Finite Group Databasebeta

← #11817818

Subgroups — #11817818

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64088C211yesmaximal, characteristic, complemented
2C2×#63841C211yesmaximal, characteristic, complemented
3C3×#4956C211yesmaximal, characteristic
4C3×#4949C211yesmaximal, characteristic, complemented
5#10591708C211yesmaximal, characteristic
6#10591707C211yesmaximal, characteristic
7#10591702C211yesmaximal, characteristic, complemented
8#10591702C211yesmaximal, characteristic, complemented
9#10591358C211yesmaximal, characteristic, complemented
10#10591303C211yesmaximal, characteristic, complemented
11#10591283C211yesmaximal, characteristic, complemented
12#10591278C211yesmaximal, characteristic, complemented
13#10591271C211yesmaximal, characteristic, complemented
14#10591256C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#78027—31nomaximal
17#74734—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64088—24no—
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63841—24no—
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#892—31no—
57C2×#879—31no—
58C2×#879—31no—
59C2×#879—61no—
60C3×#399—31no—
61C3×#386—31no—
62#5222—31no—
63#5221—31no—
64#5210—31no—
65#4993—31no—
66#4990—31no—
67#4983—31no—
68#4976—31no—
69Dic3×C4⋊C4—31no—
70#4959—31no—
71#4957—31no—
72#4956D311yescharacteristic
73#4951—31no—
74#4951—31no—
75#4949—31no—
76#4949D311yescharacteristic, complemented
77#4945—31no—
78#4945—31no—
79#4945—31no—
80#4668—31no—
81#4661—31no—
82#4654—31no—
83#4653—31no—
84#4649—31no—
85#4647—31no—
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×C3×#67—22no—
95C2×C3×#67—22no—
96C2×C3×#67—41no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C32×C22⋊C4—22no—
108#3757—22no—
109#3757—22no—
110C4⋊(C3⋊Dic3)D414yescomplemented
111#3750—22no—
112#3750—22no—
113C4×C3⋊Dic3—22no—
114C3×#217—22no—
115C3×#217—22no—
116C3×#217—41no—
117C3×(C2×D3)⋊C4—41no—
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—41no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129Dic32—22no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×C3×D4—31no—
134C23×C3×C4—31no—
135C22×#67C2×D311yescharacteristic
136C22×C4×D3C2×D311yescharacteristic
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—31no—
154C2×#217—31no—
155C2×#217—61no—
156C2×#217—61no—
157C2×#217C2×D311yescharacteristic
158C2×#217C2×D311yescharacteristic
159C2×#217C2×D311yescharacteristic
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4C2×D311yescharacteristic
165#926—64no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—61no—
172C2×C4⋊Dic3C2×D311yescharacteristic
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—61no—
183C2×Dic3⋊C4—61no—
184C2×Dic3⋊C4C2×D311yescharacteristic
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
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—61no—
195#892—64no—
196#879—64no—
197#879—64no—
198#879—68no—
199C3×#95—31no—
200C3×#95—31no—
201C3×#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95C2×D311yescharacteristic
213C3⋊#95C2×D311yescharacteristic
214C3⋊#95C2×D311yescharacteristic
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32C2411yescharacteristic
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3#4112yes—
230C2×C32×C4—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2×D412yes—
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—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D412yes—
247C2×C3⋊Dic3C2×D412yes—
248C3×#67—44no—
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×Dic3—21no—
267C2×C3×Dic3#4112yes—
268C2×C3×Dic3#4112yes—
269C2×C3×Dic3#4112yes—
270C3×C4×D3—28no—
271C2×#126—91no—
272C2×#117—91no—
273#399—31no—
274#399—91no—
275#398—91no—
276#394—91no—
277#390—91no—
278#389—91no—
279#388—91no—
280#388—91no—
281#388—91no—
282#387—91no—
283#386—31no—
284#385—91no—
285C4×C4⋊C4—91no—
286C24×C3—21no—
287C24×C3—31no—
288C24×C3C22×D311yescharacteristic
289C24×C3C22×D311yescharacteristic
290C23×D3C22×D311yescharacteristic
