Finite Group Databasebeta

← #11808929

Subgroups — #11808929

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592365C211yesmaximal, characteristic
2C3×#4660C211yesmaximal, characteristic, complemented
3C3×#4659C211yesmaximal, characteristic, complemented
4#10591326C211yesmaximal, characteristic
5#10591311C211yesmaximal, characteristic
6#10591274C211yesmaximal, characteristic, complemented
7#10591260C211yesmaximal, characteristic
8#10591260C211yesmaximal, characteristic
9#10591252C211yesmaximal, characteristic, complemented
10#10591241C211yesmaximal, characteristic, complemented
11#10591241C211yesmaximal, characteristic, complemented
12#10591228C211yesmaximal, characteristic, complemented
13#10591208C211yesmaximal, characteristic
14#10591207C211yesmaximal, characteristic, complemented
15#10591204C211yesmaximal, characteristic
16#78132—31nomaximal
17#78132—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C2×Dic32C2211yescharacteristic
34C2×Dic32C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#400—31no—
54C3×#400—31no—
55#4994—31no—
56#4994—31no—
57#4992—31no—
58#4992—31no—
59Dic3×C4⋊C4—31no—
60Dic3×C4⋊C4—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63#4675—31no—
64#4675—31no—
65#4674—31no—
66#4674—31no—
67#4666—31no—
68#4666—31no—
69#4666—31no—
70#4666—31no—
71#4666—31no—
72#4666—31no—
73#4666—61no—
74C3⋊#401—31no—
75C3⋊#401—31no—
76#4660—31no—
77#4660D311yescharacteristic, complemented
78#4659—31no—
79#4659D311yescharacteristic, complemented
80#4649—31no—
81#4649—31no—
82#4648—31no—
83#4648—31no—
84C23×C3⋊D3C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C2×C4×C3⋊D3—22no—
92C2×C4×C3⋊D3—22no—
93C2×C4×C3⋊D3—22no—
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102#3752—22no—
103#3752—22no—
104C4×C3⋊Dic3—22no—
105C4×C3⋊Dic3—22no—
106C3×C4⋊Dic3—22no—
107C3×C4⋊Dic3—22no—
108C3×Dic3⋊C4—22no—
109C3×Dic3⋊C4—22no—
110Dic3⋊Dic3—22no—
111Dic3⋊Dic3—22no—
112#3722—22no—
113#3722—22no—
114#3722—22no—
115#3722—22no—
116Dic32—22no—
117Dic32—22no—
118Dic32—22no—
119Dic32—22no—
120#2401—91noSylow
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—61no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—61no—
141C2×(C2×D3)⋊C4—61no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4C2×D311yescharacteristic
149C2×Dic3⋊C4C2×D311yescharacteristic
150C2×C4×Dic3—31no—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157C2×C4×Dic3—31no—
158C2×C4×Dic3—31no—
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—61no—
163C2×C4×Dic3—61no—
164C3×#95—21no—
165C3×#95—31no—
166C3×#95—31no—
167C3×#95—31no—
168C3×#95—31no—
169C3×#95—31no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—31no—
173C3×#95C2×D311yescharacteristic
174C3×#95C2×D311yescharacteristic
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
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—61no—
190C3⋊#95C2×D311yescharacteristic
191C3⋊#95C2×D311yescharacteristic
192C3⋊#95C2×D311yescharacteristic
193C3⋊#95C2×D311yescharacteristic
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32C2411yescharacteristic
199C22×C3⋊D3—21no—
200C22×C3⋊D3—21no—
201C22×C3⋊D3—21no—
202C22×C3⋊D3—21no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3#4112yes—
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4#4112yes—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3#4112yes—
222C2×C3⋊Dic3#4112yes—
223C2×C3⋊Dic3#4112yes—
224C4×C3⋊D3—44no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
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—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3#4112yes—
248C2×C3×Dic3#4112yes—
249#401—91no—
