Finite Group Databasebeta

← #13148507

Subgroups — #13148507

Order 1728.

921 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721735C211yesmaximal, characteristic, complemented
2C22⋊C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
3#64088⋊C3C211yesmaximal, characteristic, complemented
4#11721310C211yesmaximal, characteristic
5#11721310C211yesmaximal, characteristic
6#11721297C211yesmaximal, characteristic, complemented
7#11721297C211yesmaximal, characteristic, complemented
8#11721129C211yesmaximal, characteristic, complemented
9#11721119C211yesmaximal, characteristic, complemented
10#11721119C211yesmaximal, characteristic, complemented
11C4×((C3⋊D3)⋊C3)⋊C4C211yesmaximal, characteristic, complemented
12#11721112C211yesmaximal, characteristic, complemented
13#11721111C211yesmaximal, characteristic, complemented
14#11721109C211yesmaximal, characteristic, complemented
15#11721108C211yesmaximal, characteristic, complemented
16#10594154—31nomaximal
17D3×#879—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
22C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
23C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
24C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
25C22⋊C4×H(3,𝔽3)C2211yescharacteristic
26#88552C2211yescharacteristic
27#88552C2211yescharacteristic
28C4⋊#1084C2211yescharacteristic, complemented
29#88540C2211yescharacteristic, complemented
30#88540C2211yescharacteristic, complemented
31C4×#1084C2211yescharacteristic, complemented
32#3757⋊C3C2211yescharacteristic
33#3757⋊C3C2211yescharacteristic
34#3757⋊C3C2211yescharacteristic
35#3752⋊C3C2211yescharacteristic
36#3752⋊C3C2211yescharacteristic
37C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
38#3750⋊C3C2211yescharacteristic, complemented
39#3750⋊C3C2211yescharacteristic, complemented
40C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
41#88450C2211yescharacteristic
42#88450C2211yescharacteristic
43#88450C2211yescharacteristic
44#88450C2211yescharacteristic
45#88449C2211yescharacteristic, complemented
46#88449C2211yescharacteristic, complemented
47#88448C2211yescharacteristic, complemented
48#88448C2211yescharacteristic, complemented
49#88448C2211yescharacteristic, complemented
50#88448C2211yescharacteristic, complemented
51#88447C2211yescharacteristic, complemented
52#88447C2211yescharacteristic, complemented
53C22⋊C4×C3⋊D3D311yescharacteristic
54#64088D311yescharacteristic, complemented
55C3×D3×C22⋊C4—31no—
56C3×#879—31no—
57C3×#879—31no—
58C3×#879—31no—
59C3×#879—61no—
60#63974—31no—
61#63974—31no—
62D3×#217—31no—
63D3×#217—31no—
64#63956—31no—
65#63956—31no—
66#63956—31no—
67#63956—31no—
68#63900—31no—
69D3×C4⋊Dic3—31no—
70#63883—31no—
71#63883—31no—
72C4×#624—31no—
73D3×Dic3⋊C4—31no—
74D3×Dic3⋊C4—31no—
75C4×D3×Dic3—31no—
76#63868—31no—
77#63868—31no—
78#63862—31no—
79#63861—31no—
80#63859—31no—
81#63858—31no—
82#63848—31no—
83#63848—31no—
84C23×H(3,𝔽3)C2311yescharacteristic
85C22×(C3⋊D3)⋊C3—22no—
86C22×(C3⋊D3)⋊C3—22no—
87C22×(C3⋊D3)⋊C3—22no—
88C22×(C3⋊D3)⋊C3C2311yescharacteristic
89C22×(C3⋊D3)⋊C3C2311yescharacteristic
90C2×C4×H(3,𝔽3)C2311yescharacteristic
91C2×C4×H(3,𝔽3)C2311yescharacteristic
92C2×#1084C2311yescharacteristic
93C2×#1084C2311yescharacteristic
94C2×#1084C2311yescharacteristic
95C2×#1084C2311yescharacteristic
96C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
97C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
98C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
99C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
100C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
101C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
102C4×(C3⋊D3)⋊C3—22no—
103C4×(C3⋊D3)⋊C3—22no—
104((C3⋊D3)⋊C3)⋊C4—22no—
105((C3⋊D3)⋊C3)⋊C4—22no—
106((C3⋊D3)⋊C3)⋊C4—22no—
107((C3⋊D3)⋊C3)⋊C4—22no—
108D3×#126—91no—
109D3×#126—91no—
110C2×#879—91no—
