Finite Group Databasebeta

← #13148707

Subgroups — #13148707

Order 1728.

1277 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88676C211yesmaximal, characteristic
2#11721737C211yesmaximal, characteristic, complemented
3#64090⋊C3C211yesmaximal, characteristic, complemented
4C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
5#11721315C211yesmaximal, characteristic, complemented
6C2×#88450C211yesmaximal, characteristic, complemented
7#11721293C211yesmaximal, characteristic, complemented
8#11721161C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721154C211yesmaximal, characteristic, complemented
11C4×#6200C211yesmaximal, characteristic, complemented
12C4×#6198C211yesmaximal, characteristic, complemented
13#11721122C211yesmaximal, characteristic, complemented
14#11721121C211yesmaximal, characteristic, complemented
15#11721120C211yesmaximal, characteristic, complemented
16#10594256—31nomaximal
17#10594254—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C2×#6235C2211yescharacteristic
21C22×#1084C2211yescharacteristic, complemented
22C2×C4×#272C2211yescharacteristic, complemented
23C2×#638⋊C3C2211yescharacteristic
24C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
25C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28#88676C418yescomplemented
29C2×#6200C2211yescharacteristic
30C2×#6199C2211yescharacteristic, complemented
31C2×#6198C2211yescharacteristic
32C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
33C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
34C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
35#88542C2211yescharacteristic, complemented
36#88540C2211yescharacteristic, complemented
37C4×#1084C2211yescharacteristic, complemented
38#3757⋊C3C2211yescharacteristic, complemented
39#3752⋊C3C2211yescharacteristic
40#3752⋊C3C2211yescharacteristic
41#3752⋊C3C2211yescharacteristic, complemented
42#3750⋊C3C2211yescharacteristic, complemented
43C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
44#88451C2211yescharacteristic, complemented
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88450C2211yescharacteristic, complemented
48#88450C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53#88447C2211yescharacteristic, complemented
54C2×#3811—31no—
55C2×D3×#67—31no—
56#64090D311yescharacteristic, complemented
57C22⋊C4×C3⋊D3D311yescharacteristic, complemented
58C3×#67⋊C4—31no—
59C3×#67⋊C4—31no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4—61no—
62C3×D3×C22⋊C4—31no—
63#67⋊Dic3—31no—
64Dic3×#67—31no—
65Dic3×#67—31no—
66C2×#3722—31no—
67C2×(C2×D3)⋊Dic3—31no—
68#63952—31no—
69#63921—31no—
70D3×(C2×D3)⋊C4—31no—
71D3×(C2×D3)⋊C4—31no—
72D3×(C2×D3)⋊C4—31no—
73#63904—31no—
74C4×#626—31no—
75C4×#626—31no—
76C4×#626—31no—
77C4×#625—31no—
78#63881—31no—
79#63881—31no—
80#63879—31no—
81#63878—31no—
82#63877—31no—
83#63836—31no—
84#63836—31no—
85C23×H(3,𝔽3)C2311yescharacteristic
86C22×#272C2311yescharacteristic
87C22×(C3⋊D3)⋊C3—41no—
88C22×(C3⋊D3)⋊C3—41no—
89C22×(C3⋊D3)⋊C3C2×C414yescomplemented
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C2×((C3⋊D3)⋊C3)⋊C2—41no—
94C2×((C3⋊D3)⋊C3)⋊C2—41no—
95C2×((C3⋊D3)⋊C3)⋊C2C2×C414yescomplemented
96C2×C4×H(3,𝔽3)C2311yescharacteristic
97C2×C4×H(3,𝔽3)C2311yescharacteristic
98#6235C2×C414yescomplemented
99C2×#1084—41no—
100C2×#1084C2311yescharacteristic
101C2×#1084C2311yescharacteristic
102C2×#1084C2311yescharacteristic
103C4×#272—41no—