250#400—31no—
251#400—31no—
252#400—91no—
253#397—91no—
254#397—91no—
255#397—91no—
256#396—91no—
257C4×C4⋊C4—91no—
258C4×C4⋊C4—91no—
259C4×C4⋊C4—91no—
260C4×C22⋊C4—91no—
261C4×C22⋊C4—91no—
262C4×C22⋊C4—91no—
263#376—91no—
264C23×D3—31no—
265C23×D3—31no—
266C23×D3—61no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C22×Dic3C22×D311yescharacteristic
296C22×Dic3C22×D311yescharacteristic
297C22×Dic3C22×D311yescharacteristic
298C22×Dic3C22×D311yescharacteristic
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C2×C4×D3—62no—
302C2×C4×D3—62no—
303C2×C4×D3—62no—
304C2×C4×D3—62no—
305C2×C4×D3—62no—
306C2×C4×D3—62no—
307C2×C4×D3—64no—
308C2×C4×D3—122no—
309C2×C4×D3—122no—
310C3×C4⋊C4—62no—
311C3×C4⋊C4—62no—
312C3×C4⋊C4—62no—
313C3×C4⋊C4—62no—
314(C2×D3)⋊C4—62no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—62no—
321(C2×D3)⋊C4—62no—
322(C2×D3)⋊C4—64no—
323(C2×D3)⋊C4—64no—
324(C2×D3)⋊C4—62no—
325(C2×D3)⋊C4—62no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—62no—
328C4⋊Dic3—22no—
329C4⋊Dic3—22no—
330C4⋊Dic3—62no—
331C4⋊Dic3—62no—
332Dic3⋊C4—22no—
333Dic3⋊C4—22no—
334Dic3⋊C4—62no—
335Dic3⋊C4—62no—
336C4×Dic3—62no—
337C4×Dic3—62no—
338C4×Dic3—62no—
339C4×Dic3—62no—
340C4×Dic3—62no—
341C4×Dic3—62no—
342C4×Dic3—62no—
343C4×Dic3—62no—
344C4×Dic3—62no—
345C4×Dic3—62no—
346C4×Dic3—62no—
347C4×Dic3—62no—
348C4×Dic3—122no—
349C4×Dic3—122no—
350C22×C32C2×#4111yescharacteristic
351C22×C32C2×#4111yescharacteristic
352C22×C32C2×#4111yescharacteristic
353C22×C32C2×#4111yescharacteristic
354C22×C32C2×#4111yescharacteristic
355C22×C32C2×#4111yescharacteristic
356C22×C32C2×#4111yescharacteristic
357C2×C3⋊D3—22no—
358C2×C3⋊D3—22no—
359C2×C3⋊D3—22no—
360C2×C3⋊D3—41no—
361C2×C3⋊D3—41no—
362C2×C3⋊D3—41no—
363C2×C3⋊D3—41no—
364C32×C4—22no—
365C32×C4—41no—
366C32×C4—41no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3#12614yes—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C23×C4—91no—
379C2×C4⋊C4—31no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C22⋊C4—91no—
386C2×C22⋊C4—91no—
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C42—91no—
392C2×C42—91no—
393C2×C42—91no—
394C2×C42—91no—
395C2×C42—91no—
396C2×C42—91no—
397#95—31no—
398#95—31no—
399#95—31no—
400#95—31no—
401#95—31no—
402#95—31no—
403#95—31no—
404#95—31no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411#95—91no—
412#95D3211yescharacteristic
413C23×C3—21no—
414C23×C3C23×D311yescharacteristic
415C23×C3C23×D311yescharacteristic
416C22×D3—32no—
417C22×D3—32no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—61no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
429C22×D3—61no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—121no—
434C22×D3—121no—
435C22×D3—121no—
436C22×D3—121no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—32no—
457C2×C3×C4—32no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4#23712yes—
487C2×C3×C4#23912yes—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3#23712yes—
538C2×Dic3#23912yes—
539C4×D3—124no—
540C4×D3—124no—
541C4×D3—128no—
542C2×C32C2×#12611yescharacteristic
543C2×C32#52911yescharacteristic
544C2×C32#52911yescharacteristic
545C2×C32#52911yescharacteristic
546C2×C32#52911yescharacteristic
547C2×C32#52911yescharacteristic
548C2×C32#52911yescharacteristic
549C3⋊D3—42no—
550C24—91no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—182no—
563C22×C4—182no—
564C22×C4—182no—
565C22×C4C2×D3211yescharacteristic
566C22×C4C2×D3211yescharacteristic
567C22×C4C2×D3211yescharacteristic
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—62no—
572C4⋊C4—182no—
573C4⋊C4—182no—
574C22⋊C4—182no—
575C22⋊C4—182no—
