Finite Group Databasebeta

← #13177375

Subgroups — #13177375

Order 1728.

2500 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6289C211yesmaximal, characteristic, complemented
2C2×#89028C211yesmaximal, characteristic, complemented
3#11723978C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C32×#939C211yesmaximal, characteristic, complemented
6#11723640C211yesmaximal, characteristic, complemented
7#11723638C211yesmaximal, characteristic, complemented
8#11723628C211yesmaximal, characteristic, complemented
9#11723622C211yesmaximal, characteristic, complemented
10#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
11#11723599C211yesmaximal, characteristic, complemented
12#11723485C211yesmaximal, characteristic, complemented
13#11723469C211yesmaximal, characteristic, complemented
14#11723461C211yesmaximal, characteristic, complemented
15#11723422C211yesmaximal, characteristic, complemented
16#10596077—31nomaximal
17#10595138—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C2×C33×D4C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic
27C2×#6293C2211yescharacteristic, complemented
28C2×#6291C2211yescharacteristic
29C2×#6291C2211yescharacteristic
30C2×#6289—24no—
31C2×#6289C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×#6289C2211yescharacteristic
35#89028—24no—
36C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
37#88864C2211yescharacteristic
38#88859C2211yescharacteristic
39#88859C2211yescharacteristic
40C3×#3757C2211yescharacteristic
41C3×#3757C2211yescharacteristic, complemented
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×#3830—31no—
56C22×C4×C3⋊D3—31no—
57C22×#624—34no—
58C2×#3804—34no—
59C32×#121—31no—
60#64147—31no—
61#64146—31no—
62#64146—31no—
63#64146—34no—
64#64146—64no—
65D4×C3⋊Dic3—31no—
66D4×C3⋊Dic3D311yescharacteristic, complemented
67#64133—31no—
68#64106—31no—
69#64101—31no—
70#64092—31no—
71#64092—31no—
72#64090—31no—
73#64090—31no—
74C3×#939D314yescomplemented
75C3×D4×Dic3—34no—
76#63981—34no—
77#63975—34no—
78Dic3×#67—34no—
79#63964—34no—
80#63958—34no—
81#63952—34no—
82#63895—34no—
83#63880—34no—
84#63854—34no—
85#63836—34no—
86C23×C33C2311yescharacteristic
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)—22no—
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C33×D4—22no—
95C2×C33×C4C2311yescharacteristic
96#6312—22no—
97#6312—22no—
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3×C3⋊Dic3—22no—
101C2×C3×C3⋊Dic3—22no—
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C32×#67—22no—
107C32×#67—22no—
108C2×C32×Dic3—22no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112#6293—22no—
113#6291—22no—
114#6291—22no—
115#6289—22no—
116#6289—22no—
117#6289—22no—
118#6289D414yescomplemented
119D3×C3⋊Dic3—22no—
120#5606—94no—
121#5547—91no—
122C23×C3⋊D3—31no—
123C23×C3⋊D3—34no—
124C23×C3⋊D3—64no—
125C2×C32×D4—24no—
126C2×C32×D4—31no—
127C2×C32×D4—31no—
128C2×C32×D4C2×D314yes—
129C2×C32×D4C2×D311yescharacteristic
130C22×C32×C4—31no—
131C2×#638—31no—
132C2×#638—31no—
133C2×#638—34no—
134C2×#638—34no—
135C2×#638—31no—
136C2×#638—31no—
137C2×#638—64no—
138C2×#638—64no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3C2×D311yescharacteristic
141C22×C3⋊Dic3C2×D311yescharacteristic, complemented
142#3830—64no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—31no—
147C2×C4×C3⋊D3—64no—
148C2×#634—31no—
149C2×C3×#67C2×D314yes—
150C2×C3×#67C2×D314yescomplemented
151C22×C3×Dic3—34no—
152C22×C3×Dic3—34no—
153C22×C3×Dic3C2×D314yes—
