Finite Group Databasebeta

← #13150886

Subgroups — #13150886

Order 1728.

1263 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88676C211yesmaximal, characteristic, complemented
2C2×#88671C211yesmaximal, characteristic, complemented
3#11721830C211yesmaximal, characteristic, complemented
4C4×#638⋊C3C211yesmaximal, characteristic, complemented
5C2×#3752⋊C3C211yesmaximal, characteristic, complemented
6#11721321C211yesmaximal, characteristic, complemented
7#11721301C211yesmaximal, characteristic, complemented
8#11721163C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721157C211yesmaximal, characteristic, complemented
11#11721140C211yesmaximal, characteristic, complemented
12#11721133C211yesmaximal, characteristic, complemented
13#11721131C211yesmaximal, characteristic, complemented
14#11721123C211yesmaximal, characteristic, complemented
15#11721103C211yesmaximal, characteristic, complemented
16#10595083—31nomaximal
17#10595075—31nomaximal
18C23×(C3⋊D3)⋊C3C2211yescharacteristic
19C22×((C3⋊D3)⋊C3)⋊C2C2211yescharacteristic
20C22×C4×H(3,𝔽3)C2211yescharacteristic, complemented
21C2×#6235C2211yescharacteristic
22C2×#6235C2211yescharacteristic, complemented
23C2×C4⋊#272C2211yescharacteristic, complemented
24C2×#638⋊C3C2211yescharacteristic
25C22×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27#88676—24no—
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic, complemented
31C2×#6200C2211yescharacteristic, complemented
32C2×#6199C2211yescharacteristic, complemented
33C2×#6198C2211yescharacteristic
34#88671—24no—
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38#88542C2211yescharacteristic, complemented
39#88542C2211yescharacteristic, complemented
40C4⋊#1084C2211yescharacteristic, complemented
41#3757⋊C3C2211yescharacteristic, complemented
42#3752⋊C3C2211yescharacteristic
43#3752⋊C3C2211yescharacteristic
44#3752⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46#3752⋊C3C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
49#88451C2211yescharacteristic, complemented
50#88451C2211yescharacteristic, complemented
51#88450C2211yescharacteristic
52#88450C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×#3811—31no—
56C2×D3×#67—31no—
57C2×#3805—31no—
58C2×#3804—31no—
59C4×#638D311yescharacteristic, complemented
60C2×#3752D311yescharacteristic, complemented
61C3×#930—31no—
62C3×#930—31no—
63C3×#930—61no—
64C3×C4×#67—31no—
65C2×C3×(C2×D3)⋊C4—31no—
66#63981—31no—
67#63976—31no—
68#63962—31no—
69#63961—31no—
70#63922—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63915—31no—
75#63912—31no—
76#63906—31no—
77#63902—31no—
78#63899—31no—
79#63895—31no—
80#63890—31no—
81#63886—31no—
82#63885—31no—
83#63880—31no—
84#63854—31no—
85#63852—31no—
86C23×H(3,𝔽3)C2311yescharacteristic
87C22×#272C2311yescharacteristic
88C22×#272C2311yescharacteristic
89C22×(C3⋊D3)⋊C3—22no—
90C22×(C3⋊D3)⋊C3—22no—
91C22×(C3⋊D3)⋊C3—41no—
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)—41no—
99C2×C4×H(3,𝔽3)C2311yescharacteristic
100C2×C4×H(3,𝔽3)C2311yescharacteristic
101#6235—22no—
102#6235—22no—
103C2×#1084C2311yescharacteristic
104C2×#1084C2311yescharacteristic
105C4⋊#272—41no—
106#638⋊C3D414yescomplemented
107C2×(C3⋊Dic3)⋊C3—22no—
108C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
109C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
110C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
111C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
112C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
113C4×(C3⋊D3)⋊C3—41no—
114#6200—22no—
115#6200—22no—
116#6200—22no—
117#6200—41no—
118#6199—22no—
119#6198—22no—
120((C3⋊D3)⋊C3)⋊C4—22no—
