Finite Group Databasebeta

← #13175966

Subgroups — #13175966

Order 1728.

1864 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723926C211yesmaximal, characteristic, complemented
2C3×#64091C211yesmaximal, characteristic, complemented
3C32×#885C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723636C211yesmaximal, characteristic, complemented
6#11723634C211yesmaximal, characteristic, complemented
7#11723591C211yesmaximal, characteristic, complemented
8#11723541C211yesmaximal, characteristic, complemented
9#11723541C211yesmaximal, characteristic, complemented
10#11723530C211yesmaximal, characteristic, complemented
11#11723528C211yesmaximal, characteristic, complemented
12#11723439C211yesmaximal, characteristic, complemented
13#11723436C211yesmaximal, characteristic, complemented
14#11723416C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596154—31nomaximal
17#10594309—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic, complemented
19C22×D3×C3⋊D3C2211yescharacteristic, complemented
20C2×#6312C2211yescharacteristic
21C2×#6308C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic
26C2×C32×Dic6C2211yescharacteristic, complemented
27C2×#6293C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C33×C22⋊C4C2211yescharacteristic, complemented
33#88864C2211yescharacteristic, complemented
34#88859C2211yescharacteristic, complemented
35#88859C2211yescharacteristic, complemented
36C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic, complemented
39C32×#217C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C32×C4×Dic3C2211yescharacteristic, complemented
43#88804C2211yescharacteristic, complemented
44#88803C2211yescharacteristic, complemented
45#88803C2211yescharacteristic, complemented
46#88803C2211yescharacteristic, complemented
47#88803C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, 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#64094—31no—
62#64094—34no—
63#64094—64no—
64#64091—31no—
65#64091—31no—
66#64091—31no—
67#64091D311yescharacteristic, complemented
68#64084—31no—
69#64084—31no—
70C3×#885D314yescomplemented
71C3×#882—34no—
72#63983—34no—
73#63977—34no—
74#63976—34no—
75#63959—34no—
76#63922—34no—
77#63922—34no—
78#63915—34no—
79#63913—34no—
80#63907—34no—
81#63863—34no—
82#63860—34no—
83#63852—34no—
84C23×C33C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3—41no—
87C22×C3×C3⋊D3—41no—
88C22×C3×C3⋊D3—41no—
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C3×C3⋊D3C2311yescharacteristic
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
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102#6308—41no—
103C3×#638—41no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C3×C4⋊(C3⋊D3)—41no—
106C3×C4⋊(C3⋊D3)—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#6290—41no—
116#6290—41no—
117#5683—94no—
118#5594—91no—
119C23×C3⋊D3—31no—
120C23×C3⋊D3C2×D311yescharacteristic, complemented
121C23×C3×D3—34no—
122C22×D32—34no—
123C2×C32×Q8—31no—
124C2×C32×D4—31no—
125C2×#638—31no—
126C2×#638—34no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—64no—
130C2×#638C2×D311yescharacteristic
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
135C2×#634—31no—
136C2×#634—34no—
137C2×#634—31no—
138C2×#634—64no—
139C2×C3×#67—34no—
140C2×C3×#67C2×D314yes—
141C2×C3×D12—34no—
142C2×C3×D12—34no—
143C2×C3×Dic6C2×D314yescomplemented
144C2×#627—34no—
145C2×#626—34no—
146C2×#626—34no—
147C2×#625—34no—
148C2×#625—34no—
149C32×C22⋊C4—24no—
150C32×C22⋊C4—31no—
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153C32×C22⋊C4C2×D314yescomplemented
154C32×C22⋊C4C2×D311yescharacteristic, complemented
155C32×C42—31no—
156#3757—31no—
157#3757—34no—
158#3757—31no—
159#3757—64no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—34no—
170#3752—34no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic, complemented
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—34no—
