Finite Group Databasebeta

← #13148718

Subgroups — #13148718

Order 1728.

1299 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88677C211yesmaximal, characteristic, complemented
2C2×#88671C211yesmaximal, characteristic, complemented
3#11721738C211yesmaximal, characteristic, complemented
4#64095⋊C3C211yesmaximal, characteristic, complemented
5#64090⋊C3C211yesmaximal, characteristic, complemented
6#11721322C211yesmaximal, characteristic, complemented
7C2×#88451C211yesmaximal, characteristic, complemented
8#11721163C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721157C211yesmaximal, characteristic, complemented
11#11721156C211yesmaximal, characteristic, complemented
12#11721150C211yesmaximal, characteristic, complemented
13#11721149C211yesmaximal, characteristic, complemented
14#11721130C211yesmaximal, characteristic, complemented
15#11721103C211yesmaximal, characteristic, complemented
16#10594294—31nomaximal
17#10594292—31nomaximal
18C23×#272C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C2×#6235C2211yescharacteristic, complemented
21C2×C4⋊#272C2211yescharacteristic
22C2×C4⋊#272C2211yescharacteristic, complemented
23C2×#638⋊C3C2211yescharacteristic
24C2×#638⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
26C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
27C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
28#88677—24no—
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic, complemented
32C2×#6200C2211yescharacteristic, complemented
33C2×#6199C2211yescharacteristic
34C2×#6199C2211yescharacteristic, complemented
35#88671—24no—
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38C22⋊C4×H(3,𝔽3)C2211yescharacteristic, complemented
39#88542C2211yescharacteristic
40#88542C2211yescharacteristic, complemented
41#3752⋊C3C2211yescharacteristic, complemented
42#3752⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
45C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
46#3750⋊C3C2211yescharacteristic, complemented
47C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
48#88451C2211yescharacteristic
49#88451C2211yescharacteristic
50#88451C2211yescharacteristic, complemented
51#88451C2211yescharacteristic, complemented
52#88451C2211yescharacteristic, complemented
53#88450C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×#67—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59#64095D311yescharacteristic, complemented
60#64090D311yescharacteristic, complemented
61C3×#886—31no—
62C3×#882—31no—
63C3×#882—31no—
64C3×#882—61no—
65C3×#67⋊C4—31no—
66#63980—31no—
67#63978—31no—
68C2×(C2×D3)⋊Dic3—31no—
69C2×(C2×D3)⋊Dic3—31no—
70#63922—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63916—31no—
75#63915—31no—
76#63908—31no—
77#63899—31no—
78#63898—31no—
79#63893—31no—
80Dic3×D12—31no—
81#63891—31no—
82#63886—31no—
83#63885—31no—
84#63854—31no—
85#63852—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272—22no—
88C22×#272—22no—
89C22×#272—41no—
90C22×#272C2311yescharacteristic
91C22×#272C2311yescharacteristic
92C22×#272C2311yescharacteristic
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)C2311yescharacteristic
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100#6235—22no—
101C2×#1084C2311yescharacteristic
102C4⋊#272—22no—
103C4⋊#272—41no—
104#638⋊C3—22no—
105#638⋊C3D414yescomplemented
106C2×(C3⋊Dic3)⋊C3—22no—
107C2×(C3⋊Dic3)⋊C3—41no—
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
114C4×(C3⋊D3)⋊C3—41no—
115#6200—22no—
116#6200—22no—
117#6200—22no—
118#6200—41no—
119#6199—22no—
120#6199—22no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122#6196—22no—
123#5654—91no—
124#5591—91no—
125#5554—91no—
126C23×C3×D3—31no—
127C23×C3×D3—31no—
128C23×C3×D3—61no—
129C22×D32—31no—
130C22×D32—31no—
131C2×#638C2×D311yescharacteristic
132C2×#638C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic, complemented
