Finite Group Databasebeta

← #11812886

Subgroups — #11812886

Order 1152.

1467 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×#67C211yesmaximal, characteristic, complemented
2C2×#63971C211yesmaximal, characteristic
3C2×#63966C211yesmaximal, characteristic, complemented
4C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10592660C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7C3×#4950C211yesmaximal, characteristic, complemented
8#10591717C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591364C211yesmaximal, characteristic, complemented
12#10591351C211yesmaximal, characteristic, complemented
13#10591350C211yesmaximal, characteristic, complemented
14#10591266C211yesmaximal, characteristic, complemented
15#10591250C211yesmaximal, characteristic, complemented
16#74703—31nomaximal
17#74608—31nomaximal
18C22×#638C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35Dic3×#67—24no—
36#63971—24no—
37C2×#3724C2211yescharacteristic
38#63966—24no—
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×Dic32C2211yescharacteristic
48D3×C4⋊Dic3—24no—
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#939—31no—
58C2×D4×Dic3—31no—
59C2×#929—31no—
60C2×C4×#67—31no—
61C22×C4⋊Dic3—31no—
62C2×D3×C4⋊C4—31no—
63C2×#886—31no—
64C2×#884—31no—
65C3×#386—31no—
66C3×#385—31no—
67#5213—31no—
68#4993—31no—
69#4990—31no—
70#4989—31no—
71#4961—31no—
72#4961—31no—
73#4961—61no—
74#4958—31no—
75#4956D311yescharacteristic, complemented
76#4953—31no—
77#4952—31no—
78#4950—31no—
79#4950D311yescharacteristic, complemented
80#4677—31no—
81#4670—31no—
82#4665—31no—
83#4665—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
93C2×#638—22no—
94C2×#638—22no—
95C2×#638—41no—
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67D414yes—
102C22×C3×Dic3—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—41no—
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×#626—22no—
116C2×#626—22no—
117C2×#626—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C32×C22⋊C4—22no—
125#3757—22no—
126#3752—22no—
127#3752—41no—
128C4⋊(C3⋊Dic3)—22no—
129C3×#217—22no—
130C3×#217—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×C4⋊Dic3—22no—
133C3×C4⋊Dic3—41no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3D414yescomplemented
139#3722—22no—
140#3722—22no—
141#3722—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67—61no—
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3C2×D311yescharacteristic
156C22×D12—31no—
157C22×C4×D3—31no—
158C22×C4×D3—31no—
159C22×C4×D3C2×D311yescharacteristic
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4C2×D311yescharacteristic
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×#217—31no—
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—61no—
172C2×#217C2×D311yescharacteristic
173C2×#217C2×D311yescharacteristic
174#939—64no—
175D4×Dic3—64no—
176#929—64no—
177C4×#67—64no—
178C2×(C2×D3)⋊C4—31no—
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)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3—64no—
200C2×C4⋊Dic3C2×D311yescharacteristic
201C2×C4⋊Dic3C2×D311yescharacteristic
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210D3×C4⋊C4—64no—
211#886—64no—
212#884—64no—
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—31no—
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×C32—21no—
235C23×C32—21no—
236C23×C32C2×D412yes—
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×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4#4112yes—
258#638—44no—
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⋊Dic3C2×D412yes—
268C3×#67—28no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
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—44no—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C3×C4×D3—28no—
292#626—44no—
293D3×Dic3—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—91no—
307#386—91no—
308#385—31no—
309#385—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—61no—
317C23×D3C22×D311yescharacteristic
318C2×C3×D4—34no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—121no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—22no—
341C2×#67—22no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—122no—
350C2×#67—122no—
351C2×#67—121no—
352C2×#67—121no—
353C2×#67—122no—
354C2×#67D1214yes—
355C22×Dic3—22no—
356C22×Dic3—22no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—41no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—62no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370C22×Dic3—62no—
