Finite Group Databasebeta

← #13148682

Subgroups — #13148682

Order 1728.

1000 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊C4×#272C211yesmaximal, characteristic, complemented
2#64095⋊C3C211yesmaximal, characteristic, complemented
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721323C211yesmaximal, characteristic
5#11721314C211yesmaximal, characteristic, complemented
6C2×#88451C211yesmaximal, characteristic, complemented
7#11721296C211yesmaximal, characteristic, complemented
8#11721155C211yesmaximal, characteristic, complemented
9#11721130C211yesmaximal, characteristic, complemented
10#11721124C211yesmaximal, characteristic, complemented
11#11721104C211yesmaximal, characteristic, complemented
12#11721094C211yesmaximal, characteristic, complemented
13#11721089C211yesmaximal, characteristic, complemented
14#11721088C211yesmaximal, characteristic, complemented
15#11721088C211yesmaximal, characteristic, complemented
16#10594214—31nomaximal
17#10594211—31nomaximal
18C23×#272C2211yescharacteristic
19C2×C4×#272C2211yescharacteristic
20C2×C4×#272C2211yescharacteristic
21C2×#638⋊C3C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic, complemented
25C2×#6200C2211yescharacteristic
26C2×#6200C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#88552C2211yescharacteristic
30#88542C2211yescharacteristic
31#88542C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3752⋊C3C2211yescharacteristic, complemented
34#3752⋊C3C2211yescharacteristic, complemented
35C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88450C2211yescharacteristic, complemented
47#88448C2211yescharacteristic, complemented
48#88448C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88447C2211yescharacteristic, complemented
51#88447C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64095D311yescharacteristic, complemented
54#64087D311yescharacteristic, complemented
55C3×#886—31no—
56C3×D3×C22⋊C4—31no—
57C3×D3×C22⋊C4—31no—
58C3×D3×C22⋊C4—61no—
59C3×#878—31no—
60#63977—31no—
61#63976—31no—
62#67⋊Dic3—31no—
63C2×(C2×D3)⋊Dic3—31no—
64C2×(C2×D3)⋊Dic3—31no—
65#63957—31no—
66#63955—31no—
67#63952—31no—
68#63913—31no—
69#63907—31no—
70#63905—31no—
71#63904—31no—
72#63891—31no—
73#63879—31no—
74#63861—31no—
75#63861—31no—
76#63858—31no—
77#63858—31no—
78#63857—31no—
79#63856—31no—
80#63854—31no—
81#63850—31no—
82#63841—31no—
83#63841—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272—22no—
86C22×#272—22no—
87C22×#272—41no—
88C22×#272C2311yescharacteristic
89C22×#272C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×#1084C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C4×#272—22no—
96C4×#272—41no—
97#638⋊C3—22no—
98C2×(C3⋊Dic3)⋊C3—22no—
99C2×(C3⋊Dic3)⋊C3—41no—
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107#634⋊C3—41no—
108#6200—22no—
109#6200—41no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5658—91no—
112#5637—91no—
113#5495—91no—
114C23×C3×D3—31no—
115C23×C3×D3—31no—
116C23×C3×D3—61no—
117C2×#638C2×D311yescharacteristic
118C22×C3⋊Dic3C2×D311yescharacteristic
119C22×C3⋊Dic3C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic, complemented
121C2×C3×#67—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C2×C3×C4×D3—31no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3—61no—
129C2×C3×C4×D3—61no—
130C2×C3×Dic6—31no—
131C2×#626—31no—
132C2×#626—31no—
133C2×#625—31no—
134C2×#625—31no—
135C2×#624—31no—
136C2×D3×Dic3—31no—
137C32×C22⋊C4—21no—
138C32×C22⋊C4C2×D311yescharacteristic
139C32×C22⋊C4C2×D311yescharacteristic
140#3757C2×D311yescharacteristic
141#3752C2×D311yescharacteristic, complemented
142#3752C2×D311yescharacteristic, complemented
143C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
144C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
145C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
146#3750C2×D311yescharacteristic, complemented