104#638⋊C3C2×C414yescomplemented
105C2×(C3⋊Dic3)⋊C3—41no—
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C4×(C3⋊D3)⋊C3—41no—
112C4×(C3⋊D3)⋊C3—41no—
113C4×(C3⋊D3)⋊C3—41no—
114#6200C2×C414yescomplemented
115#6199—41no—
116#6198C2×C414yescomplemented
117((C3⋊D3)⋊C3)⋊C4—41no—
118((C3⋊D3)⋊C3)⋊C4C2×C414yescomplemented
119#5545—91no—
120#5545—91no—
121#5486—91no—
122C23×C3⋊D3C2×D311yescharacteristic
123C23×C3×D3—31no—
124C22×D32—31no—
125C22×D32—31no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic, complemented
128C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
129C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
130C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—61no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—61no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—61no—
145#3811—38no—
146D3×#67—38no—
147C2×#626—31no—
148C2×#626—31no—
149C2×#626—31no—
150C2×#625—31no—
151C2×#624—31no—
152C2×#624—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C32×C22⋊C4—21no—
158C32×C22⋊C4C2×D311yescharacteristic, complemented
159C32×C22⋊C4C2×D311yescharacteristic, complemented
160#3757C2×D311yescharacteristic, complemented
161#3752C2×D311yescharacteristic
162#3752C2×D311yescharacteristic
163#3752C2×D311yescharacteristic, complemented
164#3750C2×D311yescharacteristic, complemented
165C4×C3⋊Dic3C2×D311yescharacteristic, complemented
166C3×#217—31no—
167C3×(C2×D3)⋊C4—31no—
168C3×(C2×D3)⋊C4—31no—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—31no—
171C3×(C2×D3)⋊C4—31no—
172C3×(C2×D3)⋊C4—61no—
173C3×Dic3⋊C4—31no—
174C3×Dic3⋊C4—31no—
175C3×Dic3⋊C4—31no—
176C3×Dic3⋊C4—61no—
177C3×C4×Dic3—31no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—61no—
181#3724—31no—
182Dic3⋊Dic3—31no—
183Dic3⋊Dic3—31no—
184Dic3⋊Dic3—31no—
185#3722—31no—
186#3722—31no—
187#3722—31no—
188#3722—31no—
189#3722—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192(C2×D3)⋊Dic3—31no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—31no—
196(C2×D3)⋊Dic3—31no—
197Dic32—31no—
198Dic32—31no—
199Dic32—31no—
200Dic32—31no—
201C22×H(3,𝔽3)—21no—
202C22×H(3,𝔽3)—21no—
203C22×H(3,𝔽3)C22×C412yes—
204C22×H(3,𝔽3)C2411yescharacteristic
205C2×#272—21no—
206C2×#272—21no—
207C2×#272C22×C412yes—
208C2×(C3⋊D3)⋊C3—21no—
209C2×(C3⋊D3)⋊C3—21no—
210C2×(C3⋊D3)⋊C3—21no—
211C2×(C3⋊D3)⋊C3—21no—
212C2×(C3⋊D3)⋊C3—21no—
213C2×(C3⋊D3)⋊C3—21no—
214C2×(C3⋊D3)⋊C3—44no—
215C2×(C3⋊D3)⋊C3C22×C412yes—
216C2×(C3⋊D3)⋊C3C22×C412yes—
217C2×(C3⋊D3)⋊C3C22×C412yes—
218((C3⋊D3)⋊C3)⋊C2—44no—
219C4×H(3,𝔽3)—21no—
220C4×H(3,𝔽3)—21no—
221#1084—21no—
222#1084—21no—
223#1084C22×C412yes—
224(C3⋊Dic3)⋊C3—21no—
225(C3⋊Dic3)⋊C3—21no—
226(C3⋊Dic3)⋊C3—21no—
227(C3⋊Dic3)⋊C3—21no—
228(C3⋊Dic3)⋊C3C22×C412yes—
229C22×#67—91no—
230C2×D3×D4—91no—
231C2×D3×D4—91no—
232C3×C4×D4—91no—
233C3×C4×D4—91no—
234C2×C3×C22⋊C4—91no—
235C2×#217—91no—
236D4×Dic3—91no—
237D4×Dic3—91no—
238C4×#67—91no—
239C4×#67—91no—
240C4×#67—91no—
241C4×#67—91no—
242C4×#67—91no—
243C4×#67—91no—
244C4×#67—91no—
245C4×#67—91no—
246C2×(C2×D3)⋊C4—91no—
247C2×(C2×D3)⋊C4—91no—
248C2×(C2×D3)⋊C4—91no—
249C2×(C2×D3)⋊C4—91no—
250#893—91no—
251#893—91no—
252#892—91no—
253#892—91no—
254#67⋊C4—31no—
255#67⋊C4—31no—
256#67⋊C4—31no—
257#67⋊C4—61no—
258#67⋊C4—91no—
259#67⋊C4—91no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262#67⋊C4—91no—
263D3×C22⋊C4—31no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266D3×C22⋊C4—91no—
