Finite Group Databasebeta

← #13151450

Subgroups — #13151450

Order 1728.

998 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721847C211yesmaximal, characteristic
2#64144⋊C3C211yesmaximal, characteristic, complemented
3D4×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
4#11721320C211yesmaximal, characteristic, complemented
5#11721319C211yesmaximal, characteristic, complemented
6C2×#88451C211yesmaximal, characteristic, complemented
7#11721301C211yesmaximal, characteristic, complemented
8#11721299C211yesmaximal, characteristic, complemented
9#11721296C211yesmaximal, characteristic, complemented
10#11721294C211yesmaximal, characteristic, complemented
11#11721293C211yesmaximal, characteristic, complemented
12#11721150C211yesmaximal, characteristic, complemented
13#11721092C211yesmaximal, characteristic, complemented
14#11721088C211yesmaximal, characteristic, complemented
15#11721076C211yesmaximal, characteristic, complemented
16#10595177—31nomaximal
17#10595175—31nomaximal
18C23×#272C2211yescharacteristic
19C2×D4×H(3,𝔽3)C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C2×#6235C2211yescharacteristic
22C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
23C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×#6199C2211yescharacteristic
26C2×#6199C2211yescharacteristic
27C2×#6196C2211yescharacteristic, complemented
28#88552C2211yescharacteristic
29#88542C2211yescharacteristic
30#88542C2211yescharacteristic
31#3757⋊C3C2211yescharacteristic
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic, complemented
34#3757⋊C3C2211yescharacteristic, complemented
35#3757⋊C3C2211yescharacteristic, complemented
36C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
37#3750⋊C3C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
40#88451C2211yescharacteristic
41#88451C2211yescharacteristic
42#88451C2211yescharacteristic
43#88451C2211yescharacteristic
44#88451C2211yescharacteristic
45#88451C2211yescharacteristic
46#88449C2211yescharacteristic, complemented
47#88448C2211yescharacteristic, complemented
48#88448C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88447C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#64144D311yescharacteristic, complemented
54D4×C3⋊Dic3D311yescharacteristic, complemented
55C3×#937—31no—
56C3×#937—31no—
57C3×#937—61no—
58C3×#935—31no—
59C3×D4×Dic3—31no—
60#63982—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63#63969—31no—
64#63969—31no—
65D3×#217—31no—
66D3×#217—31no—
67#63964—31no—
68#63962—31no—
69#63961—31no—
70C2×(C2×D3)⋊Dic3—31no—
71C2×(C2×D3)⋊Dic3—31no—
72#63959—31no—
73#63959—31no—
74#63957—31no—
75#63955—31no—
76#63899—31no—
77#63893—31no—
78#63878—31no—
79#63877—31no—
80#63862—31no—
81#63861—31no—
82#63859—31no—
83#63858—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×#272—22no—
87C22×#272—22no—
88C22×#272—41no—
89C22×#272C2311yescharacteristic
90C22×#272C2311yescharacteristic
91D4×H(3,𝔽3)—22no—
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93#6235—22no—
94#6235—41no—
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3—22no—
98C2×(C3⋊Dic3)⋊C3—41no—
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
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108#6199—22no—
109#6199—41no—
110#6196—41no—
111#5658—91no—
112#5587—91no—
113#5556—91no—
114C23×C3×D3—31no—
115C23×C3×D3—31no—
116C23×C3×D3—61no—
117C2×C32×D4—21no—
118C2×C32×D4C2×D311yescharacteristic
119C2×C32×D4C2×D311yescharacteristic
120C22×C3⋊Dic3C2×D311yescharacteristic
121C22×C3⋊Dic3C2×D311yescharacteristic
122C22×C3⋊Dic3C2×D311yescharacteristic, complemented
123C2×C3×#67—31no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—61no—
128C2×C3×#67—61no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C22×C3×Dic3—31no—
132C2×#627—31no—
133C2×#627—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138#3757C2×D311yescharacteristic
139#3757C2×D311yescharacteristic
140#3757C2×D311yescharacteristic, complemented
141#3757C2×D311yescharacteristic, complemented
142#3757C2×D311yescharacteristic, complemented
143C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