576C22⋊C4—182no—
577C22⋊C4—182no—
578C22⋊C4—182no—
579C22⋊C4—182no—
580C42—182no—
581C42—182no—
582C42—182no—
583C42—182no—
584C42—182no—
585C42—182no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3C2×#23711yescharacteristic
594C22×C3C2×#23711yescharacteristic
595C22×C3C2×#23911yescharacteristic
596C22×C3C2×#23911yescharacteristic
597C22×C3D3×#4111yescharacteristic
598C22×C3D3×#4111yescharacteristic
599C22×C3D3×#4111yescharacteristic
600C22×C3D3×#4111yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3D3×#4111yescharacteristic
604C22×C3D3×#4111yescharacteristic
605C22×C3D3×#4111yescharacteristic
606C22×C3D3×#4111yescharacteristic
607C2×D3—64no—
608C2×D3—62no—
609C2×D3—62no—
610C2×D3—62no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—62no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—121no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—42no—
631C3×C4—42no—
632C3×C4—42no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—62no—
638C3×C4—62no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645Dic3—22no—
646Dic3—22no—
647Dic3—34no—
648Dic3—34no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—64no—
656Dic3—122no—
657Dic3—122no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662C32#240111yescharacteristic, complemented, Sylow
663C23—92no—
664C23—181no—
665C23—181no—
666C23—181no—
667C23—181no—
668C23—181no—
669C23—181no—
670C23C22×D3211yescharacteristic
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—92no—
704C2×C4—92no—
705C2×C4—92no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—364no—
713C2×C4#379612yes—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3#562411yescharacteristic
722C2×C3#562411yescharacteristic
723C2×C3#564911yescharacteristic
724C2×C3#564911yescharacteristic
725C2×C3#568011yescharacteristic
726C2×C3#568011yescharacteristic
727C2×C3#569111yescharacteristic
728C2×C3#569111yescharacteristic
729C2×C3#569111yescharacteristic
730C2×C3#569111yescharacteristic
731C2×C3D3×#12611yescharacteristic
732C2×C3D3×#12611yescharacteristic
733C2×C3#570611yescharacteristic
734C2×C3#570611yescharacteristic
735D3—124no—
736D3—122no—
737D3—122no—
738C22—182no—
739C22—182no—
740C22—182no—
741C22—361no—
742C22—361no—
743C22—361no—
744C22—361no—
745C22C2×#379611yescharacteristic
746C22#6430611yescharacteristic
747C22#6430611yescharacteristic
748C22D3×#23711yescharacteristic
749C22#6431211yescharacteristic
750C22#6431211yescharacteristic
751C22D3×#23911yescharacteristic
752C4—22no—
753C4—41no—
754C4—41no—
755C4—62no—
756C4—62no—
757C4—94no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4—361no—
766C3—21no—
767C3#7813211yescharacteristic, complemented
768C3#7813211yescharacteristic, complemented
769C2—362no—
770C2#1059394311yescharacteristic
771C2#1059413711yescharacteristic
772C2#1059414411yescharacteristic
773C2#1059415411yescharacteristic
774C2#1059444111yescharacteristic
775C2#1059445311yescharacteristic
776C2#1059446511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2401
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C3×#4660C2semidirect
3. C3×#4659C2semidirect
6. #10591274C2semidirect
9. #10591252C2semidirect
10. #10591241C2semidirect
11. #10591241C2semidirect
12. #10591228C2semidirect
14. #10591207C2semidirect
77. #4660D3semidirect
79. #4659D3semidirect
662. C32#2401semidirect
767. C3#78132semidirect
768. C3#78132semidirect

Maximal subgroups

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

subgroupindex
#105923652
C3×#46602
C3×#46592
#105913262
#105913112
#105912742
#105912602
#105912522
#105912412
#105912282
#105912082
#105912072
#105912042
#781323