Finite Group Databasebeta

← #13148529

Subgroups — #13148529

Order 1728.

921 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721734C211yesmaximal, characteristic, complemented
2C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
3#64087⋊C3C211yesmaximal, characteristic, complemented
4#11721310C211yesmaximal, characteristic
5#11721309C211yesmaximal, characteristic, complemented
6C2×#88450C211yesmaximal, characteristic
7#11721299C211yesmaximal, characteristic, complemented
8#11721135C211yesmaximal, characteristic, complemented
9#11721134C211yesmaximal, characteristic, complemented
10#11721133C211yesmaximal, characteristic, complemented
11#11721128C211yesmaximal, characteristic, complemented
12#11721107C211yesmaximal, characteristic, complemented
13#11721106C211yesmaximal, characteristic, complemented
14#11721101C211yesmaximal, characteristic, complemented
15#11721101C211yesmaximal, characteristic, complemented
16#10594180—31nomaximal
17#10594170—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)⋊C4C2211yescharacteristic
26C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
27C2×#6196C2211yescharacteristic, complemented
28C2×#6196C2211yescharacteristic, complemented
29C22⋊C4×H(3,𝔽3)C2211yescharacteristic
30#88552C2211yescharacteristic
31C4⋊#1084C2211yescharacteristic, complemented
32#88540C2211yescharacteristic, complemented
33#88540C2211yescharacteristic, complemented
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
41#88450C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88450C2211yescharacteristic
46#88450C2211yescharacteristic
47#88449C2211yescharacteristic, complemented
48#88449C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88448C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3D311yescharacteristic
54#64087D311yescharacteristic, complemented
55C3×D3×C22⋊C4—31no—
56C3×#878—31no—
57C3×#878—31no—
58C3×#878—31no—
59C3×#878—61no—
60#63982—31no—
61#63974—31no—
62D3×#217—31no—
63#63964—31no—
64#63964—31no—
65#63964—31no—
66C2×#3722—31no—
67C2×(C2×D3)⋊Dic3—31no—
68#63899—31no—
69#63896—31no—
70#63895—31no—
71#63895—31no—
72#63893—31no—
73#63888—31no—
74#63888—31no—
75#63887—31no—
76#63871—31no—
77#63871—31no—
78#63865—31no—
79#63865—31no—
80#63857—31no—
81#63856—31no—
82#63851—31no—
83#63851—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3—41no—
86C22×(C3⋊D3)⋊C3—41no—
87C22×(C3⋊D3)⋊C3Q814yescomplemented
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×#1084—41no—
93C2×#1084C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×#1084C2311yescharacteristic
97#6229—41no—
98C2×(C3⋊Dic3)⋊C3—41no—
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
103C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
104C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
105C4×(C3⋊D3)⋊C3—41no—
106C4×(C3⋊D3)⋊C3—41no—
107#634⋊C3—41no—
108((C3⋊D3)⋊C3)⋊C4—41no—
109((C3⋊D3)⋊C3)⋊C4—41no—
110#6196—41no—
111#6196—41no—
112#5634—91no—
113#5634—91no—
114#5483—91no—
115C23×C3⋊D3C2×D311yescharacteristic
116C23×C3×D3—31no—
117C22×C3⋊Dic3C2×D311yescharacteristic
118C2×C4×C3⋊D3C2×D311yescharacteristic
119C2×C4×C3⋊D3C2×D311yescharacteristic
120C2×#634C2×D311yescharacteristic, complemented
121C22×C3×Dic3—31no—
122C22×C3×Dic3—31no—
123C22×C3×Dic3—31no—
124C22×C3×Dic3—61no—
125C2×C3×C4×D3—31no—
126C2×C3×C4×D3—31no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—61no—
131C2×#627—31no—
132C2×#627—31no—
133C2×#627—31no—
134C2×#627—31no—
135C2×#624—31no—
136C2×#624—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C32×C22⋊C4—21no—
140C32×C22⋊C4C2×D311yescharacteristic
141C32×C22⋊C4C2×D311yescharacteristic
142#3757C2×D311yescharacteristic
143#3757C2×D311yescharacteristic
144#3752C2×D311yescharacteristic
145#3752C2×D311yescharacteristic
146C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
147#3750C2×D311yescharacteristic, complemented
148#3750C2×D311yescharacteristic, complemented
