Finite Group Databasebeta

← #13150881

Subgroups — #13150881

Order 1728.

1301 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3828⋊C3C211yesmaximal, characteristic, complemented
2C2×#88677C211yesmaximal, characteristic, complemented
3C2×#88542C211yesmaximal, characteristic, complemented
4#64138⋊C3C211yesmaximal, characteristic, complemented
5#11721323C211yesmaximal, characteristic, complemented
6#11721318C211yesmaximal, characteristic, complemented
7#11721315C211yesmaximal, characteristic, complemented
8#11721162C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721155C211yesmaximal, characteristic, complemented
11#11721154C211yesmaximal, characteristic, complemented
12#11721148C211yesmaximal, characteristic, complemented
13#11721140C211yesmaximal, characteristic, complemented
14#11721127C211yesmaximal, characteristic, complemented
15#11721100C211yesmaximal, characteristic, complemented
16#10595077—31nomaximal
17#10595065—31nomaximal
18C23×#272C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C22×#1084C2211yescharacteristic, complemented
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic, complemented
25#3828⋊C3—24no—
26C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
29C2×#634⋊C3C2211yescharacteristic, complemented
30#88677—24no—
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic
33C2×#6200C2211yescharacteristic
34C2×#6200C2211yescharacteristic, complemented
35C2×#6199C2211yescharacteristic
36C2×#6198C2211yescharacteristic, complemented
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
38#88542C2211yescharacteristic
39#88542C2211yescharacteristic
40#88542C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45#3750⋊C3C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47#88451C2211yescharacteristic
48#88451C2211yescharacteristic, complemented
49#88450C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88449C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C2×#3828D311yescharacteristic, complemented
56C2×C3×#235—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59#64138D311yescharacteristic, complemented
60C3×#929—31no—
61C2×C3×(C2×D3)⋊C4—31no—
62C2×C3×(C2×D3)⋊C4—31no—
63C2×C3×(C2×D3)⋊C4—61no—
64#63978—31no—
65#63978—31no—
66#63977—31no—
67#63976—31no—
68Dic3×#67—31no—
69#63952—31no—
70#63923—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63913—31no—
75#63912—31no—
76#63910—31no—
77#63907—31no—
78#63906—31no—
79#63905—31no—
80#63896—31no—
81#63887—31no—
82#63885—31no—
83#63881—31no—
84#63879—31no—
85#63853—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272—22no—
88C22×#272—22no—
89C22×#272—41no—
90C22×#272C2311yescharacteristic
91C22×#272C2311yescharacteristic
92C22×(C3⋊D3)⋊C3C2311yescharacteristic
93C22×(C3⋊D3)⋊C3C2311yescharacteristic
94C22×(C3⋊D3)⋊C3C2311yescharacteristic
95C2×((C3⋊D3)⋊C3)⋊C2—22no—
96C2×((C3⋊D3)⋊C3)⋊C2—22no—
97C2×((C3⋊D3)⋊C3)⋊C2—41no—
98C2×C4×H(3,𝔽3)—22no—
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101C2×#1084—41no—
102C2×#1084C2311yescharacteristic
103C2×#1084C2311yescharacteristic
104#638⋊C3—22no—
105#638⋊C3—22no—
106#638⋊C3D414yescomplemented
107C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C4⋊((C3⋊D3)⋊C3)—22no—
113C4×(C3⋊D3)⋊C3—22no—
114C4×(C3⋊D3)⋊C3—22no—
115#634⋊C3—22no—