134C22×C3⋊Dic3C2×D311yescharacteristic, complemented
135C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—31no—
147C2×C3×D12—61no—
148C2×C3×D12—61no—
149C2×C3×C4×D3—31no—
150D3×#67—64no—
151D3×#67—64no—
152C2×#627—31no—
153C2×#627—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—31no—
161C2×#625—31no—
162C2×#624—31no—
163#3805—64no—
164#3804—64no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C32×C22⋊C4—21no—
171C32×C22⋊C4C2×D311yescharacteristic, complemented
172C32×C22⋊C4C2×D311yescharacteristic, complemented
173#3752C2×D311yescharacteristic, complemented
174#3752C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic, complemented
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
177C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
178#3750C2×D311yescharacteristic, complemented
179C4×C3⋊Dic3C2×D311yescharacteristic, complemented
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—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—61no—
188C3×(C2×D3)⋊C4—61no—
189C3×C4⋊Dic3—31no—
190C3×C4⋊Dic3—31no—
191C3×Dic3⋊C4—31no—
192C3×C4×Dic3—31no—
193#3724—31no—
194Dic3⋊Dic3—31no—
195#3722—31no—
196(C2×D3)⋊Dic3—31no—
197(C2×D3)⋊Dic3—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—
205(C2×D3)⋊Dic3—31no—
206(C2×D3)⋊Dic3—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—21no—
217C2×#272—21no—
218C2×#272—21no—
219C2×#272—44no—
220C2×#272#4112yescomplemented
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(C3⋊Dic3)⋊C3—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—
237C22×#67—91no—
238C2×#237—91no—
239C2×#237—91no—
240C2×D3×D4—91no—
241C2×D3×D4—91no—
242C2×#235—91no—
243C3×#123—91no—
244C3×#120—91no—
245C3×C4×D4—91no—
246C2×#217—91no—
247#939—91no—
248#939—91no—
249#939—91no—
250#938—91no—
251#937—91no—
252D4×Dic3—91no—
253#930—91no—
254#930—91no—
255C2×(C2×D3)⋊C4—91no—
256C2×(C2×D3)⋊C4—91no—
257C2×(C2×D3)⋊C4—91no—
258#897—91no—
259#896—91no—
260#895—91no—
261#895—91no—
262#894—91no—
263#893—91no—
264#886—31no—
265#886—91no—
266#886—91no—
267#885—91no—
268#885—91no—
269#884—91no—
270#883—91no—
271#882—31no—
272#882—31no—
273#882—61no—
274#882—91no—
275#882—91no—
276#67⋊C4—31no—
277#67⋊C4—91no—
278D3×C22⋊C4—91no—
279D3×C22⋊C4—91no—
280#878—91no—
281#875—91no—
282C4×D12—91no—
283C23×C32—21no—
284C23×C32C22×D311yescharacteristic
285C23×C32C22×D311yescharacteristic
286C22×C3⋊D3C22×D311yescharacteristic
287C22×C3⋊D3C22×D311yescharacteristic
288C22×C3×D3—31no—
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—61no—
299C22×C3×D3—62no—
300C22×C3×D3—62no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—122no—
304C22×C3×D3—122no—
305C22×C3×D3—121no—
306C22×C3×D3—121no—
307C22×C3×D3—122no—
308C2×D32—62no—
309C2×D32—62no—
310C2×D32—62no—
311C2×D32—62no—
312C2×D32—121no—
313C2×D32—121no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319C2×C32×C4C22×D311yescharacteristic
320#638—22no—
321#638D1214yescomplemented
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3—41no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4×C3⋊D3—41no—
331C3×#67—34no—
332C3×#67—62no—
333C3×#67—62no—
334C3×#67—62no—
335C3×#67—122no—
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—62no—
346C2×C3×Dic3—121no—
347C3×D12—62no—
348C3×D12—62no—
349C3×D12—122no—
350C3×D12—121no—
351C3×D12—121no—
352C3×D12—122no—
353C3×C4×D3—121no—
354#627—62no—
355#627—62no—
356#626—62no—
357#626—62no—
358#626—62no—
359#626—121no—
360#625—62no—
361#625—62no—
362#625—62no—
363#625—121no—
364#624—62no—
365D3×Dic3—62no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—62no—
369D3×Dic3—62no—
370#546—271noSylow
371C2×H(3,𝔽3)—22no—
372C2×H(3,𝔽3)C22×D411yescharacteristic
373C2×H(3,𝔽3)C2×#4111yescharacteristic
374C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
375#272—22no—
376#272—41no—
377#272—41no—
378(C3⋊D3)⋊C3—22no—
