Finite Group Databasebeta

← #11824491

Subgroups — #11824491

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C211yesmaximal, characteristic
3C2×#63964C211yesmaximal, characteristic, complemented
4C2×#63893C211yesmaximal, characteristic, complemented
5C2×#63887C211yesmaximal, characteristic, complemented
6C2×#63839C211yesmaximal, characteristic, complemented
7#10592648C211yesmaximal, characteristic, complemented
8C3×#4957C211yesmaximal, characteristic
9#10591715C211yesmaximal, characteristic, complemented
10#10591707C211yesmaximal, characteristic
11#10591349C211yesmaximal, characteristic, complemented
12#10591324C211yesmaximal, characteristic, complemented
13#10591303C211yesmaximal, characteristic, complemented
14#10591244C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16#82780—31nomaximal
17#76349—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C3×#878—24no—
39Dic3×#67—24no—
40C2×#3724C2211yescharacteristic
41C2×#3724C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic3⋊Dic3C2211yescharacteristic
44C2×Dic3⋊Dic3C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48#63964—24no—
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×Dic32C2211yescharacteristic
53C2×Dic32C2211yescharacteristic
54#63893—24no—
55#63887—24no—
56#63839—24no—
57#63658C2211yescharacteristic
58#63579C2211yescharacteristic
59C2×C3×C22⋊Q8—31no—
60C2×#946—31no—
61C2×#944—31no—
62C2×D4×Dic3—31no—
63C2×C4×#67—31no—
64C2×#924—31no—
65C2×#897—31no—
66C2×#888—31no—
67C2×#878—31no—
68C2×#878—31no—
69C2×#878—31no—
70C2×#878D311yescharacteristic, complemented
71C3×#390—31no—
72#5221—31no—
73#4993—31no—
74#4993—31no—
75#4975—31no—
76#4975—31no—
77#4975—31no—
78Dic3×C4⋊C4—31no—
79#4957—31no—
80#4957D311yescharacteristic
81#4949—31no—
82#4949—31no—
83#4949—31no—
84#4949—31no—
85#4949—31no—
86#4949—31no—
87#4949—61no—
88#4935—31no—
89C4×Dic3⋊C4—31no—
90C24×C32C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67Q814yescomplemented
101C22×C3×Dic3—22no—
102C22×C3×Dic3—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—22no—
114C2×#627—22no—
115C2×#627—22no—
116C2×#627—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C32×C22⋊C4—22no—
121#3757—22no—
122#3757—22no—
123C4⋊(C3⋊Dic3)—22no—
124#3750—22no—
125#3750—22no—
126C3×#217—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4D414yescomplemented
134C3×C4×Dic3—22no—
135#3724—22no—
136#3724—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3D414yescomplemented
143(C2×D3)⋊Dic3—22no—
144(C2×D3)⋊Dic3—22no—
145(C2×D3)⋊Dic3—22no—
146Dic32—22no—
147Dic32D414yes—
148#2542—91noSylow
149C22×C3×Q8—31no—
150C22×C3×D4—31no—
151C23×C3×C4—31no—
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3C2×D311yescharacteristic
155C22×C4×D3—31no—
156C22×Dic6—31no—
157C22×Dic6—31no—
158C22×Dic6C2×D311yescharacteristic
159C3×C22⋊Q8—64no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C22⋊C4—21no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4C2×D311yescharacteristic
170C2×C3×C22⋊C4C2×D311yescharacteristic
171C2×C3×C42—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—31no—
178C2×#217—31no—
179C2×#217—61no—
180C2×#217—61no—
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183#946—64no—
184#944—64no—
185D4×Dic3—64no—
186C4×#67—64no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
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—31no—
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—61no—
201C2×C4⋊Dic3C2×D311yescharacteristic