116#6200—22no—
117#6200—22no—
118#6200—22no—
119#6200—41no—
120#6199—22no—
121#6198—41no—
122((C3⋊D3)⋊C3)⋊C4—41no—
123#5829—91no—
124#5654—91no—
125#5490—91no—
126C23×C3×D3—31no—
127C23×C3×D3—31no—
128C23×C3×D3—61no—
129C22×D32—31no—
130C22×D32—31no—
131C22×C32×C4—21no—
132C22×C32×C4C2×D311yescharacteristic, complemented
133C22×C32×C4C2×D311yescharacteristic, complemented
134C2×#638C2×D311yescharacteristic
135C2×#638C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic, complemented
137#3828—24no—
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
139C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
140C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
141C2×#634C2×D311yescharacteristic, complemented
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—61no—
148C3×#235—64no—
149C2×C3×D12—31no—
150C2×C3×C4×D3—31no—
151C2×C3×C4×D3—31no—
152C2×C3×Dic6—31no—
153D3×#67—64no—
154D3×#67—64no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#625—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#625—31no—
165C2×#624—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169#3757C2×D311yescharacteristic, complemented
170#3752C2×D311yescharacteristic, complemented
171#3752C2×D311yescharacteristic, complemented
172#3750C2×D311yescharacteristic, complemented
173#3750C2×D311yescharacteristic, complemented
174C3×#217—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—31no—
178C3×(C2×D3)⋊C4—31no—
179C3×(C2×D3)⋊C4—31no—
180C3×(C2×D3)⋊C4—31no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—61no—
186C3×(C2×D3)⋊C4—61no—
187C3×(C2×D3)⋊C4—61no—
188C3×(C2×D3)⋊C4—61no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191#3724—31no—
192Dic3⋊Dic3—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196#3722—31no—
197#3722—31no—
198(C2×D3)⋊Dic3—31no—
199(C2×D3)⋊Dic3—31no—
200(C2×D3)⋊Dic3—31no—
201(C2×D3)⋊Dic3—31no—
202(C2×D3)⋊Dic3—31no—
203(C2×D3)⋊Dic3—31no—
204(C2×D3)⋊Dic3—31no—
205Dic32—31no—
206Dic32—31no—
207C22×H(3,𝔽3)—21no—
208C22×H(3,𝔽3)—21no—
209C22×H(3,𝔽3)C2×D412yes—
210C22×H(3,𝔽3)C2411yescharacteristic
211C2×#272—21no—
212C2×#272—21no—
213C2×#272—21no—
214C2×#272—21no—
215C2×#272—21no—
216C2×#272—44no—
217C2×#272#4112yescomplemented
218C2×(C3⋊D3)⋊C3—21no—
219C2×(C3⋊D3)⋊C3—21no—
220C2×(C3⋊D3)⋊C3—21no—
221C2×(C3⋊D3)⋊C3—21no—
222C2×(C3⋊D3)⋊C3—21no—
223C2×(C3⋊D3)⋊C3—21no—
224C2×(C3⋊D3)⋊C3—21no—
225C2×(C3⋊D3)⋊C3—21no—
226C2×(C3⋊D3)⋊C3C2×D412yes—
227((C3⋊D3)⋊C3)⋊C2—44no—
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230#1084—21no—
231#1084—21no—
232(C3⋊Dic3)⋊C3—21no—
233(C3⋊Dic3)⋊C3—21no—
234(C3⋊Dic3)⋊C3—21no—
235(C3⋊Dic3)⋊C3—21no—
236(C3⋊Dic3)⋊C3C2×D412yes—
237C2×C3×#41—91no—
238C22×#67—91no—
239C2×D3×D4—91no—
240C2×D3×D4—91no—
241C2×#235—31no—
242C2×#235—91no—
243C3×#123—91no—
244C2×C3×C22⋊C4—91no—
245#953—91no—
246#947—91no—
247#946—91no—
248#939—91no—
249#939—91no—
250#939—91no—
251#937—91no—
252#937—91no—
253D4×Dic3—91no—
254#930—91no—
255#930—91no—
256#929—31no—
257#929—91no—
258#929—91no—
259C4×#67—91no—
260C4×#67—91no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—61no—
264C2×(C2×D3)⋊C4—91no—
265#896—91no—
266#895—91no—
267#894—91no—
268#893—91no—
269#885—91no—
270#885—91no—
271#884—91no—
272#884—91no—
273#884—91no—
274#883—91no—
275#882—91no—