371C22×Dic3—121no—
372C22×Dic3—121no—
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C2×D12—62no—
381C2×D12—62no—
382C2×D12—62no—
383C2×C4×D3—22no—
384C2×C4×D3—22no—
385C2×C4×D3—22no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—121no—
391C2×C4×D3—121no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—121no—
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—42no—
397C3×C22⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400#217—22no—
401#217—22no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—122no—
406(C2×D3)⋊C4—22no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
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—
416(C2×D3)⋊C4—122no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—122no—
420C4⋊Dic3—22no—
421C4⋊Dic3—34no—
422C4⋊Dic3—41no—
423C4⋊Dic3—62no—
424C4⋊Dic3—62no—
425C4⋊Dic3—62no—
426C4⋊Dic3—62no—
427C4⋊Dic3—62no—
428C4⋊Dic3—122no—
429Dic3⋊C4—34no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435C4×Dic3—62no—
436C4×Dic3—62no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32C22×D411yescharacteristic
445C22×C32C22×D411yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32H(5,𝔽2)11yescharacteristic
450C22×C322−1+411yescharacteristic
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3#12314yescomplemented
465C32×C4—22no—
466C32×C4—41no—
467C3⋊Dic3—22no—
468C3⋊Dic3—41no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C22×D4—31no—
478C22×D4—91no—
479C22×D4—91no—
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—91no—
483C23×C4—91no—
484#123—184no—
485#121—184no—
486C4×D4—184no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—184no—
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⋊C4—91no—
506C2×C22⋊C4D3211yescharacteristic
507C2×C42—91no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
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—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—22no—
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—32no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—41no—
538C23×C3—41no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3C2×D1212yes—
544C23×C3D3×D412yes—
545C23×C3C23×D311yescharacteristic
546C23×C3C23×D311yescharacteristic
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—62no—
552C22×D3—61no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—61no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—61no—
566C22×D3—121no—
567C22×D3—121no—
568C22×D3—121no—
569C22×D3—121no—
570C22×D3—121no—
571C22×D3—121no—
572C22×D3C2×D1212yes—
573C22×D3#23712yes—
574C22×D3#23712yes—
575C3×D4—68no—
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—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—22no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—68no—
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—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—124no—
615C2×C3×C4#23512yes—
616C2×C3×C4#23712yes—
617#67—28no—
618#67—124no—
619#67—124no—
620#67—124no—
621#67—128no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—44no—
643C2×Dic3—62no—
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—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3—121no—
664C2×Dic3—121no—
665C2×Dic3—121no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—124no—
669C2×Dic3—124no—
670C2×Dic3C2×D1212yes—
671C2×Dic3D3×D412yes—
672C2×Dic3D3×D412yes—
673D12—124no—
674C4×D3—28no—
675C4×D3—124no—
676C4×D3—124no—
677C2×C32—42no—
678C2×C32C2×#12311yescharacteristic
679C2×C32#52511yescharacteristic
680C2×C32#53911yescharacteristic
681C2×C32D4211yescharacteristic
682C2×C32#54711yescharacteristic
683C2×C32#54811yescharacteristic
684C2×C32#55311yescharacteristic
685C3⋊D3—81no—
686C3×D3—24no—
687C24—31no—
688C24—91no—
689C24C2×D3211yescharacteristic
690C2×D4—34no—
691C2×D4—62no—
692C2×D4—62no—
693C2×D4—182no—
694C2×D4—182no—
695C2×D4—182no—
696C2×D4—182no—
697C2×D4—182no—
698C2×D4—361no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—91no—
712C22×C4—91no—
713C22×C4—91no—
714C22×C4—121no—
715C22×C4—182no—
716C22×C4—182no—
717C22×C4—182no—
718C22×C4—182no—
719C22×C4—361no—
720C22×C4—361no—
721C22×C4C2×D3211yescharacteristic
722C22×C4C2×D3211yescharacteristic
723C4⋊C4—62no—
724C4⋊C4—94no—
725C4⋊C4—121no—
726C4⋊C4—182no—
727C4⋊C4—182no—
728C4⋊C4—182no—
729C4⋊C4—182no—
730C4⋊C4—182no—
731C22⋊C4—22no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—62no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C22⋊C4—182no—
738C22⋊C4—182no—
739C22⋊C4—182no—
