Finite Group Databasebeta

← #13175969

Subgroups — #13175969

Order 1728.

2080 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723923C211yesmaximal, characteristic, complemented
2C3×#64094C211yesmaximal, characteristic, complemented
3C32×#885C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723639C211yesmaximal, characteristic, complemented
6#11723638C211yesmaximal, characteristic, complemented
7#11723592C211yesmaximal, characteristic, complemented
8#11723542C211yesmaximal, characteristic, complemented
9#11723542C211yesmaximal, characteristic, complemented
10#11723521C211yesmaximal, characteristic, complemented
11#11723441C211yesmaximal, characteristic, complemented
12#11723440C211yesmaximal, characteristic, complemented
13#11723419C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596154—31nomaximal
17#10594311—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
22C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic, complemented
33#88859C2211yescharacteristic, complemented
34#88859C2211yescharacteristic, complemented
35C3×#3757C2211yescharacteristic, complemented
36C3×#3752C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic, complemented
38C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88804C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C32×#124—31no—
54#64156—31no—
55#64156—31no—
56#64146—31no—
57#64146—31no—
58#64094—31no—
59#64094—31no—
60#64094—31no—
61#64094D311yescharacteristic, complemented
62#64091—31no—
63#64091—31no—
64#64091—31no—
65#64091—31no—
66#64091—34no—
67#64091—64no—
68#64084—31no—
69#64084—31no—
70C3×#885—34no—
71C3×#885D314yescomplemented
72#63983—34no—
73#63981—34no—
74#63981—34no—
75#63953—34no—
76#63923—34no—
77#63923—34no—
78#63907—34no—
79#63907—34no—
80#63864—34no—
81#63864—34no—
82#63852—34no—
83#63852—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)—41no—
86C22×C3⋊(C3⋊D3)—41no—
87C22×C3⋊(C3⋊D3)—41no—
88C22×C3⋊(C3⋊D3)C2311yescharacteristic
89C22×C3⋊(C3⋊D3)C2311yescharacteristic
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C32×D3C2311yescharacteristic
93C2×D3×C3⋊D3—41no—
94C2×D3×C3⋊D3—41no—
95C2×D3×C3⋊D3—41no—
96C2×C33×C4C2311yescharacteristic
97C2×C33×C4C2311yescharacteristic
98#6312—41no—
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C4⋊(C3⋊(C3⋊D3))—41no—
101C4⋊(C3⋊(C3⋊D3))—41no—
102C3×#638—41no—
103C2×C3×C3⋊Dic3C2311yescharacteristic
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×#634—41no—
107C32×#67—41no—
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×Dic6—41no—
112#6293—41no—
113#6292—41no—
114#6292—41no—
115#6291—41no—
116#6291—41no—
117#5683—94no—
118#5683—91no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3—34no—
121C23×C3⋊D3—31no—
122C23×C3⋊D3—64no—
123C22×D32—34no—
124C2×C32×Q8—31no—
125C2×C32×D4—31no—
126C2×#638—31no—
127C2×#638—34no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—64no—
131C2×#638C2×D311yescharacteristic
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—31no—
135C2×C4⋊(C3⋊D3)—31no—
136C2×C4⋊(C3⋊D3)—34no—
137C2×C4⋊(C3⋊D3)—34no—
138C2×C4⋊(C3⋊D3)—64no—
139C2×C4⋊(C3⋊D3)—64no—
140C2×#634—31no—
141C2×#634C2×D311yescharacteristic, complemented
142C2×C3×#67—34no—
143C2×C3×#67C2×D314yes—
144C2×C3×Dic6—34no—
145C2×C3×Dic6C2×D314yescomplemented
146C2×#627—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C32×C22⋊C4—24no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4—31no—