178C4×C3⋊Dic3—31no—
179C4×C3⋊Dic3—64no—
180C3×#217C2×D314yescomplemented
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yescomplemented
184C3×(C2×D3)⋊C4C2×D314yescomplemented
185C3×C4×Dic3C2×D314yescomplemented
186#3722—34no—
187(C2×D3)⋊Dic3—34no—
188(C2×D3)⋊Dic3—34no—
189(C2×D3)⋊Dic3—34no—
190(C2×D3)⋊Dic3—34no—
191(C2×D3)⋊Dic3—34no—
192(C2×D3)⋊Dic3—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—21no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3—44no—
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×#120—91no—
228#953—91no—
229#953—91no—
230#947—94no—
231#947—94no—
232#937—94no—
233#937—94no—
234#937—91no—
235#937—91no—
236#937—91no—
237#936—91no—
238#936—91no—
239#936—91no—
240#885—94no—
241#885—94no—
242#885—94no—
243#885—91no—
244#885—94no—
245#885—91no—
246#885—91no—
247#885—91no—
248#885—91no—
249#885—184no—
250#885C3⋊D311yescharacteristic, complemented
251#882—34no—
252#882—94no—
253#882—94no—
254#882—94no—
255#875—94no—
256#875—94no—
257C23×C32—24no—
258C23×C32—31no—
259C23×C32C22×D314yes—
260C23×C32C22×D311yescharacteristic
261C22×C3⋊D3—31no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—41no—
264C22×C3⋊D3—41no—
265C22×C3⋊D3—41no—
266C22×C3⋊D3—64no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3—121no—
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3⋊D3C22×D311yescharacteristic
273C22×C3×D3—34no—
274C22×C3×D3—34no—
275C22×C3×D3—34no—
276C22×C3×D3—124no—
277C22×C3×D3—124no—
278C22×C3×D3—124no—
279C22×C3×D3C22×D314yes—
280C2×D32—124no—
281C2×D32—124no—
282C2×D32—124no—
283C32×Q8—121no—
284C32×D4—121no—
285C2×C32×C4—24no—
286C2×C32×C4—24no—
287C2×C32×C4—31no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4C22×D314yes—
291C2×C32×C4C22×D314yes—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294#638—41no—
295#638—121no—
296#638—121no—
297#638—121no—
298#638—124no—
299#638—128no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C4⋊(C3⋊D3)—41no—
311C4⋊(C3⋊D3)—41no—
312C4⋊(C3⋊D3)—121no—
313C4⋊(C3⋊D3)—121no—
314#634—121no—
315#634—121no—
316#634—124no—
317#634—128no—
318C3×#67—44no—
319C3×#67—124no—
320C2×C3×Dic3—34no—
321C2×C3×Dic3C22×D314yes—
322C2×C3×Dic3C22×D314yes—
323C2×C3×Dic3C22×D314yes—
324C3×D12—124no—
325C3×D12—124no—
326C3×Dic6—44no—
327#627—124no—
328#626—124no—
329#626—124no—
330#625—124no—
331#625—124no—
332H(3,𝔽4)—271noSylow
333C2×C33—41no—
334C2×C33H(5,𝔽2)11yescharacteristic
335C2×C33H(5,𝔽2)11yescharacteristic
336C2×C33H(5,𝔽2)11yescharacteristic
337C3⋊(C3⋊D3)—41no—
338C3×C3⋊D3—41no—
339C3×C3⋊D3—41no—
340C3×C3⋊D3—41no—
341C32×D3—41no—
342C24×C3—91no—
343C23×D3—34no—
344C23×D3—94no—
345C23×D3—91no—
346C2×C3×Q8—34no—
347C2×C3×D4—34no—
348C2×C3×D4—91no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×#67—34no—
352C2×#67—94no—
353C2×#67—94no—
354C2×#67—94no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—184no—
361C2×#67C2×C3⋊D311yescharacteristic
362C2×D12—34no—
363C2×D12—34no—
364C2×D12—94no—
365C2×D12—94no—
366C2×Dic6—94no—
367C2×Dic6—94no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—184no—
371C2×Dic6C2×C3⋊D311yescharacteristic, complemented
372C3×C22⋊C4—24no—
373C3×C22⋊C4—34no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4D3214yescomplemented
379C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
380C3×C42—34no—
381#217—94no—
382#217—94no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387#217—91no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—184no—
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—184no—
410(C2×D3)⋊C4—184no—
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
412(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
413C4×Dic3—94no—
414C4×Dic3—94no—
415C4×Dic3—91no—
416C4×Dic3—91no—
417C4×Dic3—184no—
418C4×Dic3C2×C3⋊D311yescharacteristic, complemented
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—24no—
423C22×C32—24no—
424C22×C32—24no—
425C22×C32—24no—
426C22×C32—44no—
