Finite Group Databasebeta

← #13150878

Subgroups — #13150878

Order 1728.

1247 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3828⋊C3C211yesmaximal, characteristic, complemented
2C2×#88676C211yesmaximal, characteristic, complemented
3#11721829C211yesmaximal, characteristic, complemented
4C2×#3752⋊C3C211yesmaximal, characteristic, complemented
5#11721322C211yesmaximal, characteristic, complemented
6#11721316C211yesmaximal, characteristic, complemented
7#11721314C211yesmaximal, characteristic, complemented
8#11721162C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721155C211yesmaximal, characteristic, complemented
11#11721140C211yesmaximal, characteristic, complemented
12#11721139C211yesmaximal, characteristic, complemented
13#11721128C211yesmaximal, characteristic, complemented
14#11721126C211yesmaximal, characteristic, complemented
15#11721122C211yesmaximal, characteristic, complemented
16#10595077—31nomaximal
17#10595068—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C2×#6235C2211yescharacteristic
22C2×#638⋊C3C2211yescharacteristic
23C2×#638⋊C3C2211yescharacteristic, complemented
24C22×(C3⋊Dic3)⋊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#88676—24no—
31C2×#6200C2211yescharacteristic
32C2×#6200C2211yescharacteristic, complemented
33C2×#6198C2211yescharacteristic
34C2×#6198C2211yescharacteristic
35C2×#6198C2211yescharacteristic, complemented
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
37C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
38#88552C2211yescharacteristic, complemented
39#88542C2211yescharacteristic, complemented
40#88542C2211yescharacteristic, complemented
41#88540C2211yescharacteristic, complemented
42#88540C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic
45#3752⋊C3C2211yescharacteristic, complemented
46#3752⋊C3C2211yescharacteristic, complemented
47#88451C2211yescharacteristic, complemented
48#88450C2211yescharacteristic
49#88450C2211yescharacteristic, complemented
50#88450C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88448C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88447C2211yescharacteristic, complemented
55C2×#3828D311yescharacteristic, complemented
56C2×C3×#235—31no—
57C2×#3811—31no—
58C2×D3×#67—31no—
59C2×#3752D311yescharacteristic, complemented
60C3×#929—31no—
61C3×#929—31no—
62C3×#929—61no—
63C2×C3×(C2×D3)⋊C4—31no—
64#63981—31no—
65#63980—31no—
66#63978—31no—
67#63977—31no—
68#67⋊Dic3—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#63904—31no—
80#63896—31no—
81#63888—31no—
82#63886—31no—
83#63881—31no—
84#63853—31no—
85#63850—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×(C3⋊D3)⋊C3—22no—
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—41no—
91C22×(C3⋊D3)⋊C3C2311yescharacteristic
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
101#6235—22no—
102C2×#1084C2311yescharacteristic
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105#638⋊C3—22no—
106#638⋊C3D414yescomplemented
107C2×(C3⋊Dic3)⋊C3—41no—
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—41no—
118#6198—22no—
119#6198—22no—
120#6198—41no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122((C3⋊D3)⋊C3)⋊C4—41no—
123#5829—91no—
124#5654—91no—
125#5490—91no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—31no—
128C22×D32—31no—
129C22×D32—31no—
130C22×C32×C4—21no—
131C22×C32×C4C2×D311yescharacteristic, complemented
132C22×C32×C4C2×D311yescharacteristic, complemented
133C2×#638C2×D311yescharacteristic
134C2×#638C2×D311yescharacteristic, complemented
135C22×C3⋊Dic3C2×D311yescharacteristic, complemented
136#3828—24no—