154C32×C22⋊C4—31no—
155C32×C22⋊C4C2×D314yescomplemented
156C32×C22⋊C4C2×D311yescharacteristic, complemented
157C32×C42—31no—
158#3757—31no—
159#3757C2×D311yescharacteristic, complemented
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—34no—
164#3752—34no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic, complemented
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3C2×D311yescharacteristic, complemented
178C3×#217—34no—
179C3×#217C2×D314yescomplemented
180C3×(C2×D3)⋊C4—34no—
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4C2×D314yescomplemented
183C3×(C2×D3)⋊C4C2×D314yescomplemented
184C3×C4×Dic3—34no—
185C3×C4×Dic3C2×D314yescomplemented
186#3722—34no—
187#3722—34no—
188#3722—34no—
189#3722—34no—
190#3722—34no—
191#3722—34no—
192#3722—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—34no—
195Dic32—34no—
196C22×C33—21no—
197C22×C33—21no—
198C22×C33—21no—
199C22×C33C2411yescharacteristic
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—44no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216D3×C3⋊D3—44no—
217C33×C4—21no—
218C33×C4—21no—
219C3⋊(C3⋊Dic3)—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3—21no—
222C3×C3⋊Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C32×Dic3—21no—
226C3×#124—34no—
227C3×#124—91no—
228#947—94no—
229#947—94no—
230#947—91no—
231#947—91no—
232#937—94no—
233#937—94no—
234#937—91no—
235#937—91no—
236#885—34no—
237#885—94no—
238#885—94no—
239#885—94no—
240#885—91no—
241#885—91no—
242#885—91no—
243#885C3⋊D311yescharacteristic, complemented
244#882—94no—
245#882—94no—
246#882—94no—
247#882—91no—
248#882—94no—
249#882—91no—
250#882—91no—
251#882—91no—
252#882—184no—
253#875—94no—
254#875—94no—
255#875—91no—
256#875—91no—
257C23×C32—24no—
258C23×C32—31no—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3⋊D3—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—64no—
270C22×C3⋊D3—121no—
271C22×C3⋊D3—121no—
272C22×C3⋊D3—121no—
273C22×C3⋊D3—121no—
274C22×C3⋊D3—121no—
275C22×C3⋊D3—121no—
276C22×C3⋊D3—124no—
277C22×C3⋊D3—124no—
278C22×C3⋊D3—124no—
279C22×C3⋊D3—128no—
280C22×C3⋊D3—128no—
281C22×C3⋊D3—128no—
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—34no—
284C22×C3×D3C22×D314yes—
285C2×D32—124no—
286C2×D32—124no—
287C2×D32—124no—
288C32×Q8—121no—
289C32×D4—121no—
290C2×C32×C4—24no—
291C2×C32×C4—24no—
292C2×C32×C4—31no—
293C2×C32×C4—31no—
294C2×C32×C4—31no—
295C2×C32×C4C22×D314yes—
296C2×C32×C4C22×D314yes—
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299#638—41no—
300#638—121no—
301#638—121no—
302#638—121no—
303#638—124no—
304#638—128no—
305C2×C3⋊Dic3—31no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3C22×D311yescharacteristic
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C4⋊(C3⋊D3)—121no—
312C4⋊(C3⋊D3)—121no—
313C4⋊(C3⋊D3)—124no—
314C4⋊(C3⋊D3)—124no—
315C4⋊(C3⋊D3)—128no—
316C4⋊(C3⋊D3)—128no—
317C4⋊(C3⋊D3)—121no—
318C4⋊(C3⋊D3)—121no—
319#634—41no—
320#634—121no—
321C3×#67—44no—
322C3×#67—124no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3C22×D314yes—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×Dic6—44no—
330C3×Dic6—124no—
331#627—124no—
332#626—124no—
333#626—124no—
334#626—124no—
335#626—124no—
336H(3,𝔽4)—271noSylow
337C2×C33—41no—
338C2×C33H(5,𝔽2)11yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C2×C33H(5,𝔽2)11yescharacteristic
341C3⋊(C3⋊D3)—41no—
