Finite Group Databasebeta

← #13148490

Subgroups — #13148490

Order 1728.

1201 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
1C22×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic
2C2×((C3⋊D3)⋊C3)⋊Q8C211yesmaximal, characteristic, complemented
3#11721734C211yesmaximal, characteristic, complemented
4C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
5#64087⋊C3C211yesmaximal, characteristic, complemented
6#11721310C211yesmaximal, characteristic
7#11721309C211yesmaximal, characteristic, complemented
8#11721299C211yesmaximal, characteristic, complemented
9#11721135C211yesmaximal, characteristic, complemented
10#11721134C211yesmaximal, characteristic, complemented
11#11721133C211yesmaximal, characteristic, complemented
12#11721129C211yesmaximal, characteristic, complemented
13#11721128C211yesmaximal, characteristic, complemented
14#11721119C211yesmaximal, characteristic, complemented
15#11721119C211yesmaximal, characteristic, complemented
16#10594067—31nomaximal
17D3×#878—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×#1084C2211yescharacteristic
20C2×#6229C2211yescharacteristic, complemented
21C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
24C2×#634⋊C3C2211yescharacteristic, complemented
25C2×((C3⋊D3)⋊C3)⋊C4—24no—
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
28C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
29C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
30C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
31C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
32C2×#6196C2211yescharacteristic, complemented
33C2×#6196C2211yescharacteristic, complemented
34((C3⋊D3)⋊C3)⋊Q8—24no—
35C22⋊C4×H(3,𝔽3)C2211yescharacteristic
36#88552C2211yescharacteristic
37C4⋊#1084C2211yescharacteristic, complemented
38#88540C2211yescharacteristic, complemented
39#88540C2211yescharacteristic, complemented
40#3757⋊C3C2211yescharacteristic
41#3757⋊C3C2211yescharacteristic
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#88450C2211yescharacteristic
48#88450C2211yescharacteristic
49#88449C2211yescharacteristic, complemented
50#88449C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C22×#624—31no—
56C22×D3×Dic3—31no—
57C2×#3797—31no—
58C2×D3×Dic6—31no—
59C22⋊C4×C3⋊D3D311yescharacteristic
60#64087D311yescharacteristic, complemented
61C3×D3×C22⋊C4—31no—
62C3×#878—31no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#63982—31no—
67#63974—31no—
68D3×#217—31no—
69#63964—31no—
70#63964—31no—
71#63964—31no—
72#63900—31no—
73#63899—31no—
74#63896—31no—
75#63895—31no—
76#63895—31no—
77#63893—31no—
78D3×C4⋊Dic3—31no—
79#63888—31no—
80#63888—31no—
81#63887—31no—
82#63883—31no—
83#63883—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×(C3⋊D3)⋊C3—22no—
88C22×(C3⋊D3)⋊C3—22no—
89C22×(C3⋊D3)⋊C3Q814yescomplemented
90C22×(C3⋊D3)⋊C3C2311yescharacteristic
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
92C2×C4×H(3,𝔽3)C2311yescharacteristic