154C2×#627—34no—
155C2×#626—34no—
156C2×#626—34no—
157C2×#624—34no—
158C2×#624—34no—
159C2×#624—34no—
160C2×#624—34no—
161C2×#624—616no—
162#3804—616no—
163C2×D3×Dic3—34no—
164C32×C4⋊C4—31no—
165C32×C22⋊C4—31no—
166C32×C22⋊C4—31no—
167#3757—31no—
168#3757—34no—
169#3757—31no—
170#3757—64no—
171#3757C2×D311yescharacteristic
172#3757C2×D311yescharacteristic, complemented
173#3752—31no—
174#3752—31no—
175#3752—34no—
176#3752—34no—
177#3752—31no—
178#3752—31no—
179#3752—64no—
180#3752—64no—
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)—31no—
183C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
184#3750—31no—
185#3750—31no—
186C4×C3⋊Dic3—31no—
187C4×C3⋊Dic3C2×D311yescharacteristic, complemented
188C3×#217—34no—
189C3×#217—34no—
190C3×#217C2×D314yescomplemented
191C3×(C2×D3)⋊C4C2×D314yescomplemented
192C3×C4⋊Dic3—34no—
193C3×Dic3⋊C4C2×D314yescomplemented
194C3×C4×Dic3—34no—
195#3724—34no—
196Dic3⋊Dic3—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202Dic32—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33#4112yescomplemented
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—28no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3⋊(C3⋊D3)—21no—
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)C2×D412yes—
216C2×C3⋊(C3⋊D3)#4112yescomplemented
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3—21no—
220C33×C4—21no—
221C3⋊(C3⋊Dic3)—21no—
222C3⋊(C3⋊Dic3)—21no—
223C3×C3⋊Dic3—21no—
224C3×C3⋊Dic3—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3C2×D412yes—
227C32×Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3C2×D412yes—
230C2×#237—94no—
231C2×#235—91no—
232C22×C4×D3—94no—
233C22×C4×D3—91no—
234C3×#121—34no—
235C3×C4×D4—91no—
236#939C3⋊D311yescharacteristic, complemented
237#938—94no—
238#937—94no—
239#937—94no—
240#937—91no—
241#937—184no—
242D4×Dic3—34no—
243D4×Dic3—94no—
244C4×#67—91no—
245C4×#67—91no—
246#924—94no—
247#897—94no—
248#896—91no—
249#894—91no—
250#892—94no—
251#884—91no—
252#883—94no—
253#883—94no—
254#883—91no—
255#882—91no—
256#67⋊C4—94no—
257#67⋊C4—94no—
258#878—91no—
259C4×D12—91no—
260#872—91no—
261C23×C32—24no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32C22×D314yes—
265C23×C32C22×D314yes—
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3⋊D3—34no—
271C22×C3⋊D3—34no—
272C22×C3⋊D3—64no—
273C22×C3⋊D3—64no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3—62no—
277C22×C3⋊D3—68no—
278C22×C3⋊D3—68no—
279C22×C3⋊D3—68no—
280C22×C3⋊D3—128no—
281C22×C3⋊D3—128no—
282C22×C3⋊D3—128no—
283C22×C3×D3C22×D314yes—
284C32×D4—22no—
285C32×D4—28no—
286C32×D4—48no—
287C32×D4—62no—
288C32×D4—62no—
289C2×C32×C4—24no—
290C2×C32×C4—31no—
291C2×C32×C4—31no—
292C2×C32×C4—31no—
293C2×C32×C4—62no—
294C2×C32×C4C22×D314yes—
295C2×C32×C4C22×D311yescharacteristic
296#638—62no—
297#638—62no—
298#638—62no—
299#638—62no—
300#638—68no—
301#638—68no—
302#638—128no—
303#638—128no—
304C2×C3⋊Dic3—22no—
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3—31no—
307C2×C3⋊Dic3—31no—
308C2×C3⋊Dic3—34no—
309C2×C3⋊Dic3—34no—
310C2×C3⋊Dic3—64no—
311C2×C3⋊Dic3—64no—
312C2×C3⋊Dic3—62no—
313C2×C3⋊Dic3C22×D311yescharacteristic
314C2×C3⋊Dic3C22×D311yescharacteristic
315C2×C3⋊Dic3C22×D311yescharacteristic
316C2×C3⋊Dic3C22×D311yescharacteristic
317C4×C3⋊D3—34no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—62no—
321#634—62no—
322C3×#67—28no—
323C3×#67—28no—
324C2×C3×Dic3—28no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3—34no—
329C2×C3×Dic3—68no—
330C2×C3×Dic3—68no—
