Finite Group Databasebeta

← #13178239

Subgroups — #13178239

Order 1728.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89049C211yesmaximal, characteristic, complemented
2C2×#89041C211yesmaximal, characteristic, complemented
3C3×#64094C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C3×#64091C211yesmaximal, characteristic, complemented
6#11723725C211yesmaximal, characteristic, complemented
7#11723725C211yesmaximal, characteristic, complemented
8#11723723C211yesmaximal, characteristic, complemented
9#11723701C211yesmaximal, characteristic, complemented
10#11723700C211yesmaximal, characteristic, complemented
11#11723691C211yesmaximal, characteristic, complemented
12#11723690C211yesmaximal, characteristic, complemented
13#11723688C211yesmaximal, characteristic, complemented
14#11723687C211yesmaximal, characteristic, complemented
15#11723685C211yesmaximal, characteristic, complemented
16#10594282—31nomaximal
17#10594281—31nomaximal
18#10594274—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C22×#1113C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×#634C2211yescharacteristic, complemented
28#89049—24no—
29C2×#6295C2211yescharacteristic
30C2×#6295C2211yescharacteristic
31C2×#6295C2211yescharacteristic, complemented
32C2×#6295C2211yescharacteristic, complemented
33C2×#6294C2211yescharacteristic
34C2×#6294C2211yescharacteristic, complemented
35C2×#6294C2211yescharacteristic, complemented
36C2×#6294C2211yescharacteristic, complemented
37C2×#6294C2211yescharacteristic, complemented
38#89041—24no—
39C33×C22⋊C4C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3757C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic
43C3×#3752C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3752C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48C3×#3750C2211yescharacteristic, complemented
49C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
50#88815C2211yescharacteristic, complemented
51#88815C2211yescharacteristic, complemented
52#88814C2211yescharacteristic
53#88814C2211yescharacteristic
54#88814C2211yescharacteristic, complemented
55#88814C2211yescharacteristic, complemented
56C2×#3811—31no—
57C2×D3×#67—31no—
58C2×D3×#67—31no—
59C2×#3799—31no—
60C2×#3796—31no—
61C2×#3795—31no—
62#64094D311yescharacteristic, complemented
63#64092D311yescharacteristic, complemented
64#64091D311yescharacteristic, complemented
65C3×#885—31no—
66C3×#885—31no—
67C3×#885—61no—
68C3×#883—31no—
69C3×#883—31no—
70C3×#883—61no—
71C3×#882—31no—
72C3×#882—31no—
73C3×#882—61no—
74#63974—31no—
75#63971—31no—
76#63971—31no—
77#63970—31no—
78#63970—31no—
79D3×#217—31no—
80D3×#217—31no—
81#63958—31no—
82#63958—31no—
83#63923—31no—
84#63922—31no—
85#63922—31no—
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63910—31no—
90#63902—31no—
91#63898—31no—
92#63896—31no—
93#63894—31no—
94Dic3×D12—31no—
95#63891—31no—
96#63890—31no—
97#63888—31no—
98#63887—31no—
99#63886—31no—
100#63885—31no—
101#63880—31no—
102#63880—31no—
103#63854—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3—22no—
106C22×C3×C3⋊D3—22no—
107C22×C3×C3⋊D3—41no—
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C3×C3⋊D3C2311yescharacteristic
110C22×C3×C3⋊D3C2311yescharacteristic
111C22×C3×C3⋊D3C2311yescharacteristic
