Finite Group Databasebeta

← #13147918

Subgroups — #13147918

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721718C211yesmaximal, characteristic, complemented
2#64084⋊C3C211yesmaximal, characteristic, complemented
3#64081⋊C3C211yesmaximal, characteristic, complemented
4#11721162C211yesmaximal, characteristic
5#11721161C211yesmaximal, characteristic, complemented
6#11721160C211yesmaximal, characteristic, complemented
7#11721148C211yesmaximal, characteristic, complemented
8#11721139C211yesmaximal, characteristic, complemented
9#11721138C211yesmaximal, characteristic, complemented
10#11721128C211yesmaximal, characteristic, complemented
11#11721125C211yesmaximal, characteristic, complemented
12#11721123C211yesmaximal, characteristic, complemented
13#11721112C211yesmaximal, characteristic, complemented
14#11721109C211yesmaximal, characteristic, complemented
15#11721104C211yesmaximal, characteristic, complemented
16#10594016—31nomaximal
17#10594014—31nomaximal
18C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×#634⋊C3C2211yescharacteristic, complemented
23C2×#6200C2211yescharacteristic
24C2×#6199C2211yescharacteristic
25C2×#6198C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
28C42×H(3,𝔽3)C2211yescharacteristic, complemented
29#88542C2211yescharacteristic
30#88542C2211yescharacteristic
31#88540C2211yescharacteristic, complemented
32#88540C2211yescharacteristic, complemented
33C4×#1084C2211yescharacteristic, complemented
34#3752⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38#3752⋊C3C2211yescharacteristic, complemented
39#3752⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41#3750⋊C3C2211yescharacteristic, complemented
42C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
43#88451C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic, complemented
49#88449C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#64084D311yescharacteristic, complemented
54#64081D311yescharacteristic, complemented
55C3×#875—31no—
56C3×#872—31no—
57C3×#872—31no—
58C3×#872—31no—
59C3×#872—61no—
60#63923—31no—
61#63922—31no—
62#63921—31no—
63D3×(C2×D3)⋊C4—31no—
64D3×(C2×D3)⋊C4—31no—
65D3×(C2×D3)⋊C4—31no—
66#63905—31no—
67#63902—31no—
68#63897—31no—
69#63896—31no—
70#63896—31no—
71#63888—31no—
72#63887—31no—
73#63884—31no—
74#63880—31no—
75#63880—31no—
76#63880—31no—
77#63868—31no—
78#63868—31no—
79#63862—31no—
80#63859—31no—
81#63853—31no—
82#63850—31no—
83#63850—31no—
84C22×#272C2311yescharacteristic
85C22×(C3⋊D3)⋊C3C2311yescharacteristic
86C22×(C3⋊D3)⋊C3C2311yescharacteristic
87C22×(C3⋊D3)⋊C3C2311yescharacteristic
88C2×((C3⋊D3)⋊C3)⋊C2—22no—
89C2×((C3⋊D3)⋊C3)⋊C2—22no—
90C2×((C3⋊D3)⋊C3)⋊C2—41no—
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C4×#272—22no—
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C4⋊((C3⋊D3)⋊C3)—41no—
104C4×(C3⋊D3)⋊C3—22no—
105#634⋊C3—41no—
106#6200—22no—
107#6199—41no—
108#6198—22no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5679—91no—
112#5527—91no—
113#5527—91no—
114C22×D32—31no—
115C22×D32—31no—
116C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
117C2×C4×C3⋊D3C2×D311yescharacteristic
118C2×#634C2×D311yescharacteristic, complemented
119C2×C3×D12—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×C4×D3—61no—
124C2×C3×Dic6—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C2×#624—31no—
130C2×#624—31no—
131C2×D3×Dic3—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C32×C42—21no—
136C32×C42C2×D311yescharacteristic, complemented
137C32×C42C2×D311yescharacteristic, complemented
138#3752C2×D311yescharacteristic
139#3752C2×D311yescharacteristic
140#3752C2×D311yescharacteristic
141#3752C2×D311yescharacteristic
142#3752C2×D311yescharacteristic, complemented
143#3752C2×D311yescharacteristic, complemented
144#3750C2×D311yescharacteristic, complemented
145#3750C2×D311yescharacteristic, complemented
