Finite Group Databasebeta

← #13148509

Subgroups — #13148509

Order 1728.

944 conjugacy classes of subgroups.

The subgroup lattice has 847 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721741C211yesmaximal, characteristic, complemented
2C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3#64088⋊C3C211yesmaximal, characteristic, complemented
4#11721321C211yesmaximal, characteristic
5#11721319C211yesmaximal, characteristic, complemented
6#11721310C211yesmaximal, characteristic, complemented
7#11721297C211yesmaximal, characteristic, complemented
8#11721154C211yesmaximal, characteristic, complemented
9#11721135C211yesmaximal, characteristic, complemented
10#11721130C211yesmaximal, characteristic, complemented
11#11721123C211yesmaximal, characteristic, complemented
12#11721121C211yesmaximal, characteristic, complemented
13#11721107C211yesmaximal, characteristic, complemented
14#11721105C211yesmaximal, characteristic, complemented
15#11721100C211yesmaximal, characteristic, complemented
16#10594153—31nomaximal
17#10594092—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×#6235C2211yescharacteristic
20C2×#6229C2211yescharacteristic, complemented
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#6200C2211yescharacteristic
24C2×#6200C2211yescharacteristic
25C2×#6199C2211yescharacteristic, complemented
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
28C22⋊C4×H(3,𝔽3)C2211yescharacteristic
29#88552C2211yescharacteristic
30#88542C2211yescharacteristic, complemented
31#88542C2211yescharacteristic, complemented
32C4×#1084C2211yescharacteristic, complemented
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3757⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37#3752⋊C3C2211yescharacteristic
38C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40#3750⋊C3C2211yescharacteristic, complemented
41C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
42#88451C2211yescharacteristic, complemented
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88449C2211yescharacteristic, complemented
48#88448C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3D311yescharacteristic, complemented
54#64088D311yescharacteristic, complemented
55C3×#885—31no—
56C3×#885—31no—
57C3×#885—61no—
58C3×D3×C22⋊C4—31no—
59C3×#879—31no—
60#63981—31no—
61#63976—31no—
62#63974—31no—
63#63969—31no—
64#63969—31no—
65D3×#217—31no—
66#63956—31no—
67#63956—31no—
68#63905—31no—
69#63902—31no—
70#63891—31no—
71#63888—31no—
72#63887—31no—
73#63881—31no—
74#63880—31no—
75#63879—31no—
76#63877—31no—
77#63874—31no—
78#63871—31no—
79#63856—31no—
80#63855—31no—
81#63854—31no—
82#63853—31no—
83#63836—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×#272C2311yescharacteristic
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—22no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93#6235—41no—
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97#6229—41no—
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C4×(C3⋊D3)⋊C3—22no—
105C4×(C3⋊D3)⋊C3—41no—
106#6200—22no—
107#6200—22no—
108#6199—41no—
109((C3⋊D3)⋊C3)⋊C4—22no—
110((C3⋊D3)⋊C3)⋊C4—41no—
111#5705—91no—
112#5679—91no—
113#5495—91no—
114C23×C3⋊D3C2×D311yescharacteristic
115C23×C3×D3—31no—
116C2×C4×C3⋊D3C2×D311yescharacteristic
117C2×C4×C3⋊D3C2×D311yescharacteristic
118C2×C3×#67—31no—
119C2×C3×#67—31no—
120C2×C3×#67—61no—
121C2×C3×C4×D3—31no—
122C2×C3×C4×D3—31no—
123C2×C3×Dic6—31no—
124C2×C3×Dic6—31no—
125C2×C3×Dic6—61no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#625—31no—
129C2×#625—31no—
130C2×#624—31no—
131C2×#624—31no—
132C2×D3×Dic3—31no—
133C2×D3×Dic3—31no—
134C2×D3×Dic3—31no—
135C2×D3×Dic3—31no—
136C32×C22⋊C4—21no—
137C32×C22⋊C4C2×D311yescharacteristic
138C32×C22⋊C4C2×D311yescharacteristic
139#3757C2×D311yescharacteristic
140#3757C2×D311yescharacteristic
141#3757C2×D311yescharacteristic
142#3752C2×D311yescharacteristic
143#3752C2×D311yescharacteristic