202#924—64no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—61no—
218C2×Dic3⋊C4—61no—
219C2×Dic3⋊C4C2×D311yescharacteristic
220C2×Dic3⋊C4C2×D311yescharacteristic
221C2×Dic3⋊C4C2×D311yescharacteristic
222C2×C4×Dic3—31no—
223C2×C4×Dic3—31no—
224C2×C4×Dic3—31no—
225C2×C4×Dic3—31no—
226C2×C4×Dic3C2×D311yescharacteristic
227#897—64no—
228#888—64no—
229#878—24no—
230#878—64no—
231#878—64no—
232#878—64no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—61no—
238C23×C32—21no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32C2×Q812yes—
245C23×C32C2411yescharacteristic
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3C2×Q812yes—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D412yes—
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⋊Dic3C2×D412yes—
270C2×C3⋊Dic3C2×D412yes—
271C3×#67—28no—
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—44no—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3C2×D412yes—
291C2×C3×Dic3C2×D412yes—
292C2×C3×Dic3C2×Q812yes—
293C2×C3×Dic3#4112yes—
294C3×Dic6—44no—
295#627—44no—
296D3×Dic3—44no—
297C2×C4⋊Q8—91no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8—91no—
300C2×C22⋊Q8—91no—
301C2×C22⋊Q8—91no—
302C2×C4×D4—91no—
303#399—91no—
304#399—91no—
305#399—91no—
306#399—91no—
307#390—31no—
308#390—91no—
309#384—91no—
310#384—91no—
311C4×C4⋊C4—91no—
312C24×C3—21no—
313C24×C3—31no—
314C24×C3C22×D311yescharacteristic
315C24×C3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8—62no—
320C2×C3×D4—34no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—31no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C2×#67—22no—
340C2×#67—22no—
341C2×#67Dic614yescomplemented
342C22×Dic3—22no—
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—62no—
358C22×Dic3—62no—
359C22×Dic3—62no—
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×Dic6—22no—
371C2×Dic6—22no—
372C2×Dic6—22no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—62no—
377C2×Dic6—62no—
378C2×Dic6—62no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—62no—
381C3×C4⋊C4—62no—
382C3×C4⋊C4—62no—
383C3×C22⋊C4—22no—
384C3×C22⋊C4—22no—
385C3×C22⋊C4—42no—
386C3×C22⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C42—62no—
391#217—22no—
392#217—22no—
393#217—62no—
394#217—62no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—62no—
399#217—62no—
400#217—122no—
401#217—122no—
402(C2×D3)⋊C4—22no—
403(C2×D3)⋊C4—22no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407C4⋊Dic3—22no—
408C4⋊Dic3—34no—
409C4⋊Dic3—62no—
410C4⋊Dic3—62no—
411C4⋊Dic3—62no—
412C4⋊Dic3—62no—
413C4⋊Dic3—62no—
414C4⋊Dic3—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—122no—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—34no—
420Dic3⋊C4—62no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—122no—
434Dic3⋊C4—122no—
435Dic3⋊C4#6714yescomplemented
436C4×Dic3—22no—
437C4×Dic3—34no—
438C4×Dic3—34no—
439C4×Dic3—62no—
440C4×Dic3—62no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32C22×D411yescharacteristic
449C22×C32C22×D411yescharacteristic
450C22×C32C22×D411yescharacteristic
451C22×C32C22×Q811yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C22×C322−1+411yescharacteristic
454C22×C322−1+411yescharacteristic
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—41no—
464C3⋊Dic3—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3C22⋊Q814yescomplemented
474C3×Dic3#12714yes—
475C22×Q8—31no—
476C22×Q8—91no—
477C22×D4—31no—
478C23×C4—31no—
479C23×C4—91no—
480C4⋊Q8—184no—