146C4×C3⋊Dic3C2×D311yescharacteristic, complemented
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4—31no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—61no—
158C3×(C2×D3)⋊C4—61no—
159C3×Dic3⋊C4—31no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—61no—
166C3×Dic3⋊C4—61no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—61no—
171#3724—31no—
172#3724—31no—
173#3724—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179#3722—31no—
180#3722—31no—
181#3722—31no—
182#3722—31no—
183#3722—31no—
184(C2×D3)⋊Dic3—31no—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191C22×H(3,𝔽3)C2411yescharacteristic
192C2×#272—21no—
193C2×#272—21no—
194C2×#272#4112yes—
195C2×(C3⋊D3)⋊C3—21no—
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—21no—
201C2×(C3⋊D3)⋊C3—21no—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3#4112yes—
204((C3⋊D3)⋊C3)⋊C2—44no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207C4×H(3,𝔽3)—21no—
208#1084—21no—
209#1084—21no—
210#1084—21no—
211(C3⋊Dic3)⋊C3—21no—
212(C3⋊Dic3)⋊C3—21no—
213(C3⋊Dic3)⋊C3—21no—
214(C3⋊Dic3)⋊C3—21no—
215(C3⋊Dic3)⋊C3—21no—
216C3×#124—91no—
217C3×#117—91no—
218C3×#117—91no—
219#946—91no—
220#946—91no—
221#937—91no—
222#935—91no—
223#929—91no—
224#929—91no—
225C2×(C2×D3)⋊C4—91no—
226C2×(C2×D3)⋊C4—91no—
227#898—91no—
228#898—91no—
229#896—91no—
230#896—91no—
231#894—91no—
232#894—91no—
233#894—91no—
234#894—91no—
235#883—91no—
236#883—91no—
237#882—91no—
238#882—91no—
239#67⋊C4—91no—
240#67⋊C4—91no—
241#67⋊C4—91no—
242#67⋊C4—91no—
243D3×C22⋊C4—91no—
244D3×C22⋊C4—91no—
245D3×C22⋊C4—91no—
246D3×C22⋊C4—91no—
247#879—91no—
248#879—91no—
249#878—91no—
250#878—91no—
251#876—91no—
252#876—91no—
253#875—31no—
254#875—91no—
255C4×D12—91no—
256C4×D12—91no—
257#872—31no—
258#872—31no—
259#872—31no—
260#872—61no—
261#872—91no—
262C22×C3⋊D3C22×D311yescharacteristic
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—61no—
271C2×D32—62no—
272C2×D32—62no—
273C2×D32—62no—
274C2×D32—62no—
275C2×D32—121no—
276C2×D32—121no—
277C2×C32×C4—21no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C2×C3⋊Dic3C22×D311yescharacteristic
291C4⋊(C3⋊D3)—41no—
292C4×C3⋊D3—22no—
293#634—41no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C3×D12—121no—
309C3×C4×D3—62no—
310C3×C4×D3—62no—
311C3×C4×D3—62no—
312C3×C4×D3—64no—
313C3×Dic6—121no—
314#626—62no—
315#626—62no—
316#626—62no—
317#625—62no—
318#624—121no—
319#624—121no—
320D3×Dic3—121no—
321D3×Dic3—121no—
322D3×Dic3—121no—
323D3×Dic3—121no—
324#551—271noSylow
325C2×H(3,𝔽3)C2×#4111yescharacteristic
326C2×H(3,𝔽3)C2×#4111yescharacteristic
327C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
328#272—22no—
329(C3⋊D3)⋊C3—22no—
330(C3⋊D3)⋊C3—41no—
331(C3⋊D3)⋊C3—41no—
332C23×D3—91no—
333C23×D3—91no—
334C23×D3—91no—
335C2×C3×Q8—91no—
336C2×C3×D4—91no—
337C22×C3×C4—91no—
338C22×C3×C4—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C22×Dic3—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C2×D12—31no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×C4×D3—31no—
351C2×C4×D3—31no—
352C2×C4×D3—31no—
353C2×C4×D3—61no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×Dic6—31no—
362C2×Dic6—91no—
363C3×C4⋊C4—91no—
364C3×C4⋊C4—91no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370C3×C22⋊C4—91no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C42—31no—
376C3×C42—31no—
377C3×C42—61no—
378C3×C42—91no—
379C3×C42—91no—
380C3×C42D3211yescharacteristic
381#217—91no—
382#217—91no—
383#217—91no—
384#217—91no—
385#217—91no—
386#217—91no—
387(C2×D3)⋊C4—31no—
388(C2×D3)⋊C4—31no—
389(C2×D3)⋊C4—31no—
390(C2×D3)⋊C4—31no—
391(C2×D3)⋊C4—31no—
392(C2×D3)⋊C4—31no—
393(C2×D3)⋊C4—31no—
394(C2×D3)⋊C4—31no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
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—91no—