379(C3⋊D3)⋊C3—41no—
380C24×C3—91no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—61no—
384C23×D3—91no—
385C23×D3—91no—
386C23×D3—91no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C2×C3×D4—91no—
391C2×C3×D4—91no—
392C22×C3×C4—91no—
393C22×C3×C4—91no—
394C22×C3×C4—91no—
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—184no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—91no—
414C22×Dic3—91no—
415C22×Dic3—91no—
416C22×Dic3—91no—
417C22×Dic3—91no—
418#237—184no—
419#237—184no—
420D3×D4—184no—
421D3×D4—184no—
422#235—184no—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—31no—
426C2×D12—31no—
427C2×D12—61no—
428C2×D12—61no—
429C2×D12—91no—
430C2×D12—91no—
431C2×D12—91no—
432C2×D12—91no—
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×C4×D3—91no—
441C2×Dic6—91no—
442C2×Dic6—91no—
443C2×Dic6—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C22⋊C4—31no—
448C3×C22⋊C4—31no—
449C3×C22⋊C4—61no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C22⋊C4D3211yescharacteristic
456C3×C42—91no—
457#217—91no—
458#217—91no—
459#217—91no—
460#217—91no—
461#217—91no—
462#217—91no—
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—31no—
469(C2×D3)⋊C4—31no—
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—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492Dic3⋊C4—31no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496C4×Dic3—31no—
497C4×Dic3—91no—
498C22×C32—21no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—21no—
502C22×C32—21no—
503C22×C32—22no—
504C22×C32—41no—
505C22×C32—41no—
506C22×C32C2×D1212yes—
507C22×C32D3×D412yes—
508C22×C32C23×D311yescharacteristic
509C22×C32C23×D311yescharacteristic
510C2×C3⋊D3—21no—
511C2×C3⋊D3—21no—
512C2×C3⋊D3—21no—
513C2×C3⋊D3—21no—
514C2×C3⋊D3—21no—
515C2×C3⋊D3C2×D1212yes—
516C2×C3×D3—32no—
517C2×C3×D3—32no—
518C2×C3×D3—32no—
519C2×C3×D3—62no—
520C2×C3×D3—61no—
521C2×C3×D3—61no—
522C2×C3×D3—61no—
523C2×C3×D3—61no—
524C2×C3×D3—61no—
525C2×C3×D3—61no—
526C2×C3×D3—62no—
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—61no—
538C2×C3×D3—61no—
539C2×C3×D3—61no—
540C2×C3×D3—61no—
541C2×C3×D3—61no—
542C2×C3×D3—121no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C2×C3×D3—121no—
546C2×C3×D3—121no—
547C2×C3×D3—121no—
548C2×C3×D3—121no—
549C2×C3×D3—124no—
550C2×C3×D3—124no—
551C2×C3×D3—128no—
552D32—124no—
553D32—124no—
554C32×C4—21no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—41no—
559C32×C4—41no—
560C3⋊Dic3—21no—
561C3⋊Dic3—21no—
562C3⋊Dic3—21no—
563C3⋊Dic3—21no—
564C3⋊Dic3—21no—
565C3⋊Dic3C2×D1212yes—
566C3×Dic3—32no—
567C3×Dic3—61no—
568C3×Dic3—61no—
569C3×Dic3—61no—
570C3×Dic3—61no—
571C3×Dic3—61no—
572C3×Dic3—61no—
573C3×Dic3—61no—
574C3×Dic3—121no—
575C2×#41—271no—
576C22×D4—271no—
577#124—271no—
578#123—91no—
579#123—271no—
580C22⋊Q8—271no—
581#121—271no—
582#121—271no—
583#121—271no—
584#120—91no—
585#120—271no—
586C4×D4—91no—
587C4×D4—271no—
588C2×C22⋊C4—271no—
589C2×C22⋊C4—271no—
590H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
591C23×C3—31no—
592C23×C3—31no—
593C23×C3—61no—
594C23×C3—91no—
595C23×C3—91no—
596C23×C3—91no—
597C23×C3—91no—
598C23×C3—91no—
599C23×C3—182no—
600C23×C3—182no—
601C23×C3—361no—
602C23×C3C2×D3211yescharacteristic
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—31no—
607C22×D3—31no—
608C22×D3—31no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—61no—
612C22×D3—61no—
613C22×D3—61no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—91no—
619C22×D3—91no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—122no—
625C22×D3—182no—
626C22×D3—182no—
627C22×D3—182no—
628C22×D3—182no—
629C22×D3—182no—
630C22×D3—182no—
631C22×D3—361no—
632C22×D3—361no—
633C22×D3—361no—
634C3×D4—94no—
635C3×D4—182no—
636C3×D4—182no—
637C3×D4—182no—
638C3×D4—361no—
639C2×C3×C4—31no—
640C2×C3×C4—31no—
641C2×C3×C4—31no—