342C3⋊(C3⋊D3)—41no—
343C3⋊(C3⋊D3)—41no—
344C3×C3⋊D3—41no—
345C32×D3—41no—
346C23×D3—94no—
347C23×D3—94no—
348C23×D3—91no—
349C23×D3—91no—
350C23×D3—184no—
351C2×C3×Q8—34no—
352C2×C3×Q8—91no—
353C2×C3×D4—34no—
354C2×C3×D4—91no—
355C2×#67—34no—
356C2×#67—94no—
357C2×#67—94no—
358C2×#67—94no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—184no—
363C2×#67C2×C3⋊D311yescharacteristic
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—94no—
369C2×D12—94no—
370C2×D12—91no—
371C2×D12—91no—
372C2×D12—184no—
373C2×D12—184no—
374C2×Dic6—34no—
375C2×Dic6—94no—
376C2×Dic6—91no—
377C2×Dic6C2×C3⋊D311yescharacteristic, complemented
378C3×C22⋊C4—24no—
379C3×C22⋊C4—34no—
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C22⋊C4D3214yescomplemented
386C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
387C3×C42—34no—
388C3×C42—91no—
389#217—34no—
390#217—94no—
391#217—91no—
392#217C2×C3⋊D311yescharacteristic, complemented
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—94no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—184no—
416(C2×D3)⋊C4—184no—
417(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
418(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
419C4×Dic3—34no—
420C4×Dic3—94no—
421C4×Dic3—91no—
422C4×Dic3C2×C3⋊D311yescharacteristic, complemented
423C22×C32—28no—
424C22×C32—21no—
425C22×C32—24no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—24no—
429C22×C32—24no—
430C22×C32—24no—
431C22×C32—44no—
432C22×C32—44no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32C23×D314yes—
437C22×C32C23×D311yescharacteristic
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—68no—
442C2×C3⋊D3—68no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3⋊D3—64no—
455C2×C3⋊D3—64no—
456C2×C3⋊D3—64no—
457C2×C3⋊D3—64no—
458C2×C3⋊D3—64no—
459C2×C3⋊D3—64no—
460C2×C3⋊D3—64no—
461C2×C3⋊D3—124no—
462C2×C3⋊D3—124no—
463C2×C3⋊D3—124no—
464C2×C3⋊D3—124no—
465C2×C3⋊D3—124no—
466C2×C3⋊D3—124no—
467C2×C3⋊D3—124no—
468C2×C3⋊D3—124no—
469C2×C3⋊D3—1232no—
470C2×C3⋊D3—1216no—
471C2×C3⋊D3—124no—
472C2×C3×D3—24no—
473C2×C3×D3—24no—
474C2×C3×D3—24no—
475C2×C3×D3—64no—
476C2×C3×D3—64no—
477C2×C3×D3—64no—
478D32—1216no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—24no—
482C32×C4—24no—
483C32×C4—44no—
484C32×C4—44no—
485C32×C4—61no—
486C32×C4—61no—
487C32×C4—61no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—61no—
492C3⋊Dic3—64no—
493C3⋊Dic3—124no—
494C3×Dic3—24no—
495C3×Dic3—24no—
496C3×Dic3—24no—
497C3×Dic3—64no—
498C3×Dic3—64no—
499C3×Dic3—64no—
500#124—31no—
501#124—91no—
502#124—271no—
503#124—271no—
504#124—271no—
505#124—271no—
506#124—271no—
507#124—271no—
508#124—271no—
509#120—271no—
510#120—271no—
511#120—271no—
512#120—271no—
513#120—271no—
514#120—271no—
515C33H(3,𝔽4)11yescharacteristic, complemented, Sylow
516C23×C3—24no—
517C23×C3—34no—
518C23×C3—91no—
519C23×C3C2×D3214yes—
520C23×C3C22×C3⋊D311yescharacteristic
521C22×D3—34no—
522C22×D3—94no—
523C22×D3—94no—
524C22×D3—94no—
525C22×D3—91no—
526C22×D3—91no—
527C22×D3—91no—
528C22×D3—184no—
529C22×D3—184no—
530C22×D3—184no—
531C22×D3—361no—
532C22×D3—361no—
533C22×D3—361no—
534C22×D3—364no—
535C22×D3—364no—
536C22×D3—364no—
537C22×D3—364no—
538C22×D3—364no—
539C22×D3—364no—
540C22×D3—361no—
541C22×D3—361no—
542C22×D3—361no—
543C22×D3—368no—
544C22×D3—368no—
545C22×D3—368no—
546C22×D3C22×C3⋊D311yescharacteristic
547C3×Q8—124no—