93C2×C4×H(3,𝔽3)C2311yescharacteristic
94C2×#1084—22no—
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97C2×#1084C2311yescharacteristic
98C2×#1084C2311yescharacteristic
99#6229—22no—
100C2×(C3⋊Dic3)⋊C3—22no—
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
106C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
107C4×(C3⋊D3)⋊C3—22no—
108C4×(C3⋊D3)⋊C3—22no—
109#634⋊C3—22no—
110((C3⋊D3)⋊C3)⋊C4—22no—
111((C3⋊D3)⋊C3)⋊C4—22no—
112((C3⋊D3)⋊C3)⋊C4—22no—
113((C3⋊D3)⋊C3)⋊C4—22no—
114((C3⋊D3)⋊C3)⋊C4—22no—
115((C3⋊D3)⋊C3)⋊C4D414yes—
116#6196—22no—
117#6196—22no—
118D3×C22⋊Q8—91no—
119D3×C22⋊Q8—91no—
120C2×#878—91no—
121C23×C3⋊D3C2×D311yescharacteristic
122C23×C3×D3—31no—
123C22×C3⋊Dic3C2×D311yescharacteristic
124C2×C4×C3⋊D3C2×D311yescharacteristic
125C2×C4×C3⋊D3C2×D311yescharacteristic
126C2×#634C2×D311yescharacteristic, complemented
127C22×C3×Dic3—31no—
128C22×C3×Dic3—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—61no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—61no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—31no—
144C2×#624—31no—
145C2×#624—31no—
146C2×#624—31no—
147C2×#624—64no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—31no—
151C2×D3×Dic3—31no—
152C2×D3×Dic3—31no—
153C2×D3×Dic3—31no—
154C2×D3×Dic3—64no—
155#3797—64no—
156D3×Dic6—64no—
157C32×C22⋊C4—21no—
158C32×C22⋊C4C2×D311yescharacteristic
159C32×C22⋊C4C2×D311yescharacteristic
160#3757C2×D311yescharacteristic
161#3757C2×D311yescharacteristic
162#3752C2×D311yescharacteristic
163#3752C2×D311yescharacteristic
164C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
165#3750C2×D311yescharacteristic, complemented
166#3750C2×D311yescharacteristic, complemented
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—61no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—61no—
178C3×Dic3⋊C4—31no—
179C3×Dic3⋊C4—31no—
180C3×Dic3⋊C4—31no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—61no—
185C3×Dic3⋊C4—61no—
186#3724—31no—
187#3724—31no—
188#3724—31no—
189#3724—31no—
190Dic3⋊Dic3—31no—
191Dic3⋊Dic3—31no—
192Dic3⋊Dic3—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195Dic3⋊Dic3—31no—
196Dic3⋊Dic3—31no—
197Dic3⋊Dic3—31no—
198#3722—31no—
199#3722—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202C22×H(3,𝔽3)—21no—
203C22×H(3,𝔽3)—21no—
204C22×H(3,𝔽3)C2×Q812yescomplemented
205C22×H(3,𝔽3)C2411yescharacteristic
206C2×(C3⋊D3)⋊C3—21no—
207C2×(C3⋊D3)⋊C3—21no—
208C2×(C3⋊D3)⋊C3—28no—
209C2×(C3⋊D3)⋊C3C2×D412yes—
210C2×(C3⋊D3)⋊C3C2×Q812yes—
211C2×(C3⋊D3)⋊C3C2×Q812yescomplemented
212C2×(C3⋊D3)⋊C3#4112yes—
213C4×H(3,𝔽3)—21no—
214C4×H(3,𝔽3)—21no—
215#1084—21no—
216#1084—21no—
217#1084—21no—
218#1084C2×D412yes—
219(C3⋊Dic3)⋊C3—21no—
220(C3⋊Dic3)⋊C3—21no—
221(C3⋊Dic3)⋊C3—21no—
222(C3⋊Dic3)⋊C3—21no—
223(C3⋊Dic3)⋊C3—21no—
224(C3⋊Dic3)⋊C3C2×D412yes—
225C23×Dic3—91no—
226C2×D3×Q8—91no—
227C2×D3×Q8—91no—
228C22×C4×D3—91no—
229C22×C4×D3—91no—
230C22×Dic6—91no—
231C3×C22⋊Q8—91no—
232C3×C22⋊Q8—91no—