147#3750C2×D311yescharacteristic, complemented
148C3×#217—31no—
149C3×#217—31no—
150C3×#217—31no—
151C3×#217—61no—
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—31no—
158C3×(C2×D3)⋊C4—61no—
159C3×(C2×D3)⋊C4—61no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—31no—
162C3×C4⋊Dic3—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171#3722—31no—
172(C2×D3)⋊Dic3—31no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—31no—
178(C2×D3)⋊Dic3—31no—
179(C2×D3)⋊Dic3—31no—
180(C2×D3)⋊Dic3—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—31no—
184(C2×D3)⋊Dic3—31no—
185Dic32—31no—
186Dic32—31no—
187Dic32—31no—
188Dic32—31no—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)#4112yes—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×#272—21no—
196C2×#272—21no—
197C2×#272—21no—
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—44no—
201C2×#272#4112yes—
202C2×(C3⋊D3)⋊C3—21no—
203C2×(C3⋊D3)⋊C3—21no—
204C2×(C3⋊D3)⋊C3—21no—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209(C3⋊Dic3)⋊C3—21no—
210(C3⋊Dic3)⋊C3—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×#123—91no—
217C3×C22⋊Q8—91no—
218C2×C3×C22⋊C4—91no—
219#953—91no—
220C2×#217—91no—
221#947—91no—
222#946—91no—
223#937—91no—
224D4×Dic3—91no—
225#929—91no—
226C4×#67—91no—
227C4×#67—91no—
228C2×(C2×D3)⋊C4—91no—
229C2×(C2×D3)⋊C4—91no—
230#926—91no—
231#926—91no—
232#924—91no—
233#898—91no—
234#898—91no—
235#898—91no—
236#898—91no—
237#897—91no—
238#894—91no—
239#894—91no—
240#893—91no—
241#892—91no—
242#892—91no—
243#886—31no—
244#886—91no—
245#886—91no—
246#885—91no—
247#885—91no—
248#883—91no—
249#883—91no—
250#882—91no—
251#67⋊C4—91no—
252#67⋊C4—91no—
253D3×C22⋊C4—31no—
254D3×C22⋊C4—31no—
255D3×C22⋊C4—61no—
256#879—91no—
257#879—91no—
258#878—31no—
259#878—91no—
260#877—91no—
261#877—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3C22×D311yescharacteristic
266C22×C3×D3—31no—
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—61no—
272C22×C3×D3—61no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—64no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—122no—
279C22×C3×D3—121no—
280C22×C3×D3—121no—
281C22×C3×D3—122no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288#638—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—41no—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298#634—41no—
299C3×#67—62no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—121no—
315C3×C4×D3—62no—
316C3×C4×D3—62no—
317C3×C4×D3—122no—
318C3×C4×D3—121no—
319C3×C4×D3—121no—
320C3×C4×D3—122no—
321C3×Dic6—121no—
322#626—62no—
323#626—121no—
324#625—62no—
325#625—121no—
326#624—121no—
327D3×Dic3—121no—
328#551—271noSylow
329C2×H(3,𝔽3)—22no—
330C2×H(3,𝔽3)C2×#4111yescharacteristic
331C2×H(3,𝔽3)C2×#4111yescharacteristic
332C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
333#272—22no—
334#272—41no—
335(C3⋊D3)⋊C3—41no—
336C24×C3—91no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—61no—
340C2×C3×Q8—91no—
341C2×C3×D4—91no—
342C22×C3×C4—91no—
343C22×C3×C4—91no—
344C22×C3×C4—91no—
345C22×C3×C4—91no—
346C2×#67—31no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—91no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—91no—
355C22×Dic3—91no—
356C22×Dic3—91no—
357C2×D12—91no—
358C2×D12—91no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×Dic6—31no—
368C2×Dic6—91no—
369C3×C4⋊C4—91no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C22⋊C4—31no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C22⋊C4—91no—
383C3×C22⋊C4D3211yescharacteristic
384#217—31no—
385#217—31no—
386#217—31no—
387#217—61no—
388#217—91no—
389#217—91no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—31no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
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—
417(C2×D3)⋊C4—91no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—91no—