548C3×Q8—361no—
549C3×D4—124no—
550C3×D4—361no—
551C2×C3×C4—24no—
552C2×C3×C4—24no—
553C2×C3×C4—34no—
554C2×C3×C4—34no—
555C2×C3×C4—34no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4C2×D3214yes—
560C2×C3×C4C2×D3214yes—
561C2×C3×C4C22×C3⋊D311yescharacteristic
562C2×C3×C4C22×C3⋊D311yescharacteristic
563#67—41no—
564#67—124no—
565#67—361no—
566#67—361no—
567#67—364no—
568#67—364no—
569#67—364no—
570#67—361no—
571#67—368no—
572C2×Dic3—34no—
573C2×Dic3—34no—
574C2×Dic3—34no—
575C2×Dic3—94no—
576C2×Dic3—91no—
577C2×Dic3—184no—
578C2×Dic3C22×C3⋊D311yescharacteristic
579C2×Dic3C22×C3⋊D311yescharacteristic
580C2×Dic3C22×C3⋊D311yescharacteristic
581D12—364no—
582D12—364no—
583D12—361no—
584D12—361no—
585D12—368no—
586D12—368no—
587D12—364no—
588D12—364no—
589D12—361no—
590D12—361no—
591Dic6—41no—
592Dic6—124no—
593Dic6—361no—
594Dic6—364no—
595C2×C32—24no—
596C2×C32—24no—
597C2×C32—24no—
598C2×C32—48no—
599C2×C32—44no—
600C2×C32—41no—
601C2×C32—121no—
602C2×C32#100414yes—
603C2×C32#100411yescharacteristic
604C2×C32#100914yes—
605C2×C32#100914yes—
606C2×C32#100911yescharacteristic
607C2×C32#100911yescharacteristic
608C3⋊D3—41no—
609C3⋊D3—128no—
610C3⋊D3—128no—
611C3⋊D3—124no—
612C3⋊D3—124no—
613C3⋊D3—121no—
614C3⋊D3—121no—
615C3⋊D3—121no—
616C3⋊D3—124no—
617C3⋊D3—244no—
618C3×D3—44no—
619C3×D3—124no—
620C24—271no—
621C24—271no—
622C2×Q8—31no—
623C2×Q8—91no—
624C2×Q8—271no—
625C2×D4—31no—
626C2×D4—91no—
627C2×D4—271no—
628C2×D4—271no—
629C2×D4—271no—
630C2×D4—271no—
631C2×D4—271no—
632C2×D4—271no—
633C2×D4—271no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22⋊C4—271no—
649C22⋊C4—271no—
650C22⋊C4—271no—
651C22⋊C4D3×C3⋊D311yescharacteristic, complemented
652C42—31no—
653C42—91no—
654C42—271no—
655C22×C3—28no—
656C22×C3—24no—
657C22×C3—24no—
658C22×C3—24no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—24no—
663C22×C3—44no—
664C22×C3—44no—
665C22×C3—64no—
666C22×C3—64no—
667C22×C3—64no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3C22×D3214yes—
672C22×C3C23×C3⋊D311yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—64no—
677C2×D3—64no—
678C2×D3—64no—
679C2×D3—188no—
680C2×D3—188no—
681C2×D3—184no—
682C2×D3—184no—
683C2×D3—184no—
684C2×D3—184no—
685C2×D3—184no—
686C2×D3—184no—
687C2×D3—184no—
688C2×D3—184no—
689C2×D3—184no—
690C2×D3—181no—
691C2×D3—181no—
692C2×D3—181no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—364no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—364no—
703C2×D3—364no—
704C2×D3—364no—
705C2×D3—364no—
706C2×D3—364no—
707C2×D3—3616no—
708C2×D3—3632no—
709C2×D3—3616no—
710C2×D3—364no—
711C3×C4—24no—
712C3×C4—24no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—44no—
716C3×C4—44no—
717C3×C4—64no—
718C3×C4—64no—
719C3×C4—64no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723Dic3—21no—
724Dic3—21no—
725Dic3—21no—
726Dic3—64no—
727Dic3—64no—
728Dic3—64no—
729Dic3—184no—
730Dic3—181no—
731Dic3—364no—
732C32—24no—
733C32#568314yescomplemented
734C32#568311yescharacteristic, complemented
735C23—31no—
736C23—91no—
737C23—271no—
738C23—271no—
739C23—271no—
740C23—1081no—
741C23—1081no—
742C23—1081no—
743C23—1081no—
744C23—1081no—
745C23—1081no—
746C23C2×D3×C3⋊D311yescharacteristic
747Q8—121no—
748Q8—361no—
749Q8—1081no—
750D4—121no—
751D4—361no—
752D4—1081no—
753D4—1081no—
754D4—1081no—
755D4—1081no—
756D4—1081no—
757D4—1081no—