642C2×C3×C4—31no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
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—91no—
652C2×C3×C4—182no—
653C2×C3×C4—361no—
654C2×C3×C4—361no—
655C2×C3×C4C2×D3211yescharacteristic
656C2×C3×C4C2×D3211yescharacteristic
657#67—34no—
658#67—62no—
659#67—62no—
660#67—62no—
661#67—94no—
662#67—122no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—182no—
667#67—182no—
668#67—182no—
669#67—182no—
670#67—361no—
671#67—361no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—61no—
681C2×Dic3—62no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—121no—
689C2×Dic3—182no—
690C2×Dic3—182no—
691C2×Dic3—182no—
692C2×Dic3—182no—
693C2×Dic3—361no—
694D12—62no—
695D12—62no—
696D12—122no—
697D12—121no—
698D12—121no—
699D12—122no—
700D12—182no—
701D12—182no—
702D12—182no—
703D12—361no—
704C4×D3—121no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—182no—
708C4×D3—182no—
709C4×D3—182no—
710C4×D3—182no—
711C4×D3—361no—
712Dic6—182no—
713Dic6—182no—
714Dic6—182no—
715C2×C32—22no—
716C2×C32—22no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—42no—
721C2×C32C22×D1211yescharacteristic
722C2×C32C2×D3×D411yescharacteristic
723C2×C32#100411yescharacteristic
724C2×C32D3×#4111yescharacteristic
725C2×C32D3×#4111yescharacteristic
726C2×C32#100911yescharacteristic
727C3⋊D3—22no—
728C3⋊D3—41no—
729C3×D3—62no—
730C3×D3—62no—
731C3×D3—62no—
732C3×D3—122no—
733C3×D3—122no—
734C3×D3—121no—
735C3×D3—121no—
736C3×D3—121no—
737C3×D3—121no—
738C3×D3—121no—
739C3×D3—241no—
740C24—91no—
741C24—271no—
742#41—544no—
743C2×Q8—271no—
744C2×D4—91no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—91no—
748C2×D4—91no—
749C2×D4—271no—
750C2×D4—271no—
751C2×D4—271no—
752C2×D4—271no—
753C2×D4—544no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—271no—
758C22×C4—271no—
759C22×C4—271no—
760C4⋊C4—91no—
761C4⋊C4—91no—
762C4⋊C4—91no—
763C4⋊C4—271no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—91no—
768C22⋊C4—91no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C22⋊C4—271no—
772C22⋊C4—271no—
773C22⋊C4—271no—
774C22⋊C4—271no—
775C22⋊C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
776C42—91no—
777C22×C3—21no—
778C22×C3—21no—
779C22×C3—31no—
780C22×C3—31no—
781C22×C3—32no—
782C22×C3—32no—
783C22×C3—61no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—62no—
789C22×C3—92no—
790C22×C3—92no—
791C22×C3—121no—
792C22×C3—121no—
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—181no—
802C22×C3—181no—
803C22×C3—181no—
804C22×C3—181no—
805C22×C3—181no—
806C22×C3—364no—
807C22×C3D3×D1212yes—
808C22×C3C22×D3211yescharacteristic
809C2×D3—32no—
810C2×D3—32no—
811C2×D3—32no—
812C2×D3—62no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—61no—
816C2×D3—61no—
817C2×D3—61no—
818C2×D3—61no—
819C2×D3—61no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—61no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—61no—
828C2×D3—61no—
829C2×D3—61no—
830C2×D3—61no—
831C2×D3—62no—
832C2×D3—61no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—92no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—124no—
844C2×D3—124no—
845C2×D3—128no—
846C2×D3—181no—
847C2×D3—181no—
848C2×D3—181no—
849C2×D3—181no—
850C2×D3—181no—
851C2×D3—364no—
852C2×D3—364no—
853C2×D3—364no—
854C3×C4—21no—
855C3×C4—21no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—61no—
860C3×C4—92no—
861C3×C4—121no—
862C3×C4—121no—
863C3×C4—181no—
864C3×C4—181no—
865C3×C4—181no—
866C3×C4—181no—
867C3×C4—181no—
868C3×C4—181no—
869Dic3—32no—
870Dic3—61no—
871Dic3—61no—
872Dic3—61no—
873Dic3—61no—
874Dic3—61no—
875Dic3—61no—
876Dic3—61no—
877Dic3—92no—
878Dic3—121no—
879Dic3—181no—
880Dic3—181no—
881Dic3—181no—
882Dic3—181no—
883Dic3—181no—
884C32—21no—
885C32#555411yescharacteristic, complemented
886C32#565411yescharacteristic, complemented
887C23—91no—
888C23—91no—