424C4⋊Dic3—91no—
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427C4⋊Dic3—91no—
428C4⋊Dic3—91no—
429Dic3⋊C4—31no—
430Dic3⋊C4—31no—
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—91no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—22no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32#23712yes—
457C22×C32#23912yes—
458C22×C32C23×D311yescharacteristic
459C22×C32C23×D311yescharacteristic
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3×D3—32no—
464C2×C3×D3—32no—
465C2×C3×D3—62no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—61no—
472C2×C3×D3—62no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—61no—
481C2×C3×D3—61no—
482C2×C3×D3—121no—
483C2×C3×D3—121no—
484C2×C3×D3—124no—
485C2×C3×D3—124no—
486C2×C3×D3—128no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4—21no—
491C32×C4—41no—
492C32×C4—41no—
493C3⋊Dic3—21no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3×Dic3—61no—
501C3×Dic3—61no—
502C3×Dic3—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—61no—
506C3×Dic3—61no—
507C3×Dic3—61no—
508C3×Dic3—61no—
509C3×Dic3—61no—
510C3×Dic3—61no—
511C3×Dic3—121no—
512C3×Dic3—121no—
513#126—271no—
514#126—271no—
515#124—271no—
516#123—91no—
517#123—271no—
518#123—271no—
519C22⋊Q8—91no—
520C22⋊Q8—271no—
521#120—271no—
522C4×D4—271no—
523C4×D4—271no—
524#117—271no—
525#117—271no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—271no—
528H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—61no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—91no—
535C23×C3—182no—
536C23×C3—182no—
537C23×C3—361no—
538C23×C3C2×D3211yescharacteristic
539C22×D3—31no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—64no—
551C22×D3—91no—
552C22×D3—122no—
553C22×D3—121no—
554C22×D3—121no—
555C22×D3—122no—
556C3×Q8—361no—
557C3×D4—182no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—182no—
574C2×C3×C4—182no—
575C2×C3×C4—361no—
576C2×C3×C4—361no—
577C2×C3×C4C2×D3211yescharacteristic
578C2×C3×C4C2×D3211yescharacteristic
579#67—62no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—361no—
584#67—361no—
585C2×Dic3—31no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—91no—
602C2×Dic3—91no—
603C2×Dic3—91no—
604C2×Dic3—91no—
605C2×Dic3—91no—
606C2×Dic3—121no—
607C2×Dic3—182no—
608C2×Dic3—361no—
609C2×Dic3—361no—
610D12—182no—
611D12—361no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—122no—
615C4×D3—121no—
616C4×D3—121no—
617C4×D3—122no—
618C4×D3—361no—
619C4×D3—361no—
620Dic6—121no—
621Dic6—361no—
622C2×C32—22no—
623C2×C32—22no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—42no—
628C2×C32C2×#23711yescharacteristic
629C2×C32#100411yescharacteristic
630C2×C32C2×#23911yescharacteristic
631C2×C32D3×#4111yescharacteristic
632C2×C32D3×#4111yescharacteristic
633C2×C32#100911yescharacteristic
634C3⋊D3—41no—
635C3×D3—64no—
636C3×D3—62no—
637C3×D3—62no—
638C3×D3—122no—
639C3×D3—121no—
640C3×D3—121no—
641C3×D3—121no—
642C24—91no—
643C2×Q8—91no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—271no—
652C4⋊C4—91no—
653C4⋊C4—91no—
654C4⋊C4—91no—
655C4⋊C4—91no—
656C4⋊C4—91no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C4⋊C4—271no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—91no—
664C22⋊C4—91no—
665C22⋊C4—91no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4—271no—
672C22⋊C4—271no—
673C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
674C42—271no—
675C42—271no—
676C42—271no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—31no—
680C22×C3—31no—
681C22×C3—32no—
682C22×C3—32no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—62no—
689C22×C3—92no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3—181no—
699C22×C3—181no—
700C22×C3—364no—
701C22×C3#379612yes—
702C22×C3C22×D3211yescharacteristic
703C2×D3—32no—
704C2×D3—32no—
705C2×D3—62no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—61no—
