Finite Group Databasebeta

← #11817806

Subgroups — #11817806

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C2×#63861C211yesmaximal, characteristic, complemented
3C3×#5213C211yesmaximal, characteristic
4C3×#5210C211yesmaximal, characteristic, complemented
5#10591715C211yesmaximal, characteristic, complemented
6#10591708C211yesmaximal, characteristic
7#10591707C211yesmaximal, characteristic
8#10591702C211yesmaximal, characteristic, complemented
9#10591353C211yesmaximal, characteristic, complemented
10#10591328C211yesmaximal, characteristic, complemented
11#10591317C211yesmaximal, characteristic, complemented
12#10591286C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591271C211yesmaximal, characteristic, complemented
15#10591241C211yesmaximal, characteristic, complemented
16#74734—31nomaximal
17#74451—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22#64135—24no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46#63861—24no—
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#926—31no—
56C2×#926—31no—
57C2×#926—61no—
58C2×#898—31no—
59C2×#879—31no—
60C3×#386—31no—
61C3×#385—31no—
62#5222—31no—
63#5221—31no—
64#5213D311yescharacteristic
65#5210D311yescharacteristic, complemented
66#4990—31no—
67#4981—31no—
68Dic3×C4⋊C4—31no—
69#4959—31no—
70#4957—31no—
71#4951—31no—
72#4951—31no—
73#4949—31no—
74#4949—31no—
75#4949—31no—
76#4945—31no—
77#4945—31no—
78#4677—31no—
79#4669—31no—
80#4661—31no—
81#4654—31no—
82#4653—31no—
83#4649—31no—
84#4647—31no—
85#4647—31no—
86C24×C32C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C22×C32×C4—22no—
89C22×C32×C4—22no—
90C22×C32×C4—22no—
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107#3757—22no—
108#3757—22no—
109C4⋊(C3⋊Dic3)—22no—
110C4⋊(C3⋊Dic3)D414yescomplemented
111C4×C3⋊Dic3—22no—
112C4×C3⋊Dic3—22no—
113C3×#217—22no—
114C3×#217—22no—
115C3×#217—41no—
116C3×(C2×D3)⋊C4—22no—
117C3×(C2×D3)⋊C4—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4—22no—
120#3724—22no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—41no—
124Dic3⋊Dic3—41no—
125Dic3⋊Dic3—41no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128(C2×D3)⋊Dic3—22no—
129(C2×D3)⋊Dic3—41no—
130Dic32—22no—
131Dic32—22no—
132#2479—91noSylow
133C22×C3×D4—31no—
134C23×C3×C4—21no—
135C23×C3×C4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C22×#67C2×D311yescharacteristic
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C22⋊C4—31no—
141C2×C3×C22⋊C4—31no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×#217—31no—
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×#217—61no—
154C2×#217—61no—
155C2×#217C2×D311yescharacteristic
156C2×#217C2×D311yescharacteristic
157C2×#217C2×D311yescharacteristic
158C2×(C2×D3)⋊C4—31no—
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
164#926—64no—
165#926—64no—
166#926—68no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—61no—
176C2×C4⋊Dic3—61no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4C2×D311yescharacteristic
186C2×Dic3⋊C4C2×D311yescharacteristic
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—31no—
195C2×C4×Dic3—61no—
196C2×C4×Dic3—61no—
197#898—64no—
198#879—64no—
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⋊#95C2×D311yescharacteristic
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#4112yes—
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—21no—
230C2×C32×C4—28no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2×D412yes—
236C2×C32×C4#4112yes—
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⋊Dic3—21no—
247C2×C3⋊Dic3C2×D412yes—
248C2×C3⋊Dic3C2×D412yes—
249C3×#67—44no—
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—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3#4112yes—
270C2×C3×Dic3#4112yes—
271C2×#126—91no—
272C2×#117—91no—
273#399—91no—
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—31no—