137C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
138C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
139C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
140C2×#634C2×D311yescharacteristic, complemented
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C22×C3×Dic3—31no—
147C3×#235—64no—
148C2×C3×D12—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—31no—
151C2×C3×Dic6—31no—
152#3811—64no—
153D3×#67—64no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#625—31no—
163C2×#625—31no—
164C2×#624—31no—
165C2×#624—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168#3752C2×D311yescharacteristic
169#3752C2×D311yescharacteristic
170#3752C2×D311yescharacteristic, complemented
171#3752C2×D311yescharacteristic, complemented
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—61no—
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—61no—
184C3×(C2×D3)⋊C4—61no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—61no—
190C3×Dic3⋊C4—61no—
191#3724—31no—
192#3724—31no—
193Dic3⋊Dic3—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196#3722—31no—
197#3722—31no—
198#3722—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×(C3⋊D3)⋊C3—21no—
215C2×(C3⋊D3)⋊C3—21no—
216C2×(C3⋊D3)⋊C3—21no—
217C2×(C3⋊D3)⋊C3—21no—
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—44no—
225C2×(C3⋊D3)⋊C3C2×D412yes—
226C2×(C3⋊D3)⋊C3#4112yescomplemented
227((C3⋊D3)⋊C3)⋊C2—44no—
228C4×H(3,𝔽3)—21no—
229C4×H(3,𝔽3)—21no—
230#1084—21no—
231#1084—21no—
232#1084—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—31no—
258#929—61no—
259#929—91no—
260C4×#67—91no—
261C4×#67—91no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—91no—
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⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—41no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—31no—
294C22×C3×D3—31no—
295C22×C3×D3—31no—
296C22×C3×D3—31no—
297C22×C3×D3—31no—
298C22×C3×D3—31no—
299C22×C3×D3—61no—
300C22×C3×D3—62no—
301C22×C3×D3—62no—
302C22×C3×D3—121no—
303C2×D32—62no—
304C2×D32—62no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—121no—
308C2×D32—121no—
309C2×C32×C4—22no—
310C2×C32×C4—22no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—42no—
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318#638—22no—
319#638#6714yescomplemented
320C2×C3⋊Dic3—41no—
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C4⋊(C3⋊D3)—22no—
326C4×C3⋊D3—22no—
327C4×C3⋊D3—22no—
328#634—22no—
329C3×#67—34no—
330C3×#67—62no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—122no—
334C2×C3×Dic3—31no—
335C2×C3×Dic3—31no—
336C2×C3×Dic3—31no—
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—61no—
345C2×C3×Dic3—61no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—121no—
348C3×D12—62no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×Dic6—62no—
352#626—62no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—121no—
358#626—121no—
359#626—121no—
360#625—62no—
361#625—121no—
362#624—62no—
363#624—121no—
364D3×Dic3—62no—
365D3×Dic3—121no—
366#546—271noSylow
367C2×H(3,𝔽3)—22no—
368C2×H(3,𝔽3)C22×D411yescharacteristic
369C2×H(3,𝔽3)C2×#4111yescharacteristic
370C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
371#272—41no—
372(C3⋊D3)⋊C3—22no—
373(C3⋊D3)⋊C3—22no—
374(C3⋊D3)⋊C3—41no—
375(C3⋊D3)⋊C3—41no—
376C24×C3—91no—
377C23×D3—31no—
378C23×D3—91no—
379C23×D3—91no—
380C23×D3—91no—
381C23×D3—91no—
382C3×#41—184no—
383C2×C3×Q8—91no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—61no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C22×C3×C4—91no—
394C22×C3×C4D3211yescharacteristic
395C2×#67—31no—
396C2×#67—31no—