233C2×C3×C22⋊C4—91no—
234C2×#217—91no—
235#946—91no—
236#946—91no—
237C2×C4⋊Dic3—91no—
238#924—91no—
239#924—91no—
240C2×Dic3⋊C4—91no—
241C2×Dic3⋊C4—91no—
242#897—91no—
243#897—91no—
244#896—91no—
245#896—91no—
246#896—91no—
247#896—91no—
248D3×C4⋊C4—91no—
249D3×C4⋊C4—91no—
250D3×C4⋊C4—91no—
251D3×C4⋊C4—91no—
252D3×C4⋊C4—91no—
253D3×C4⋊C4—91no—
254D3×C22⋊C4—31no—
255D3×C22⋊C4—91no—
256D3×C22⋊C4—91no—
257D3×C22⋊C4—91no—
258#878—31no—
259#878—31no—
260#878—31no—
261#878—61no—
262#878—91no—
263#878—91no—
264#878—91no—
265#878—91no—
266#878—91no—
267#878—91no—
268#878—91no—
269#878—91no—
270#878—91no—
271C23×C32—21no—
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3Dic614yescomplemented
277C22×C3⋊D3C22×D311yescharacteristic
278C22×C3⋊D3C22×D311yescharacteristic
279C22×C3×D3—31no—
280C22×C3×D3—34no—
281C22×C3×D3—31no—
282C22×C3×D3—62no—
283C22×C3×D3—62no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3C22×D311yescharacteristic
292C2×C3⋊Dic3C22×D311yescharacteristic
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C4×C3⋊D3—22no—
298C4×C3⋊D3—22no—
299#634—22no—
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—31no—
312C2×C3×Dic3—31no—
313C2×C3×Dic3—31no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—62no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—122no—
322C3×C4×D3—62no—
323C3×C4×D3—62no—
324C3×Dic6—62no—
325C3×Dic6—62no—
326C3×Dic6—62no—
327C3×Dic6—122no—
328#627—62no—
329#627—62no—
330#627—62no—
331#627—62no—
332#624—34no—
333#624—62no—
334#624—62no—
335#624—62no—
336#624—62no—
337#624—62no—
338D3×Dic3—34no—
339D3×Dic3—62no—
340D3×Dic3—62no—
341D3×Dic3—62no—
342D3×Dic3—62no—
343D3×Dic3—62no—
344C2×C22⋊Q8—271noSylow
345C2×H(3,𝔽3)—22no—
346C2×H(3,𝔽3)C22×D411yescharacteristic
347C2×H(3,𝔽3)C22×Q811yescharacteristic
348C2×H(3,𝔽3)C2×#4111yescharacteristic
349(C3⋊D3)⋊C3—22no—
350(C3⋊D3)⋊C3C22⋊Q814yescomplemented
351C24×C3—91no—
352C23×D3—31no—
353C23×D3—91no—
354C2×C3×Q8—91no—
355C2×C3×Q8—91no—
356C22×C3×C4—91no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—91no—
369C22×Dic3—91no—
370C22×Dic3—91no—
371C22×Dic3—184no—
372D3×Q8—184no—
373D3×Q8—184no—
374C2×C4×D3—31no—
375C2×C4×D3—31no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—91no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—184no—
391C2×C4×D3—184no—
392C2×Dic6—31no—
393C2×Dic6—31no—
394C2×Dic6—31no—
395C2×Dic6—61no—
396C2×Dic6—91no—
397C2×Dic6—91no—
398C2×Dic6—91no—
399C2×Dic6—91no—
400C2×Dic6—91no—
401C2×Dic6—91no—
402C2×Dic6—91no—
403C2×Dic6—184no—
404C3×C4⋊C4—91no—
405C3×C4⋊C4—91no—
406C3×C4⋊C4—91no—
407C3×C4⋊C4—91no—
408C3×C4⋊C4—91no—
409C3×C4⋊C4—91no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412C3×C22⋊C4—61no—
413C3×C22⋊C4—91no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4D3211yescharacteristic
419#217—31no—
420#217—31no—
421#217—31no—
422#217—31no—
423#217—61no—
424#217—91no—
425#217—91no—
426#217—91no—
427#217—91no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—91no—