267D3×C22⋊C4—91no—
268D3×C22⋊C4—91no—
269#877—91no—
270#877—91no—
271C4×D12—91no—
272C4×D12—91no—
273#872—91no—
274#872—91no—
275C23×C32—21no—
276C23×C32C22×D311yescharacteristic
277C23×C32C22×D311yescharacteristic
278C22×C3⋊D3—41no—
279C22×C3⋊D3—41no—
280C22×C3⋊D3C4×D314yescomplemented
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3⋊D3C22×D311yescharacteristic
284C22×C3×D3—31no—
285C22×C3×D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—31no—
288C22×C3×D3—31no—
289C22×C3×D3—34no—
290C22×C3×D3—61no—
291C22×C3×D3—121no—
292C22×C3×D3—121no—
293C2×D32—34no—
294C2×D32—34no—
295C2×D32—121no—
296C2×D32—121no—
297C2×D32—121no—
298C2×D32—121no—
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4C22×D311yescharacteristic
302C2×C32×C4C22×D311yescharacteristic
303C2×C32×C4C22×D311yescharacteristic
304C2×C32×C4C22×D311yescharacteristic
305#638C4×D314yescomplemented
306C2×C3⋊Dic3—41no—
307C2×C3⋊Dic3C22×D311yescharacteristic
308C2×C3⋊Dic3C22×D311yescharacteristic
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C4×C3⋊D3—41no—
313C4×C3⋊D3—41no—
314C4×C3⋊D3—41no—
315C3×#67—34no—
316C3×#67—34no—
317C3×#67—34no—
318C3×#67—64no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—31no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—31no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—31no—
330C2×C3×Dic3—61no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—61no—
333C2×C3×Dic3—121no—
334C2×C3×Dic3—121no—
335C2×C3×Dic3—121no—
336C2×C3×Dic3—122no—
337C3×C4×D3—121no—
338C3×C4×D3—121no—
339C3×C4×D3—121no—
340C3×C4×D3—121no—
341C3×C4×D3—121no—
342C3×C4×D3—122no—
343#626—34no—
344#626—34no—
345#626—34no—
346#625—34no—
347#624—34no—
348#624—121no—
349D3×Dic3—34no—
350D3×Dic3—121no—
351D3×Dic3—121no—
352D3×Dic3—121no—
353#518—271noSylow
354C2×H(3,𝔽3)—22no—
355C2×H(3,𝔽3)C23×C411yescharacteristic
356C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
357C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
358#272—22no—
359(C3⋊D3)⋊C3—22no—
360(C3⋊D3)⋊C3—22no—
361(C3⋊D3)⋊C3—22no—
362C24×C3—91no—
363C23×D3—31no—
364C23×D3—91no—
365C23×D3—91no—
366C23×D3—91no—
367C23×D3—91no—
368C2×C3×D4—91no—
369C2×C3×D4—91no—
370C22×C3×C4—91no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C22×C3×C4—91no—
374C22×C3×C4—91no—
375C22×C3×C4—91no—
376C2×#67—31no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—61no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—98no—
385C2×#67—91no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394D3×D4—98no—
395D3×D4—98no—
396C2×D12—91no—
397C2×D12—91no—
398C2×C4×D3—31no—
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—61no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—91no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C22⋊C4—31no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4D3211yescharacteristic
424C3×C42—91no—
425C3×C42—91no—
426#217—31no—
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—91no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—91no—
447(C2×D3)⋊C4—91no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—91no—
450(C2×D3)⋊C4—91no—
451(C2×D3)⋊C4—91no—
452(C2×D3)⋊C4—91no—
453(C2×D3)⋊C4—91no—
454(C2×D3)⋊C4—91no—
455C4⋊Dic3—91no—
456C4⋊Dic3—91no—
457Dic3⋊C4—31no—
458Dic3⋊C4—31no—
459Dic3⋊C4—31no—
460Dic3⋊C4—61no—
461Dic3⋊C4—91no—
462Dic3⋊C4—91no—
463Dic3⋊C4—91no—
464Dic3⋊C4—91no—
465Dic3⋊C4—91no—
466C4×Dic3—31no—
467C4×Dic3—31no—