112C22×C3×C3⋊D3C2311yescharacteristic
113C2×#1113—22no—
114C2×#1113—22no—
115C2×#1113—41no—
116C2×C33×C4C2311yescharacteristic
117C2×C33×C4C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C2×C3×C3⋊Dic3C2311yescharacteristic
127C2×C3×C3⋊Dic3C2311yescharacteristic
128C3×C4⋊(C3⋊D3)—22no—
129C3×C4⋊(C3⋊D3)—22no—
130C3×C4×C3⋊D3—22no—
131C3×#634—22no—
132#6295—22no—
133#6295—22no—
134#6295—41no—
135#6295D414yescomplemented
136#6294—22no—
137#6294—22no—
138#6294—22no—
139#6294—41no—
140#6294—41no—
141#5676—91no—
142#5654—91no—
143#5591—91no—
144C23×C3⋊D3C2×D311yescharacteristic
145C23×C3×D3—31no—
146C23×C3×D3—31no—
147C23×C3×D3—61no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C2×#638C2×D311yescharacteristic
152C2×#638C2×D311yescharacteristic
153C2×#638C2×D311yescharacteristic, complemented
154C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
155C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
156C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
157C2×#634C2×D311yescharacteristic, complemented
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C2×C3×#67—61no—
167C2×C3×D12—31no—
168C2×C3×D12—31no—
169C2×C3×D12—31no—
170C2×C3×D12—31no—
171C2×C3×D12—61no—
172C2×C3×D12—61no—
173C2×C3×C4×D3—31no—
174C2×C3×C4×D3—31no—
175C2×C3×C4×D3—61no—
176C2×C3×Dic6—31no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—61no—
179#3811—64no—
180D3×#67—64no—
181D3×#67—64no—
182C2×#626—31no—
183C2×#626—31no—
184C2×#626—31no—
185C2×#626—31no—
186C2×#626—31no—
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#625—31no—
191C2×#625—31no—
192C2×#625—31no—
193C2×#625—31no—
194C2×#624—31no—
195C2×#624—31no—
196C2×#624—31no—
197C2×#624—31no—
198C2×#624—31no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—31no—
206C2×D3×Dic3—31no—
207C2×D3×Dic3—31no—
208C2×D3×Dic3—31no—
209#3799—64no—
210#3796—64no—
211#3795—64no—
212C32×C22⋊C4—21no—
213C32×C22⋊C4—21no—
214C32×C22⋊C4—21no—
215C32×C22⋊C4—41no—
216C32×C22⋊C4C2×D311yescharacteristic, complemented
217C32×C22⋊C4C2×D311yescharacteristic, complemented
218C32×C22⋊C4C2×D311yescharacteristic, complemented
219#3757C2×D311yescharacteristic, complemented
220#3757C2×D311yescharacteristic, complemented
221#3752C2×D311yescharacteristic
222#3752C2×D311yescharacteristic, complemented
223#3752C2×D311yescharacteristic, complemented
224#3752C2×D311yescharacteristic, complemented
225#3752C2×D311yescharacteristic, complemented
226C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
227#3750C2×D311yescharacteristic, complemented
228C4×C3⋊Dic3C2×D311yescharacteristic, complemented
229C3×#217—31no—
230C3×#217—31no—
231C3×#217—31no—
232C3×#217—31no—
233C3×#217—61no—
234C3×#217—61no—
235C3×(C2×D3)⋊C4—31no—
236C3×(C2×D3)⋊C4—31no—
237C3×(C2×D3)⋊C4—31no—
238C3×(C2×D3)⋊C4—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×(C2×D3)⋊C4—31no—
245C3×(C2×D3)⋊C4—61no—
246C3×(C2×D3)⋊C4—61no—
247C3×(C2×D3)⋊C4—61no—
248C3×(C2×D3)⋊C4—61no—
249C3×(C2×D3)⋊C4—61no—
250C3×C4⋊Dic3—31no—
251C3×C4⋊Dic3—31no—
252C3×C4⋊Dic3—61no—
253C3×Dic3⋊C4—31no—
254C3×Dic3⋊C4—31no—
255C3×Dic3⋊C4—61no—
256C3×C4×Dic3—31no—
257C3×C4×Dic3—31no—
258C3×C4×Dic3—61no—
259#3724—31no—
260#3724—31no—
261Dic3⋊Dic3—31no—
262Dic3⋊Dic3—31no—
263Dic3⋊Dic3—31no—
264Dic3⋊Dic3—31no—
265#3722—31no—
266#3722—31no—
267#3722—31no—