121((C3⋊D3)⋊C3)⋊C4—22no—
122#6196—22no—
123#5610—91no—
124#5554—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
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—31no—
141C2×C3×#67—61no—
142C2×C3×#67—61no—
143C22×C3×Dic3—31no—
144C2×C3×D12—31no—
145C2×C3×D12—31no—
146C2×C3×D12—61no—
147C2×C3×C4×D3—31no—
148#3811—64no—
149D3×#67—64no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#626—31no—
153C2×#626—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—
163C2×#624—31no—
164#3805—64no—
165#3804—64no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170#3757C2×D311yescharacteristic, complemented
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173#3752C2×D311yescharacteristic, complemented
174#3752C2×D311yescharacteristic, complemented
175#3752C2×D311yescharacteristic, complemented
176#3750C2×D311yescharacteristic, complemented
177C4×C3⋊Dic3C2×D311yescharacteristic, complemented
178C3×#217—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—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—61no—
189C3×(C2×D3)⋊C4—61no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—61no—
193C3×Dic3⋊C4—31no—
194C3×C4×Dic3—31no—
195#3724—31no—
196#3724—31no—
197Dic3⋊Dic3—31no—
198Dic3⋊Dic3—31no—
199#3722—31no—
200#3722—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×(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(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×#121—91no—
244C3×C4×D4—91no—
245C2×C3×C22⋊C4—91no—
246#953—91no—
247#939—91no—
248#937—91no—
249#937—91no—
250#935—91no—
251#930—31no—
252#930—31no—
253#930—61no—
254#930—91no—
255#929—91no—
256C4×#67—31no—
257C4×#67—91no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—91no—
260C2×(C2×D3)⋊C4—91no—
261#897—91no—
262#896—91no—
263#895—91no—
264#894—91no—
265#886—91no—
266#886—91no—
267#885—91no—
268#885—91no—
269#884—91no—
270#884—91no—
271#884—91no—
272#883—91no—
273#882—91no—
274#882—91no—
275#882—91no—
276#67⋊C4—91no—
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⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—41no—
289C22×C3⋊D3C22×D311yescharacteristic
290C22×C3⋊D3C22×D311yescharacteristic
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3×D3—31no—
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—61no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—121no—
304C2×D32—62no—
305C2×D32—62no—
306C2×D32—62no—
307C2×D32—62no—
308C2×D32—121no—
309C2×D32—121no—
310C2×C32×C4—21no—
311C2×C32×C4—21no—
312C2×C32×C4—41no—
313C2×C32×C4—41no—
314C2×C32×C4—42no—
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C22×D311yescharacteristic
317C2×C32×C4C22×D311yescharacteristic
318C2×C32×C4C22×D311yescharacteristic
319#638D1214yescomplemented
320C2×C3⋊Dic3—22no—
321C2×C3⋊Dic3C22×D311yescharacteristic
322C2×C3⋊Dic3C22×D311yescharacteristic
323C2×C3⋊Dic3C22×D311yescharacteristic
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C4×C3⋊D3—41no—
327C3×#67—34no—
328C3×#67—62no—
329C3×#67—62no—
330C3×#67—62no—
331C3×#67—62no—
332C3×#67—122no—
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—61no—
344C2×C3×Dic3—61no—
345C2×C3×Dic3—62no—
346C3×D12—121no—
347C3×D12—121no—
348C3×D12—122no—
349C3×C4×D3—121no—
350#627—62no—
351#627—62no—
352#626—62no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—121no—
358#625—62no—
359#625—62no—
360#625—62no—
361#625—121no—
362#624—62no—
363#624—62no—
364D3×Dic3—62no—
365D3×Dic3—62no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368#546—271noSylow
369C2×H(3,𝔽3)—22no—
370C2×H(3,𝔽3)C22×D411yescharacteristic
371C2×H(3,𝔽3)C2×#4111yescharacteristic
372C2×H(3,𝔽3)H(5,𝔽2)11yescharacteristic
373#272—41no—
374#272—41no—
375(C3⋊D3)⋊C3—22no—