713C2×D3—61no—
714C2×D3—61no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—61no—
718C2×D3—62no—
719C2×D3—61no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—121no—
723C2×D3—121no—
724C2×D3—124no—
725C2×D3—124no—
726C2×D3—128no—
727C2×D3—181no—
728C2×D3—181no—
729C2×D3—181no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—61no—
733C3×C4—61no—
734C3×C4—61no—
735C3×C4—61no—
736C3×C4—121no—
737C3×C4—121no—
738C3×C4—181no—
739C3×C4—181no—
740C3×C4—181no—
741C3×C4—181no—
742C3×C4—181no—
743C3×C4—181no—
744C3×C4—181no—
745C3×C4—181no—
746C3×C4—181no—
747Dic3—61no—
748Dic3—61no—
749Dic3—61no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—121no—
759Dic3—121no—
760Dic3—181no—
761Dic3—181no—
762Dic3—181no—
763Dic3—181no—
764Dic3—181no—
765Dic3—181no—
766Dic3—181no—
767C32—21no—
768C32#563711yescharacteristic, complemented
769C32#565811yescharacteristic, complemented
770C23—91no—
771C23—91no—
772C23—91no—
773C23—182no—
774C23—182no—
775C23—361no—
776C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
777Q8—361no—
778D4—182no—
779D4—542no—
780D4—1081no—
781C2×C4—91no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4—361no—
793C2×C4—361no—
794C2×C4—1081no—
795C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
796C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
797C2×C3—22no—
798C2×C3—31no—
799C2×C3—31no—
800C2×C3—31no—
801C2×C3—31no—
802C2×C3—31no—
803C2×C3—31no—
804C2×C3—62no—
805C2×C3—62no—
806C2×C3—61no—
807C2×C3—61no—
808C2×C3—61no—
809C2×C3—122no—
810C2×C3—182no—
811C2×C3—361no—
812C2×C3—361no—
813C2×C3C2×#379611yescharacteristic
814C2×C3#6431211yescharacteristic
815C2×C3#6431411yescharacteristic
816D3—62no—
817D3—62no—
818D3—64no—
819D3—121no—
820D3—121no—
821D3—122no—
822D3—121no—
823D3—361no—
824C22—21no—
825C22—21no—
826C22—92no—
827C22—181no—
828C22—181no—
829C22—181no—
830C22—181no—
831C22—181no—
832C22—181no—
833C22—181no—
834C22—181no—
835C22—364no—
836C22#8864912yes—
837C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
838C4—21no—
839C4—21no—
840C4—181no—
841C4—181no—
842C4—181no—
843C4—181no—
844C4—181no—
845C4—181no—
846C4—181no—
847C4—181no—
848C4—181no—
849C3—31no—
850C3—31no—
851C3—61no—
852C3#1059416411yescharacteristic
853C2—22no—
854C2—182no—
855C2—361no—
856C2—361no—
857C2C2×#8864911yescharacteristic
858C2#1172250511yescharacteristic
859C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radical#11721323C2
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22⋊C4×#272C2semidirect
2. #64095⋊C3C2semidirect
3. #64087⋊C3C2semidirect
5. #11721314C2semidirect
6. C2×#88451C2semidirect
7. #11721296C2semidirect
8. #11721155C2semidirect
9. #11721130C2semidirect
10. #11721124C2semidirect
11. #11721104C2semidirect
12. #11721094C2semidirect
13. #11721089C2semidirect
14. #11721088C2semidirect
15. #11721088C2semidirect
24. C2×#634⋊C3C22semidirect
27. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
33. #3752⋊C3C22semidirect
34. #3752⋊C3C22semidirect
35. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
46. #88450C22semidirect
47. #88448C22semidirect
48. #88448C22semidirect
49. #88448C22semidirect
50. #88447C22semidirect
51. #88447C22semidirect
52. #88447C22semidirect
53. #64095D3semidirect
54. #64087D3semidirect
120. C2×#634C2×D3semidirect
141. #3752C2×D3semidirect
142. #3752C2×D3semidirect
143. C4⋊(C3⋊Dic3)C2×D3semidirect
144. C4⋊(C3⋊Dic3)C2×D3semidirect
145. C4⋊(C3⋊Dic3)C2×D3semidirect
146. #3750C2×D3semidirect
147. #3750C2×D3semidirect
528. H(3,𝔽3)#551semidirect
768. C32#5637semidirect
769. C32#5658semidirect

Maximal subgroups

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

subgroupindex
C22⋊C4×#2722
#64095⋊C32
#64087⋊C32
#117213232
#117213142
C2×#884512
#117212962
#117211552
#117211302
#117211242
#117211042
#117210942
#117210892
#117210882
#105942143
#105942113