Finite Group Databasebeta

← #13150888

Subgroups — #13150888

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×#88677C211yesmaximal, characteristic, complemented
2C2×#88672C211yesmaximal, characteristic, complemented
3C2×#88542C211yesmaximal, characteristic, complemented
4#64139⋊C3C211yesmaximal, characteristic, complemented
5C4×#638⋊C3C211yesmaximal, characteristic, complemented
6#11721323C211yesmaximal, characteristic, complemented
7#11721307C211yesmaximal, characteristic, complemented
8#11721162C211yesmaximal, characteristic, complemented
9#11721160C211yesmaximal, characteristic, complemented
10#11721150C211yesmaximal, characteristic, complemented
11#11721140C211yesmaximal, characteristic, complemented
12#11721130C211yesmaximal, characteristic, complemented
13#11721127C211yesmaximal, characteristic, complemented
14#11721123C211yesmaximal, characteristic, complemented
15#11721103C211yesmaximal, characteristic, complemented
16#10595083—31nomaximal
17#10595073—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
25C2×C4⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
26C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
27#88677—24no—
28C2×#6200C2211yescharacteristic
29C2×#6200C2211yescharacteristic
30C2×#6200C2211yescharacteristic
31C2×#6200C2211yescharacteristic, complemented
32C2×#6199C2211yescharacteristic
33C2×#6198C2211yescharacteristic, complemented
34#88672—24no—
35C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
36C2×((C3⋊D3)⋊C3)⋊C4C2211yescharacteristic, complemented
37C2×#6196C2211yescharacteristic, complemented
38#88542C2211yescharacteristic
39#88542C2211yescharacteristic
40#88542C2211yescharacteristic, complemented
41#88542C2211yescharacteristic, complemented
42#3757⋊C3C2211yescharacteristic, complemented
43#3752⋊C3C2211yescharacteristic, complemented
44#3752⋊C3C2211yescharacteristic, complemented
45#3752⋊C3C2211yescharacteristic, complemented
46C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
47#3750⋊C3C2211yescharacteristic, complemented
48C4×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
49#88451C2211yescharacteristic
50#88451C2211yescharacteristic, complemented
51#88450C2211yescharacteristic, complemented
52#88450C2211yescharacteristic, complemented
53#88448C2211yescharacteristic, complemented
54#88448C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×D3×#67—31no—
57C2×#3804—31no—
58C2×#3804—31no—
59#64139D311yescharacteristic, complemented
60C4×#638D311yescharacteristic, complemented
61C3×#930—31no—
62C3×C4×#67—31no—
63C2×C3×(C2×D3)⋊C4—31no—
64C2×C3×(C2×D3)⋊C4—31no—
65C2×C3×(C2×D3)⋊C4—61no—
66#63977—31no—
67#63976—31no—
68#63966—31no—
69#63961—31no—
70#63923—31no—
71#63922—31no—
72#63921—31no—
73D3×(C2×D3)⋊C4—31no—
74#63915—31no—
75#63912—31no—
76#63910—31no—
77#63906—31no—
78#63902—31no—
79#63899—31no—
80#63893—31no—
81#63891—31no—
82#63885—31no—
83#63880—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×(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
101C2×#1084—22no—
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)—41no—
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×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
137C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
138C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—61no—
145C2×C3×D12—31no—
146C2×C3×C4×D3—31no—
147D3×#67—64no—
148D3×#67—64no—
149C2×#627—31no—
150C2×#627—31no—
151C2×#626—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#625—31no—
158C2×#625—31no—
159C2×#625—31no—
160C2×#625—31no—
161C2×#624—31no—
162C2×#624—31no—
163#3804—64no—
164#3804—64no—
165C2×D3×Dic3—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#3752C2×D311yescharacteristic, complemented
173C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
174#3750C2×D311yescharacteristic, complemented