144#3750C2×D311yescharacteristic, complemented
145#3750C2×D311yescharacteristic, complemented
146C4×C3⋊Dic3C2×D311yescharacteristic, complemented
147C3×#217—31no—
148C3×#217—31no—
149C3×#217—31no—
150C3×#217—31no—
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—31no—
154C3×#217—61no—
155C3×(C2×D3)⋊C4—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—61no—
160C3×(C2×D3)⋊C4—61no—
161C3×C4⋊Dic3—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×C4×Dic3—31no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168#3724—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊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—
185(C2×D3)⋊Dic3—31no—
186(C2×D3)⋊Dic3—31no—
187Dic32—31no—
188Dic32—31no—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)—21no—
195C22×H(3,𝔽3)—21no—
196C22×H(3,𝔽3)#4112yes—
197C22×H(3,𝔽3)C2411yescharacteristic
198C2×#272—21no—
199C2×#272—21no—
200C2×#272—21no—
201C2×#272—21no—
202C2×#272—21no—
203C2×#272—44no—
204C2×#272#4112yes—
205C4×H(3,𝔽3)—21no—
206#1084—21no—
207#1084—21no—
208(C3⋊Dic3)⋊C3—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×#120—91no—
218C3×C4×D4—91no—
219C2×#217—91no—
220C2×#217—91no—
221#937—31no—
222#937—31no—
223#937—61no—
224#936—91no—
225#935—31no—
226#935—91no—
227#935—91no—
228#935—91no—
229D4×Dic3—31no—
230D4×Dic3—91no—
231D4×Dic3—91no—
232#929—91no—
233C4×#67—91no—
234C2×(C2×D3)⋊C4—91no—
235C2×(C2×D3)⋊C4—91no—
236#926—91no—
237#924—91no—
238#898—91no—
239#898—91no—
240#898—91no—
241#897—91no—
242#896—91no—
243#892—91no—
244#886—91no—
245#885—91no—
246#885—91no—
247#883—91no—
248#883—91no—
249#67⋊C4—91no—
250D3×C22⋊C4—91no—
251D3×C22⋊C4—91no—
252#879—91no—
253#879—91no—
254#878—91no—
255#878—91no—
256#878—91no—
257#877—91no—
258#877—91no—
259#877—91no—
260#876—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32C22×D311yescharacteristic
265C23×C32C22×D311yescharacteristic
266C23×C32C22×D311yescharacteristic
267C23×C32C22×D311yescharacteristic
268C22×C3×D3—31no—
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—61no—
273C22×C3×D3—61no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—122no—
279C22×C3×D3—122no—
280C22×C3×D3—121no—
281C22×C3×D3—121no—
282C22×C3×D3—122no—
283C32×D4—22no—
284C32×D4—22no—
285C32×D4—42no—
286C2×C32×C4—21no—
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—41no—
291C2×C3⋊Dic3—41no—
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C2×C3⋊Dic3C22×D311yescharacteristic
298C2×C3⋊Dic3C22×D311yescharacteristic
299C2×C3⋊Dic3C22×D311yescharacteristic
300C3×#67—62no—
301C3×#67—62no—
302C3×#67—122no—
303C3×#67—121no—
304C3×#67—121no—
305C3×#67—122no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—31no—
310C2×C3×Dic3—31no—
311C2×C3×Dic3—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—31no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—121no—
322C2×C3×Dic3—121no—
323#627—121no—
324#627—121no—
325D3×Dic3—62no—
326D3×Dic3—62no—
327D3×Dic3—121no—
328D3×Dic3—121no—
329#551—271noSylow
330C2×H(3,𝔽3)—22no—
331C2×H(3,𝔽3)—41no—
332C2×H(3,𝔽3)C2×#4111yescharacteristic
333C2×H(3,𝔽3)C2×#4111yescharacteristic
334C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
335#272—22no—
336#272—41no—
337C24×C3—91no—
338C23×D3—31no—
339C23×D3—31no—
340C23×D3—61no—
341C2×C3×D4—31no—
342C2×C3×D4—31no—
343C2×C3×D4—61no—
344C2×C3×D4—91no—
345C2×C3×D4—91no—
346C2×C3×D4D3211yescharacteristic
347C22×C3×C4—91no—
348C22×C3×C4—91no—
349C22×C3×C4—91no—
350C2×#67—31no—
351C2×#67—31no—
352C2×#67—31no—
353C2×#67—31no—
354C2×#67—61no—
355C2×#67—61no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361C22×Dic3—91no—
362C22×Dic3—91no—
363C22×Dic3—91no—
364C2×C4×D3—91no—
365C2×C4×D3—91no—
366C2×C4×D3—91no—
367C2×C4×D3—91no—
368C2×Dic6—91no—
369C2×Dic6—91no—
370C2×Dic6—91no—
371C3×C4⋊C4—91no—
372C3×C4⋊C4—91no—
373C3×C4⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380C3×C22⋊C4—91no—
381C3×C22⋊C4—91no—
382C3×C42—91no—
383#217—31no—
384#217—31no—
385#217—31no—
386#217—31no—
387#217—31no—
388#217—31no—
389#217—31no—
390#217—61no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217—91no—
396#217—91no—
397#217—91no—