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—61no—
400C2×#67—91no—
401C2×#67—91no—
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—184no—
413C22×Dic3—31no—
414C22×Dic3—91no—
415C22×Dic3—91no—
416C22×Dic3—91no—
417D3×D4—184no—
418D3×D4—184no—
419#235—64no—
420#235—184no—
421C2×D12—31no—
422C2×D12—91no—
423C2×D12—91no—
424C2×D12—91no—
425C2×D12—91no—
426C2×D12—91no—
427C2×D12—91no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×Dic6—31no—
437C2×Dic6—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C22⋊C4—91no—
441C3×C22⋊C4—91no—
442C3×C22⋊C4—91no—
443C3×C22⋊C4—91no—
444C3×C22⋊C4—91no—
445C3×C22⋊C4—91no—
446C3×C22⋊C4—91no—
447#217—31no—
448#217—31no—
449#217—61no—
450#217—91no—
451#217—91no—
452#217—91no—
453#217—91no—
454#217—91no—
455(C2×D3)⋊C4—31no—
456(C2×D3)⋊C4—31no—
457(C2×D3)⋊C4—31no—
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—61no—
464(C2×D3)⋊C4—61no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
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—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481Dic3⋊C4—31no—
482Dic3⋊C4—31no—
483Dic3⋊C4—31no—
484Dic3⋊C4—31no—
485Dic3⋊C4—61no—
486Dic3⋊C4—61no—
487Dic3⋊C4—91no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491C4×Dic3—91no—
492C4×Dic3—91no—
493C4×Dic3—91no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—22no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32D3×D412yes—
503C22×C32C2×#6712yes—
504C22×C32C23×D311yescharacteristic
505C22×C32C23×D311yescharacteristic
506C2×C3⋊D3—21no—
507C2×C3⋊D3—21no—
508C2×C3⋊D3—21no—
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—44no—
517C2×C3⋊D3#23512yescomplemented
518C2×C3⋊D3C2×#6712yes—
519C2×C3×D3—32no—
520C2×C3×D3—32no—
521C2×C3×D3—61no—
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—61no—
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—121no—
538C2×C3×D3—121no—
539C2×C3×D3—121no—
540C2×C3×D3—124no—
541D32—124no—
542D32—124no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4—41no—
548C32×C4—41no—
549C3⋊Dic3—21no—
550C3⋊Dic3—21no—
551C3⋊Dic3—21no—
552C3⋊Dic3C2×#6712yes—
553C3×Dic3—32no—
554C3×Dic3—61no—
555C3×Dic3—61no—
556C3×Dic3—61no—
557C3×Dic3—61no—
558C3×Dic3—61no—
559C3×Dic3—61no—
560C3×Dic3—61no—
561C3×Dic3—61no—
562C3×Dic3—61no—
563C3×Dic3—121no—
564C3×Dic3—121no—
565C3×Dic3—121no—
566C2×#41—91no—
567C22×D4—271no—
568#124—271no—
569#123—91no—
570#123—271no—
571C22⋊Q8—271no—
572#121—271no—
573#121—271no—
574#121—271no—
575#120—271no—
576#120—271no—
577C4×D4—271no—
578C4×D4—271no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—271no—
581H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—61no—
585C23×C3—91no—
586C23×C3—91no—
587C23×C3—91no—
588C23×C3—91no—
589C23×C3—91no—
590C23×C3—182no—
591C23×C3—182no—
592C23×C3—361no—
593C23×C3C2×D3211yescharacteristic
594C22×D3—31no—
595C22×D3—31no—
596C22×D3—31no—
597C22×D3—31no—
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—61no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—91no—
604C22×D3—91no—
605C22×D3—91no—
606C22×D3—91no—
607C22×D3—121no—
608C22×D3—182no—
609C22×D3—182no—
610C22×D3—182no—
611C22×D3—182no—
612C22×D3—182no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—361no—
617C22×D3—361no—
618C22×D3—361no—
619C22×D3—361no—
620C3×Q8—182no—
621C3×D4—94no—
622C3×D4—182no—
623C3×D4—182no—
624C3×D4—182no—
625C2×C3×C4—22no—
626C2×C3×C4—31no—
627C2×C3×C4—31no—
628C2×C3×C4—31no—
629C2×C3×C4—31no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—91no—
635C2×C3×C4—91no—
636C2×C3×C4—91no—
637C2×C3×C4—91no—
638C2×C3×C4—91no—
639C2×C3×C4—91no—
640C2×C3×C4—91no—
641C2×C3×C4—122no—