276#882—91no—
277#882—91no—
278#67⋊C4—91no—
279#67⋊C4—91no—
280D3×C22⋊C4—91no—
281D3×C22⋊C4—91no—
282#878—91no—
283C23×C32—21no—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3C22×D311yescharacteristic
287C22×C3⋊D3C22×D311yescharacteristic
288C22×C3⋊D3C22×D311yescharacteristic
289C22×C3×D3—31no—
290C22×C3×D3—31no—
291C22×C3×D3—31no—
292C22×C3×D3—31no—
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—61no—
297C22×C3×D3—61no—
298C22×C3×D3—62no—
299C22×C3×D3—62no—
300C22×C3×D3—64no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—122no—
304C22×C3×D3—121no—
305C22×C3×D3—121no—
306C22×C3×D3—122no—
307C2×D32—62no—
308C2×D32—62no—
309C2×D32—62no—
310C2×D32—62no—
311C2×D32—121no—
312C2×D32—121no—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4—21no—
316C2×C32×C4—21no—
317C2×C32×C4—42no—
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320C2×C32×C4C22×D311yescharacteristic
321C2×C32×C4C22×D311yescharacteristic
322#638—22no—
323#638—22no—
324#638#6714yescomplemented
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—22no—
331C4×C3⋊D3—22no—
332C4×C3⋊D3—22no—
333#634—22no—
334C3×#67—34no—
335C3×#67—62no—
336C3×#67—62no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—31no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—31no—
341C2×C3×Dic3—31no—
342C2×C3×Dic3—31no—
343C2×C3×Dic3—31no—
344C2×C3×Dic3—31no—
345C2×C3×Dic3—31no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—61no—
348C2×C3×Dic3—121no—
349C2×C3×Dic3—121no—
350C2×C3×Dic3—122no—
351C3×D12—62no—
352C3×C4×D3—62no—
353C3×C4×D3—62no—
354C3×Dic6—62no—
355#626—62no—
356#626—62no—
357#626—62no—
358#626—121no—
359#626—121no—
360#626—121no—
361#625—62no—
362#625—62no—
363#625—62no—
364#625—121no—
365#624—121no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—121no—
369#546—271noSylow
370C2×H(3,𝔽3)—22no—
371C2×H(3,𝔽3)C22×D411yescharacteristic
372C2×H(3,𝔽3)C2×#4111yescharacteristic
373C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
374#272—22no—
375#272—41no—
376(C3⋊D3)⋊C3—22no—
377(C3⋊D3)⋊C3—41no—
378(C3⋊D3)⋊C3—41no—
379C24×C3—91no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—61no—
383C23×D3—91no—
384C23×D3—91no—
385C23×D3—91no—
386C3×#41—184no—
387C2×C3×Q8—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C2×C3×D4—91no—
391C2×C3×D4—91no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C22×C3×C4—61no—
395C22×C3×C4—91no—
396C22×C3×C4—91no—
397C22×C3×C4—91no—
398C22×C3×C4D3211yescharacteristic
399C2×#67—31no—
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—91no—
405C2×#67—91no—
406C2×#67—91no—
407C2×#67—91no—
408C2×#67—91no—
409C2×#67—91no—
410C2×#67—91no—
411C2×#67—91no—
412C2×#67—91no—
413C2×#67—91no—
414C2×#67—91no—
415C2×#67—184no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—61no—
419C22×Dic3—91no—
420C22×Dic3—91no—
421D3×D4—184no—
422D3×D4—184no—
423#235—64no—
424#235—184no—
425C2×D12—31no—
426C2×D12—91no—
427C2×D12—91no—
428C2×D12—91no—
429C2×D12—91no—
430C2×D12—91no—
431C2×D12—91no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×C4×D3—91no—
440C2×Dic6—31no—
441C2×Dic6—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C22⋊C4—91no—
445C3×C22⋊C4—91no—
446C3×C22⋊C4—91no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451#217—31no—
452#217—91no—
453#217—91no—