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—24no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—22no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—22no—
302C22×C3×C4—22no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—22no—
317C2×#67—22no—
318C2×#67—41no—
319C22×Dic3—31no—
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3C22×D311yescharacteristic
332C22×Dic3C22×D311yescharacteristic
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D311yescharacteristic
335C22×Dic3C22×D311yescharacteristic
336C22×Dic3C22×D311yescharacteristic
337C22×Dic3C22×D311yescharacteristic
338C3×C4⋊C4—62no—
339C3×C4⋊C4—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—62no—
343C3×C22⋊C4—62no—
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—64no—
355#217—64no—
356#217—62no—
357#217—121no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—22no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—121no—
364C4⋊Dic3—34no—
365C4⋊Dic3—34no—
366C4⋊Dic3—64no—
367C4⋊Dic3—62no—
368C4⋊Dic3—64no—
369C4⋊Dic3—62no—
370C4⋊Dic3—62no—
371C4⋊Dic3—121no—
372C4⋊Dic3—121no—
373C4⋊Dic3—121no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—62no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383Dic3⋊C4—121no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—62no—
387C4×Dic3—62no—
388C4×Dic3—62no—
389C4×Dic3—62no—
390C4×Dic3—62no—
391C4×Dic3—64no—
392C4×Dic3—64no—
393C4×Dic3—62no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C22×C32C2×#4111yescharacteristic
403C22×C32C2×#4111yescharacteristic
404C22×C32C2×#4111yescharacteristic
405C22×C32C2×#4111yescharacteristic
406C22×C32H(5,𝔽2)11yescharacteristic
407C22×C322−1+411yescharacteristic
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C32×C4—22no—
416C32×C4—22no—
417C3⋊Dic3—22no—
418C3⋊Dic3—22no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×D4—31no—
429C23×C4D3211yescharacteristic
430#126—184no—
431#117—184no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
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×C4⋊C4—91no—
441C2×C4⋊C4—91no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—91no—
448C2×C22⋊C4—91no—
449C2×C22⋊C4—91no—
450C2×C22⋊C4—91no—
451C2×C22⋊C4—91no—
452C2×C22⋊C4—91no—
453C2×C42—91no—
454C2×C42—91no—
455C2×C42—91no—
456C2×C42—91no—
457#95—31no—
458#95—31no—
459#95—31no—
460#95—31no—
461#95—91no—
462#95—91no—
463#95—91no—
464#95—91no—
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—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—22no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3#23712yes—
493C23×C3#23712yes—
494C23×C3C23×D311yescharacteristic
495C23×C3C23×D311yescharacteristic
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C3×D4—124no—
504C2×C3×C4—22no—
505C2×C3×C4—216no—
506C2×C3×C4—28no—
507C2×C3×C4—28no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
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×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4D3×D412yes—
543C2×C3×C4D3×D412yes—
544C2×C3×C4#23712yes—
545C2×C3×C4#23712yes—
546#67—44no—
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—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—62no—
571C2×Dic3—62no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—62no—
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—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3#23512yes—
603C2×Dic3#23512yes—
604C2×C32—42no—
605C2×C32#52511yescharacteristic
606C2×C32#52911yescharacteristic
607C2×C32#54211yescharacteristic
608C2×C32#54711yescharacteristic
609C2×C32#55011yescharacteristic
610C2×C32#55111yescharacteristic
611C2×C32#55211yescharacteristic
612C3×D3—81no—
613C24—31no—
614C24C2×D3211yescharacteristic
615C2×D4—62no—
616C2×D4—62no—
617C2×D4—121no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—91no—
629C22×C4—91no—
630C22×C4—91no—
631C22×C4—91no—
632C22×C4C2×D3211yescharacteristic
633C22×C4C2×D3211yescharacteristic
634C4⋊C4—62no—
635C4⋊C4—62no—
636C4⋊C4—94no—
637C4⋊C4—182no—