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C2×C3×D4—121no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—62no—
304C22×C3×C4—62no—
305C22×C3×C4—62no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—22no—
311C2×#67—22no—
312C2×#67—41no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—31no—
317C22×Dic3—31no—
318C22×Dic3—31no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C22×Dic3C22×D311yescharacteristic
332C2×C4×D3—22no—
333C2×C4×D3—22no—
334C2×C4×D3—22no—
335C3×C4⋊C4—62no—
336C3×C4⋊C4—62no—
337C3×C4⋊C4—121no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—22no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—121no—
344C3×C22⋊C4—121no—
345#217—22no—
346#217—22no—
347#217—41no—
348#217—62no—
349#217—62no—
350#217—62no—
351#217—62no—
352#217—62no—
353#217—62no—
354#217—62no—
355#217—64no—
356#217—64no—
357#217—62no—
358(C2×D3)⋊C4—41no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363C4⋊Dic3—22no—
364C4⋊Dic3—34no—
365C4⋊Dic3—34no—
366C4⋊Dic3—64no—
367C4⋊Dic3—62no—
368C4⋊Dic3—121no—
369C4⋊Dic3—121no—
370Dic3⋊C4—22no—
371Dic3⋊C4—41no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—64no—
377Dic3⋊C4—64no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—64no—
391C4×Dic3—62no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32C22×D411yescharacteristic
400C22×C32C2×#4111yescharacteristic
401C22×C32C2×#4111yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32H(5,𝔽2)11yescharacteristic
405C22×C322−1+411yescharacteristic
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—22no—
414C32×C4—41no—
415C3⋊Dic3—22no—
416C3⋊Dic3—22no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—22no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—31no—
427C23×C4—31no—
428#126—184no—
429#117—184no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—31no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—91no—
434C2×C4⋊C4—91no—
435C2×C4⋊C4—91no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—91no—
438C2×C4⋊C4—91no—
439C2×C4⋊C4—91no—
440C2×C22⋊C4—31no—
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—91no—
445C2×C22⋊C4—91no—
446C2×C22⋊C4—91no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4D3211yescharacteristic
451C2×C42—91no—
452C2×C42—91no—
453C2×C42—91no—
454C2×C42—91no—
455#95—31no—
456#95—31no—
457#95—31no—
458#95—91no—
459#95—91no—
460#95—91no—
461#95—91no—
462#95—91no—
463C23×C3—22no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
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—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—32no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
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×D3#23712yes—
501C3×D4—124no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
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—22no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—68no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
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×C4D3×D412yes—
541C2×C3×C4D3×D412yes—
542#67—44no—
543C2×Dic3—21no—
544C2×Dic3—21no—
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—32no—
562C2×Dic3—32no—
563C2×Dic3—32no—
564C2×Dic3—32no—
565C2×Dic3—62no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—61no—
578C2×Dic3—61no—
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—121no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3—121no—
593C2×Dic3—121no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3#23512yes—
598C2×Dic3#23712yes—
599C2×Dic3#23712yes—
600C4×D3—28no—
601C2×C32—81no—
602C2×C32#52511yescharacteristic
603C2×C32#52911yescharacteristic
604C2×C32#54211yescharacteristic
605C2×C32#54711yescharacteristic
606C2×C32#55011yescharacteristic
607C2×C32#55111yescharacteristic
608C2×C32#55211yescharacteristic
609C3×D3—42no—
610C24—31no—
611C24C2×D3211yescharacteristic
612C2×D4—62no—
613C2×D4—62no—
614C2×D4—121no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—62no—
623C22×C4—62no—
624C22×C4—62no—