454#217—91no—
455#217—91no—
456#217—91no—
457#217—91no—
458(C2×D3)⋊C4—31no—
459(C2×D3)⋊C4—31no—
460(C2×D3)⋊C4—31no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—31no—
468(C2×D3)⋊C4—61no—
469(C2×D3)⋊C4—61no—
470(C2×D3)⋊C4—61no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486Dic3⋊C4—31no—
487Dic3⋊C4—31no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494C4×Dic3—91no—
495C4×Dic3—91no—
496C4×Dic3—91no—
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—21no—
504C22×C32—22no—
505C22×C32D3×D412yes—
506C22×C32C2×#6712yes—
507C22×C32C23×D311yescharacteristic
508C22×C32C23×D311yescharacteristic
509C2×C3⋊D3—21no—
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3—21no—
516C2×C3⋊D3—21no—
517C2×C3⋊D3C2×#6712yes—
518C2×C3×D3—32no—
519C2×C3×D3—32no—
520C2×C3×D3—32no—
521C2×C3×D3—62no—
522C2×C3×D3—61no—
523C2×C3×D3—61no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—61no—
527C2×C3×D3—61no—
528C2×C3×D3—62no—
529C2×C3×D3—61no—
530C2×C3×D3—61no—
531C2×C3×D3—61no—
532C2×C3×D3—61no—
533C2×C3×D3—61no—
534C2×C3×D3—61no—
535C2×C3×D3—61no—
536C2×C3×D3—61no—
537C2×C3×D3—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—121no—
542C2×C3×D3—121no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C2×C3×D3—124no—
546C2×C3×D3—124no—
547C2×C3×D3—128no—
548D32—124no—
549D32—124no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—41no—
555C32×C4—41no—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3—21no—
559C3⋊Dic3—21no—
560C3⋊Dic3C2×#6712yes—
561C3×Dic3—32no—
562C3×Dic3—61no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—61no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—121no—
571C3×Dic3—121no—
572C2×#41—91no—
573C22×D4—271no—
574#124—271no—
575#123—91no—
576#123—271no—
577C22⋊Q8—271no—
578#121—271no—
579#121—271no—
580#121—271no—
581#120—271no—
582#120—271no—
583C4×D4—271no—
584C4×D4—271no—
585C2×C22⋊C4—91no—
586C2×C22⋊C4—271no—
587H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—61no—
591C23×C3—91no—
592C23×C3—91no—
593C23×C3—91no—
594C23×C3—91no—
595C23×C3—91no—
596C23×C3—182no—
597C23×C3—182no—
598C23×C3—361no—
599C23×C3C2×D3211yescharacteristic
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—64no—
614C22×D3—91no—
615C22×D3—91no—
616C22×D3—91no—
617C22×D3—122no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—122no—
621C22×D3—182no—
622C22×D3—182no—
623C22×D3—182no—
624C22×D3—182no—
625C22×D3—182no—
626C22×D3—182no—
627C22×D3—361no—
628C22×D3—361no—
629C22×D3—361no—
630C3×Q8—182no—
631C3×D4—94no—
632C3×D4—182no—
633C3×D4—182no—
634C3×D4—182no—
635C2×C3×C4—22no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—91no—
649C2×C3×C4—91no—
650C2×C3×C4—91no—
651C2×C3×C4—122no—
652C2×C3×C4—182no—
653C2×C3×C4—182no—
654C2×C3×C4—361no—
655C2×C3×C4C2×D3211yescharacteristic
656C2×C3×C4C2×D3211yescharacteristic
657#67—34no—
658#67—62no—
659#67—62no—
660#67—94no—
661#67—182no—
662#67—182no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—361no—
670#67—361no—
671#67—361no—
672#67—361no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—61no—
683C2×Dic3—61no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—91no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—122no—
692C2×Dic3—182no—
693C2×Dic3—361no—
694D12—62no—