175C4×C3⋊Dic3C2×D311yescharacteristic, complemented
176C3×#217—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—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—61no—
189C3×(C2×D3)⋊C4—61no—
190C3×(C2×D3)⋊C4—61no—
191C3×(C2×D3)⋊C4—61no—
192C3×C4⋊Dic3—31no—
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—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—
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—91no—
253#930—91no—
254#929—91no—
255C4×#67—31no—
256C4×#67—91no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—61no—
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⋊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—21no—
314C2×C32×C4—21no—
315C2×C32×C4—41no—
316C2×C32×C4—41no—
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#638D1214yescomplemented
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C2×C3⋊Dic3C22×D311yescharacteristic
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—41no—
331C4×C3⋊D3—41no—
332C3×#67—34no—
333C3×#67—62no—
334C3×#67—62no—
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—62no—
347C2×C3×Dic3—62no—
348C2×C3×Dic3—122no—
349C3×D12—121no—
350C3×C4×D3—121no—
351#627—62no—
352#627—62no—
353#626—62no—
354#626—62no—
355#626—62no—
356#626—62no—
357#626—62no—
358#626—121no—
359#625—62no—
360#625—62no—
361#625—62no—
362#625—121no—
363#624—62no—
364#624—62no—
365D3×Dic3—62no—
366D3×Dic3—62no—
367D3×Dic3—62no—
368D3×Dic3—62no—
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—
386C2×C3×D4—91no—
387C2×C3×D4—91no—
388C2×C3×D4—91no—
389C2×C3×D4—91no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—61no—
393C22×C3×C4—91no—
394C22×C3×C4—91no—
395C22×C3×C4D3211yescharacteristic
396C2×#67—31no—
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—91no—
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—31no—
415C22×Dic3—61no—
416C22×Dic3—91no—
417C22×Dic3—91no—
418C22×Dic3—91no—
419#237—184no—
420#237—184no—
421D3×D4—184no—
422D3×D4—184no—
423#235—184no—
424C2×D12—31no—
425C2×D12—91no—
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—31no—
469(C2×D3)⋊C4—31no—
470(C2×D3)⋊C4—61no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—61no—
473(C2×D3)⋊C4—61no—
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—
485C4⋊Dic3—31no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489Dic3⋊C4—31no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495C4×Dic3—31no—
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×C32C2×D1212yes—
506C22×C32D3×D412yes—
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×D1212yes—
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×D1212yes—
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—271no—
573C22×D4—271no—
574#124—271no—
575#123—271no—
576#123—271no—
577C22⋊Q8—271no—
578#121—91no—
579#121—271no—
580#121—271no—
581#120—271no—
582#120—271no—
583C4×D4—91no—
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×D4—94no—
631C3×D4—182no—
632C3×D4—182no—
633C3×D4—361no—
634C2×C3×C4—31no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—41no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—91no—
642C2×C3×C4—91no—
643C2×C3×C4—91no—
644C2×C3×C4—91no—
645C2×C3×C4—91no—
646C2×C3×C4—91no—
647C2×C3×C4—91no—
648C2×C3×C4—121no—
649C2×C3×C4—121no—
650C2×C3×C4—122no—
651C2×C3×C4—182no—
652C2×C3×C4—361no—
653C2×C3×C4C2×D3211yescharacteristic
654C2×C3×C4C2×D3211yescharacteristic
655#67—34no—
656#67—62no—
657#67—62no—
658#67—94no—
659#67—182no—
660#67—182no—
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—
671C2×Dic3—31no—
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—61no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—91no—
685C2×Dic3—91no—
686C2×Dic3—91no—
687C2×Dic3—91no—
688C2×Dic3—91no—
689C2×Dic3—122no—
690C2×Dic3—182no—
691C2×Dic3—182no—
692C2×Dic3—182no—
693D12—121no—