398#217—91no—
399#217—91no—
400#217—91no—
401#217—91no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—31no—
404(C2×D3)⋊C4—31no—
405(C2×D3)⋊C4—31no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
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—91no—
422C4⋊Dic3—91no—
423C4⋊Dic3—91no—
424C4⋊Dic3—91no—
425C4⋊Dic3—91no—
426C4⋊Dic3—91no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
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—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441C4×Dic3—31no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C4×Dic3—91no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—22no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32#23512yes—
467C22×C32#23712yes—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C2×C3×D3—32no—
471C2×C3×D3—32no—
472C2×C3×D3—62no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—62no—
478C2×C3×D3—61no—
479C2×C3×D3—61no—
480C2×C3×D3—61no—
481C2×C3×D3—61no—
482C2×C3×D3—61no—
483C2×C3×D3—61no—
484C2×C3×D3—121no—
485C2×C3×D3—121no—
486C2×C3×D3—121no—
487C2×C3×D3—121no—
488C2×C3×D3—124no—
489C2×C3×D3—124no—
490C2×C3×D3—128no—
491C32×C4—21no—
492C32×C4—21no—
493C32×C4—41no—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3—21no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—21no—
501C3⋊Dic3—21no—
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—61no—
512C3×Dic3—61no—
513C3×Dic3—61no—
514C3×Dic3—121no—
515C3×Dic3—121no—
516#126—271no—
517#126—271no—
518#124—271no—
519#123—91no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523C22⋊Q8—271no—
524#120—91no—
525C4×D4—91no—
526C4×D4—271no—
527#117—271no—
528#117—271no—
529C2×C22⋊C4—271no—
530C2×C22⋊C4—271no—
531H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—91no—
539C23×C3—91no—
540C23×C3—182no—
541C23×C3—182no—
542C23×C3—361no—
543C23×C3C2×D3211yescharacteristic
544C23×C3C2×D3211yescharacteristic
545C22×D3—31no—
546C22×D3—31no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—121no—
558C22×D3—121no—
559C22×D3—122no—
560C3×D4—22no—
561C3×D4—62no—
562C3×D4—62no—
563C3×D4—122no—
564C3×D4—182no—
565C3×D4—361no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—61no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—182no—
580C2×C3×C4—361no—
581C2×C3×C4—361no—
582C2×C3×C4C2×D3211yescharacteristic
583#67—62no—
584#67—62no—
585#67—122no—
586#67—121no—
587#67—121no—
588#67—122no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—62no—
604C2×Dic3—91no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—91no—
608C2×Dic3—91no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—91no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—182no—
615C2×Dic3—182no—
616C2×Dic3—361no—
617C2×Dic3—361no—
618C2×Dic3—361no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—361no—
622C4×D3—361no—
623Dic6—361no—
624Dic6—361no—
625Dic6—361no—
626C2×C32—22no—
627C2×C32—22no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—42no—
632C2×C32—41no—
633C2×C32—41no—
634C2×C32—81no—
635C2×C32C2×#23511yescharacteristic
636C2×C32C2×#23711yescharacteristic
637C2×C32#100411yescharacteristic
638C2×C32D3×#4111yescharacteristic
639C2×C32D3×#4111yescharacteristic
640C2×C32#100911yescharacteristic
641C3×D3—62no—
642C3×D3—62no—
643C3×D3—122no—
644C3×D3—122no—
645C3×D3—121no—
646C3×D3—121no—
647C24—91no—
648C2×Q8—271no—
649C2×D4—91no—
650C2×D4—91no—
651C2×D4((C3⋊D3)⋊C3)⋊C211yescharacteristic
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—271no—
656C22×C4—271no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—91no—
660C4⋊C4—271no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—91no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—91no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C42—91no—
680C42—271no—
681C42—271no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—31no—
688C22×C3—31no—
689C22×C3—32no—
690C22×C3—32no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—62no—
703C22×C3—92no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—181no—
710C22×C3—181no—
711C22×C3—181no—
712C22×C3—181no—
713C22×C3—181no—
714C22×C3—364no—