481C22⋊Q8—64no—
482C22⋊Q8—184no—
483C22⋊Q8—184no—
484C22⋊Q8—184no—
485C4×D4—184no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—91no—
497C2×C4⋊C4—91no—
498C2×C4⋊C4—91no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C22⋊C4—31no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4D3211yescharacteristic
511C2×C42—31no—
512C2×C42—91no—
513C2×C42—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—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—41no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3C2×Dic612yes—
544C23×C3D3×Q812yes—
545C23×C3C23×D311yescharacteristic
546C23×C3C23×D311yescharacteristic
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3C2×Dic612yes—
554C3×Q8—124no—
555C3×D4—68no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—32no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—124no—
594C2×C3×C4D3×D412yes—
595C2×C3×C4C2×#6712yes—
596#67—28no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—44no—
615C2×Dic3—62no—
616C2×Dic3—62no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—121no—
638C2×Dic3—121no—
639C2×Dic3—121no—
640C2×Dic3—121no—
641C2×Dic3—121no—
642C2×Dic3—121no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—124no—
648C2×Dic3C2×Dic612yes—
649C2×Dic3D3×D412yes—
650C2×Dic3D3×D412yes—
651C2×Dic3D3×D412yes—
652C2×Dic3D3×D412yes—
653C2×Dic3#23712yes—
654C2×Dic3C2×#6712yes—
655C2×Dic3C2×#6712yes—
656C4×D3—124no—
657Dic6—44no—
658Dic6—124no—
659Dic6—124no—
660C2×C32—42no—
661C2×C32C2×C22⋊Q811yescharacteristic
662C2×C32C2×#12711yescharacteristic
663C2×C32#53611yescharacteristic
664C2×C32#54711yescharacteristic
665C2×C32#54711yescharacteristic
666C2×C32D4×Q811yescharacteristic
667C2×C32D4×Q811yescharacteristic
668C3×D3—42no—
669C24—31no—
670C24C2×D3211yescharacteristic
671C2×Q8—62no—
672C2×Q8—62no—
673C2×Q8—62no—
674C2×Q8—182no—
675C2×Q8—182no—
676C2×Q8—182no—
677C2×D4—34no—
678C2×D4—62no—
679C2×D4—62no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—182no—
695C22×C4—182no—
696C22×C4—182no—
697C22×C4C2×D3211yescharacteristic
698C22×C4C2×D3211yescharacteristic
699C4⋊C4—34no—
700C4⋊C4—62no—
701C4⋊C4—62no—
702C4⋊C4—62no—
703C4⋊C4—94no—
704C4⋊C4—182no—
705C4⋊C4—182no—
706C4⋊C4—182no—
707C4⋊C4—182no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C4⋊C4—182no—
711C4⋊C4—182no—
712C4⋊C4—182no—
713C4⋊C4—182no—
714C22⋊C4—22no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—182no—
720C22⋊C4—182no—
721C22⋊C4—182no—
722C22⋊C4—182no—
723C22⋊C4—182no—
724C42—62no—
725C42—94no—
726C42—182no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—41no—
747C22×C3—41no—
748C22×C3—41no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—81no—
755C22×C3—81no—
756C22×C3—81no—
757C22×C3—81no—
758C22×C3—121no—
759C22×C3—121no—
760C22×C3—121no—
761C22×C3—121no—
762C22×C3C22×Dic611yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C22×C3C2×D3×D411yescharacteristic
765C22×C3C2×D3×D411yescharacteristic
766C22×C3C2×D3×D411yescharacteristic
767C22×C3C2×D3×D411yescharacteristic
768C22×C3C2×#23711yescharacteristic
769C22×C3C2×D3×Q811yescharacteristic
770C22×C3#100711yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3#101011yescharacteristic
773C22×C3#101011yescharacteristic
774C22×C3#101011yescharacteristic
775C22×C3C22×#6711yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—34no—
786C3×C4—34no—
787C3×C4—42no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—62no—
791C3×C4—62no—
792C3×C4—81no—
793C3×C4—121no—
794C3×C4—121no—