694D12—182no—
695D12—182no—
696D12—182no—
697D12—182no—
698D12—361no—
699D12—361no—
700C4×D3—121no—
701C4×D3—182no—
702C4×D3—182no—
703C4×D3—182no—
704C4×D3—182no—
705C4×D3—182no—
706C4×D3—182no—
707C4×D3—361no—
708Dic6—182no—
709Dic6—182no—
710Dic6—182no—
711C2×C32—24no—
712C2×C32—22no—
713C2×C32—22no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32C22×D1211yescharacteristic
718C2×C32C2×D3×D411yescharacteristic
719C2×C32#100411yescharacteristic
720C2×C32#100411yescharacteristic
721C2×C32D3×#4111yescharacteristic
722C2×C32D3×#4111yescharacteristic
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—544no—
738C2×Q8—271no—
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—271no—
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—91no—
767C22⋊C4—271no—
768C22⋊C4—271no—
769C22⋊C4—271no—
770C22⋊C4—271no—
771C42—91no—
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×D1212yes—
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#555411yescharacteristic, complemented
879C32#561011yescharacteristic, 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—542no—
893D4—94no—
894D4—182no—
895D4—182no—
896D4—361no—
897D4—542no—
898D4—542no—
899D4—542no—
900D4—542no—
901D4—1081no—
902C2×C4—41no—
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—361no—
912C2×C4—542no—
913C2×C4—542no—
914C2×C4—542no—
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×C3C2×D3×D1211yescharacteristic
936C2×C3#6430611yescharacteristic
937C2×C3#6433011yescharacteristic
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#8865412yes—
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#1059507511yescharacteristic
984C2—22no—
985C2—182no—
986C2—182no—
987C2—361no—
988C2—361no—
989C2—361no—
990C2C2×#8865411yescharacteristic
991C2#1172249111yescharacteristic
992C2#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×#88677C2semidirect
2. C2×#88672C2semidirect
3. C2×#88542C2semidirect
4. #64139⋊C3C2semidirect
5. C4×#638⋊C3C2semidirect
6. #11721323C2semidirect
7. #11721307C2semidirect
8. #11721162C2semidirect
9. #11721160C2semidirect
10. #11721150C2semidirect
11. #11721140C2semidirect
12. #11721130C2semidirect
13. #11721127C2semidirect
14. #11721123C2semidirect
15. #11721103C2semidirect
20. C22×C4×H(3,𝔽3)C22semidirect
21. C22×#1084C22semidirect
24. C2×#638⋊C3C22semidirect
25. C2×C4⋊((C3⋊D3)⋊C3)C22semidirect
26. C2×C4×(C3⋊D3)⋊C3C22semidirect
31. C2×#6200C22semidirect
33. C2×#6198C22semidirect
35. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
36. C2×((C3⋊D3)⋊C3)⋊C4C22semidirect
37. C2×#6196C22semidirect
40. #88542C22semidirect
41. #88542C22semidirect
42. #3757⋊C3C22semidirect
43. #3752⋊C3C22semidirect
44. #3752⋊C3C22semidirect
45. #3752⋊C3C22semidirect
46. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
47. #3750⋊C3C22semidirect
48. C4×(C3⋊Dic3)⋊C3C22semidirect
50. #88451C22semidirect
51. #88450C22semidirect
52. #88450C22semidirect
53. #88448C22semidirect
54. #88448C22semidirect
59. #64139D3semidirect
60. C4×#638D3semidirect
106. #638⋊C3D4semidirect
132. C22×C32×C4C2×D3semidirect
133. C22×C32×C4C2×D3semidirect
136. C2×#638C2×D3semidirect
137. C2×C4⋊(C3⋊D3)C2×D3semidirect
138. C2×C4×C3⋊D3C2×D3semidirect
169. #3757C2×D3semidirect
170. #3752C2×D3semidirect
171. #3752C2×D3semidirect
172. #3752C2×D3semidirect
173. C4⋊(C3⋊Dic3)C2×D3semidirect
174. #3750C2×D3semidirect
175. C4×C3⋊Dic3C2×D3semidirect
217. C2×#272#41semidirect
324. #638D12semidirect
587. H(3,𝔽3)#546semidirect
754. C22×C4((C3⋊D3)⋊C3)⋊C2semidirect
878. C32#5554semidirect
879. C32#5610semidirect

Maximal subgroups

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

subgroupindex
C2×#886772
C2×#886722
C2×#885422
#64139⋊C32
C4×#638⋊C32
#117213232
#117213072
#117211622
#117211602
#117211502
#117211402
#117211302
#117211272
#117211232
#117211032
#105950833
#105950733