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—61no—
440C4⋊Dic3—91no—
441C4⋊Dic3—91no—
442C4⋊Dic3—91no—
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445C4⋊Dic3—91no—
446C4⋊Dic3—91no—
447Dic3⋊C4—31no—
448Dic3⋊C4—31no—
449Dic3⋊C4—31no—
450Dic3⋊C4—31no—
451Dic3⋊C4—31no—
452Dic3⋊C4—31no—
453Dic3⋊C4—61no—
454Dic3⋊C4—61no—
455Dic3⋊C4—91no—
456Dic3⋊C4—91no—
457Dic3⋊C4—91no—
458Dic3⋊C4—91no—
459Dic3⋊C4—91no—
460Dic3⋊C4—91no—
461Dic3⋊C4—91no—
462Dic3⋊C4—91no—
463Dic3⋊C4—91no—
464Dic3⋊C4—91no—
465Dic3⋊C4—91no—
466Dic3⋊C4—91no—
467Dic3⋊C4—91no—
468Dic3⋊C4—91no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—22no—
475C22×C32—41no—
476C22×C32—41no—
477C22×C32C2×Dic612yescomplemented
478C22×C32D3×Q812yescomplemented
479C22×C32C23×D311yescharacteristic
480C22×C32C23×D311yescharacteristic
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—28no—
484C2×C3⋊D3C2×Dic612yes—
485C2×C3⋊D3C2×Dic612yescomplemented
486C2×C3⋊D3D3×D412yes—
487C2×C3⋊D3#23712yes—
488C2×C3×D3—32no—
489C2×C3×D3—32no—
490C2×C3×D3—32no—
491C2×C3×D3—32no—
492C2×C3×D3—68no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C32×C4—21no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—41no—
500C32×C4—41no—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—21no—
505C3⋊Dic3—21no—
506C3⋊Dic3D3×D412yes—
507C3×Dic3—32no—
508C3×Dic3—32no—
509C3×Dic3—32no—
510C3×Dic3—62no—
511C3×Dic3—61no—
512C3×Dic3—61no—
513C3×Dic3—61no—
514C3×Dic3—61no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—61no—
522C3×Dic3—121no—
523C3×Dic3—121no—
524C3×Dic3—121no—
525C22×Q8—271no—
526C23×C4—271no—
527C22⋊Q8—91no—
528C22⋊Q8—91no—
529C22⋊Q8—271no—
530C22⋊Q8—271no—
531C22⋊Q8—271no—
532C22⋊Q8—271no—
533C22⋊Q8—271no—
534C22⋊Q8—271no—
535C2×C4⋊C4—271no—
536C2×C4⋊C4—271no—
537C2×C4⋊C4—271no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—271no—
540H(3,𝔽3)C2×C22⋊Q811yescharacteristic, complemented, Sylow
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—61no—
544C23×C3—91no—
545C23×C3—91no—
546C23×C3—94no—
547C23×C3—182no—
548C23×C3—182no—
549C23×C3C2×D3211yescharacteristic
550C22×D3—31no—
551C22×D3—31no—
552C22×D3—34no—
553C22×D3—62no—
554C22×D3—62no—
555C22×D3—91no—
556C22×D3—94no—
557C22×D3—91no—
558C22×D3—182no—
559C22×D3—182no—
560C3×Q8—182no—
561C3×Q8—182no—
562C2×C3×C4—31no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—91no—
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—182no—
579C2×C3×C4—182no—
580C2×C3×C4—182no—
581C2×C3×C4—182no—
582C2×C3×C4C2×D3211yescharacteristic
583C2×C3×C4C2×D3211yescharacteristic
584C2×Dic3—31no—
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—31no—
597C2×Dic3—31no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—91no—
608C2×Dic3—91no—
609C2×Dic3—91no—
610C2×Dic3—91no—
611C2×Dic3—94no—
612C2×Dic3—122no—
613C2×Dic3—182no—
614C2×Dic3—182no—
615C2×Dic3—182no—
616C2×Dic3—182no—
617C2×Dic3—182no—
618C2×Dic3—182no—
619C4×D3—62no—
620C4×D3—62no—