268#3722—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—31no—
274(C2×D3)⋊Dic3—31no—
275(C2×D3)⋊Dic3—31no—
276(C2×D3)⋊Dic3—31no—
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C3×C3⋊D3—44no—
294C2×C3×C3⋊D3C2×D412yes—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C3×C3⋊D3#4112yescomplemented
297#1113—44no—
298C33×C4—21no—
299C33×C4—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C3×C3⋊Dic3—21no—
303C3×C3⋊Dic3—21no—
304C3×C3⋊Dic3—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3C2×D412yes—
307C22×#67—91no—
308C2×#239—91no—
309C2×#237—91no—
310C2×D3×D4—91no—
311C2×D3×D4—91no—
312C2×#235—91no—
313C3×#124—91no—
314C3×#123—91no—
315C3×#120—91no—
316C2×#217—91no—
317#946—91no—
318#939—91no—
319#939—91no—
320#939—91no—
321#938—91no—
322#938—91no—
323#937—91no—
324D4×Dic3—91no—
325C2×(C2×D3)⋊C4—91no—
326#896—91no—
327#895—91no—
328#894—91no—
329#893—91no—
330#886—91no—
331#885—31no—
332#885—31no—
333#885—61no—
334#884—91no—
335#884—91no—
336#884—91no—
337#883—31no—
338#883—31no—
339#883—61no—
340#883—91no—
341#882—31no—
342#882—31no—
343#882—61no—
344#882—91no—
345#882—91no—
346#67⋊C4—91no—
347#67⋊C4—91no—
348D3×C22⋊C4—91no—
349D3×C22⋊C4—91no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352#878—91no—
353C4×D12—91no—
354C4×D12—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—41no—
359C23×C32C22×D311yescharacteristic
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C22×C3⋊D3—22no—
363C22×C3⋊D3—22no—
364C22×C3⋊D3—41no—
365C22×C3⋊D3C22×D311yescharacteristic
366C22×C3⋊D3C22×D311yescharacteristic
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3⋊D3C22×D311yescharacteristic
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—31no—
375C22×C3×D3—31no—
376C22×C3×D3—31no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—62no—
386C22×C3×D3—62no—
387C22×C3×D3—62no—
388C22×C3×D3—62no—
389C22×C3×D3—122no—
390C22×C3×D3—122no—
391C22×C3×D3—121no—
392C22×C3×D3—121no—
393C22×C3×D3—122no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—121no—
403C2×C32×C4—21no—
404C2×C32×C4—21no—
405C2×C32×C4—21no—
406C2×C32×C4—21no—
407C2×C32×C4—21no—
408C2×C32×C4—21no—
409C2×C32×C4—41no—
410C2×C32×C4—41no—
411C2×C32×C4C22×D311yescharacteristic
412C2×C32×C4C22×D311yescharacteristic
413C2×C32×C4C22×D311yescharacteristic
414C2×C32×C4C22×D311yescharacteristic
415C2×C32×C4C22×D311yescharacteristic
416C2×C32×C4C22×D311yescharacteristic
417#638—22no—
418#638—22no—
419#638—41no—
420C2×C3⋊Dic3C22×D311yescharacteristic
421C2×C3⋊Dic3C22×D311yescharacteristic
422C2×C3⋊Dic3C22×D311yescharacteristic
423C2×C3⋊Dic3C22×D311yescharacteristic
424C2×C3⋊Dic3C22×D311yescharacteristic
425C2×C3⋊Dic3C22×D311yescharacteristic
426C2×C3⋊Dic3C22×D311yescharacteristic
427C4⋊(C3⋊D3)—22no—
428C4⋊(C3⋊D3)—22no—
429C4×C3⋊D3—22no—
430#634—22no—
431C3×#67—62no—
432C3×#67—62no—
433C3×#67—62no—
434C3×#67—62no—
435C3×#67—122no—
436C3×#67—122no—
437C3×#67—121no—
438C3×#67—121no—
439C3×#67—122no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—31no—
442C2×C3×Dic3—31no—
443C2×C3×Dic3—31no—
444C2×C3×Dic3—31no—
445C2×C3×Dic3—31no—
446C2×C3×Dic3—31no—
447C2×C3×Dic3—31no—
448C2×C3×Dic3—31no—
449C2×C3×Dic3—31no—
450C2×C3×Dic3—31no—
451C2×C3×Dic3—31no—
452C2×C3×Dic3—31no—
453C2×C3×Dic3—31no—
454C2×C3×Dic3—61no—