331C2×C3×Dic3C22×D314yes—
332C2×C3×Dic3C22×D314yes—
333C2×C3×Dic3C22×D314yes—
334#627—68no—
335#626—68no—
336#626—68no—
337#624—316no—
338#624—68no—
339#624—68no—
340#624—68no—
341D3×Dic3—68no—
342#525—271noSylow
343C2×C33—22no—
344C2×C33—41no—
345C2×C33C22×D411yescharacteristic
346C2×C33C2×#4111yescharacteristic
347C2×C33C2×#4111yescharacteristic
348C3⋊(C3⋊D3)—22no—
349C3⋊(C3⋊D3)—22no—
350C32×D3—41no—
351C23×D3—94no—
352C23×D3—91no—
353C23×D3—184no—
354C2×C3×D4—24no—
355C2×C3×D4—34no—
356C2×C3×D4—34no—
357C2×C3×D4D3214yes—
358C2×C3×D4C2×C3⋊D311yescharacteristic
359C22×C3×C4—34no—
360C22×C3×C4—91no—
361C22×C3×C4—91no—
362C2×#67—94no—
363C2×#67—94no—
364C2×#67—94no—
365C2×#67—94no—
366C2×#67—91no—
367C2×#67—91no—
368C2×#67—184no—
369C2×#67—184no—
370C2×#67C2×C3⋊D311yescharacteristic
371C2×#67C2×C3⋊D311yescharacteristic, complemented
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—94no—
375C22×Dic3C2×C3⋊D311yescharacteristic
376#237—1816no—
377#235—184no—
378C2×D12—91no—
379C2×D12—91no—
380C2×C4×D3—94no—
381C2×C4×D3—91no—
382C2×C4×D3—94no—
383C2×C4×D3—94no—
384C2×C4×D3—94no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—184no—
390C2×C4×D3—1816no—
391C2×Dic6—94no—
392C2×Dic6—91no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—91no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—91no—
398C3×C22⋊C4—91no—
399C3×C42—91no—
400#217—34no—
401#217—34no—
402#217—94no—
403#217—94no—
404#217—91no—
405#217—184no—
406#217C2×C3⋊D311yescharacteristic, complemented
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—94no—
411(C2×D3)⋊C4—94no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—184no—
417(C2×D3)⋊C4—184no—
418(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
419C4⋊Dic3—34no—
420C4⋊Dic3—94no—
421C4⋊Dic3—94no—
422C4⋊Dic3—91no—
423Dic3⋊C4—94no—
424Dic3⋊C4—94no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
429C4×Dic3—34no—
430C4×Dic3—94no—
431C4×Dic3—91no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—24no—
438C22×C32—28no—
439C22×C32—24no—
440C22×C32—24no—
441C22×C32—24no—
442C22×C32—24no—
443C22×C32—24no—
444C22×C32—44no—
445C22×C32—44no—
446C22×C32—44no—
447C22×C32—44no—
448C22×C32—44no—
449C22×C32—61no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32#23512yescomplemented
453C22×C32#23718yescomplemented
454C22×C32C23×D314yes—
455C22×C32C23×D311yescharacteristic
456C2×C3⋊D3—32no—
457C2×C3⋊D3—32no—
458C2×C3⋊D3—38no—
459C2×C3⋊D3—38no—
460C2×C3⋊D3—68no—
461C2×C3⋊D3—68no—
462C2×C3⋊D3—68no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—632no—
468C2×C3⋊D3—64no—
469C2×C3⋊D3—64no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—64no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3—124no—
476C2×C3⋊D3—1232no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C32×C4—21no—
481C32×C4—24no—
482C32×C4—32no—
483C32×C4—44no—
484C32×C4—61no—
485C32×C4—61no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—61no—
490C3⋊Dic3—61no—
491C3⋊Dic3—64no—
492C3⋊Dic3—64no—
493C3⋊Dic3—124no—
494C3⋊Dic3—124no—
495C3⋊Dic3D3×D412yes—
496C3×Dic3—24no—
497C3×Dic3—24no—
498C3×Dic3—38no—
499C3×Dic3—64no—
500C3×Dic3—64no—
501C3×Dic3—64no—
502C3×Dic3D3×D418yes—
503C2×#41—271no—
504C23×C4—271no—
505#123—271no—
506#123—271no—
507C22⋊Q8—271no—
508C22⋊Q8—271no—
509#121—31no—
510#121—271no—
511#120—271no—
512#120—271no—
513C4×D4—91no—
514C4×D4—271no—
515C4×D4—271no—
516C4×D4—271no—
517#117—271no—
518C33#52511yescharacteristic, complemented, Sylow
519C23×C3—24no—
520C23×C3—24no—