111C23×C3⋊D3C2×D311yescharacteristic
112C23×C3×D3—31no—
113C2×C4×C3⋊D3C2×D311yescharacteristic
114C2×C4×C3⋊D3C2×D311yescharacteristic
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×#624—31no—
118C2×#624—31no—
119C2×#624—31no—
120C2×#624—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C2×D3×Dic3—31no—
124C2×D3×Dic3—31no—
125C32×C22⋊C4—21no—
126C32×C22⋊C4C2×D311yescharacteristic
127C32×C22⋊C4C2×D311yescharacteristic
128#3757C2×D311yescharacteristic
129#3757C2×D311yescharacteristic
130#3757C2×D311yescharacteristic
131#3752C2×D311yescharacteristic
132#3752C2×D311yescharacteristic
133C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
134#3750C2×D311yescharacteristic, complemented
135#3750C2×D311yescharacteristic, complemented
136C4×C3⋊Dic3C2×D311yescharacteristic, complemented
137C3×#217—31no—
138C3×#217—31no—
139C3×#217—31no—
140C3×#217—31no—
141C3×#217—31no—
142C3×#217—31no—
143C3×#217—31no—
144C3×#217—61no—
145C3×#217—61no—
146C3×(C2×D3)⋊C4—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×C4⋊Dic3—31no—
149C3×C4⋊Dic3—31no—
150C3×C4⋊Dic3—31no—
151C3×C4⋊Dic3—61no—
152C3×Dic3⋊C4—31no—
153C3×Dic3⋊C4—31no—
154C3×Dic3⋊C4—31no—
155C3×Dic3⋊C4—31no—
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4—31no—
158C3×Dic3⋊C4—61no—
159C3×Dic3⋊C4—61no—
160C3×C4×Dic3—31no—
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—61no—
164#3724—31no—
165#3724—31no—
166#3724—31no—
167#3724—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—31no—
171Dic3⋊Dic3—31no—
172Dic3⋊Dic3—31no—
173Dic3⋊Dic3—31no—
174Dic3⋊Dic3—31no—
175Dic3⋊Dic3—31no—
176#3722—31no—
177#3722—31no—
178#3722—31no—
179#3722—31no—
180(C2×D3)⋊Dic3—31no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—31no—
184Dic32—31no—
185Dic32—31no—
186Dic32—31no—
187Dic32—31no—
188C22×H(3,𝔽3)—21no—
189C22×H(3,𝔽3)—21no—
190C22×H(3,𝔽3)—21no—
191C22×H(3,𝔽3)C2411yescharacteristic
192C2×(C3⋊D3)⋊C3—21no—
193C2×(C3⋊D3)⋊C3—21no—
194C2×(C3⋊D3)⋊C3—21no—
195C2×(C3⋊D3)⋊C3—44no—
196C2×(C3⋊D3)⋊C3#4112yes—
197C2×(C3⋊D3)⋊C3#4112yes—
198C2×(C3⋊D3)⋊C3#4112yes—
199C4×H(3,𝔽3)—21no—
200C4×H(3,𝔽3)—21no—
201#1084—21no—
202#1084—21no—
203#1084—21no—
204#1084—21no—
205(C3⋊Dic3)⋊C3—21no—
206(C3⋊Dic3)⋊C3—21no—
207(C3⋊Dic3)⋊C3—21no—
208(C3⋊Dic3)⋊C3—21no—
209(C3⋊Dic3)⋊C3—21no—
210(C3⋊Dic3)⋊C3—21no—
211C3×#126—91no—
212C3×#126—91no—
213C2×C3×C22⋊C4—91no—
214C2×#217—91no—
215C2×#217—91no—
216C2×C4⋊Dic3—91no—
217C2×Dic3⋊C4—91no—
218C2×Dic3⋊C4—91no—
219C2×C4×Dic3—91no—
220#898—91no—
221#898—91no—
222#898—91no—
223#898—91no—
224#898—91no—
225#898—91no—
226D3×C4⋊C4—91no—
227D3×C4⋊C4—91no—
228D3×C4⋊C4—91no—
229D3×C4⋊C4—91no—
230D3×C4⋊C4—91no—
231D3×C4⋊C4—91no—
232D3×C22⋊C4—31no—
233D3×C22⋊C4—91no—
234D3×C22⋊C4—91no—
235D3×C22⋊C4—91no—
236D3×C22⋊C4—91no—
237D3×C22⋊C4—91no—
238#879—31no—
239#879—31no—
240#879—31no—
241#879—61no—
242#879—91no—
243#879—91no—
244#879—91no—
245#879—91no—
246#879—91no—
247#879—91no—
248#879—91no—
249#879—91no—
250#879—91no—
251#879—91no—
252#879—91no—
253#876—91no—
254#876—91no—
255C42×D3—91no—
256C42×D3—91no—
257C23×C32—21no—
258C23×C32C22×D311yescharacteristic
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3—22no—
261C22×C3⋊D3—22no—
262C22×C3⋊D3—22no—
263C22×C3⋊D3C22×D311yescharacteristic
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3×D3—31no—
266C22×C3×D3—31no—
267C22×C3×D3—62no—
268C22×C3×D3—62no—
269C22×C3×D3—62no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4C22×D311yescharacteristic
273C2×C32×C4C22×D311yescharacteristic
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D311yescharacteristic
279C2×C3⋊Dic3C22×D311yescharacteristic
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D311yescharacteristic
282C4×C3⋊D3—22no—
283C4×C3⋊D3—22no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
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—61no—
299C2×C3×Dic3—61no—
300C2×C3×Dic3—61no—