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×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—31no—
159C3×C4⋊Dic3—61no—
160C3×Dic3⋊C4—31no—
161C3×Dic3⋊C4—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×Dic3⋊C4—31no—
166C3×Dic3⋊C4—61no—
167C3×Dic3⋊C4—61no—
168#3724—31no—
169#3724—31no—
170#3724—31no—
171#3724—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176Dic3⋊Dic3—31no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179Dic3⋊Dic3—31no—
180#3722—31no—
181#3722—31no—
182#3722—31no—
183#3722—31no—
184#3722—31no—
185#3722—31no—
186(C2×D3)⋊Dic3—31no—
187(C2×D3)⋊Dic3—31no—
188(C2×D3)⋊Dic3—31no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—31no—
192C22×H(3,𝔽3)—21no—
193C22×H(3,𝔽3)—21no—
194C22×H(3,𝔽3)C2×Q812yes—
195C22×H(3,𝔽3)C2411yescharacteristic
196C2×(C3⋊D3)⋊C3—21no—
197C2×(C3⋊D3)⋊C3—21no—
198C2×(C3⋊D3)⋊C3—21no—
199C2×(C3⋊D3)⋊C3—21no—
200C2×(C3⋊D3)⋊C3—44no—
201C2×(C3⋊D3)⋊C3C2×Q812yes—
202C2×(C3⋊D3)⋊C3C2×Q812yes—
203C4×H(3,𝔽3)—21no—
204C4×H(3,𝔽3)—21no—
205#1084—21no—
206#1084—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—
215C3×C22⋊Q8—91no—
216C3×C22⋊Q8—91no—
217C2×C3×C22⋊C4—91no—
218C2×#217—91no—
219C2×#217—91no—
220#946—91no—
221#946—91no—
222#946—91no—
223#946—91no—
224C2×(C2×D3)⋊C4—91no—
225C2×(C2×D3)⋊C4—91no—
226#924—91no—
227#924—91no—
228#924—91no—
229#924—91no—
230#924—91no—
231#924—91no—
232#897—91no—
233#897—91no—
234#897—91no—
235#897—91no—
236#896—91no—
237#896—91no—
238#896—91no—
239#896—91no—
240#896—91no—
241#896—91no—
242#896—91no—
243#896—91no—
244D3×C22⋊C4—31no—
245D3×C22⋊C4—91no—
246D3×C22⋊C4—91no—
247D3×C22⋊C4—91no—
248#878—31no—
249#878—31no—
250#878—31no—
251#878—61no—
252#878—91no—
253#878—91no—
254#878—91no—
255#878—91no—
256#878—91no—
257#878—91no—
258#878—91no—
259#878—91no—
260#878—91no—
261C23×C32—21no—
262C23×C32C22×D311yescharacteristic
263C23×C32C22×D311yescharacteristic
264C22×C3⋊D3—41no—
265C22×C3⋊D3—41no—
266C22×C3⋊D3Dic614yescomplemented
267C22×C3⋊D3C22×D311yescharacteristic
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3×D3—31no—
270C22×C3×D3—31no—
271C22×C3×D3—34no—
272C22×C3×D3—121no—
273C22×C3×D3—121no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C22×D311yescharacteristic
278C2×C32×C4C22×D311yescharacteristic
279C2×C32×C4C22×D311yescharacteristic
280C2×C3⋊Dic3—41no—
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C4×C3⋊D3—41no—
288C4×C3⋊D3—41no—
289#634—41no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
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—61no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—121no—
309C2×C3×Dic3—121no—
310C2×C3×Dic3—121no—
311C2×C3×Dic3—122no—
312C3×C4×D3—121no—
313C3×C4×D3—121no—
314C3×Dic6—121no—
315C3×Dic6—121no—
316C3×Dic6—121no—
317C3×Dic6—122no—
318#627—121no—
319#627—121no—
320#627—121no—
321#627—121no—
322#624—121no—
323#624—121no—
324D3×Dic3—121no—
325D3×Dic3—121no—
326#543—271noSylow
327C2×H(3,𝔽3)—22no—
328C2×H(3,𝔽3)C22×Q811yescharacteristic
329C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
330C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
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×Q8—91no—
338C22×C3×C4—91no—
339C22×C3×C4—91no—
340C22×C3×C4—91no—
341C22×C3×C4—91no—
342C22×Dic3—31no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—91no—
347C22×Dic3—91no—
348C22×Dic3—91no—
349C2×C4×D3—31no—
350C2×C4×D3—31no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3—91no—
356C2×C4×D3—91no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—61no—
361C2×Dic6—91no—
362C2×Dic6—91no—
363C2×Dic6—91no—
364C2×Dic6—91no—
365C2×Dic6—91no—
366C2×Dic6—91no—
367C2×Dic6—91no—
368C3×C4⋊C4—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⋊C4D3211yescharacteristic
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—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
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—