715C22×C3#380412yes—
716C22×C3C22×D3211yescharacteristic
717C2×D3—32no—
718C2×D3—32no—
719C2×D3—62no—
720C2×D3—61no—
721C2×D3—61no—
722C2×D3—61no—
723C2×D3—61no—
724C2×D3—61no—
725C2×D3—61no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—62no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—124no—
736C2×D3—124no—
737C2×D3—128no—
738C3×C4—21no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4—121no—
742C3×C4—181no—
743C3×C4—181no—
744C3×C4—181no—
745C3×C4—181no—
746C3×C4—181no—
747C3×C4—181no—
748C3×C4—181no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4—181no—
752Dic3—61no—
753Dic3—61no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—61no—
759Dic3—61no—
760Dic3—61no—
761Dic3—61no—
762Dic3—61no—
763Dic3—61no—
764Dic3—121no—
765Dic3—121no—
766Dic3—181no—
767Dic3—181no—
768Dic3—181no—
769Dic3—181no—
770Dic3—181no—
771Dic3—181no—
772Dic3—181no—
773Dic3—181no—
774C32—21no—
775C32#555611yescharacteristic, complemented
776C32#565811yescharacteristic, complemented
777C23—91no—
778C23—91no—
779C23—182no—
780C23—182no—
781C23—361no—
782C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
783C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
784Q8—1081no—
785D4—22no—
786D4—182no—
787D4—361no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—182no—
799C2×C4—361no—
800C2×C4—361no—
801C2×C4—542no—
802C2×C4—1081no—
803C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
804C2×C3—22no—
805C2×C3—31no—
806C2×C3—31no—
807C2×C3—31no—
808C2×C3—31no—
809C2×C3—31no—
810C2×C3—31no—
811C2×C3—41no—
812C2×C3—62no—
813C2×C3—62no—
814C2×C3—61no—
815C2×C3—61no—
816C2×C3—61no—
817C2×C3—122no—
818C2×C3—121no—
819C2×C3—121no—
820C2×C3—182no—
821C2×C3—241no—
822C2×C3—361no—
823C2×C3#6431211yescharacteristic
824C2×C3#6431411yescharacteristic
825C2×C3C2×#380411yescharacteristic
826D3—62no—
827D3—62no—
828D3—122no—
829D3—121no—
830D3—121no—
831D3—122no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—92no—
838C22—181no—
839C22—181no—
840C22—181no—
841C22—181no—
842C22—181no—
843C22—364no—
844C22#8867112yes—
845C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
846C4—21no—
847C4—181no—
848C4—181no—
849C4—181no—
850C4—181no—
851C4—181no—
852C4—181no—
853C4—181no—
854C4—181no—
855C4—181no—
856C4—181no—
857C3—31no—
858C3—31no—
859C3—61no—
860C3#1059511811yescharacteristic
861C2—22no—
862C2—41no—
863C2—182no—
864C2—361no—
865C2#1172250511yescharacteristic
866C2#1172250711yescharacteristic
867C2C2×#8867111yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
prime radical#11721847C2
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#551
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #64144⋊C3C2semidirect
3. D4×(C3⋊Dic3)⋊C3C2semidirect
4. #11721320C2semidirect
5. #11721319C2semidirect
6. C2×#88451C2semidirect
7. #11721301C2semidirect
8. #11721299C2semidirect
9. #11721296C2semidirect
10. #11721294C2semidirect
11. #11721293C2semidirect
12. #11721150C2semidirect
13. #11721092C2semidirect
14. #11721088C2semidirect
15. #11721076C2semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×#6196C22semidirect
33. #3757⋊C3C22semidirect
34. #3757⋊C3C22semidirect
35. #3757⋊C3C22semidirect
36. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
37. #3750⋊C3C22semidirect
38. #3750⋊C3C22semidirect
39. C4×(C3⋊Dic3)⋊C3C22semidirect
46. #88449C22semidirect
47. #88448C22semidirect
48. #88448C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88447C22semidirect
52. #88447C22semidirect
53. #64144D3semidirect
54. D4×C3⋊Dic3D3semidirect
122. C22×C3⋊Dic3C2×D3semidirect
140. #3757C2×D3semidirect
141. #3757C2×D3semidirect
142. #3757C2×D3semidirect
143. C4⋊(C3⋊Dic3)C2×D3semidirect
144. #3750C2×D3semidirect
145. #3750C2×D3semidirect
146. C4×C3⋊Dic3C2×D3semidirect
531. H(3,𝔽3)#551semidirect
775. C32#5556semidirect
776. C32#5658semidirect

Maximal subgroups

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

subgroupindex
#117218472
#64144⋊C32
D4×(C3⋊Dic3)⋊C32
#117213202
#117213192
C2×#884512
#117213012
#117212992
#117212962
#117212942
#117212932
#117211502
#117210922
#117210882
#117210762
#105951773
#105951753