301C2×C3×Dic3—61no—
302C3×C4×D3—62no—
303C3×C4×D3—62no—
304#624—62no—
305#624—62no—
306#624—62no—
307#624—62no—
308D3×Dic3—62no—
309D3×Dic3—62no—
310D3×Dic3—62no—
311D3×Dic3—62no—
312C2×#126—271noSylow
313C2×H(3,𝔽3)—41no—
314C2×H(3,𝔽3)C2×#4111yescharacteristic
315C2×H(3,𝔽3)C2×#4111yescharacteristic
316C2×H(3,𝔽3)C2×#4111yescharacteristic
317(C3⋊D3)⋊C3—41no—
318(C3⋊D3)⋊C3#12614yescomplemented
319C24×C3—91no—
320C23×D3—31no—
321C23×D3—91no—
322C22×C3×C4—91no—
323C22×C3×C4—91no—
324C22×Dic3—91no—
325C22×Dic3—91no—
326C22×Dic3—91no—
327C22×Dic3—91no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C3×C4⋊C4—91no—
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C4⋊C4—91no—
344C3×C4⋊C4—91no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
354C3×C22⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C22⋊C4D3211yescharacteristic
357C3×C42—91no—
358C3×C42—91no—
359#217—31no—
360#217—31no—
361#217—31no—
362#217—31no—
363#217—31no—
364#217—31no—
365#217—31no—
366#217—61no—
367#217—61no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—91no—
392C4⋊Dic3—91no—
393C4⋊Dic3—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398Dic3⋊C4—31no—
399Dic3⋊C4—31no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—91no—
407Dic3⋊C4—91no—
408Dic3⋊C4—91no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C4×Dic3—91no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C23×D311yescharacteristic
442C22×C32C23×D311yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3—21no—
446C2×C3⋊D3—44no—
447C2×C3⋊D3#23512yes—
448C2×C3⋊D3#23712yes—
449C2×C3⋊D3#23712yes—
450C2×C3×D3—32no—
451C2×C3×D3—32no—
452C2×C3×D3—32no—
453C2×C3×D3—61no—
454C2×C3×D3—61no—
455C2×C3×D3—61no—
456C2×C3×D3—124no—
457C32×C4—21no—
458C32×C4—21no—
459C32×C4—21no—
460C32×C4—21no—
461C32×C4—41no—
462C32×C4—41no—
463C3⋊Dic3—21no—
464C3⋊Dic3—21no—
465C3⋊Dic3—21no—
466C3⋊Dic3—21no—
467C3⋊Dic3—21no—
468C3⋊Dic3—21no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—61no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3—61no—
483C3×Dic3—121no—
484C3×Dic3—121no—
485C3×Dic3—121no—
486C3×Dic3—121no—
487#126—91no—
488#126—91no—
489#126—271no—
490#126—271no—
491#126—271no—
492#126—271no—
493#126—271no—
494#126—271no—
495C2×C4⋊C4—271no—
496C2×C4⋊C4—271no—
497C2×C4⋊C4—271no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—271no—
500C2×C22⋊C4—271no—
501C2×C42—271no—
502H(3,𝔽3)C2×#12611yescharacteristic, complemented, Sylow
503C23×C3—31no—
504C23×C3—31no—
505C23×C3—61no—
506C23×C3—91no—
507C23×C3—91no—
508C23×C3—182no—
509C23×C3—182no—
510C23×C3—182no—
511C23×C3C2×D3211yescharacteristic
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—62no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—182no—
520C22×D3—182no—
521C22×D3—182no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—91no—
532C2×C3×C4—91no—
533C2×C3×C4—91no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—182no—
539C2×C3×C4—182no—
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—31no—
555C2×Dic3—31no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—182no—
567C2×Dic3—182no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C4×D3—62no—
571C4×D3—62no—
572C4×D3—182no—
573C4×D3—182no—
574C4×D3—182no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—182no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—41no—
586C2×C32—41no—
587C2×C32—81no—
588C2×C32C2×#23511yescharacteristic
589C2×C32C2×#23711yescharacteristic
590C2×C32C2×#23711yescharacteristic
591C2×C32D3×#4111yescharacteristic
592C2×C32D3×#4111yescharacteristic
593C2×C32D3×#4111yescharacteristic
594C3⋊D3—41no—
595C3⋊D3#87914yescomplemented
596C3×D3—34no—
597C3×D3—121no—
598C24—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—271no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—271no—
605C4⋊C4—91no—