521C23×C3—34no—
522C23×C3C2×D3214yes—
523C23×C3C2×D3214yes—
524C23×C3C22×C3⋊D311yescharacteristic
525C23×C3C22×C3⋊D311yescharacteristic
526C22×D3—94no—
527C22×D3—94no—
528C22×D3—91no—
529C22×D3—91no—
530C22×D3—184no—
531C22×D3—184no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—188no—
535C22×D3—188no—
536C22×D3—188no—
537C22×D3—182no—
538C22×D3—368no—
539C22×D3—368no—
540C22×D3—368no—
541C22×D3C22×C3⋊D311yescharacteristic
542C3×D4—28no—
543C3×D4—22no—
544C3×D4—48no—
545C3×D4—68no—
546C3×D4—68no—
547C2×C3×C4—24no—
548C2×C3×C4—34no—
549C2×C3×C4—34no—
550C2×C3×C4—34no—
551C2×C3×C4—68no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—182no—
557C2×C3×C4—182no—
558C2×C3×C4C2×D3214yes—
559C2×C3×C4C22×C3⋊D311yescharacteristic
560#67—22no—
561#67—22no—
562#67—188no—
563#67—188no—
564#67—182no—
565#67—182no—
566#67—188no—
567#67—188no—
568#67—368no—
569#67—368no—
570C2×Dic3—22no—
571C2×Dic3—34no—
572C2×Dic3—34no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—68no—
576C2×Dic3—68no—
577C2×Dic3—94no—
578C2×Dic3—94no—
579C2×Dic3—91no—
580C2×Dic3—91no—
581C2×Dic3—184no—
582C2×Dic3—184no—
583C2×Dic3—188no—
584C2×Dic3C22×C3⋊D311yescharacteristic
585C2×Dic3C22×C3⋊D311yescharacteristic
586C2×Dic3C22×C3⋊D311yescharacteristic
587D12—182no—
588D12—182no—
589C4×D3—916no—
590C4×D3—94no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—188no—
594C4×D3—188no—
595C4×D3—188no—
596C4×D3—182no—
597C4×D3—182no—
598Dic6—188no—
599Dic6—182no—
600C2×C32—22no—
601C2×C32—24no—
602C2×C32—24no—
603C2×C32—24no—
604C2×C32—28no—
605C2×C32—48no—
606C2×C32—41no—
607C2×C32—44no—
608C2×C32—84no—
609C2×C32—121no—
610C2×C32C2×#23511yescharacteristic
611C2×C32C2×D3×D414yes—
612C2×C32C2×D3×D411yescharacteristic
613C2×C32C2×#23714yes—
614C2×C32D3×#4114yes—
615C2×C32D3×#4111yescharacteristic
616C3⋊D3—62no—
617C3⋊D3—62no—
618C3⋊D3—68no—
619C3⋊D3—68no—
620C3⋊D3—128no—
621C3⋊D3—128no—
622C3×D3—44no—
623C24—271no—
624#41—544no—
625C2×Q8—271no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4D3×C3⋊D311yescharacteristic
633C22×C4—31no—
634C22×C4—91no—
635C22×C4—91no—
636C22×C4—271no—
637C22×C4—271no—
638C22×C4—271no—
639C22×C4—271no—
640C22×C4—271no—
641C22×C4—544no—
642C4⋊C4—31no—
643C4⋊C4—91no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C22⋊C4—31no—
649C22⋊C4—31no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C42—91no—
659C42—271no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—24no—
665C22×C3—24no—
666C22×C3—24no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—24no—
671C22×C3—28no—
672C22×C3—44no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—64no—
678C22×C3—64no—
679C22×C3—64no—
680C22×C3#380418yescomplemented
681C22×C3#383012yescomplemented
682C22×C3C22×D3214yes—
683C22×C3C23×C3⋊D311yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—98no—
688C2×D3—98no—
689C2×D3—92no—
690C2×D3—92no—
691C2×D3—188no—
692C2×D3—188no—
693C2×D3—188no—
694C2×D3—1832no—
695C2×D3—184no—
696C2×D3—184no—
697C2×D3—184no—
698C2×D3—184no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—364no—
704C2×D3—364no—
705C2×D3—364no—
706C2×D3—364no—
707C2×D3—3632no—
708C3×C4—24no—
709C3×C4—21no—
710C3×C4—38no—
711C3×C4—44no—
712C3×C4—64no—
713C3×C4—64no—
714C3×C4—92no—
715C3×C4—181no—
716C3×C4—181no—
717C3×C4—181no—
718Dic3—21no—
719Dic3—21no—
720Dic3—38no—
721Dic3—64no—
722Dic3—64no—
723Dic3—64no—
724Dic3—184no—
725Dic3—184no—
726Dic3—181no—
727Dic3—181no—
728Dic3—364no—
729Dic3—364no—
730Dic3D4×C3⋊D312yes—
731C32—24no—