795C3×C4—121no—
796Dic3—22no—
797Dic3—22no—
798Dic3—41no—
799Dic3—41no—
800Dic3—41no—
801Dic3—62no—
802Dic3—62no—
803Dic3—62no—
804Dic3—62no—
805Dic3—122no—
806Dic3—122no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810Dic3—121no—
811Dic3—241no—
812Dic3—241no—
813Dic3#87814yescomplemented
814Dic3#94014yes—
815C32#254211yescharacteristic, complemented, Sylow
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—32no—
823C23—61no—
824C23—61no—
825C23—61no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23D3×Dic612yes—
830C23C22×D3211yescharacteristic
831Q8—124no—
832Q8—364no—
833D4—68no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—32no—
840C2×C4—32no—
841C2×C4—32no—
842C2×C4—32no—
843C2×C4—32no—
844C2×C4—32no—
845C2×C4—32no—
846C2×C4—32no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—61no—
858C2×C4—61no—
859C2×C4—61no—
860C2×C4—92no—
861C2×C4—92no—
862C2×C4—124no—
863C2×C4—181no—
864C2×C4—181no—
865C2×C4—181no—
866C2×C4—181no—
867C2×C4—181no—
868C2×C4—181no—
869C2×C4—181no—
870C2×C4—181no—
871C2×C4—181no—
872C2×C4—181no—
873C2×C4—364no—
874C2×C4D3×#6712yes—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—42no—
883C2×C3—42no—
884C2×C3—82no—
885C2×C3—122no—
886C2×C3C2×#87811yescharacteristic
887C2×C3D4×Dic611yescharacteristic
888C2×C3D4×Dic611yescharacteristic
889C2×C3#561111yescharacteristic
890C2×C3#561111yescharacteristic
891C2×C3D3×C22⋊Q811yescharacteristic
892C2×C3#562811yescharacteristic
893C2×C3#563111yescharacteristic
894C2×C3#563211yescharacteristic
895C2×C3#567511yescharacteristic
896C2×C3D3×#12711yescharacteristic
897C2×C3C2×#94011yescharacteristic
898C2×C3Q8×#6711yescharacteristic
899C2×C3#582411yescharacteristic
900D3—42no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—121no—
912C22—121no—
913C22—121no—
914C22—121no—
915C22C2×D3×Dic611yescharacteristic
916C22#6429711yescharacteristic
917C22#6430911yescharacteristic
918C22D32×D411yescharacteristic
919C22D32×D411yescharacteristic
920C22D3×#23711yescharacteristic
921C22C2×D3×#6711yescharacteristic
922C4—22no—
923C4—34no—
924C4—34no—
925C4—41no—
926C4—62no—
927C4—62no—
928C4—121no—
929C4—121no—
930C4—121no—
931C4—182no—
932C4—182no—
933C4—361no—
934C4—361no—
935C3—21no—
936C3#7634911yescharacteristic, complemented
937C3#8278011yescharacteristic, complemented
938C2—42no—
939C2—122no—
940C2D3×#87811yescharacteristic
941C2#1059406511yescharacteristic
942C2#1059407011yescharacteristic
943C2#1059407111yescharacteristic
944C2Dic6×#6711yescharacteristic
945C2#1059515111yescharacteristic
946C2D3×#94011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2542
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×C3×#878C2semidirect
3. C2×#63964C2semidirect
4. C2×#63893C2semidirect
5. C2×#63887C2semidirect
6. C2×#63839C2semidirect
7. #10592648C2semidirect
9. #10591715C2semidirect
11. #10591349C2semidirect
12. #10591324C2semidirect
13. #10591303C2semidirect
14. #10591244C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
70. C2×#878D3semidirect
100. C2×C3×#67Q8semidirect
133. C3×Dic3⋊C4D4semidirect
142. Dic3⋊Dic3D4semidirect
341. C2×#67Dic6semidirect
435. Dic3⋊C4#67semidirect
473. C3×Dic3C22⋊Q8semidirect
813. Dic3#878semidirect
815. C32#2542semidirect
936. C3#76349semidirect
937. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
C2×Dic3×#672
C2×#639642
C2×#638932
C2×#638872
C2×#638392
#105926482
C3×#49572
#105917152
#105917072
#105913492
#105913242
#105913032
#105912442
Dic3×Dic3⋊C42
#827803
#763493