740C22⋊C4—182no—
741C22⋊C4—361no—
742C42—182no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—34no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—81no—
775C22×C3—81no—
776C22×C3—81no—
777C22×C3—81no—
778C22×C3C22×D1211yescharacteristic
779C22×C3C2×#23511yescharacteristic
780C22×C3C2×D3×D411yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×#23711yescharacteristic
784C22×C3C2×#23711yescharacteristic
785C22×C3C2×#23711yescharacteristic
786C22×C3#100411yescharacteristic
787C22×C3#100711yescharacteristic
788C22×C3D3×#4111yescharacteristic
789C22×C3D3×#4111yescharacteristic
790C22×C3#100911yescharacteristic
791C22×C3#101011yescharacteristic
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—22no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—121no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—121no—
815C2×D3—241no—
816C2×D3—241no—
817C2×D3—241no—
818C2×D3—241no—
819C2×D3#88614yescomplemented
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—42no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—81no—
829C3×C4—121no—
830C3×C4—121no—
831C3×C4—121no—
832C3×C4—121no—
833Dic3—22no—
834Dic3—22no—
835Dic3—22no—
836Dic3—41no—
837Dic3—41no—
838Dic3—41no—
839Dic3—41no—
840Dic3—62no—
841Dic3—62no—
842Dic3—122no—
843Dic3—121no—
844Dic3—121no—
845Dic3—121no—
846Dic3—121no—
847Dic3—241no—
848Dic3—241no—
849C32#244311yescharacteristic, complemented, Sylow
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—32no—
857C23—32no—
858C23—32no—
859C23—61no—
860C23—61no—
861C23—61no—
862C23—61no—
863C23—181no—
864C23—181no—
865C23—181no—
866C23—181no—
867C23—181no—
868C23—181no—
869C23—181no—
870C23D3×D1212yes—
871C23C22×D3211yescharacteristic
872D4—68no—
873D4—364no—
874D4—364no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—32no—
881C2×C4—32no—
882C2×C4—32no—
883C2×C4—68no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—92no—
903C2×C4—124no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—364no—
913C2×C4—364no—
914C2×C4#380412yes—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—42no—
923C2×C3—42no—
924C2×C3—64no—
925C2×C3—82no—
926C2×C3C2×#88611yescharacteristic
927C2×C3#550711yescharacteristic
928C2×C3#554711yescharacteristic
929C2×C3D4×D1211yescharacteristic
930C2×C3#555511yescharacteristic
931C2×C3#555811yescharacteristic
932C2×C3#558611yescharacteristic
933C2×C3#559011yescharacteristic
934C2×C3#559811yescharacteristic
935C2×C3#561811yescharacteristic
936C2×C3#563311yescharacteristic
937C2×C3#563811yescharacteristic
938C2×C3D3×#12311yescharacteristic
939C2×C3#566511yescharacteristic
940D3—24no—
941D3—242no—
942D3—241no—
943D3—241no—
944C22—22no—
945C22—22no—
946C22—22no—
947C22—34no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—361no—
959C22—361no—
960C22—361no—
961C22—361no—
962C22—361no—
963C22—361no—
964C22—361no—
965C22#6429711yescharacteristic
966C22C2×D3×D1211yescharacteristic
967C22D32×D411yescharacteristic
968C22D3×#23711yescharacteristic
969C22D3×#23711yescharacteristic
970C22#6431411yescharacteristic
971C22C2×#380411yescharacteristic
972C4—22no—
973C4—41no—
974C4—62no—
975C4—62no—
976C4—62no—
977C4—121no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—182no—
982C4—361no—
983C4—361no—
984C3—21no—
985C3#7460811yescharacteristic, complemented
986C3#7470311yescharacteristic, complemented
987C2—42no—
988C2—64no—
989C2—721no—
990C2#1059407411yescharacteristic
991C2#1059412911yescharacteristic
992C2#1059427711yescharacteristic
993C2D3×#88611yescharacteristic
994C2#1059490611yescharacteristic
995C2#1059512911yescharacteristic
996C2#1059518211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63971C2
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
1. C2×Dic3×#67C2semidirect
3. C2×#63966C2semidirect
4. C2×D3×C4⋊Dic3C2semidirect
5. #10592660C2semidirect
6. C3×#4956C2semidirect
7. C3×#4950C2semidirect
8. #10591717C2semidirect
9. #10591382C2semidirect
10. #10591377C2semidirect
11. #10591364C2semidirect
12. #10591351C2semidirect
13. #10591350C2semidirect
14. #10591266C2semidirect
15. #10591250C2semidirect
75. #4956D3semidirect
79. #4950D3semidirect
138. Dic3⋊Dic3D4semidirect
464. C2×C3×D3#123semidirect
819. C2×D3#886semidirect
849. C32#2443semidirect
985. C3#74608semidirect
986. C3#74703semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×#672
C2×#639712
C2×#639662
C2×D3×C4⋊Dic32
#105926602
C3×#49562
C3×#49502
#105917172
#105913822
#105913772
#105913642
#105913512
#105913502
#105912662
#105912502
#747033
#746083