642C2×C3×C4—182no—
643C2×C3×C4—182no—
644C2×C3×C4—361no—
645C2×C3×C4C2×D3211yescharacteristic
646C2×C3×C4C2×D3211yescharacteristic
647#67—34no—
648#67—62no—
649#67—62no—
650#67—62no—
651#67—94no—
652#67—122no—
653#67—182no—
654#67—182no—
655#67—182no—
656#67—182no—
657#67—182no—
658#67—182no—
659#67—182no—
660#67—361no—
661#67—361no—
662#67—361no—
663#67—361no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—91no—
678C2×Dic3—91no—
679C2×Dic3—91no—
680C2×Dic3—91no—
681C2×Dic3—121no—
682C2×Dic3—182no—
683C2×Dic3—361no—
684C2×Dic3—361no—
685D12—62no—
686D12—182no—
687D12—182no—
688D12—182no—
689D12—182no—
690D12—361no—
691D12—361no—
692C4×D3—62no—
693C4×D3—62no—
694C4×D3—182no—
695C4×D3—182no—
696C4×D3—182no—
697C4×D3—182no—
698C4×D3—361no—
699C4×D3—361no—
700Dic6—62no—
701Dic6—182no—
702C2×C32—22no—
703C2×C32—22no—
704C2×C32—21no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—42no—
708C2×C32C2×#23511yescharacteristic
709C2×C32C2×D3×D411yescharacteristic
710C2×C32#100411yescharacteristic
711C2×C32D3×#4111yescharacteristic
712C2×C32#100911yescharacteristic
713C2×C32C22×#6711yescharacteristic
714C3⋊D3—22no—
715C3⋊D3—22no—
716C3⋊D3—41no—
717C3⋊D3—41no—
718C3×D3—62no—
719C3×D3—62no—
720C3×D3—121no—
721C3×D3—121no—
722C3×D3—121no—
723C3×D3—121no—
724C3×D3—241no—
725C24—91no—
726C24—271no—
727#41—184no—
728C2×Q8—91no—
729C2×D4—91no—
730C2×D4—91no—
731C2×D4—91no—
732C2×D4—91no—
733C2×D4—271no—
734C2×D4—271no—
735C2×D4—271no—
736C2×D4—271no—
737C2×D4—271no—
738C2×D4—544no—
739C22×C4—91no—
740C22×C4—91no—
741C22×C4—91no—
742C22×C4—271no—
743C22×C4—271no—
744C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4—271no—
748C4⋊C4—271no—
749C22⋊C4—91no—
750C22⋊C4—91no—
751C22⋊C4—91no—
752C22⋊C4—91no—
753C22⋊C4—91no—
754C22⋊C4—91no—
755C22⋊C4—91no—
756C22⋊C4—271no—
757C22⋊C4—271no—
758C22⋊C4—271no—
759C22⋊C4—271no—
760C22⋊C4—271no—
761C42—271no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—31no—
765C22×C3—31no—
766C22×C3—32no—
767C22×C3—32no—
768C22×C3—61no—
769C22×C3—61no—
770C22×C3—61no—
771C22×C3—61no—
772C22×C3—61no—
773C22×C3—62no—
774C22×C3—92no—
775C22×C3—92no—
776C22×C3—121no—
777C22×C3—121no—
778C22×C3—181no—
779C22×C3—181no—
780C22×C3—181no—
781C22×C3—181no—
782C22×C3—181no—
783C22×C3—181no—
784C22×C3—181no—
785C22×C3—181no—
786C22×C3—181no—
787C22×C3—181no—
788C22×C3—181no—
789C22×C3—181no—
790C22×C3—181no—
791C22×C3—364no—
792C22×C3D3×#6712yes—
793C22×C3C22×D3211yescharacteristic
794C2×D3—32no—
795C2×D3—32no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—61no—
799C2×D3—61no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—61no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—92no—
813C2×D3—92no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—124no—
818C2×D3—181no—
819C2×D3—181no—
820C2×D3—181no—
821C2×D3—181no—
822C2×D3—181no—
823C2×D3—181no—
824C2×D3—181no—
825C2×D3—181no—
826C2×D3—181no—
827C2×D3—181no—
828C2×D3—364no—
829C2×D3—364no—
830C2×D3—364no—
831C2×D3—364no—
832C3×C4—21no—
833C3×C4—21no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—61no—
838C3×C4—92no—
839C3×C4—121no—
840C3×C4—121no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845C3×C4—181no—
846C3×C4—181no—
847Dic3—32no—
848Dic3—61no—
849Dic3—61no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—92no—
858Dic3—121no—
859Dic3—121no—
860Dic3—121no—
861Dic3—181no—
862Dic3—181no—
863Dic3—181no—
864C32—21no—
865C32#549011yescharacteristic, complemented
866C32#582911yescharacteristic, complemented
867C23—91no—
868C23—91no—
869C23—91no—
870C23—91no—
871C23—91no—
872C23—182no—
873C23—182no—
874C23—361no—