758D4—1081no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—271no—
766C2×C4C2×D3×C3⋊D311yescharacteristic
767C2×C4C2×D3×C3⋊D311yescharacteristic
768C2×C3—24no—
769C2×C3—24no—
770C2×C3—24no—
771C2×C3—48no—
772C2×C3—44no—
773C2×C3—41no—
774C2×C3—124no—
775C2×C3—361no—
776C2×C3#6430814yes—
777C2×C3#6431414yes—
778C2×C3#6431414yes—
779C2×C3#6436111yescharacteristic
780C2×C3#6436611yescharacteristic
781C2×C3#6436611yescharacteristic
782D3—41no—
783D3—124no—
784D3—368no—
785D3—368no—
786D3—364no—
787D3—364no—
788D3—364no—
789D3—361no—
790D3—361no—
791D3—361no—
792D3—724no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—61no—
797C22—61no—
798C22—61no—
799C22—181no—
800C22—181no—
801C22—181no—
802C22—541no—
803C22—541no—
804C22—541no—
805C22—541no—
806C22—541no—
807C22—541no—
808C22—541no—
809C22—541no—
810C22—541no—
811C22—1084no—
812C22—1084no—
813C22C22×D3×C3⋊D311yescharacteristic
814C4—21no—
815C4—21no—
816C4—61no—
817C4—61no—
818C4—61no—
819C4—181no—
820C4—181no—
821C4—181no—
822C4—541no—
823C3—24no—
824C3#1059431114yescomplemented
825C3#1059615411yescharacteristic, complemented
826C2—41no—
827C2—121no—
828C2—361no—
829C2—1081no—
830C2—1081no—
831C2—1081no—
832C2#1172458111yescharacteristic
833C2#1172458811yescharacteristic
834C2#1172458911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33H(3,𝔽4)
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723923C2semidirect
2. C3×#64094C2semidirect
3. C32×#885C2semidirect
4. #11723643C2semidirect
5. #11723639C2semidirect
6. #11723638C2semidirect
7. #11723592C2semidirect
8. #11723542C2semidirect
9. #11723542C2semidirect
10. #11723521C2semidirect
11. #11723441C2semidirect
12. #11723440C2semidirect
13. #11723419C2semidirect
14. #11723416C2semidirect
15. #11723392C2semidirect
18. C23×C3⋊(C3⋊D3)C22semidirect
19. C22×D3×C3⋊D3C22semidirect
24. C2×C3×#634C22semidirect
26. C2×C32×Dic6C22semidirect
27. C2×#6293C22semidirect
32. C33×C22⋊C4C22semidirect
33. #88859C22semidirect
34. #88859C22semidirect
35. C3×#3757C22semidirect
36. C3×#3752C22semidirect
37. C3×#3752C22semidirect
38. C3×C4×C3⋊Dic3C22semidirect
39. C32×#217C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88804C22semidirect
44. #88804C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. #88804C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
61. #64094D3semidirect
71. C3×#885D3semidirect
141. C2×#634C2×D3semidirect
145. C2×C3×Dic6C2×D3semidirect
155. C32×C22⋊C4C2×D3semidirect
156. C32×C22⋊C4C2×D3semidirect
159. #3757C2×D3semidirect
174. #3752C2×D3semidirect
175. #3752C2×D3semidirect
177. C4×C3⋊Dic3C2×D3semidirect
179. C3×#217C2×D3semidirect
182. C3×(C2×D3)⋊C4C2×D3semidirect
183. C3×(C2×D3)⋊C4C2×D3semidirect
185. C3×C4×Dic3C2×D3semidirect
243. #885C3⋊D3semidirect
377. C2×Dic6C2×C3⋊D3semidirect
385. C3×C22⋊C4D32semidirect
386. C3×C22⋊C4C2×C3⋊D3semidirect
392. #217C2×C3⋊D3semidirect
417. (C2×D3)⋊C4C2×C3⋊D3semidirect
418. (C2×D3)⋊C4C2×C3⋊D3semidirect
422. C4×Dic3C2×C3⋊D3semidirect
515. C33H(3,𝔽4)semidirect
651. C22⋊C4D3×C3⋊D3semidirect
733. C32#5683semidirect
734. C32#5683semidirect
824. C3#10594311semidirect
825. C3#10596154semidirect

Maximal subgroups

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

subgroupindex
#117239232
C3×#640942
C32×#8852
#117236432
#117236392
#117236382
#117235922
#117235422
#117235212
#117234412
#117234402
#117234192
#117234162
#117233922
#105961543
#105943113