416(C2×D3)⋊C4—91no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421Dic3⋊C4—31no—
422Dic3⋊C4—31no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—31no—
426Dic3⋊C4—31no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439C4×Dic3—31no—
440C4×Dic3—31no—
441C4×Dic3—31no—
442C4×Dic3—61no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32C23×D311yescharacteristic
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—21no—
451C2×C3⋊D3—21no—
452C2×C3⋊D3—21no—
453C2×C3⋊D3—21no—
454C2×C3⋊D3—21no—
455C2×C3⋊D3#23512yes—
456C2×C3×D3—32no—
457C2×C3×D3—32no—
458C2×C3×D3—32no—
459C2×C3×D3—62no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—121no—
473C2×C3×D3—121no—
474D32—124no—
475D32—124no—
476C32×C4—22no—
477C32×C4—21no—
478C32×C4—21no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—41no—
484C32×C4—41no—
485C3⋊Dic3—21no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—62no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—61no—
499C3×Dic3—61no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—121no—
503C3×Dic3—121no—
504#126—271no—
505#126—271no—
506#124—91no—
507#123—271no—
508#123—271no—
509#123—271no—
510C22⋊Q8—271no—
511C22⋊Q8—271no—
512#120—271no—
513C4×D4—271no—
514C4×D4—271no—
515#117—91no—
516#117—91no—
517C2×C22⋊C4—271no—
518C2×C22⋊C4—271no—
519H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
520C23×C3—91no—
521C23×C3—91no—
522C23×C3—91no—
523C23×C3—91no—
524C22×D3—31no—
525C22×D3—31no—
526C22×D3—31no—
527C22×D3—31no—
528C22×D3—31no—
529C22×D3—61no—
530C22×D3—91no—
531C22×D3—91no—
532C22×D3—91no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3—182no—
537C22×D3—182no—
538C22×D3—182no—
539C22×D3—361no—
540C22×D3—361no—
541C22×D3—361no—
542C3×Q8—361no—
543C3×D4—361no—
544C2×C3×C4—31no—
545C2×C3×C4—31no—
546C2×C3×C4—31no—
547C2×C3×C4—31no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—91no—
554C2×C3×C4—91no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—91no—
559C2×C3×C4—91no—
560C2×C3×C4—91no—
561C2×C3×C4—182no—
562C2×C3×C4—182no—
563C2×C3×C4C2×D3211yescharacteristic
564C2×C3×C4C2×D3211yescharacteristic
565C2×C3×C4C2×D3211yescharacteristic
566#67—182no—
567#67—182no—
568#67—182no—
569#67—182no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—91no—
585C2×Dic3—91no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—361no—
590C2×Dic3—361no—
591C2×Dic3—361no—
592D12—121no—
593D12—182no—
594D12—182no—
595D12—361no—
596C4×D3—62no—
597C4×D3—62no—
598C4×D3—62no—
599C4×D3—64no—
600C4×D3—182no—
601C4×D3—361no—
602C4×D3—361no—
603C4×D3—361no—
604C4×D3—361no—
605C4×D3—361no—
606C4×D3—361no—
607Dic6—121no—
608Dic6—361no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32C2×#23511yescharacteristic
613C2×C32#100411yescharacteristic
614C2×C32D3×#4111yescharacteristic
615C2×C32D3×#4111yescharacteristic
616C2×C32D3×#4111yescharacteristic
617C2×C32#100911yescharacteristic
618C3⋊D3—22no—
619C3⋊D3—41no—
620C3⋊D3—41no—
621C3×D3—62no—
622C3×D3—62no—
623C3×D3—62no—
624C3×D3—122no—
625C3×D3—121no—
626C3×D3—121no—
627C24—271no—
628C2×Q8—91no—
629C2×D4—91no—
630C2×D4—271no—
631C2×D4—271no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—271no—
635C22×C4—271no—
636C22×C4—271no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—271no—
642C4⋊C4—271no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C42—91no—
660C42—91no—
661C42((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
662C22×C3—31no—
663C22×C3—31no—
664C22×C3—61no—
665C22×C3—92no—
666C22×C3—92no—
667C22×C3—181no—
668C22×C3—181no—
669C22×C3—181no—
670C22×C3—181no—
671C22×C3—181no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3—181no—
675C22×C3—181no—
676C22×C3—181no—
677C22×C3C22×D3211yescharacteristic
678C2×D3—32no—
679C2×D3—32no—
680C2×D3—32no—
681C2×D3—62no—
682C2×D3—61no—
683C2×D3—61no—
684C2×D3—61no—
685C2×D3—61no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—61no—