144C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
145#3750C2×D311yescharacteristic, complemented
146#3750C2×D311yescharacteristic, complemented
147C4×C3⋊Dic3C2×D311yescharacteristic, complemented
148C3×#217—31no—
149C3×#217—31no—
150C3×#217—31no—
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—61no—
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×(C2×D3)⋊C4—61no—
161C3×(C2×D3)⋊C4—61no—
162C3×C4⋊Dic3—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×C4×Dic3—31no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—61no—
169#3724—31no—
170#3724—31no—
171#3724—31no—
172#3724—31no—
173Dic3⋊Dic3—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(C2×D3)⋊Dic3—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—
189Dic32—31no—
190Dic32—31no—
191C22×H(3,𝔽3)—21no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)C2411yescharacteristic
195C2×#272—21no—
196C2×#272—21no—
197C2×#272—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—44no—
203C2×(C3⋊D3)⋊C3#4112yes—
204C2×(C3⋊D3)⋊C3#4112yes—
205C4×H(3,𝔽3)—21no—
206C4×H(3,𝔽3)—21no—
207#1084—21no—
208#1084—21no—
209#1084—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×#126—91no—
217C3×#124—91no—
218C2×C3×C22⋊C4—91no—
219#953—91no—
220C2×#217—91no—
221#946—91no—
222#946—91no—
223#937—91no—
224#935—91no—
225#929—91no—
226C4×#67—91no—
227#926—91no—
228#924—91no—
229#897—91no—
230#896—91no—
231#894—91no—
232#894—91no—
233#893—91no—
234#892—91no—
235#886—91no—
236#885—31no—
237#885—31no—
238#885—61no—
239#883—91no—
240#883—91no—
241#883—91no—
242#883—91no—
243#882—91no—
244#67⋊C4—91no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247D3×C22⋊C4—31no—
248D3×C22⋊C4—91no—
249D3×C22⋊C4—91no—
250D3×C22⋊C4—91no—
251#879—31no—
252#879—91no—
253#879—91no—
254#879—91no—
255#879—91no—
256#878—91no—
257#877—91no—
258C4×D12—91no—
259#872—91no—
260#872—91no—
261#872—91no—
262C23×C32—21no—
263C23×C32C22×D311yescharacteristic
264C23×C32C22×D311yescharacteristic
265C22×C3⋊D3—22no—
266C22×C3⋊D3—22no—
267C22×C3⋊D3—41no—
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3×D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—31no—
274C22×C3×D3—61no—
275C22×C3×D3—62no—
276C22×C3×D3—62no—
277C22×C3×D3—121no—
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×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C2×C3⋊Dic3C22×D311yescharacteristic
288C2×C3⋊Dic3C22×D311yescharacteristic
289C2×C3⋊Dic3C22×D311yescharacteristic
290C4×C3⋊D3—22no—
291C4×C3⋊D3—41no—
292C3×#67—121no—
293C3×#67—121no—
294C3×#67—122no—
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—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C3×C4×D3—62no—
311C3×C4×D3—121no—
312C3×Dic6—121no—
313C3×Dic6—121no—
314C3×Dic6—122no—
315#626—62no—
316#626—62no—
317#625—62no—
318#625—62no—
319#624—62no—
320#624—121no—
321D3×Dic3—62no—
322D3×Dic3—121no—
323D3×Dic3—121no—
324D3×Dic3—121no—
325#551—271noSylow
326C2×H(3,𝔽3)—41no—
327C2×H(3,𝔽3)C2×#4111yescharacteristic
328C2×H(3,𝔽3)C2×#4111yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330#272—41no—
331(C3⋊D3)⋊C3—22no—
332(C3⋊D3)⋊C3—22no—
333C24×C3—91no—
334C23×D3—31no—
335C23×D3—91no—
336C2×C3×Q8—91no—
337C2×C3×D4—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C2×#67—31no—
341C2×#67—31no—
342C2×#67—61no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C22×Dic3—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×C4×D3—31no—
353C2×C4×D3—31no—
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×C4×D3—91no—
362C2×Dic6—31no—
363C2×Dic6—31no—
364C2×Dic6—61no—
365C3×C4⋊C4—91no—
366C3×C4⋊C4—91no—
367C3×C4⋊C4—91no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—91no—
372C3×C22⋊C4—91no—
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C22⋊C4—91no—
377C3×C22⋊C4—91no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4D3211yescharacteristic
380C3×C42—91no—
381C3×C42—91no—
382#217—31no—
383#217—31no—