468C4×Dic3—31no—
469C4×Dic3—61no—
470C4×Dic3—91no—
471C4×Dic3—91no—
472C4×Dic3—91no—
473C4×Dic3—91no—
474C4×Dic3—91no—
475C4×Dic3—91no—
476C4×Dic3—91no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—21no—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—22no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32C2×C4×D312yes—
486C22×C32C2×C4×D312yes—
487C22×C32C23×D311yescharacteristic
488C22×C32C23×D311yescharacteristic
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3⋊D3—21no—
495C2×C3⋊D3—44no—
496C2×C3⋊D3C2×C4×D312yes—
497C2×C3⋊D3C2×C4×D312yes—
498C2×C3⋊D3C2×C4×D312yes—
499C2×C3×D3—32no—
500C2×C3×D3—32no—
501C2×C3×D3—32no—
502C2×C3×D3—32no—
503C2×C3×D3—32no—
504C2×C3×D3—62no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—61no—
509C2×C3×D3—61no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—121no—
516C2×C3×D3—121no—
517C2×C3×D3—124no—
518D32—124no—
519D32—124no—
520C32×C4—21no—
521C32×C4—21no—
522C32×C4—21no—
523C32×C4—21no—
524C32×C4—41no—
525C32×C4—41no—
526C3⋊Dic3—21no—
527C3⋊Dic3—21no—
528C3⋊Dic3—21no—
529C3⋊Dic3—21no—
530C3⋊Dic3C2×C4×D312yes—
531C3×Dic3—32no—
532C3×Dic3—32no—
533C3×Dic3—32no—
534C3×Dic3—62no—
535C3×Dic3—62no—
536C3×Dic3—61no—
537C3×Dic3—61no—
538C3×Dic3—61no—
539C3×Dic3—61no—
540C3×Dic3—61no—
541C3×Dic3—61no—
542C3×Dic3—61no—
543C3×Dic3—61no—
544C3×Dic3—121no—
545C22×D4—271no—
546C4×D4—91no—
547C4×D4—91no—
548C4×D4—271no—
549C4×D4—271no—
550C4×D4—271no—
551C4×D4—271no—
552C4×D4—271no—
553C4×D4—271no—
554#117—271no—
555#117—271no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—271no—
558C2×C22⋊C4—271no—
559C2×C22⋊C4—271no—
560H(3,𝔽3)#51811yescharacteristic, complemented, Sylow
561C23×C3—31no—
562C23×C3—31no—
563C23×C3—61no—
564C23×C3—91no—
565C23×C3—91no—
566C23×C3—91no—
567C23×C3—94no—
568C23×C3—91no—
569C23×C3—361no—
570C23×C3—361no—
571C23×C3C2×D3211yescharacteristic
572C22×D3—31no—
573C22×D3—31no—
574C22×D3—31no—
575C22×D3—31no—
576C22×D3—31no—
577C22×D3—34no—
578C22×D3—61no—
579C22×D3—91no—
580C22×D3—91no—
581C22×D3—91no—
582C22×D3—94no—
583C22×D3—94no—
584C22×D3—94no—
585C22×D3—94no—
586C22×D3—121no—
587C22×D3—121no—
588C22×D3—361no—
589C22×D3—361no—
590C22×D3—361no—
591C22×D3—361no—
592C22×D3—361no—
593C22×D3—361no—
594C22×D3—361no—
595C22×D3—361no—
596C3×D4—94no—
597C3×D4—94no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—31no—
601C2×C3×C4—31no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—91no—
605C2×C3×C4—91no—
606C2×C3×C4—91no—
607C2×C3×C4—91no—
608C2×C3×C4—91no—
609C2×C3×C4—91no—
610C2×C3×C4—91no—
611C2×C3×C4—91no—
612C2×C3×C4—361no—
613C2×C3×C4—361no—
614C2×C3×C4—361no—
615C2×C3×C4—361no—
616C2×C3×C4—361no—
617C2×C3×C4—361no—
618C2×C3×C4C2×D3211yescharacteristic
619C2×C3×C4C2×D3211yescharacteristic
620#67—34no—
621#67—34no—
622#67—34no—
623#67—64no—
624#67—94no—
625#67—94no—
626#67—94no—
627#67—94no—
628#67—94no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—31no—
632C2×Dic3—31no—
633C2×Dic3—31no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—91no—
644C2×Dic3—91no—
645C2×Dic3—91no—
646C2×Dic3—91no—
647C2×Dic3—91no—
648C2×Dic3—94no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—122no—
653C2×Dic3—361no—
654C2×Dic3—361no—
655C2×Dic3—361no—
656D12—94no—
657D12—94no—
658C4×D3—94no—
659C4×D3—94no—
660C4×D3—121no—
661C4×D3—121no—
662C4×D3—121no—
663C4×D3—121no—
664C4×D3—121no—
665C4×D3—122no—
666C4×D3—361no—
667C4×D3—361no—