376(C3⋊D3)⋊C3—22no—
377(C3⋊D3)⋊C3—41no—
378C24×C3—91no—
379C23×D3—31no—
380C23×D3—91no—
381C23×D3—91no—
382C23×D3—91no—
383C23×D3—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×C4D3211yescharacteristic
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—31no—
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—61no—
400C2×#67—61no—
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—
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—61no—
426C2×D12—91no—
427C2×D12—91no—
428C2×D12—91no—
429C2×D12—91no—
430C2×D12—91no—
431C2×C4×D3—31no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—91no—
436C2×C4×D3—91no—
437C2×C4×D3—91no—
438C2×C4×D3—91no—
439C2×Dic6—91no—
440C2×Dic6—91no—
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—
451C3×C22⋊C4—91no—
452C3×C42—91no—
453#217—31no—
454#217—91no—
455#217—91no—
456#217—91no—
457#217—91no—
458#217—91no—
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—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—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483C4⋊Dic3—31no—
484C4⋊Dic3—31no—
485C4⋊Dic3—61no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488Dic3⋊C4—31no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494C4×Dic3—31no—
495C4×Dic3—91no—
496C22×C32—21no—
497C22×C32—21no—
498C22×C32—21no—
499C22×C32—21no—
500C22×C32—21no—
501C22×C32—22no—
502C22×C32—41no—
503C22×C32—41no—
504C22×C32C2×D1212yes—
505C22×C32D3×D412yes—
506C22×C32C23×D311yescharacteristic
507C22×C32C23×D311yescharacteristic
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—44no—
516C2×C3⋊D3C2×D1212yes—
517C2×C3⋊D3#23512yescomplemented
518C2×C3×D3—32no—
519C2×C3×D3—32no—
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—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—61no—
538C2×C3×D3—61no—
539C2×C3×D3—121no—
540C2×C3×D3—121no—
541C2×C3×D3—121no—
542C2×C3×D3—121no—
543C2×C3×D3—121no—
544C2×C3×D3—121no—
545C2×C3×D3—124no—
546D32—124no—
547D32—124no—
548C32×C4—22no—
549C32×C4—21no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—41no—
554C3⋊Dic3—21no—
555C3⋊Dic3—21no—
556C3⋊Dic3—21no—
557C3⋊Dic3—21no—
558C3⋊Dic3C2×D1212yes—
559C3×Dic3—32no—
560C3×Dic3—61no—
561C3×Dic3—61no—
562C3×Dic3—61no—
563C3×Dic3—61no—
564C3×Dic3—61no—
565C3×Dic3—61no—
566C3×Dic3—61no—
567C3×Dic3—61no—
568C3×Dic3—121no—
569C3×Dic3—121no—
570C2×#41—271no—
571C22×D4—271no—
572#124—271no—
573#123—271no—
574#123—271no—
575C22⋊Q8—271no—
576#121—91no—
577#121—271no—
578#121—271no—
579#120—271no—
580#120—271no—
581C4×D4—91no—
582C4×D4—271no—
583C2×C22⋊C4—91no—
584C2×C22⋊C4—271no—
585H(3,𝔽3)#54611yescharacteristic, complemented, Sylow
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—91no—
590C23×C3—91no—
591C23×C3—91no—
592C23×C3—91no—
593C23×C3—91no—
594C23×C3—182no—
595C23×C3—182no—
596C23×C3—361no—
597C23×C3C2×D3211yescharacteristic
598C22×D3—31no—
599C22×D3—31no—
600C22×D3—31no—
601C22×D3—31no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—61no—
606C22×D3—61no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—91no—
610C22×D3—91no—
611C22×D3—91no—
612C22×D3—121no—
613C22×D3—182no—
614C22×D3—182no—
615C22×D3—182no—
616C22×D3—182no—
617C22×D3—182no—
618C22×D3—182no—
619C22×D3—182no—
620C22×D3—182no—
621C22×D3—361no—
622C22×D3—361no—
623C22×D3—361no—
624C22×D3—361no—
625C3×D4—94no—
626C3×D4—182no—
627C3×D4—182no—
628C3×D4—361no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—31no—
632C2×C3×C4—31no—
633C2×C3×C4—41no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—91no—
637C2×C3×C4—91no—
638C2×C3×C4—91no—
639C2×C3×C4—91no—
640C2×C3×C4—91no—
641C2×C3×C4—91no—
642C2×C3×C4—91no—
643C2×C3×C4—121no—
644C2×C3×C4—121no—