455C2×C3×Dic3—61no—
456C2×C3×Dic3—61no—
457C2×C3×Dic3—61no—
458C2×C3×Dic3—61no—
459C2×C3×Dic3—61no—
460C2×C3×Dic3—61no—
461C3×D12—62no—
462C3×D12—62no—
463C3×D12—62no—
464C3×D12—62no—
465C3×D12—122no—
466C3×D12—122no—
467C3×C4×D3—62no—
468C3×C4×D3—62no—
469C3×C4×D3—122no—
470C3×Dic6—62no—
471C3×Dic6—62no—
472C3×Dic6—122no—
473#626—34no—
474#626—34no—
475#626—62no—
476#626—62no—
477#626—62no—
478#626—62no—
479#626—121no—
480#626—121no—
481#625—34no—
482#625—62no—
483#625—62no—
484#625—121no—
485#624—62no—
486#624—62no—
487#624—62no—
488#624—121no—
489#624—121no—
490D3×Dic3—62no—
491D3×Dic3—62no—
492D3×Dic3—62no—
493D3×Dic3—62no—
494D3×Dic3—62no—
495D3×Dic3—62no—
496D3×Dic3—121no—
497D3×Dic3—121no—
498D3×Dic3—121no—
499D3×Dic3—121no—
500#546—271noSylow
501C2×C33—41no—
502C2×C33C22×D411yescharacteristic
503C2×C33C2×#4111yescharacteristic
504C2×C33H(5,𝔽2)11yescharacteristic
505C3×C3⋊D3—22no—
506C3×C3⋊D3—22no—
507C3×C3⋊D3—22no—
508C3×C3⋊D3—41no—
509C3×C3⋊D3—41no—
510C24×C3—91no—
511C23×D3—31no—
512C23×D3—31no—
513C23×D3—61no—
514C23×D3—91no—
515C23×D3—91no—
516C23×D3—91no—
517C2×C3×Q8—91no—
518C2×C3×D4—91no—
519C2×C3×D4—91no—
520C2×C3×D4—91no—
521C2×C3×D4—91no—
522C2×C3×D4—91no—
523C22×C3×C4—91no—
524C2×#67—31no—
525C2×#67—31no—
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—61no—
531C2×#67—61no—
532C2×#67—61no—
533C2×#67—91no—
534C2×#67—91no—
535C2×#67—91no—
536C2×#67—91no—
537C2×#67—91no—
538C2×#67—91no—
539C2×#67—91no—
540C2×#67—91no—
541C2×#67—184no—
542C22×Dic3—91no—
543C22×Dic3—91no—
544C22×Dic3—91no—
545C22×Dic3—91no—
546C22×Dic3—91no—
547#239—184no—
548#237—184no—
549D3×D4—184no—
550D3×D4—184no—
551#235—184no—
552C2×D12—31no—
553C2×D12—31no—
554C2×D12—31no—
555C2×D12—31no—
556C2×D12—61no—
557C2×D12—61no—
558C2×D12—91no—
559C2×D12—91no—
560C2×D12—91no—
561C2×D12—91no—
562C2×C4×D3—31no—
563C2×C4×D3—31no—
564C2×C4×D3—61no—
565C2×C4×D3—91no—
566C2×C4×D3—91no—
567C2×C4×D3—91no—
568C2×C4×D3—91no—
569C2×C4×D3—91no—
570C2×C4×D3—91no—
571C2×C4×D3—91no—
572C2×C4×D3—91no—
573C2×C4×D3—91no—
574C2×C4×D3—91no—
575C2×Dic6—31no—
576C2×Dic6—31no—
577C2×Dic6—61no—
578C3×C4⋊C4—91no—
579C3×C4⋊C4—91no—
580C3×C22⋊C4—21no—
581C3×C22⋊C4—21no—
582C3×C22⋊C4—21no—
583C3×C22⋊C4—41no—
584C3×C22⋊C4—91no—
585C3×C22⋊C4—91no—
586C3×C22⋊C4—91no—
587C3×C22⋊C4—91no—
588C3×C22⋊C4—91no—
589C3×C22⋊C4—91no—
590C3×C22⋊C4—91no—
591C3×C22⋊C4D3211yescharacteristic, complemented
592C3×C22⋊C4D3211yescharacteristic, complemented
593C3×C22⋊C4D3211yescharacteristic, complemented
594C3×C42—91no—
595#217—31no—
596#217—31no—
597#217—31no—
598#217—31no—
599#217—61no—
600#217—61no—
601#217—91no—
602#217—91no—
603#217—91no—
604#217—91no—
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—31no—
610(C2×D3)⋊C4—31no—
611(C2×D3)⋊C4—31no—
612(C2×D3)⋊C4—31no—
613(C2×D3)⋊C4—31no—
614(C2×D3)⋊C4—31no—
615(C2×D3)⋊C4—61no—
616(C2×D3)⋊C4—61no—
617(C2×D3)⋊C4—61no—
618(C2×D3)⋊C4—61no—
619(C2×D3)⋊C4—61no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628C4⋊Dic3—31no—
629C4⋊Dic3—31no—
630C4⋊Dic3—61no—
631C4⋊Dic3—91no—
632C4⋊Dic3—91no—
633Dic3⋊C4—31no—
634Dic3⋊C4—31no—
635Dic3⋊C4—61no—
636Dic3⋊C4—91no—
637Dic3⋊C4—91no—
638Dic3⋊C4—91no—
639Dic3⋊C4—91no—
640C4×Dic3—31no—
641C4×Dic3—31no—
642C4×Dic3—61no—
643C22×C32—21no—
644C22×C32—22no—