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—
416C4⋊Dic3—31no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—91no—
420C4⋊Dic3—91no—
421C4⋊Dic3—91no—
422C4⋊Dic3—91no—
423Dic3⋊C4—31no—
424Dic3⋊C4—31no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437C4×Dic3—31no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—61no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32C23×D311yescharacteristic
456C22×C32C23×D311yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—44no—
462C2×C3⋊D3#23512yes—
463C2×C3⋊D3#23712yes—
464C2×C3×D3—32no—
465C2×C3×D3—32no—
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—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—121no—
477C2×C3×D3—121no—
478C2×C3×D3—121no—
479C2×C3×D3—124no—
480C32×C4—21no—
481C32×C4—21no—
482C32×C4—21no—
483C32×C4—21no—
484C32×C4—41no—
485C32×C4—41no—
486C3⋊Dic3—21no—
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—21no—
492C3×Dic3—62no—
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—61no—
503C3×Dic3—61no—
504C3×Dic3—61no—
505C3×Dic3—121no—
506C3×Dic3—121no—
507#126—91no—
508#126—271no—
509#124—91no—
510#123—271no—
511#123—271no—
512#123—271no—
513C22⋊Q8—271no—
514C22⋊Q8—271no—
515#120—271no—
516C4×D4—271no—
517C4×D4—271no—
518#117—271no—
519#117—271no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—271no—
522H(3,𝔽3)#55111yescharacteristic, complemented, Sylow
523C23×C3—31no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—91no—
527C23×C3—91no—
528C23×C3—91no—
529C23×C3—182no—
530C23×C3—182no—
531C23×C3—361no—
532C23×C3C2×D3211yescharacteristic
533C22×D3—31no—
534C22×D3—31no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—61no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—91no—
541C22×D3—91no—
542C22×D3—121no—
543C22×D3—182no—
544C22×D3—182no—
545C22×D3—361no—
546C3×Q8—361no—
547C3×D4—361no—
548C2×C3×C4—31no—
549C2×C3×C4—31no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
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—91no—
562C2×C3×C4—91no—
563C2×C3×C4—182no—
564C2×C3×C4—361no—
565C2×C3×C4C2×D3211yescharacteristic
566C2×C3×C4C2×D3211yescharacteristic
567#67—121no—
568#67—121no—
569#67—122no—
570#67—182no—
571#67—182no—
572#67—182no—
573#67—182no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—31no—
578C2×Dic3—31no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—31no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—182no—
596C2×Dic3—361no—
597C2×Dic3—361no—
598D12—182no—
599D12—182no—
600C4×D3—62no—
601C4×D3—121no—
602C4×D3—182no—
603C4×D3—182no—
604C4×D3—182no—
605C4×D3—361no—
606C4×D3—361no—
607C4×D3—361no—
608C4×D3—361no—
609C4×D3—361no—
610Dic6—121no—
611Dic6—121no—
612Dic6—122no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—81no—
619C2×C32C2×#23511yescharacteristic
620C2×C32C2×#23711yescharacteristic
621C2×C32#100411yescharacteristic
622C2×C32D3×#4111yescharacteristic
623C2×C32D3×#4111yescharacteristic
624C2×C32#100911yescharacteristic
625C3⋊D3—22no—
626C3⋊D3—22no—
627C3×D3—62no—
628C3×D3—62no—
629C3×D3—121no—
630C3×D3—121no—
631C3×D3—241no—
632C24—91no—
633C2×Q8—91no—
634C2×D4—91no—
635C2×D4—271no—
636C2×D4—271no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—271no—
640C22×C4—271no—
641C22×C4—271no—
642C4⋊C4—91no—
643C4⋊C4—91no—
644C4⋊C4—91no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C4⋊C4—271no—
649C4⋊C4—271no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—91no—
655C22⋊C4—91no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—271no—
659C22⋊C4—271no—
660C22⋊C4—271no—
661C22⋊C4—271no—
662C22⋊C4—271no—
663C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
664C42—91no—
665C42—91no—
666C42—271no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—31no—
671C22×C3—31no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—61no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—61no—
679C22×C3—92no—