638C4⋊C4—182no—
639C4⋊C4—182no—
640C4⋊C4—182no—
641C4⋊C4—361no—
642C4⋊C4—361no—
643C4⋊C4—361no—
644C22⋊C4—62no—
645C22⋊C4—62no—
646C22⋊C4—62no—
647C22⋊C4—62no—
648C22⋊C4—121no—
649C22⋊C4—182no—
650C22⋊C4—182no—
651C22⋊C4—182no—
652C22⋊C4—182no—
653C22⋊C4—182no—
654C22⋊C4—361no—
655C42—182no—
656C42—182no—
657C42—182no—
658C42—182no—
659C22×C3—24no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3C2×#23511yescharacteristic
695C22×C3C2×#23511yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C22×C3C2×D3×D411yescharacteristic
698C22×C3C2×#23711yescharacteristic
699C22×C3C2×#23711yescharacteristic
700C22×C3C2×#23711yescharacteristic
701C22×C3C2×#23711yescharacteristic
702C22×C3#100411yescharacteristic
703C22×C3#100711yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3#100911yescharacteristic
707C22×C3#101011yescharacteristic
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—41no—
714C2×D3—41no—
715C3×C4—24no—
716C3×C4—24no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4—121no—
728Dic3—22no—
729Dic3—22no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—122no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3—121no—
744Dic3—121no—
745Dic3—121no—
746Dic3—121no—
747C32#247911yescharacteristic, complemented, Sylow
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23#380512yes—
762C23C22×D3211yescharacteristic
763D4—124no—
764C2×C4—28no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—32no—
770C2×C4—32no—
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—61no—
789C2×C4—61no—
790C2×C4—92no—
791C2×C4—92no—
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—181no—
801C2×C4—181no—
802C2×C4#380512yes—
803C2×C4#381112yes—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—44no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—241no—
815C2×C3#549511yescharacteristic
816C2×C3#551311yescharacteristic
817C2×C3#553811yescharacteristic
818C2×C3#555111yescharacteristic
819C2×C3#555311yescharacteristic
820C2×C3#555711yescharacteristic
821C2×C3#558611yescharacteristic
822C2×C3#558611yescharacteristic
823C2×C3#559911yescharacteristic
824C2×C3#560311yescharacteristic
825C2×C3#563111yescharacteristic
826C2×C3#564311yescharacteristic
827C2×C3#565011yescharacteristic
828C2×C3#565811yescharacteristic
829D3—81no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—121no—
838C22—121no—
839C22—121no—
840C22—121no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22#6429711yescharacteristic
845C22D3×#23511yescharacteristic
846C22D3×#23511yescharacteristic
847C22#6430711yescharacteristic
848C22C2×#380511yescharacteristic
849C22C2×#380511yescharacteristic
850C22C2×#381111yescharacteristic
851C4—22no—
852C4—22no—
853C4—62no—
854C4—62no—
855C4—121no—
856C4—121no—
857C4—121no—
858C4—121no—
859C4—121no—
860C4—182no—
861C4—182no—
862C4—361no—
863C4—361no—
864C3—21no—
865C3#7445111yescharacteristic, complemented
866C3#7473411yescharacteristic, complemented
867C2—42no—
868C2—241no—
869C2#1059483411yescharacteristic
870C2#1059491911yescharacteristic
871C2#1059493411yescharacteristic
872C2#1059494011yescharacteristic
873C2#1059495211yescharacteristic
874C2#1059498411yescharacteristic
875C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2479
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
2. C2×#63861C2semidirect
4. C3×#5210C2semidirect
5. #10591715C2semidirect
8. #10591702C2semidirect
9. #10591353C2semidirect
10. #10591328C2semidirect
11. #10591317C2semidirect
12. #10591286C2semidirect
13. #10591283C2semidirect
14. #10591271C2semidirect
15. #10591241C2semidirect
65. #5210D3semidirect
110. C4⋊(C3⋊Dic3)D4semidirect
747. C32#2479semidirect
865. C3#74451semidirect
866. C3#74734semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×#638612
C3×#52132
C3×#52102
#105917152
#105917082
#105917072
#105917022
#105913532
#105913282
#105913172
#105912862
#105912832
#105912712
#105912412
#747343
#744513