875C23—542no—
876C23—542no—
877C23—1081no—
878C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
879Q8—182no—
880D4—94no—
881D4—182no—
882D4—182no—
883D4—182no—
884D4—542no—
885D4—542no—
886D4—542no—
887D4—1081no—
888D4—1081no—
889C2×C4—22no—
890C2×C4—91no—
891C2×C4—91no—
892C2×C4—91no—
893C2×C4—91no—
894C2×C4—91no—
895C2×C4—91no—
896C2×C4—91no—
897C2×C4—182no—
898C2×C4—182no—
899C2×C4—361no—
900C2×C4—542no—
901C2×C4—1081no—
902C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
903C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
904C2×C3—22no—
905C2×C3—31no—
906C2×C3—31no—
907C2×C3—31no—
908C2×C3—31no—
909C2×C3—31no—
910C2×C3—31no—
911C2×C3—62no—
912C2×C3—62no—
913C2×C3—61no—
914C2×C3—61no—
915C2×C3—61no—
916C2×C3—122no—
917C2×C3—182no—
918C2×C3—182no—
919C2×C3—361no—
920C2×C3—361no—
921C2×C3—361no—
922C2×C3D3×#23511yescharacteristic
923C2×C3#6430711yescharacteristic
924C2×C3C2×D3×#6711yescharacteristic
925D3—62no—
926D3—62no—
927D3—121no—
928D3—121no—
929D3—121no—
930D3—121no—
931D3—182no—
932D3—182no—
933D3—241no—
934D3—361no—
935D3—361no—
936C22—21no—
937C22—21no—
938C22—92no—
939C22—92no—
940C22—181no—
941C22—181no—
942C22—181no—
943C22—181no—
944C22—181no—
945C22—181no—
946C22—181no—
947C22—181no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—364no—
954C22—1084no—
955C22#8867612yes—
956C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
957C4—21no—
958C4—21no—
959C4—92no—
960C4—181no—
961C4—181no—
962C4—181no—
963C4—181no—
964C4—181no—
965C4—181no—
966C3—31no—
967C3—31no—
968C3—61no—
969C3#1059506511yescharacteristic
970C2—22no—
971C2—182no—
972C2—182no—
973C2—361no—
974C2—361no—
975C2—361no—
976C2#1172249011yescharacteristic
977C2#1172249211yescharacteristic
978C2C2×#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×#88676C2semidirect
3. #11721829C2semidirect
4. C2×#3752⋊C3C2semidirect
5. #11721322C2semidirect
6. #11721316C2semidirect
7. #11721314C2semidirect
8. #11721162C2semidirect
9. #11721160C2semidirect
10. #11721155C2semidirect
11. #11721140C2semidirect
12. #11721139C2semidirect
13. #11721128C2semidirect
14. #11721126C2semidirect
15. #11721122C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
23. C2×#638⋊C3C22semidirect
24. C22×(C3⋊Dic3)⋊C3C22semidirect
26. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
28. C2×C4×(C3⋊D3)⋊C3C22semidirect
29. C2×#634⋊C3C22semidirect
32. C2×#6200C22semidirect
35. C2×#6198C22semidirect
37. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
38. #88552C22semidirect
39. #88542C22semidirect
40. #88542C22semidirect
41. #88540C22semidirect
42. #88540C22semidirect
45. #3752⋊C3C22semidirect
46. #3752⋊C3C22semidirect
47. #88451C22semidirect
49. #88450C22semidirect
50. #88450C22semidirect
51. #88450C22semidirect
52. #88448C22semidirect
53. #88448C22semidirect
54. #88447C22semidirect
55. C2×#3828D3semidirect
59. C2×#3752D3semidirect
106. #638⋊C3D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
134. C2×#638C2×D3semidirect
135. C22×C3⋊Dic3C2×D3semidirect
137. C2×C4⋊(C3⋊D3)C2×D3semidirect
138. C2×C4×C3⋊D3C2×D3semidirect
139. C2×C4×C3⋊D3C2×D3semidirect
140. C2×#634C2×D3semidirect
170. #3752C2×D3semidirect
171. #3752C2×D3semidirect
226. C2×(C3⋊D3)⋊C3#41semidirect
319. #638#67semidirect
517. C2×C3⋊D3#235semidirect
581. H(3,𝔽3)#546semidirect
744. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
865. C32#5490semidirect
866. 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×#886762
#117218292
C2×#3752⋊C32
#117213222
#117213162
#117213142
#117211622
#117211602
#117211552
#117211402
#117211392
#117211282
#117211262
#117211222
#105950773
#105950683