645C2×C3×C4—122no—
646C2×C3×C4—182no—
647C2×C3×C4—361no—
648C2×C3×C4C2×D3211yescharacteristic
649C2×C3×C4C2×D3211yescharacteristic
650#67—34no—
651#67—62no—
652#67—62no—
653#67—62no—
654#67—62no—
655#67—94no—
656#67—122no—
657#67—122no—
658#67—182no—
659#67—182no—
660#67—182no—
661#67—182no—
662#67—182no—
663#67—182no—
664#67—182no—
665#67—182no—
666#67—361no—
667#67—361no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—62no—
680C2×Dic3—91no—
681C2×Dic3—91no—
682C2×Dic3—91no—
683C2×Dic3—91no—
684C2×Dic3—91no—
685C2×Dic3—182no—
686C2×Dic3—182no—
687C2×Dic3—182no—
688C2×Dic3—182no—
689D12—121no—
690D12—121no—
691D12—122no—
692D12—182no—
693D12—182no—
694D12—182no—
695D12—182no—
696D12—361no—
697C4×D3—121no—
698C4×D3—182no—
699C4×D3—182no—
700C4×D3—182no—
701C4×D3—182no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—361no—
705Dic6—182no—
706Dic6—182no—
707Dic6—182no—
708C2×C32—22no—
709C2×C32—22no—
710C2×C32—21no—
711C2×C32—21no—
712C2×C32—21no—
713C2×C32—42no—
714C2×C32C22×D1211yescharacteristic
715C2×C32C2×#23511yescharacteristic
716C2×C32C2×D3×D411yescharacteristic
717C2×C32#100411yescharacteristic
718C2×C32#100411yescharacteristic
719C2×C32D3×#4111yescharacteristic
720C3⋊D3—22no—
721C3⋊D3—22no—
722C3⋊D3—41no—
723C3×D3—62no—
724C3×D3—62no—
725C3×D3—121no—
726C3×D3—121no—
727C3×D3—121no—
728C3×D3—121no—
729C3×D3—121no—
730C3×D3—241no—
731C3×D3—241no—
732C24—91no—
733C24—271no—
734#41—544no—
735C2×Q8—271no—
736C2×D4—91no—
737C2×D4—91no—
738C2×D4—91no—
739C2×D4—91no—
740C2×D4—271no—
741C2×D4—271no—
742C2×D4—271no—
743C2×D4—271no—
744C2×D4—271no—
745C2×D4—544no—
746C22×C4—91no—
747C22×C4—91no—
748C22×C4—271no—
749C22×C4—271no—
750C22×C4—271no—
751C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic, complemented
752C4⋊C4—91no—
753C4⋊C4—91no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C22⋊C4—91no—
757C22⋊C4—91no—
758C22⋊C4—91no—
759C22⋊C4—91no—
760C22⋊C4—91no—
761C22⋊C4—91no—
762C22⋊C4—91no—
763C22⋊C4—91no—
764C22⋊C4—271no—
765C22⋊C4—271no—
766C22⋊C4—271no—
767C22⋊C4—271no—
768C42—91no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—31no—
772C22×C3—31no—
773C22×C3—32no—
774C22×C3—32no—
775C22×C3—61no—
776C22×C3—61no—
777C22×C3—61no—
778C22×C3—61no—
779C22×C3—61no—
780C22×C3—62no—
781C22×C3—92no—
782C22×C3—92no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—181no—
786C22×C3—181no—
787C22×C3—181no—
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—364no—
799C22×C3D3×D1212yes—
800C22×C3C22×D3211yescharacteristic
801C2×D3—32no—
802C2×D3—32no—
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—61no—
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—92no—
823C2×D3—92no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—121no—
828C2×D3—121no—
829C2×D3—121no—
830C2×D3—124no—
831C2×D3—181no—
832C2×D3—181no—
833C2×D3—181no—
834C2×D3—181no—
835C2×D3—181no—
836C2×D3—181no—
837C2×D3—181no—
838C2×D3—364no—
839C2×D3—364no—
840C2×D3—364no—
841C2×D3—364no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—61no—
845C3×C4—61no—
846C3×C4—61no—
847C3×C4—61no—
848C3×C4—62no—
849C3×C4—92no—
850C3×C4—121no—
851C3×C4—181no—
852C3×C4—181no—
853C3×C4—181no—
854C3×C4—181no—
855C3×C4—181no—
856C3×C4—181no—
857Dic3—32no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—61no—
865Dic3—61no—
866Dic3—92no—
867Dic3—121no—
868Dic3—121no—
869Dic3—181no—
870Dic3—181no—
871Dic3—181no—
872Dic3—181no—
873C32—21no—
874C32#549011yescharacteristic, complemented
875C32#555411yescharacteristic, complemented
876C23—91no—
877C23—91no—
878C23—91no—
879C23—91no—
880C23—91no—
881C23—182no—
882C23—182no—
883C23—361no—
884C23—542no—
885C23—542no—