621C4×D3—94no—
622C4×D3—94no—
623C4×D3—182no—
624C4×D3—182no—
625C4×D3—182no—
626C4×D3—182no—
627C4×D3—182no—
628C4×D3—182no—
629C4×D3—182no—
630C4×D3—182no—
631C4×D3—182no—
632C4×D3—182no—
633C4×D3—182no—
634C4×D3—182no—
635Dic6—62no—
636Dic6—62no—
637Dic6—62no—
638Dic6—122no—
639Dic6—182no—
640Dic6—182no—
641Dic6—182no—
642Dic6—182no—
643Dic6—182no—
644Dic6—182no—
645Dic6—182no—
646C2×C32—22no—
647C2×C32—22no—
648C2×C32—21no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—42no—
652C2×C32C22×Dic611yescharacteristic
653C2×C32C2×D3×D411yescharacteristic
654C2×C32C2×D3×D411yescharacteristic
655C2×C32C2×#23711yescharacteristic
656C2×C32C2×D3×Q811yescharacteristic
657C2×C32D3×#4111yescharacteristic
658C3⋊D3—22no—
659C3⋊D3#87814yescomplemented
660C3×D3—34no—
661C3×D3—62no—
662C24—91no—
663C2×Q8—91no—
664C2×Q8—91no—
665C2×Q8—271no—
666C2×Q8—271no—
667C2×Q8—544no—
668C22×C4—91no—
669C22×C4—91no—
670C22×C4—91no—
671C22×C4—91no—
672C22×C4—271no—
673C22×C4—271no—
674C22×C4—271no—
675C22×C4—271no—
676C22×C4—271no—
677C22×C4—271no—
678C22×C4—544no—
679C4⋊C4—91no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4—271no—
686C4⋊C4—271no—
687C4⋊C4—271no—
688C4⋊C4—271no—
689C4⋊C4—271no—
690C4⋊C4—271no—
691C22⋊C4—91no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—91no—
695C22⋊C4—91no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—31no—
702C22×C3—31no—
703C22×C3—32no—
704C22×C3—32no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—62no—
711C22×C3—92no—
712C22×C3—92no—
713C22×C3—92no—
714C22×C3—92no—
715C22×C3—121no—
716C22×C3—121no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—188no—
720C22×C3D3×Dic612yes—
721C22×C3C22×D3211yescharacteristic
722C2×D3—32no—
723C2×D3—32no—
724C2×D3—32no—
725C2×D3—32no—
726C2×D3—68no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—92no—
730C2×D3—92no—
731C2×D3—92no—
732C2×D3—92no—
733C2×D3—188no—
734C2×D3—181no—
735C2×D3—181no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—92no—
743C3×C4—92no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4—181no—
747C3×C4—181no—
748C3×C4—181no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4—181no—
752C3×C4—181no—
753C3×C4—181no—
754Dic3—32no—
755Dic3—32no—
756Dic3—32no—
757Dic3—62no—
758Dic3—61no—
759Dic3—61no—
760Dic3—61no—
761Dic3—61no—
762Dic3—61no—
763Dic3—61no—
764Dic3—61no—
765Dic3—61no—
766Dic3—61no—
767Dic3—61no—
768Dic3—61no—
769Dic3—92no—
770Dic3—121no—
771Dic3—121no—
772Dic3—121no—
773Dic3—181no—
774Dic3—181no—
775Dic3—181no—
776Dic3—181no—
777Dic3—181no—
778C32—21no—
779C32C2×#87811yescharacteristic, complemented
780C32D3×C22⋊Q811yescharacteristic, complemented
781C23—91no—
782C23—91no—
783C23—94no—
784C23—182no—
785C23—182no—
786C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
787Q8—182no—
788Q8—182no—
789Q8—542no—
790Q8—542no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—91no—
799C2×C4—91no—
800C2×C4—91no—
801C2×C4—182no—
802C2×C4—182no—
803C2×C4—182no—