412C4⋊Dic3—31no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—61no—
416C4⋊Dic3—91no—
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—31no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
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—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443Dic3⋊C4—91no—
444Dic3⋊C4—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32C2×Dic612yes—
454C22×C32D3×Q812yes—
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⋊D3C2×Dic612yes—
463C2×C3⋊D3C2×Dic612yes—
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—124no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—41no—
476C32×C4—41no—
477C3⋊Dic3—21no—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3×Dic3—62no—
484C3×Dic3—61no—
485C3×Dic3—61no—
486C3×Dic3—61no—
487C3×Dic3—61no—
488C3×Dic3—61no—
489C3×Dic3—61no—
490C3×Dic3—61no—
491C3×Dic3—61no—
492C3×Dic3—61no—
493C3×Dic3—61no—
494C3×Dic3—61no—
495C3×Dic3—61no—
496C3×Dic3—61no—
497C3×Dic3—61no—
498C3×Dic3—121no—
499C3×Dic3—121no—
500C3×Dic3—121no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—271no—
504C22⋊Q8—271no—
505C22⋊Q8—271no—
506C22⋊Q8—271no—
507C22⋊Q8—271no—
508C22⋊Q8—271no—
509C22⋊Q8—271no—
510C22⋊Q8—271no—
511C22⋊Q8—271no—
512C22⋊Q8—271no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—271no—
515C2×C22⋊C4—271no—
516H(3,𝔽3)#54311yescharacteristic, complemented, Sylow
517C23×C3—31no—
518C23×C3—31no—
519C23×C3—61no—
520C23×C3—91no—
521C23×C3—91no—
522C23×C3—94no—
523C23×C3—361no—
524C23×C3—361no—
525C23×C3C2×D3211yescharacteristic
526C22×D3—31no—
527C22×D3—31no—
528C22×D3—34no—
529C22×D3—91no—
530C22×D3—91no—
531C22×D3—94no—
532C22×D3—121no—
533C22×D3—121no—
534C22×D3—361no—
535C22×D3—361no—
536C3×Q8—361no—
537C3×Q8—361no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—91no—
550C2×C3×C4—91no—
551C2×C3×C4—91no—
552C2×C3×C4—91no—
553C2×C3×C4—91no—
554C2×C3×C4—361no—
555C2×C3×C4—361no—
556C2×C3×C4—361no—
557C2×C3×C4—361no—
558C2×C3×C4C2×D3211yescharacteristic
559C2×C3×C4C2×D3211yescharacteristic
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—31no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—91no—
579C2×Dic3—91no—
580C2×Dic3—91no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—122no—
588C2×Dic3—361no—
589C2×Dic3—361no—
590C2×Dic3—361no—
591C4×D3—121no—
592C4×D3—121no—
593C4×D3—361no—
594C4×D3—361no—
595C4×D3—361no—
596C4×D3—361no—
597C4×D3—361no—
598C4×D3—361no—
599Dic6—121no—
600Dic6—121no—
601Dic6—121no—
602Dic6—122no—
603Dic6—361no—
604Dic6—361no—
605Dic6—361no—
606Dic6—361no—
607Dic6—361no—
608Dic6—361no—
609Dic6—361no—
610C2×C32—22no—
611C2×C32—22no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—42no—
616C2×C32C22×Dic611yescharacteristic
617C2×C32#100411yescharacteristic
618C2×C32#100411yescharacteristic
619C2×C32#100411yescharacteristic
620C2×C32C2×D3×Q811yescharacteristic
621C2×C32#100911yescharacteristic
622C3⋊D3—22no—
623C3⋊D3—22no—
624C3×D3—62no—
625C3×D3—62no—
626C24—91no—
627C2×Q8—91no—
628C2×Q8—91no—
629C2×Q8—271no—
630C2×Q8—271no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—91no—
635C22×C4—271no—
636C22×C4—271no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—91no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C4⋊C4—271no—
647C4⋊C4—271no—
648C4⋊C4—271no—
649C22⋊C4—91no—
650C22⋊C4—91no—
651C22⋊C4—91no—
652C22⋊C4—91no—
653C22⋊C4—91no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4—271no—
658C22⋊C4—271no—
659C22⋊C4—271no—
660C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—31no—
664C22×C3—31no—
665C22×C3—32no—
666C22×C3—32no—
667C22×C3—61no—
668C22×C3—61no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—61no—
672C22×C3—62no—
673C22×C3—92no—
674C22×C3—92no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—181no—
678C22×C3—181no—
679C22×C3—181no—
680C22×C3—181no—
681C22×C3—364no—
682C22×C3D3×Dic612yes—