695D12—182no—
696D12—182no—
697D12—182no—
698D12—182no—
699D12—361no—
700D12—361no—
701C4×D3—62no—
702C4×D3—62no—
703C4×D3—182no—
704C4×D3—182no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—361no—
708C4×D3—361no—
709Dic6—62no—
710Dic6—182no—
711C2×C32—24no—
712C2×C32—22no—
713C2×C32—22no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32C2×D3×D411yescharacteristic
718C2×C32D3×#4111yescharacteristic
719C2×C32D3×#4111yescharacteristic
720C2×C32#100911yescharacteristic
721C2×C32#100911yescharacteristic
722C2×C32C22×#6711yescharacteristic
723C3⋊D3—22no—
724C3⋊D3—41no—
725C3⋊D3—41no—
726C3×D3—62no—
727C3×D3—62no—
728C3×D3—62no—
729C3×D3—122no—
730C3×D3—122no—
731C3×D3—121no—
732C3×D3—121no—
733C3×D3—121no—
734C3×D3—121no—
735C24—91no—
736C24—271no—
737#41—184no—
738C2×Q8—91no—
739C2×D4—91no—
740C2×D4—91no—
741C2×D4—91no—
742C2×D4—91no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—271no—
746C2×D4—271no—
747C2×D4—271no—
748C2×D4—544no—
749C22×C4—91no—
750C22×C4—91no—
751C22×C4—91no—
752C22×C4—271no—
753C22×C4—271no—
754C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
755C4⋊C4—91no—
756C4⋊C4—91no—
757C4⋊C4—271no—
758C4⋊C4—271no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C22⋊C4—91no—
763C22⋊C4—91no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C42—271no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—31no—
775C22×C3—31no—
776C22×C3—32no—
777C22×C3—32no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—61no—
781C22×C3—61no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—61no—
785C22×C3—62no—
786C22×C3—92no—
787C22×C3—92no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—181no—
792C22×C3—181no—
793C22×C3—181no—
794C22×C3—181no—
795C22×C3—181no—
796C22×C3—181no—
797C22×C3—181no—
798C22×C3—181no—
799C22×C3—181no—
800C22×C3—181no—
801C22×C3—364no—
802C22×C3D3×#6712yes—
803C22×C3C22×D3211yescharacteristic
804C2×D3—32no—
805C2×D3—32no—
806C2×D3—32no—
807C2×D3—62no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—62no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—92no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—121no—
831C2×D3—121no—
832C2×D3—124no—
833C2×D3—124no—
834C2×D3—128no—
835C2×D3—181no—
836C2×D3—181no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—364no—
844C2×D3—364no—
845C2×D3—364no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—92no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4—181no—
856C3×C4—181no—
857C3×C4—181no—
858C3×C4—181no—
859C3×C4—181no—
860C3×C4—181no—
861Dic3—32no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—61no—
867Dic3—61no—
868Dic3—61no—
869Dic3—61no—
870Dic3—92no—
871Dic3—121no—
872Dic3—121no—
873Dic3—181no—
874Dic3—181no—
875Dic3—181no—
876Dic3—181no—
877C32—21no—
878C32#565411yescharacteristic, complemented
879C32#582911yescharacteristic, complemented
880C23—91no—
881C23—91no—
882C23—91no—
883C23—91no—
884C23—91no—
885C23—182no—
886C23—182no—
887C23—361no—
888C23—542no—
889C23—542no—
890C23—1081no—
891C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
892Q8—182no—
893D4—94no—
894D4—182no—
895D4—182no—
896D4—182no—
897D4—542no—
898D4—542no—
899D4—542no—
900D4—1081no—
901D4—1081no—
902C2×C4—22no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—91no—
909C2×C4—91no—