886C23—1081no—
887C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
888Q8—542no—
889D4—94no—
890D4—182no—
891D4—182no—
892D4—361no—
893D4—542no—
894D4—542no—
895D4—542no—
896D4—542no—
897D4—1081no—
898C2×C4—41no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—91no—
906C2×C4—182no—
907C2×C4—361no—
908C2×C4—542no—
909C2×C4—542no—
910C2×C4—542no—
911C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
912C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
913C2×C3—22no—
914C2×C3—31no—
915C2×C3—31no—
916C2×C3—31no—
917C2×C3—31no—
918C2×C3—31no—
919C2×C3—31no—
920C2×C3—62no—
921C2×C3—62no—
922C2×C3—61no—
923C2×C3—61no—
924C2×C3—61no—
925C2×C3—122no—
926C2×C3—182no—
927C2×C3—182no—
928C2×C3—361no—
929C2×C3—361no—
930C2×C3—361no—
931C2×C3C2×D3×D1211yescharacteristic
932C2×C3D3×#23511yescharacteristic
933C2×C3#6433011yescharacteristic
934D3—62no—
935D3—62no—
936D3—121no—
937D3—121no—
938D3—121no—
939D3—121no—
940D3—121no—
941D3—182no—
942D3—182no—
943D3—241no—
944D3—241no—
945D3—361no—
946C22—21no—
947C22—21no—
948C22—92no—
949C22—92no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—181no—
954C22—181no—
955C22—181no—
956C22—181no—
957C22—181no—
958C22—181no—
959C22—181no—
960C22—181no—
961C22—181no—
962C22—181no—
963C22—364no—
964C22—1084no—
965C22#8865412yes—
966C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
967C4—21no—
968C4—21no—
969C4—92no—
970C4—181no—
971C4—181no—
972C4—181no—
973C4—181no—
974C4—181no—
975C4—181no—
976C3—31no—
977C3—31no—
978C3—61no—
979C3#1059507311yescharacteristic
980C2—22no—
981C2—182no—
982C2—182no—
983C2—361no—
984C2—361no—
985C2—361no—
986C2C2×#8865411yescharacteristic
987C2#1172249011yescharacteristic
988C2#1172254511yescharacteristic
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×#88676C2semidirect
2. C2×#88671C2semidirect
3. #11721830C2semidirect
4. C4×#638⋊C3C2semidirect
5. C2×#3752⋊C3C2semidirect
6. #11721321C2semidirect
7. #11721301C2semidirect
8. #11721163C2semidirect
9. #11721160C2semidirect
10. #11721157C2semidirect
11. #11721140C2semidirect
12. #11721133C2semidirect
13. #11721131C2semidirect
14. #11721123C2semidirect
15. #11721103C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
22. C2×#6235C22semidirect
23. C2×C4⋊#272C22semidirect
25. C22×(C3⋊Dic3)⋊C3C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
30. C2×#6200C22semidirect
31. C2×#6200C22semidirect
32. C2×#6199C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
38. #88542C22semidirect
39. #88542C22semidirect
40. C4⋊#1084C22semidirect
41. #3757⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. #3752⋊C3C22semidirect
47. #3750⋊C3C22semidirect
48. C4×(C3⋊Dic3)⋊C3C22semidirect
49. #88451C22semidirect
50. #88451C22semidirect
52. #88450C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
59. C4×#638D3semidirect
60. C2×#3752D3semidirect
106. #638⋊C3D4semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C2×D3semidirect
134. C22×C3⋊Dic3C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
170. #3757C2×D3semidirect
173. #3752C2×D3semidirect
174. #3752C2×D3semidirect
175. #3752C2×D3semidirect
176. #3750C2×D3semidirect
177. C4×C3⋊Dic3C2×D3semidirect
226. C2×(C3⋊D3)⋊C3#41semidirect
319. #638D12semidirect
517. C2×C3⋊D3#235semidirect
585. H(3,𝔽3)#546semidirect
751. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
874. C32#5490semidirect
875. C32#5554semidirect

Maximal subgroups

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

subgroupindex
C2×#886762
C2×#886712
#117218302
C4×#638⋊C32
C2×#3752⋊C32
#117213212
#117213012
#117211632
#117211602
#117211572
#117211402
#117211332
#117211312
#117211232
#117211032
#105950833
#105950753