804C2×C4—182no—
805C2×C4—274no—
806C2×C4—542no—
807C2×C4—542no—
808C2×C4—542no—
809C2×C4—542no—
810C2×C4—542no—
811C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
812C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
813C2×C3—22no—
814C2×C3—31no—
815C2×C3—31no—
816C2×C3—31no—
817C2×C3—31no—
818C2×C3—31no—
819C2×C3—31no—
820C2×C3—62no—
821C2×C3—62no—
822C2×C3—61no—
823C2×C3—61no—
824C2×C3—61no—
825C2×C3—94no—
826C2×C3—122no—
827C2×C3—182no—
828C2×C3C2×D3×Dic611yescharacteristic
829C2×C3D32×D411yescharacteristic
830C2×C3D3×#23711yescharacteristic
831D3—34no—
832D3—62no—
833D3—94no—
834D3—182no—
835C22—21no—
836C22—21no—
837C22—92no—
838C22—92no—
839C22—92no—
840C22—92no—
841C22—188no—
842C22—181no—
843C22—181no—
844C22((C3⋊D3)⋊C3)⋊Q812yescomplemented
845C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
846C4—21no—
847C4—21no—
848C4—92no—
849C4—92no—
850C4—181no—
851C4—181no—
852C4—181no—
853C4—181no—
854C4—181no—
855C4—181no—
856C4—181no—
857C4—181no—
858C3—31no—
859C3—31no—
860C3—61no—
861C3D3×#87811yescharacteristic
862C2—22no—
863C2—94no—
864C2—182no—
865C2C2×((C3⋊D3)⋊C3)⋊Q811yescharacteristic
866C2D4×((C3⋊D3)⋊C3)⋊C211yescharacteristic
867C2#1172250411yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22⋊C4×H(3,𝔽3)C22
prime radicalC23×(C3⋊D3)⋊C3C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C22⋊Q8
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
2. C2×((C3⋊D3)⋊C3)⋊Q8C2semidirect
3. #11721734C2semidirect
5. #64087⋊C3C2semidirect
7. #11721309C2semidirect
8. #11721299C2semidirect
9. #11721135C2semidirect
10. #11721134C2semidirect
11. #11721133C2semidirect
12. #11721129C2semidirect
13. #11721128C2semidirect
14. #11721119C2semidirect
15. #11721119C2semidirect
20. C2×#6229C22semidirect
24. C2×#634⋊C3C22semidirect
32. C2×#6196C22semidirect
33. C2×#6196C22semidirect
37. C4⋊#1084C22semidirect
38. #88540C22semidirect
39. #88540C22semidirect
44. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
45. #3750⋊C3C22semidirect
46. #3750⋊C3C22semidirect
49. #88449C22semidirect
50. #88449C22semidirect
51. #88448C22semidirect
52. #88448C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
60. #64087D3semidirect
89. C22×(C3⋊D3)⋊C3Q8semidirect
126. C2×#634C2×D3semidirect
164. C4⋊(C3⋊Dic3)C2×D3semidirect
165. #3750C2×D3semidirect
166. #3750C2×D3semidirect
204. C22×H(3,𝔽3)C2×Q8semidirect
211. C2×(C3⋊D3)⋊C3C2×Q8semidirect
276. C22×C3⋊D3Dic6semidirect
350. (C3⋊D3)⋊C3C22⋊Q8semidirect
477. C22×C32C2×Dic6semidirect
478. C22×C32D3×Q8semidirect
485. C2×C3⋊D3C2×Dic6semidirect
540. H(3,𝔽3)C2×C22⋊Q8semidirect
659. C3⋊D3#878semidirect
779. C32C2×#878semidirect
780. C32D3×C22⋊Q8semidirect
844. C22((C3⋊D3)⋊C3)⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×((C3⋊D3)⋊C3)⋊C42
C2×((C3⋊D3)⋊C3)⋊Q82
#117217342
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#117213102
#117213092
#117212992
#117211352
#117211342
#117211332
#117211292
#117211282
#117211192
#105940673
D3×#8783