668C4×D3—361no—
669C4×D3—361no—
670C4×D3—361no—
671C4×D3—361no—
672C4×D3—361no—
673C2×C32—22no—
674C2×C32—22no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—42no—
679C2×C32C22×C4×D311yescharacteristic
680C2×C32C22×C4×D311yescharacteristic
681C2×C32#100411yescharacteristic
682C2×C32#100411yescharacteristic
683C2×C32#100411yescharacteristic
684C2×C32#100911yescharacteristic
685C3⋊D3—22no—
686C3⋊D3—22no—
687C3⋊D3—22no—
688C3×D3—62no—
689C3×D3—62no—
690C3×D3—62no—
691C3×D3—62no—
692C3×D3—62no—
693C3×D3—122no—
694C24—91no—
695C24—271no—
696C2×D4—91no—
697C2×D4—91no—
698C2×D4—271no—
699C2×D4—271no—
700C2×D4—278no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—91no—
706C22×C4—91no—
707C22×C4—271no—
708C22×C4—271no—
709C22×C4—271no—
710C4⋊C4—91no—
711C4⋊C4—91no—
712C4⋊C4—271no—
713C4⋊C4—271no—
714C22⋊C4—91no—
715C22⋊C4—91no—
716C22⋊C4—91no—
717C22⋊C4—91no—
718C22⋊C4—91no—
719C22⋊C4—271no—
720C22⋊C4—271no—
721C22⋊C4—271no—
722C22⋊C4—271no—
723C22⋊C4—271no—
724C22⋊C4—271no—
725C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
726C42—91no—
727C42—91no—
728C42—271no—
729C42—271no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—31no—
733C22×C3—31no—
734C22×C3—32no—
735C22×C3—32no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—62no—
742C22×C3—92no—
743C22×C3—92no—
744C22×C3—92no—
745C22×C3—92no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—181no—
749C22×C3—181no—
750C22×C3—181no—
751C22×C3—181no—
752C22×C3—181no—
753C22×C3—181no—
754C22×C3—181no—
755C22×C3—181no—
756C22×C3—364no—
757C22×C3C4×D3212yes—
758C22×C3C22×D3211yescharacteristic
759C2×D3—32no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—32no—
763C2×D3—32no—
764C2×D3—62no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—61no—
768C2×D3—61no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—61no—
775C2×D3—92no—
776C2×D3—92no—
777C2×D3—92no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—124no—
781C2×D3—181no—
782C2×D3—181no—
783C2×D3—181no—
784C2×D3—181no—
785C2×D3—181no—
786C2×D3—181no—
787C2×D3—364no—
788C2×D3—364no—
789C2×D3—364no—
790C2×D3—364no—
791C3×C4—21no—
792C3×C4—21no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—61no—
797C3×C4—92no—
798C3×C4—92no—
799C3×C4—121no—
800C3×C4—121no—
801C3×C4—181no—
802C3×C4—181no—
803C3×C4—181no—
804C3×C4—181no—
805C3×C4—181no—
806C3×C4—181no—
807Dic3—32no—
808Dic3—32no—
809Dic3—32no—
810Dic3—62no—
811Dic3—61no—
812Dic3—61no—
813Dic3—61no—
814Dic3—61no—
815Dic3—62no—
816Dic3—61no—
817Dic3—61no—
818Dic3—61no—
819Dic3—61no—
820Dic3—92no—
821Dic3—121no—
822Dic3—181no—
823Dic3—181no—
824Dic3—181no—
825Dic3—181no—
826C32—21no—
827C32#548611yescharacteristic, complemented
828C32#554511yescharacteristic, complemented
829C23—91no—
830C23—91no—
831C23—91no—
832C23—91no—
833C23—94no—
834C23—274no—
835C23—361no—
836C23—361no—
837C23—1081no—
838C23—1081no—
839C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
840D4—94no—
841D4—94no—
842D4—274no—
843D4—274no—
844C2×C4—91no—
845C2×C4—91no—
846C2×C4—91no—
847C2×C4—91no—
848C2×C4—91no—
849C2×C4—91no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—274no—
853C2×C4—361no—
854C2×C4—361no—
855C2×C4—361no—
856C2×C4—361no—
857C2×C4—361no—
858C2×C4—361no—
859C2×C4—1081no—
860C2×C4—1081no—
861C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
862C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
863C2×C3—22no—
864C2×C3—31no—
865C2×C3—31no—