889C23—91no—
890C23—91no—
891C23—91no—
892C23—182no—
893C23—182no—
894C23—361no—
895C23—542no—
896C23—542no—
897C23—1081no—
898C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
899Q8—542no—
900D4—94no—
901D4—182no—
902D4—182no—
903D4—182no—
904D4—361no—
905D4—542no—
906D4—542no—
907D4—542no—
908D4—1081no—
909C2×C4—91no—
910C2×C4—91no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—182no—
917C2×C4—361no—
918C2×C4—361no—
919C2×C4—542no—
920C2×C4—542no—
921C2×C4—542no—
922C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
923C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
924C2×C3—22no—
925C2×C3—31no—
926C2×C3—31no—
927C2×C3—31no—
928C2×C3—31no—
929C2×C3—31no—
930C2×C3—31no—
931C2×C3—62no—
932C2×C3—62no—
933C2×C3—61no—
934C2×C3—61no—
935C2×C3—61no—
936C2×C3—122no—
937C2×C3—182no—
938C2×C3—182no—
939C2×C3—361no—
940C2×C3—361no—
941C2×C3—361no—
942C2×C3C2×D3×D1211yescharacteristic
943C2×C3#6431211yescharacteristic
944C2×C3#6431411yescharacteristic
945D3—62no—
946D3—62no—
947D3—62no—
948D3—122no—
949D3—121no—
950D3—121no—
951D3—121no—
952D3—121no—
953D3—122no—
954D3—121no—
955D3—182no—
956D3—241no—
957D3—361no—
958C22—21no—
959C22—21no—
960C22—92no—
961C22—92no—
962C22—181no—
963C22—181no—
964C22—181no—
965C22—181no—
966C22—181no—
967C22—181no—
968C22—181no—
969C22—181no—
970C22—181no—
971C22—181no—
972C22—181no—
973C22—181no—
974C22—181no—
975C22—364no—
976C22—1084no—
977C22#8865412yes—
978C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
979C4—21no—
980C4—21no—
981C4—92no—
982C4—181no—
983C4—181no—
984C4—181no—
985C4—181no—
986C4—181no—
987C4—181no—
988C3—31no—
989C3—31no—
990C3—61no—
991C3#1059429311yescharacteristic
992C2—22no—
993C2—182no—
994C2—182no—
995C2—361no—
996C2—361no—
997C2—361no—
998C2C2×#8865411yescharacteristic
999C2#1172250511yescharacteristic
1000C2#1172250711yescharacteristic
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×#88677C2semidirect
2. C2×#88671C2semidirect
3. #11721738C2semidirect
4. #64095⋊C3C2semidirect
5. #64090⋊C3C2semidirect
6. #11721322C2semidirect
7. C2×#88451C2semidirect
8. #11721163C2semidirect
9. #11721160C2semidirect
10. #11721157C2semidirect
11. #11721156C2semidirect
12. #11721150C2semidirect
13. #11721149C2semidirect
14. #11721130C2semidirect
15. #11721103C2semidirect
20. C2×#6235C22semidirect
22. C2×C4⋊#272C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
26. C22×(C3⋊Dic3)⋊C3C22semidirect
27. C2×C4×(C3⋊D3)⋊C3C22semidirect
31. C2×#6200C22semidirect
32. C2×#6200C22semidirect
34. C2×#6199C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
38. C22⋊C4×H(3,𝔽3)C22semidirect
40. #88542C22semidirect
41. #3752⋊C3C22semidirect
42. #3752⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
45. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
46. #3750⋊C3C22semidirect
47. C4×(C3⋊Dic3)⋊C3C22semidirect
50. #88451C22semidirect
51. #88451C22semidirect
52. #88451C22semidirect
53. #88450C22semidirect
54. #88448C22semidirect
59. #64095D3semidirect
60. #64090D3semidirect
105. #638⋊C3D4semidirect
133. C22×C3⋊Dic3C2×D3semidirect
134. C22×C3⋊Dic3C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
171. C32×C22⋊C4C2×D3semidirect
172. C32×C22⋊C4C2×D3semidirect
173. #3752C2×D3semidirect
174. #3752C2×D3semidirect
175. #3752C2×D3semidirect
176. C4⋊(C3⋊Dic3)C2×D3semidirect
177. C4⋊(C3⋊Dic3)C2×D3semidirect
178. #3750C2×D3semidirect
179. C4×C3⋊Dic3C2×D3semidirect
220. C2×#272#41semidirect
321. #638D12semidirect
590. H(3,𝔽3)#546semidirect
775. C22⋊C4((C3⋊D3)⋊C3)⋊C2semidirect
885. C32#5554semidirect
886. C32#5654semidirect

Maximal subgroups

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

subgroupindex
C2×#886772
C2×#886712
#117217382
#64095⋊C32
#64090⋊C32
#117213222
C2×#884512
#117211632
#117211602
#117211572
#117211562
#117211502
#117211492
#117211302
#117211032
#105942943
#105942923