683C22×C3C22×D3211yescharacteristic
684C2×D3—32no—
685C2×D3—32no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—92no—
691C2×D3—92no—
692C2×D3—124no—
693C2×D3—181no—
694C2×D3—181no—
695C2×D3—181no—
696C2×D3—181no—
697C2×D3—364no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—61no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—181no—
707C3×C4—181no—
708C3×C4—181no—
709C3×C4—181no—
710C3×C4—181no—
711C3×C4—181no—
712C3×C4—181no—
713C3×C4—181no—
714C3×C4—181no—
715C3×C4—181no—
716Dic3—61no—
717Dic3—61no—
718Dic3—61no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—61no—
724Dic3—62no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—61no—
730Dic3—61no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—181no—
735Dic3—181no—
736Dic3—181no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740C32—21no—
741C32#548311yescharacteristic, complemented
742C32#563411yescharacteristic, complemented
743C23—91no—
744C23—91no—
745C23—94no—
746C23—361no—
747C23—361no—
748C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
749Q8—361no—
750Q8—361no—
751Q8—1081no—
752Q8—1081no—
753C2×C4—91no—
754C2×C4—91no—
755C2×C4—91no—
756C2×C4—91no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—91no—
761C2×C4—91no—
762C2×C4—91no—
763C2×C4—361no—
764C2×C4—361no—
765C2×C4—361no—
766C2×C4—361no—
767C2×C4—1081no—
768C2×C4—1081no—
769C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
770C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
771C2×C3—22no—
772C2×C3—31no—
773C2×C3—31no—
774C2×C3—31no—
775C2×C3—31no—
776C2×C3—31no—
777C2×C3—31no—
778C2×C3—62no—
779C2×C3—62no—
780C2×C3—61no—
781C2×C3—61no—
782C2×C3—61no—
783C2×C3—122no—
784C2×C3—182no—
785C2×C3—182no—
786C2×C3C2×D3×Dic611yescharacteristic
787C2×C3#6431311yescharacteristic
788C2×C3#6431411yescharacteristic
789D3—62no—
790D3—62no—
791D3—182no—
792D3—182no—
793C22—21no—
794C22—21no—
795C22—92no—
796C22—92no—
797C22—181no—
798C22—181no—
799C22—181no—
800C22—181no—
801C22—364no—
802C22((C3⋊D3)⋊C3)⋊Q812yes—
803C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
804C4—21no—
805C4—21no—
806C4—181no—
807C4—181no—
808C4—181no—
809C4—181no—
810C4—181no—
811C4—181no—
812C4—181no—
813C4—181no—
814C4—181no—
815C4—181no—
816C3—31no—
817C3—31no—
818C3—61no—
819C3#1059417011yescharacteristic
820C2—22no—
821C2—182no—
822C2—182no—
823C2C2×((C3⋊D3)⋊C3)⋊Q811yescharacteristic
824C2#1172250611yescharacteristic
825C2#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 radicalC23×(C3⋊D3)⋊C3C22
hypercenterC22⋊C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#543
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. #11721734C2semidirect
3. #64087⋊C3C2semidirect
5. #11721309C2semidirect
7. #11721299C2semidirect
8. #11721135C2semidirect
9. #11721134C2semidirect
10. #11721133C2semidirect
11. #11721128C2semidirect
12. #11721107C2semidirect
13. #11721106C2semidirect
14. #11721101C2semidirect
15. #11721101C2semidirect
20. C2×#6229C22semidirect
24. C2×#634⋊C3C22semidirect
27. C2×#6196C22semidirect
28. C2×#6196C22semidirect
31. C4⋊#1084C22semidirect
32. #88540C22semidirect
33. #88540C22semidirect
38. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
39. #3750⋊C3C22semidirect
40. #3750⋊C3C22semidirect
47. #88449C22semidirect
48. #88449C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88448C22semidirect
52. #88448C22semidirect
54. #64087D3semidirect
87. C22×(C3⋊D3)⋊C3Q8semidirect
120. C2×#634C2×D3semidirect
146. C4⋊(C3⋊Dic3)C2×D3semidirect
147. #3750C2×D3semidirect
148. #3750C2×D3semidirect
266. C22×C3⋊D3Dic6semidirect
516. H(3,𝔽3)#543semidirect
741. C32#5483semidirect
742. C32#5634semidirect

Maximal subgroups

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

subgroupindex
#117217342
C22⋊C4×(C3⋊D3)⋊C32
#64087⋊C32
#117213102
#117213092
C2×#884502
#117212992
#117211352
#117211342
#117211332
#117211282
#117211072
#117211062
#117211012
#105941803
#105941703