866C2×C3—31no—
867C2×C3—31no—
868C2×C3—31no—
869C2×C3—31no—
870C2×C3—62no—
871C2×C3—62no—
872C2×C3—61no—
873C2×C3—61no—
874C2×C3—61no—
875C2×C3—122no—
876C2×C3—182no—
877C2×C3—182no—
878C2×C3—182no—
879C2×C3—182no—
880C2×C3C2×C4×D3211yescharacteristic
881C2×C3#6431311yescharacteristic
882C2×C3#6431411yescharacteristic
883D3—62no—
884D3—62no—
885D3—62no—
886D3—62no—
887D3—62no—
888D3—122no—
889D3—182no—
890D3—182no—
891D3—182no—
892C22—21no—
893C22—21no—
894C22—92no—
895C22—92no—
896C22—92no—
897C22—92no—
898C22—181no—
899C22—181no—
900C22—181no—
901C22—181no—
902C22—181no—
903C22—181no—
904C22—181no—
905C22—181no—
906C22—364no—
907C22—1084no—
908C22C4×((C3⋊D3)⋊C3)⋊C212yes—
909C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
910C4—21no—
911C4—21no—
912C4—92no—
913C4—92no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4—181no—
918C4—181no—
919C4—181no—
920C3—31no—
921C3—31no—
922C3—61no—
923C3#1059425411yescharacteristic
924C2—22no—
925C2—182no—
926C2—182no—
927C2—182no—
928C2—182no—
929C2C2×C4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
930C2#1172250611yescharacteristic
931C2#1172250711yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC2×#88676C2
cosocleC22×H(3,𝔽3)C24
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#518
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11721737C2semidirect
3. #64090⋊C3C2semidirect
4. C22⋊C4×(C3⋊D3)⋊C3C2semidirect
5. #11721315C2semidirect
6. C2×#88450C2semidirect
7. #11721293C2semidirect
8. #11721161C2semidirect
9. #11721160C2semidirect
10. #11721154C2semidirect
11. C4×#6200C2semidirect
12. C4×#6198C2semidirect
13. #11721122C2semidirect
14. #11721121C2semidirect
15. #11721120C2semidirect
21. C22×#1084C22semidirect
22. C2×C4×#272C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
25. C2×C4×(C3⋊D3)⋊C3C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. #88676C4semidirect
30. C2×#6199C22semidirect
33. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
34. C22⋊C4×H(3,𝔽3)C22semidirect
35. #88542C22semidirect
36. #88540C22semidirect
37. C4×#1084C22semidirect
38. #3757⋊C3C22semidirect
41. #3752⋊C3C22semidirect
42. #3750⋊C3C22semidirect
43. C4×(C3⋊Dic3)⋊C3C22semidirect
44. #88451C22semidirect
47. #88450C22semidirect
48. #88450C22semidirect
49. #88450C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88447C22semidirect
53. #88447C22semidirect
56. #64090D3semidirect
57. C22⋊C4×C3⋊D3D3semidirect
89. C22×(C3⋊D3)⋊C3C2×C4semidirect
95. C2×((C3⋊D3)⋊C3)⋊C2C2×C4semidirect
98. #6235C2×C4semidirect
104. #638⋊C3C2×C4semidirect
114. #6200C2×C4semidirect
116. #6198C2×C4semidirect
118. ((C3⋊D3)⋊C3)⋊C4C2×C4semidirect
127. C22×C3⋊Dic3C2×D3semidirect
128. C2×C4×C3⋊D3C2×D3semidirect
129. C2×C4×C3⋊D3C2×D3semidirect
130. C2×C4×C3⋊D3C2×D3semidirect
158. C32×C22⋊C4C2×D3semidirect
159. C32×C22⋊C4C2×D3semidirect
160. #3757C2×D3semidirect
163. #3752C2×D3semidirect
164. #3750C2×D3semidirect
165. C4×C3⋊Dic3C2×D3semidirect
280. C22×C3⋊D3C4×D3semidirect
305. #638C4×D3semidirect
560. H(3,𝔽3)#518semidirect
725. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
827. C32#5486semidirect
828. C32#5545semidirect

Maximal subgroups

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

subgroupindex
C2×#886762
#117217372
#64090⋊C32
C22⋊C4×(C3⋊D3)⋊C32
#117213152
C2×#884502
#117212932
#117211612
#117211602
#117211542
C4×#62002
C4×#61982
#117211222
#117211212
#117211202
#105942563
#105942543