680C22×C3—92no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—181no—
685C22×C3—181no—
686C22×C3—181no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—364no—
692C22×C3C22×D3211yescharacteristic
693C2×D3—32no—
694C2×D3—32no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—61no—
698C2×D3—61no—
699C2×D3—61no—
700C2×D3—61no—
701C2×D3—61no—
702C2×D3—61no—
703C2×D3—61no—
704C2×D3—61no—
705C2×D3—92no—
706C2×D3—92no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—124no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—61no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—181no—
725C3×C4—181no—
726C3×C4—181no—
727C3×C4—181no—
728C3×C4—181no—
729C3×C4—181no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—61no—
738Dic3—61no—
739Dic3—62no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—61no—
745Dic3—61no—
746Dic3—121no—
747Dic3—121no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—181no—
753Dic3—181no—
754C32—21no—
755C32#549511yescharacteristic, complemented
756C32#570511yescharacteristic, complemented
757C23—91no—
758C23—91no—
759C23—91no—
760C23—182no—
761C23—182no—
762C23—361no—
763C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
764Q8—361no—
765D4—361no—
766D4—542no—
767D4—542no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—91no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—91no—
777C2×C4—182no—
778C2×C4—361no—
779C2×C4—542no—
780C2×C4—1081no—
781C2×C4—1081no—
782C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
783C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
784C2×C3—31no—
785C2×C3—31no—
786C2×C3—31no—
787C2×C3—31no—
788C2×C3—31no—
789C2×C3—31no—
790C2×C3—41no—
791C2×C3—61no—
792C2×C3—61no—
793C2×C3—61no—
794C2×C3—121no—
795C2×C3—121no—
796C2×C3—182no—
797C2×C3—182no—
798C2×C3—241no—
799C2×C3—361no—
800C2×C3D3×#23511yescharacteristic
801C2×C3D3×#23711yescharacteristic
802C2×C3#6431411yescharacteristic
803D3—62no—
804D3—62no—
805D3—121no—
806D3—121no—
807D3—182no—
808D3—182no—
809D3—241no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—92no—
814C22—92no—
815C22—181no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—181no—
822C22—364no—
823C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
824C4—21no—
825C4—21no—
826C4—181no—
827C4—181no—
828C4—181no—
829C4—181no—
830C4—181no—
831C4—181no—
832C4—181no—
833C4—181no—
834C4—181no—
835C3—31no—
836C3—31no—
837C3—61no—
838C3#1059409411yescharacteristic
839C2—41no—
840C2—182no—
841C2—182no—
842C2—361no—
843C2#1172249011yescharacteristic
844C2#1172250411yescharacteristic
845C2#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#11721321C2
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. #11721741C2semidirect
2. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
3. #64088⋊C3C2semidirect
5. #11721319C2semidirect
6. #11721310C2semidirect
7. #11721297C2semidirect
8. #11721154C2semidirect
9. #11721135C2semidirect
10. #11721130C2semidirect
11. #11721123C2semidirect
12. #11721121C2semidirect
13. #11721107C2semidirect
14. #11721105C2semidirect
15. #11721100C2semidirect
20. C2×#6229C22semidirect
25. C2×#6199C22semidirect
30. #88542C22semidirect
31. #88542C22semidirect
32. C4×#1084C22semidirect
38. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
41. C4×(C3⋊Dic3)⋊C3C22semidirect
42. #88451C22semidirect
47. #88449C22semidirect
48. #88448C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. C22⋊C4×C3⋊D3D3semidirect
54. #64088D3semidirect
144. C4⋊(C3⋊Dic3)C2×D3semidirect
145. #3750C2×D3semidirect
146. #3750C2×D3semidirect
147. C4×C3⋊Dic3C2×D3semidirect
522. H(3,𝔽3)#551semidirect
755. C32#5495semidirect
756. C32#5705semidirect

Maximal subgroups

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

subgroupindex
#117217412
C22⋊C4×(C3⋊D3)⋊C32
#64088⋊C32
#117213212
#117213192
#117213102
#117212972
#117211542
#117211352
#117211302
#117211232
#117211212
#117211072
#117211052
#117211002
#105941533
#105940923