694C2×D3—92no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—181no—
700C2×D3—181no—
701C2×D3—181no—
702C2×D3—181no—
703C2×D3—181no—
704C2×D3—181no—
705C2×D3—364no—
706C2×D3—364no—
707C2×D3—364no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—62no—
718C3×C4—121no—
719C3×C4—121no—
720C3×C4—181no—
721C3×C4—181no—
722C3×C4—181no—
723C3×C4—181no—
724C3×C4—181no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—62no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—61no—
740Dic3—121no—
741Dic3—121no—
742Dic3—181no—
743Dic3—181no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747C32—21no—
748C32#552711yescharacteristic, complemented
749C32#567911yescharacteristic, complemented
750C23—91no—
751C23—91no—
752C23—91no—
753C23—91no—
754C23—542no—
755C23—542no—
756C23—1081no—
757Q8—361no—
758D4—361no—
759D4—542no—
760D4—542no—
761C2×C4—91no—
762C2×C4—91no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—182no—
770C2×C4—182no—
771C2×C4—1081no—
772C2×C4—1081no—
773C2×C4—1081no—
774C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
775C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
776C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
777C2×C3—31no—
778C2×C3—31no—
779C2×C3—31no—
780C2×C3—31no—
781C2×C3—31no—
782C2×C3—31no—
783C2×C3—61no—
784C2×C3—61no—
785C2×C3—61no—
786C2×C3—182no—
787C2×C3—182no—
788C2×C3—361no—
789C2×C3—361no—
790C2×C3D3×#23511yescharacteristic
791C2×C3#6430611yescharacteristic
792C2×C3#6430711yescharacteristic
793D3—62no—
794D3—62no—
795D3—62no—
796D3—122no—
797D3—121no—
798D3—121no—
799D3—182no—
800D3—361no—
801D3—361no—
802C22—92no—
803C22—92no—
804C22—181no—
805C22—181no—
806C22—181no—
807C22—181no—
808C22—181no—
809C22—181no—
810C22—181no—
811C22—181no—
812C22—181no—
813C22—181no—
814C22—1084no—
815C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
816C4—21no—
817C4—21no—
818C4—21no—
819C4—181no—
820C4—181no—
821C4—181no—
822C4—181no—
823C4—181no—
824C4—181no—
825C4—181no—
826C4—181no—
827C3—31no—
828C3—31no—
829C3—61no—
830C3#1059401611yescharacteristic
831C2—182no—
832C2—182no—
833C2—361no—
834C2—361no—
835C2#1172249011yescharacteristic
836C2#1172249111yescharacteristic
837C2#1172249211yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC42×H(3,𝔽3)C22
prime radical#11721162C2
hypercenterC42((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11721718C2semidirect
2. #64084⋊C3C2semidirect
3. #64081⋊C3C2semidirect
5. #11721161C2semidirect
6. #11721160C2semidirect
7. #11721148C2semidirect
8. #11721139C2semidirect
9. #11721138C2semidirect
10. #11721128C2semidirect
11. #11721125C2semidirect
12. #11721123C2semidirect
13. #11721112C2semidirect
14. #11721109C2semidirect
15. #11721104C2semidirect
22. C2×#634⋊C3C22semidirect
27. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
28. C42×H(3,𝔽3)C22semidirect
31. #88540C22semidirect
32. #88540C22semidirect
33. C4×#1084C22semidirect
38. #3752⋊C3C22semidirect
39. #3752⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. #3750⋊C3C22semidirect
42. C4×(C3⋊Dic3)⋊C3C22semidirect
48. #88450C22semidirect
49. #88449C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88448C22semidirect
53. #64084D3semidirect
54. #64081D3semidirect
118. C2×#634C2×D3semidirect
136. C32×C42C2×D3semidirect
137. C32×C42C2×D3semidirect
142. #3752C2×D3semidirect
143. #3752C2×D3semidirect
144. #3750C2×D3semidirect
145. #3750C2×D3semidirect
146. C4×C3⋊Dic3C2×D3semidirect
519. H(3,𝔽3)#551semidirect
661. C42((C3⋊D3)⋊C3)⋊C2semidirect
748. C32#5527semidirect
749. C32#5679semidirect

Maximal subgroups

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

subgroupindex
#117217182
#64084⋊C32
#64081⋊C32
#117211622
#117211612
#117211602
#117211482
#117211392
#117211382
#117211282
#117211252
#117211232
#117211122
#117211092
#117211042
#105940163
#105940143