606C4⋊C4—91no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—271no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4—271no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—91no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
629C42—91no—
630C42—91no—
631C42—271no—
632C42—271no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—31no—
637C22×C3—31no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—92no—
646C22×C3—92no—
647C22×C3—92no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—364no—
655C22×C3C22×D3211yescharacteristic
656C2×D3—32no—
657C2×D3—32no—
658C2×D3—32no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—92no—
663C2×D3—92no—
664C2×D3—92no—
665C2×D3—124no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—364no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—181no—
679C3×C4—181no—
680C3×C4—181no—
681C3×C4—181no—
682C3×C4—181no—
683C3×C4—181no—
684C3×C4—181no—
685C3×C4—181no—
686C3×C4—181no—
687C3×C4—181no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—61no—
701Dic3—61no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—181no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—181no—
712C32—21no—
713C32C2×#87911yescharacteristic, complemented
714C32D3×#12611yescharacteristic, complemented
715C23—91no—
716C23—91no—
717C23—182no—
718C23—182no—
719C23—182no—
720C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—182no—
732C2×C4—182no—
733C2×C4—542no—
734C2×C4—542no—
735C2×C4—542no—
736C2×C4—542no—
737C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
738C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
739C2×C3—31no—
740C2×C3—31no—
741C2×C3—31no—
742C2×C3—31no—
743C2×C3—31no—
744C2×C3—31no—
745C2×C3—41no—
746C2×C3—61no—
747C2×C3—61no—
748C2×C3—61no—
749C2×C3—94no—
750C2×C3—121no—
751C2×C3—121no—
752C2×C3—241no—
753C2×C3—361no—
754C2×C3D3×#23511yescharacteristic
755C2×C3D3×#23711yescharacteristic
756C2×C3D3×#23711yescharacteristic
757D3—34no—
758D3—94no—
759D3—121no—
760D3—361no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—92no—
765C22—92no—
766C22—92no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22—364no—
771C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
772C4—21no—
773C4—21no—
774C4—181no—
775C4—181no—
776C4—181no—
777C4—181no—
778C4—181no—
779C4—181no—
780C4—181no—
781C4—181no—
782C4—181no—
783C4—181no—
784C3—31no—
785C3—31no—
786C3—61no—
787C3D3×#87911yescharacteristic
788C2—41no—
789C2—94no—
790C2—361no—
791C2#1172249011yescharacteristic
792C2#1172250411yescharacteristic
793C2#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×#126
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. #11721735C2semidirect
3. #64088⋊C3C2semidirect
6. #11721297C2semidirect
7. #11721297C2semidirect
8. #11721129C2semidirect
9. #11721119C2semidirect
10. #11721119C2semidirect
11. C4×((C3⋊D3)⋊C3)⋊C4C2semidirect
12. #11721112C2semidirect
13. #11721111C2semidirect
14. #11721109C2semidirect
15. #11721108C2semidirect
28. C4⋊#1084C22semidirect
29. #88540C22semidirect
30. #88540C22semidirect
31. C4×#1084C22semidirect
37. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
38. #3750⋊C3C22semidirect
39. #3750⋊C3C22semidirect
40. C4×(C3⋊Dic3)⋊C3C22semidirect
45. #88449C22semidirect
46. #88449C22semidirect
47. #88448C22semidirect
48. #88448C22semidirect
49. #88448C22semidirect
50. #88448C22semidirect
51. #88447C22semidirect
52. #88447C22semidirect
54. #64088D3semidirect
133. C4⋊(C3⋊Dic3)C2×D3semidirect
134. #3750C2×D3semidirect
135. #3750C2×D3semidirect
136. C4×C3⋊Dic3C2×D3semidirect
318. (C3⋊D3)⋊C3#126semidirect
502. H(3,𝔽3)C2×#126semidirect
595. C3⋊D3#879semidirect
713. C32C2×#879semidirect
714. C32D3×#126semidirect

Maximal subgroups

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

subgroupindex
#117217352
C22⋊C4×(C3⋊D3)⋊C32
#64088⋊C32
#117213102
#117212972
#117211292
#117211192
C4×((C3⋊D3)⋊C3)⋊C42
#117211122
#117211112
#117211092
#117211082
#105941543
D3×#8793