121no—
386Dic3⋊C4—121no—
387C4×Dic3—34no—
388C4×Dic3—34no—
389C4×Dic3—121no—
390C4×Dic3—121no—
391C4×Dic3—121no—
392C4×Dic3—121no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32#11714yes—
400C22×C32C23×C411yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32H(5,𝔽2)11yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
405C22×C32H(5,𝔽2)11yescharacteristic
406C22×C322−1+411yescharacteristic
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C32×C4—41no—
415C32×C4—41no—
416C3⋊Dic3—22no—
417C3⋊Dic3—22no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—31no—
428C23×C4—91no—
429C23×C4—91no—
430C23×C4—91no—
431C23×C4D3211yescharacteristic
432C4×D4—98no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C22⋊C4—31no—
439C2×C22⋊C4—31no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—91no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C42—91no—
447C2×C42—91no—
448C2×C42—91no—
449#95—31no—
450#95—31no—
451#95—31no—
452#95—31no—
453#95—91no—
454#95—91no—
455#95—91no—
456#95—91no—
457#95—91no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—32no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3C2×C4×D312yes—
487C23×C3C2×C4×D312yes—
488C23×C3#23712yes—
489C23×C3#23712yes—
490C23×C3#23712yes—
491C23×C3#23912yes—
492C23×C3C23×D311yescharacteristic
493C23×C3C23×D311yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3C2×C4×D312yes—
501C3×D4—68no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—48no—
524C2×C3×C4—44no—
525C2×C3×C4—44no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544#67—28no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—62no—
568C2×Dic3—62no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—124no—
600C2×Dic3—124no—
601C2×Dic3—124no—
602C2×Dic3—128no—
603C2×Dic3—128no—
604C2×Dic3—124no—
605C2×Dic3—124no—
606C2×Dic3C2×C4×D312yes—
607C2×Dic3C2×C4×D312yes—
608C2×Dic3C2×C4×D312yes—
609C4×D3—124no—
610C2×C32—24no—
611C2×C32C2×#11711yescharacteristic
612C2×C32#51811yescharacteristic
613C2×C32#52011yescharacteristic
614C2×C32#53811yescharacteristic
615C2×C32#53811yescharacteristic
616C2×C32#53911yescharacteristic
617C2×C32#53911yescharacteristic
618C3×D3—42no—
619C24—31no—
620C24C2×D3211yescharacteristic
621C2×D4—34no—
622C2×D4—62no—
623C2×D4—62no—
624C22×C4—22no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—94no—
635C22×C4—91no—
636C22×C4—91no—
637C22×C4—94no—
638C22×C4—91no—
639C22×C4—91no—
640C22×C4—182no—
641C22×C4—361no—
642C22×C4—361no—
643C22×C4—361no—
644C22×C4—361no—
645C22×C4—361no—
646C22×C4—361no—
647C22×C4C2×D3211yescharacteristic
648C22×C4C2×D3211yescharacteristic
649C4⋊C4—94no—
650C4⋊C4—121no—
651C4⋊C4—121no—
652C4⋊C4—361no—
653C4⋊C4—361no—
654C22⋊C4—34no—
655C22⋊C4—62no—
656C22⋊C4—62no—
657C22⋊C4—94no—
658C22⋊C4—121no—
659C22⋊C4—121no—
660C22⋊C4—361no—
661C22⋊C4—361no—
662C42—94no—
663C42—361no—
664C42—361no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—24no—
668C22×C3—24no—
669C22×C3—24no—
670C22×C3—24no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—24no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3—121no—
698C22×C3#87714yes—
699C22×C3#89214yes—
700C22×C3C22×C4×D311yescharacteristic
701C22×C3C22×C4×D311yescharacteristic
702C22×C3C2×#23711yescharacteristic
703C22×C3C2×#23711yescharacteristic
704C22×C3C2×#23711yescharacteristic
705C22×C3#100411yescharacteristic
706C22×C3#100411yescharacteristic
707C22×C3#100411yescharacteristic
708C22×C3#100411yescharacteristic
709C22×C3C2×#23911yescharacteristic
710C22×C3#100911yescharacteristic
711C22×C3#100911yescharacteristic
712C22×C3#101011yescharacteristic
713C22×C3#101011yescharacteristic
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C3×C4—42no—
722C3×C4—42no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—121no—
733C3×C4—121no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—41no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—122no—
746Dic3—122no—
747Dic3—122no—
748Dic3—122no—
749Dic3—121no—
750Dic3—121no—
751Dic3—121no—
752Dic3—121no—
753C32#231811yescharacteristic, complemented, Sylow
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—32no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23#379612yes—
766C23C4×D3212yes—
767C23#380512yes—
768C23C22×D3211yescharacteristic
769D4—68no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—44no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—92no—
799C2×C4—92no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—181no—
803C2×C4—181no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—364no—
811C2×C4—364no—
812C2×C4—364no—
813C2×C3—28no—
814C2×C3—24no—
815C2×C3—24no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—122no—
824C2×C3C2×#87711yescharacteristic
825C2×C3C2×#89211yescharacteristic
826C2×C3#554511yescharacteristic
827C2×C3#554511yescharacteristic
828C2×C3#554611yescharacteristic
829C2×C3#554611yescharacteristic
830C2×C3#559311yescharacteristic
831C2×C3#559311yescharacteristic
832C2×C3#560211yescharacteristic
833C2×C3#561711yescharacteristic
834C2×C3#564411yescharacteristic
835C2×C3#564511yescharacteristic
836C2×C3#566511yescharacteristic
837C2×C3#566511yescharacteristic
838D3—42no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22#6387814yes—
853C22C2×#379611yescharacteristic
854C22#6429811yescharacteristic
855C22C2×C4×D3211yescharacteristic
856C22#6430811yescharacteristic
857C22C2×#380511yescharacteristic
858C22#6433011yescharacteristic
859C22#6433011yescharacteristic
860C4—41no—
861C4—41no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—121no—
866C4—121no—
867C4—121no—
868C4—121no—
869C4—182no—
870C4—182no—
871C4—361no—
872C4—361no—
873C3—21no—
874C3#7438311yescharacteristic, complemented
875C3#7466311yescharacteristic, complemented
876C2—24no—
877C2—122no—
878C2C2×#6387811yescharacteristic
879C2#1059487611yescharacteristic
880C2#1059497411yescharacteristic
881C2#1059497911yescharacteristic
882C2#1059499411yescharacteristic
883C2#1059505811yescharacteristic
884C2#1059550811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63658C2semidirect
4. C3×#5210C2semidirect
5. #10591719C2semidirect
7. #10591705C2semidirect
8. #10591366C2semidirect
9. #10591362C2semidirect
10. #10591285C2semidirect
11. #10591284C2semidirect
12. #10591254C2semidirect
13. #10591253C2semidirect
14. #10591248C2semidirect
15. #10591245C2semidirect
30. #67⋊Dic3C4semidirect
60. #5210D3semidirect
114. C2×D3×Dic3C2×C4semidirect
124. Dic3⋊Dic3C2×C4semidirect
127. (C2×D3)⋊Dic3C2×C4semidirect
130. Dic32C2×C4semidirect
753. C32#2318semidirect
874. C3#74383semidirect
875. C3#74663semidirect

Maximal subgroups

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

subgroupindex
C2×#67⋊Dic32
C2×#636582
C3×#52132
C3×#52102
#105917192
#105917132
#105917052
#105913662
#105913622
#105912852
#105912842
#105912542
#105912532
#105912482
#105912452
#746633
#743833