625C22×C4—91no—
626C22×C4—91no—
627C22×C4—91no—
628C22×C4—91no—
629C22×C4C2×D3211yescharacteristic
630C22×C4C2×D3211yescharacteristic
631C4⋊C4—62no—
632C4⋊C4—62no—
633C4⋊C4—94no—
634C4⋊C4—121no—
635C4⋊C4—182no—
636C4⋊C4—182no—
637C4⋊C4—182no—
638C4⋊C4—182no—
639C4⋊C4—361no—
640C4⋊C4—361no—
641C22⋊C4—22no—
642C22⋊C4—62no—
643C22⋊C4—62no—
644C22⋊C4—121no—
645C22⋊C4—121no—
646C22⋊C4—182no—
647C22⋊C4—182no—
648C22⋊C4—182no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C42—182no—
653C42—182no—
654C42—182no—
655C42—182no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—62no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3C2×#23511yescharacteristic
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C2×#23711yescharacteristic
695C22×C3C2×#23711yescharacteristic
696C22×C3C2×#23711yescharacteristic
697C22×C3#100411yescharacteristic
698C22×C3#100411yescharacteristic
699C22×C3#100711yescharacteristic
700C22×C3D3×#4111yescharacteristic
701C22×C3D3×#4111yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C22×C3#101011yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—42no—
715C3×C4—42no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725Dic3—22no—
726Dic3—22no—
727Dic3—22no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—41no—
732Dic3—62no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—122no—
737Dic3—122no—
738Dic3—122no—
739Dic3—122no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744C32#247911yescharacteristic, complemented, Sylow
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—32no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23C22×D3211yescharacteristic
760D4—124no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—68no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
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—92no—
789C2×C4—92no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4#381112yes—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—82no—
809C2×C3—81no—
810C2×C3—81no—
811C2×C3—122no—
812C2×C3#549511yescharacteristic
813C2×C3#555111yescharacteristic
814C2×C3#555711yescharacteristic
815C2×C3#558611yescharacteristic
816C2×C3#559911yescharacteristic
817C2×C3#560311yescharacteristic
818C2×C3#563111yescharacteristic
819C2×C3#563911yescharacteristic
820C2×C3#564011yescharacteristic
821C2×C3#564911yescharacteristic
822C2×C3#565011yescharacteristic
823C2×C3#565611yescharacteristic
824C2×C3#565911yescharacteristic
825C2×C3#571811yescharacteristic
826D3—42no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22#6429711yescharacteristic
842C22D3×#23511yescharacteristic
843C22D3×#23711yescharacteristic
844C22D3×#23711yescharacteristic
845C22D3×#23711yescharacteristic
846C22#6431311yescharacteristic
847C22C2×#381111yescharacteristic
848C4—22no—
849C4—41no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—121no—
857C4—182no—
858C4—182no—
859C4—361no—
860C4—361no—
861C3—21no—
862C3#7473411yescharacteristic, complemented
863C3#7802711yescharacteristic, complemented
864C2—81no—
865C2—122no—
866C2#1059409811yescharacteristic
867C2#1059411811yescharacteristic
868C2#1059414911yescharacteristic
869C2#1059419311yescharacteristic
870C2#1059483411yescharacteristic
871C2#1059516011yescharacteristic
872C2#1059516411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64088C2semidirect
2. C2×#63841C2semidirect
4. C3×#4949C2semidirect
7. #10591702C2semidirect
8. #10591702C2semidirect
9. #10591358C2semidirect
10. #10591303C2semidirect
11. #10591283C2semidirect
12. #10591278C2semidirect
13. #10591271C2semidirect
14. #10591256C2semidirect
15. #10591241C2semidirect
76. #4949D3semidirect
110. C4⋊(C3⋊Dic3)D4semidirect
744. C32#2479semidirect
862. C3#74734semidirect
863. C3#78027semidirect

Maximal subgroups

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

subgroupindex
C2×#640882
C2×#638412
C3×#49562
C3×#49492
#105917082
#105917072
#105917022
#105913582
#105913032
#105912832
#105912782
#105912712
#105912562
#105912412
#780273
#747343