427C22×C32—44no—
428C22×C32—44no—
429C22×C32—61no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32C23×D314yes—
433C22×C32C23×D311yescharacteristic
434C2×C3⋊D3—21no—
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3—44no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3—124no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3×D3—24no—
455C2×C3×D3—24no—
456C2×C3×D3—24no—
457C2×C3×D3—64no—
458C2×C3×D3—64no—
459C2×C3×D3—64no—
460C2×C3×D3—64no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—1216no—
467D32—1216no—
468C32×C4—21no—
469C32×C4—21no—
470C32×C4—24no—
471C32×C4—24no—
472C32×C4—44no—
473C32×C4—44no—
474C32×C4—61no—
475C32×C4—61no—
476C32×C4—61no—
477C3⋊Dic3—21no—
478C3⋊Dic3—68no—
479C3⋊Dic3—61no—
480C3⋊Dic3—61no—
481C3⋊Dic3—61no—
482C3⋊Dic3—64no—
483C3⋊Dic3—64no—
484C3⋊Dic3—64no—
485C3⋊Dic3—124no—
486C3⋊Dic3—124no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—24no—
490C3×Dic3—64no—
491#124—31no—
492#124—271no—
493#124—271no—
494#124—271no—
495#124—271no—
496#124—271no—
497#124—271no—
498#124—271no—
499#124—271no—
500#120—91no—
501#120—271no—
502#120—271no—
503#120—271no—
504#120—271no—
505#120—271no—
506C33H(3,𝔽4)11yescharacteristic, complemented, Sylow
507C23×C3—24no—
508C23×C3—34no—
509C23×C3—91no—
510C23×C3—91no—
511C23×C3—91no—
512C23×C3—361no—
513C23×C3—361no—
514C23×C3—361no—
515C23×C3C2×D3214yes—
516C23×C3C22×C3⋊D311yescharacteristic
517C22×D3—34no—
518C22×D3—34no—
519C22×D3—34no—
520C22×D3—94no—
521C22×D3—91no—
522C22×D3—124no—
523C22×D3—124no—
524C22×D3—124no—
525C22×D3—184no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3—361no—
529C22×D3—364no—
530C22×D3—364no—
531C22×D3—364no—
532C22×D3C22×C3⋊D311yescharacteristic
533C3×Q8—124no—
534C3×D4—124no—
535C3×D4—361no—
536C3×D4—361no—
537C3×D4—361no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—34no—
541C2×C3×C4—34no—
542C2×C3×C4—34no—
543C2×C3×C4—91no—
544C2×C3×C4C2×D3214yes—
545C2×C3×C4C2×D3214yes—
546C2×C3×C4C22×C3⋊D311yescharacteristic
547C2×C3×C4C22×C3⋊D311yescharacteristic
548#67—41no—
549#67—124no—
550#67—361no—
551#67—361no—
552#67—361no—
553#67—361no—
554#67—364no—
555#67—364no—
556#67—364no—
557#67—361no—
558#67—368no—
559C2×Dic3—34no—
560C2×Dic3—94no—
561C2×Dic3—94no—
562C2×Dic3—94no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—184no—
567C2×Dic3—184no—
568C2×Dic3—184no—
569C2×Dic3C22×C3⋊D311yescharacteristic
570C2×Dic3C22×C3⋊D311yescharacteristic
571C2×Dic3C22×C3⋊D311yescharacteristic
572D12—124no—
573D12—124no—
574D12—364no—
575D12—364no—
576Dic6—41no—
577Dic6—361no—
578Dic6—364no—
579Dic6—364no—
580Dic6—361no—
581Dic6—368no—
582C2×C32—24no—
583C2×C32—24no—
584C2×C32—24no—
585C2×C32—41no—
586C2×C32—44no—
587C2×C32—84no—
588C2×C32—121no—
589C2×C32#100414yes—
590C2×C32#100411yescharacteristic
591C2×C32#100411yescharacteristic
592C2×C32#100411yescharacteristic
593C2×C32#100914yes—
594C2×C32#100914yes—
595C3⋊D3—41no—
596C3⋊D3—41no—
597C3⋊D3—41no—
598C3⋊D3—121no—
599C3⋊D3—124no—
600C3⋊D3—244no—
601C3×D3—44no—
602C3×D3—124no—
603C3×D3—124no—
604C3×D3—124no—
605C24—91no—
606C24—271no—
607C2×Q8—31no—
608C2×Q8—271no—
609C2×Q8—271no—
610C2×D4—31no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4D3×C3⋊D311yescharacteristic, complemented
637C42—31no—
638C42—271no—
639C42—271no—
640C22×C3—24no—
641C22×C3—24no—
642C22×C3—24no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—24no—
647C22×C3—44no—
648C22×C3—44no—
649C22×C3—44no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3—364no—
663C22×C3C22×D3214yes—
664C22×C3C23×C3⋊D311yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—64no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—64no—
674C2×D3—64no—
675C2×D3—64no—
676C2×D3—64no—
677C2×D3—1216no—
678C2×D3—184no—
679C2×D3—184no—
680C2×D3—184no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3—364no—
688C2×D3—3616no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—44no—
694C3×C4—44no—