732C32#554711yescharacteristic, complemented
733C32#560614yescomplemented
734C23—31no—
735C23—271no—
736C23—271no—
737C23—542no—
738C23—542no—
739C23—542no—
740C23C2×D3×C3⋊D311yescharacteristic
741C23C2×D3×C3⋊D311yescharacteristic
742Q8—542no—
743D4—22no—
744D4—62no—
745D4—62no—
746D4—542no—
747D4—542no—
748D4—542no—
749D4—542no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—62no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—182no—
759C2×C4—182no—
760C2×C4—274no—
761C2×C4—271no—
762C2×C4—271no—
763C2×C4—542no—
764C2×C4—542no—
765C2×C4—542no—
766C2×C4—542no—
767C2×C4C2×D3×C3⋊D311yescharacteristic
768C2×C3—28no—
769C2×C3—22no—
770C2×C3—24no—
771C2×C3—24no—
772C2×C3—24no—
773C2×C3—48no—
774C2×C3—44no—
775C2×C3—41no—
776C2×C3—84no—
777C2×C3—124no—
778C2×C3D32×D414yes—
779C2×C3#6431214yes—
780C2×C3C2×#380414yes—
781C2×C3C2×D4×C3⋊D311yescharacteristic
782C2×C3C2×#383011yescharacteristic
783C2×C3#41×C3⋊D311yescharacteristic
784D3—41no—
785D3—188no—
786D3—188no—
787D3—182no—
788D3—182no—
789D3—368no—
790D3—368no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—272no—
800C22—272no—
801C22—548no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22#8902812yescomplemented
807C22C22×D3×C3⋊D311yescharacteristic
808C4—21no—
809C4—32no—
810C4—61no—
811C4—61no—
812C4—92no—
813C4—181no—
814C4—181no—
815C4—181no—
816C4—541no—
817C4—541no—
818C3—24no—
819C3#1059513814yescomplemented
820C3#1059607711yescharacteristic, complemented
821C2—22no—
822C2—41no—
823C2—121no—
824C2—542no—
825C2—542no—
826C2D3×D4×C3⋊D311yescharacteristic
827C2#1172458611yescharacteristic
828C2C2×#8902811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4D3×C3⋊D3
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6289C2semidirect
2. C2×#89028C2semidirect
3. #11723978C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. C32×#939C2semidirect
6. #11723640C2semidirect
7. #11723638C2semidirect
8. #11723628C2semidirect
9. #11723622C2semidirect
10. #67×C3⋊Dic3C2semidirect
11. #11723599C2semidirect
12. #11723485C2semidirect
13. #11723469C2semidirect
14. #11723461C2semidirect
15. #11723422C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
27. C2×#6293C22semidirect
36. C2×D3×C3⋊Dic3C22semidirect
41. C3×#3757C22semidirect
42. C3×C4⋊(C3⋊Dic3)C22semidirect
43. C3×C4×C3⋊Dic3C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. Dic3⋊(C3⋊Dic3)C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
66. D4×C3⋊Dic3D3semidirect
74. C3×#939D3semidirect
118. #6289D4semidirect
141. C22×C3⋊Dic3C2×D3semidirect
150. C2×C3×#67C2×D3semidirect
172. #3757C2×D3semidirect
183. C4⋊(C3⋊Dic3)C2×D3semidirect
187. C4×C3⋊Dic3C2×D3semidirect
190. C3×#217C2×D3semidirect
191. C3×(C2×D3)⋊C4C2×D3semidirect
193. C3×Dic3⋊C4C2×D3semidirect
208. C22×C33#41semidirect
216. C2×C3⋊(C3⋊D3)#41semidirect
236. #939C3⋊D3semidirect
371. C2×#67C2×C3⋊D3semidirect
406. #217C2×C3⋊D3semidirect
418. (C2×D3)⋊C4C2×C3⋊D3semidirect
428. Dic3⋊C4C2×C3⋊D3semidirect
452. C22×C32#235semidirect
453. C22×C32#237semidirect
518. C33#525semidirect
680. C22×C3#3804semidirect
681. C22×C3#3830semidirect
732. C32#5547semidirect
733. C32#5606semidirect
806. C22#89028semidirect
819. C3#10595138semidirect
820. C3#10596077semidirect

Maximal subgroups

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

subgroupindex
C22×#62892
C2×#890282
#117239782
C3×D4×C3⋊Dic32
C32×#9392
#117236402
#117236382
#117236282
#117236222
#67×C3⋊Dic32
#117235992
#117234852
#117234692
#117234612
#117234222
#105960773
#105951383