910C2×C4—182no—
911C2×C4—182no—
912C2×C4—361no—
913C2×C4—542no—
914C2×C4—1081no—
915C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
916C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
917C2×C3—22no—
918C2×C3—31no—
919C2×C3—31no—
920C2×C3—31no—
921C2×C3—31no—
922C2×C3—31no—
923C2×C3—31no—
924C2×C3—62no—
925C2×C3—62no—
926C2×C3—64no—
927C2×C3—61no—
928C2×C3—61no—
929C2×C3—61no—
930C2×C3—182no—
931C2×C3—182no—
932C2×C3—361no—
933C2×C3—361no—
934C2×C3—361no—
935C2×C3#6430611yescharacteristic
936C2×C3#6430811yescharacteristic
937C2×C3C2×D3×#6711yescharacteristic
938D3—62no—
939D3—62no—
940D3—62no—
941D3—122no—
942D3—121no—
943D3—121no—
944D3—122no—
945D3—121no—
946D3—121no—
947D3—182no—
948D3—361no—
949D3—361no—
950C22—21no—
951C22—21no—
952C22—92no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—364no—
968C22—1084no—
969C22#8867612yes—
970C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
971C4—21no—
972C4—21no—
973C4—92no—
974C4—181no—
975C4—181no—
976C4—181no—
977C4—181no—
978C4—181no—
979C4—181no—
980C3—31no—
981C3—31no—
982C3—61no—
983C3#1059506811yescharacteristic
984C2—22no—
985C2—182no—
986C2—182no—
987C2—361no—
988C2—361no—
989C2—361no—
990C2#1172249111yescharacteristic
991C2#1172249311yescharacteristic
992C2C2×#8867611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)#546
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. C2×#3828⋊C3C2semidirect
2. C2×#88677C2semidirect
3. C2×#88542C2semidirect
4. #64138⋊C3C2semidirect
5. #11721323C2semidirect
6. #11721318C2semidirect
7. #11721315C2semidirect
8. #11721162C2semidirect
9. #11721160C2semidirect
10. #11721155C2semidirect
11. #11721154C2semidirect
12. #11721148C2semidirect
13. #11721140C2semidirect
14. #11721127C2semidirect
15. #11721100C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
21. C22×#1084C22semidirect
24. C2×#638⋊C3C22semidirect
26. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×#634⋊C3C22semidirect
34. C2×#6200C22semidirect
36. C2×#6198C22semidirect
37. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
40. #88542C22semidirect
41. #88542C22semidirect
42. #3757⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3750⋊C3C22semidirect
46. #3750⋊C3C22semidirect
48. #88451C22semidirect
49. #88450C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88449C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
55. C2×#3828D3semidirect
59. #64138D3semidirect
106. #638⋊C3D4semidirect
132. C22×C32×C4C2×D3semidirect
133. C22×C32×C4C2×D3semidirect
136. C2×#638C2×D3semidirect
138. C2×C4⋊(C3⋊D3)C2×D3semidirect
139. C2×C4×C3⋊D3C2×D3semidirect
140. C2×C4×C3⋊D3C2×D3semidirect
141. C2×#634C2×D3semidirect
169. #3757C2×D3semidirect
170. #3752C2×D3semidirect
171. #3752C2×D3semidirect
172. #3750C2×D3semidirect
173. #3750C2×D3semidirect
217. C2×#272#41semidirect
324. #638#67semidirect
587. H(3,𝔽3)#546semidirect
754. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
878. C32#5654semidirect
879. C32#5829semidirect

Maximal subgroups

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

subgroupindex
C2×#3828⋊C32
C2×#886772
C2×#885422
#64138⋊C32
#117213232
#117213182
#117213152
#117211622
#117211602
#117211552
#117211542
#117211482
#117211402
#117211272
#117211002
#105950773
#105950653