695C3×C4—64no—
696C3×C4—64no—
697C3×C4—64no—
698C3×C4—181no—
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—64no—
703Dic3—188no—
704Dic3—184no—
705Dic3—184no—
706Dic3—184no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—364no—
711Dic3—364no—
712C32—24no—
713C32#559411yescharacteristic, complemented
714C32#568314yescomplemented
715C23—31no—
716C23—91no—
717C23—91no—
718C23—91no—
719C23—271no—
720C23—361no—
721C23—361no—
722C23—361no—
723C23—1081no—
724C23—1081no—
725C23—1081no—
726C23C2×D3×C3⋊D311yescharacteristic
727Q8—121no—
728Q8—1081no—
729Q8—1081no—
730D4—121no—
731D4—361no—
732D4—361no—
733D4—361no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—91no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—271no—
746C2×C4C2×D3×C3⋊D311yescharacteristic
747C2×C4C2×D3×C3⋊D311yescharacteristic
748C2×C3—24no—
749C2×C3—24no—
750C2×C3—24no—
751C2×C3—44no—
752C2×C3—41no—
753C2×C3—84no—
754C2×C3—124no—
755C2×C3—361no—
756C2×C3—361no—
757C2×C3—361no—
758C2×C3#6430714yes—
759C2×C3#6431314yes—
760C2×C3#6431414yes—
761C2×C3#6436111yescharacteristic
762C2×C3#6436611yescharacteristic
763C2×C3#6436611yescharacteristic
764D3—41no—
765D3—124no—
766D3—124no—
767D3—124no—
768D3—364no—
769D3—361no—
770D3—724no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—181no—
786C22—364no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—1084no—
791C22C22×D3×C3⋊D311yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—61no—
796C4—61no—
797C4—181no—
798C4—541no—
799C4—541no—
800C4—541no—
801C3—24no—
802C3#1059430914yescomplemented
803C3#1059615411yescharacteristic, complemented
804C2—41no—
805C2—121no—
806C2—361no—
807C2—361no—
808C2—361no—
809C2—1081no—
810C2#1172458011yescharacteristic
811C2#1172458711yescharacteristic
812C2#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. #11723926C2semidirect
2. C3×#64091C2semidirect
3. C32×#885C2semidirect
4. #11723643C2semidirect
5. #11723636C2semidirect
6. #11723634C2semidirect
7. #11723591C2semidirect
8. #11723541C2semidirect
9. #11723541C2semidirect
10. #11723530C2semidirect
11. #11723528C2semidirect
12. #11723439C2semidirect
13. #11723436C2semidirect
14. #11723416C2semidirect
15. #11723392C2semidirect
18. C23×C3×C3⋊D3C22semidirect
19. C22×D3×C3⋊D3C22semidirect
21. C2×#6308C22semidirect
26. C2×C32×Dic6C22semidirect
27. C2×#6293C22semidirect
32. C33×C22⋊C4C22semidirect
33. #88864C22semidirect
34. #88859C22semidirect
35. #88859C22semidirect
36. C4×C3⋊(C3⋊Dic3)C22semidirect
37. C3×#3752C22semidirect
38. C3×#3752C22semidirect
39. C32×#217C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. C32×C4×Dic3C22semidirect
43. #88804C22semidirect
44. #88803C22semidirect
45. #88803C22semidirect
46. #88803C22semidirect
47. #88803C22semidirect
48. #88803C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. (C2×D3)⋊(C3⋊Dic3)C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
67. #64091D3semidirect
70. C3×#885D3semidirect
120. C23×C3⋊D3C2×D3semidirect
143. C2×C3×Dic6C2×D3semidirect
153. C32×C22⋊C4C2×D3semidirect
154. C32×C22⋊C4C2×D3semidirect
174. #3752C2×D3semidirect
175. #3752C2×D3semidirect
180. C3×#217C2×D3semidirect
183. C3×(C2×D3)⋊C4C2×D3semidirect
184. C3×(C2×D3)⋊C4C2×D3semidirect
185. C3×C4×Dic3C2×D3semidirect
250. #885C3⋊D3semidirect
371. C2×Dic6C2×C3⋊D3semidirect
378. C3×C22⋊C4D32semidirect
379. C3×C22⋊C4C2×C3⋊D3semidirect
392. #217C2×C3⋊D3semidirect
411. (C2×D3)⋊C4C2×C3⋊D3semidirect
412. (C2×D3)⋊C4C2×C3⋊D3semidirect
418. C4×Dic3C2×C3⋊D3semidirect
506. C33H(3,𝔽4)semidirect
636. C22⋊C4D3×C3⋊D3semidirect
713. C32#5594semidirect
714. C32#5683semidirect
802. C3#10594309semidirect
803. C3#10596154semidirect

Maximal subgroups

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

subgroupindex
#117239262
C3×#640912
C32×#8852
#117236432
#117236362
#117236342
#117235912
#117235412
#117235302
#117235282
#117234392
#117234362
#117234162
#117233922
#105961543
#105943093