645C22×C32—21no—
646C22×C32—21no—
647C22×C32—21no—
648C22×C32—21no—
649C22×C32—21no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—41no—
657C22×C32—41no—
658C22×C32—41no—
659C22×C32—42no—
660C22×C32—41no—
661C22×C32—41no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—41no—
666C22×C32—81no—
667C22×C32—81no—
668C22×C32C23×D311yescharacteristic
669C22×C32C23×D311yescharacteristic
670C22×C32C23×D311yescharacteristic
671C2×C3⋊D3—21no—
672C2×C3⋊D3—21no—
673C2×C3⋊D3—21no—
674C2×C3⋊D3—21no—
675C2×C3⋊D3—21no—
676C2×C3⋊D3—21no—
677C2×C3⋊D3—21no—
678C2×C3⋊D3—21no—
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—44no—
684C2×C3⋊D3D3×D412yes—
685C2×C3⋊D3D3×D412yes—
686C2×C3⋊D3#23712yescomplemented
687C2×C3×D3—32no—
688C2×C3×D3—32no—
689C2×C3×D3—32no—
690C2×C3×D3—32no—
691C2×C3×D3—32no—
692C2×C3×D3—32no—
693C2×C3×D3—62no—
694C2×C3×D3—62no—
695C2×C3×D3—62no—
696C2×C3×D3—61no—
697C2×C3×D3—61no—
698C2×C3×D3—61no—
699C2×C3×D3—61no—
700C2×C3×D3—61no—
701C2×C3×D3—61no—
702C2×C3×D3—61no—
703C2×C3×D3—61no—
704C2×C3×D3—61no—
705C2×C3×D3—61no—
706C2×C3×D3—61no—
707C2×C3×D3—61no—
708C2×C3×D3—61no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—61no—
714C2×C3×D3—61no—
715C2×C3×D3—61no—
716C2×C3×D3—61no—
717C2×C3×D3—61no—
718C2×C3×D3—61no—
719C2×C3×D3—61no—
720C2×C3×D3—121no—
721C2×C3×D3—121no—
722C2×C3×D3—121no—
723C2×C3×D3—121no—
724C2×C3×D3—121no—
725C2×C3×D3—121no—
726C2×C3×D3—121no—
727C2×C3×D3—121no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—121no—
731C2×C3×D3—121no—
732C2×C3×D3—124no—
733C2×C3×D3—124no—
734C2×C3×D3—128no—
735D32—124no—
736D32—124no—
737D32—124no—
738C32×C4—21no—
739C32×C4—21no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—41no—
745C32×C4—41no—
746C32×C4—41no—
747C32×C4—41no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—81no—
751C32×C4—81no—
752C3⋊Dic3—21no—
753C3⋊Dic3—21no—
754C3⋊Dic3—21no—
755C3⋊Dic3—21no—
756C3⋊Dic3—21no—
757C3⋊Dic3—21no—
758C3⋊Dic3D3×D412yes—
759C3×Dic3—32no—
760C3×Dic3—32no—
761C3×Dic3—62no—
762C3×Dic3—61no—
763C3×Dic3—61no—
764C3×Dic3—61no—
765C3×Dic3—61no—
766C3×Dic3—61no—
767C3×Dic3—61no—
768C3×Dic3—61no—
769C3×Dic3—61no—
770C3×Dic3—61no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—61no—
774C3×Dic3—121no—
775C3×Dic3—121no—
776C3×Dic3—121no—
777C3×Dic3—121no—
778C3×Dic3—121no—
779C3×Dic3—121no—
780C2×#41—271no—
781C22×D4—271no—
782#124—91no—
783#123—91no—
784#123—271no—
785C22⋊Q8—271no—
786#121—271no—
787#121—271no—
788#121—271no—
789#120—91no—
790#120—271no—
791C4×D4—271no—
792C4×D4—271no—
793C2×C22⋊C4—271no—
794C2×C22⋊C4—271no—
795C33#54611yescharacteristic, complemented, Sylow
796C23×C3—21no—
797C23×C3—21no—
798C23×C3—21no—
799C23×C3—41no—
800C23×C3—91no—
801C23×C3—91no—
802C23×C3—91no—
803C23×C3—91no—
804C23×C3—91no—
805C23×C3—182no—
806C23×C3—182no—
807C23×C3—361no—
808C23×C3C2×D3211yescharacteristic
809C23×C3C2×D3211yescharacteristic
810C23×C3C2×D3211yescharacteristic
811C22×D3—31no—
812C22×D3—31no—
813C22×D3—31no—
814C22×D3—31no—
815C22×D3—31no—
816C22×D3—31no—
817C22×D3—31no—
818C22×D3—31no—
819C22×D3—31no—
820C22×D3—31no—
821C22×D3—61no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—62no—
827C22×D3—62no—
828C22×D3—62no—
829C22×D3—62no—
830C22×D3—122no—
831C22×D3—122no—
832C22×D3—121no—
833C22×D3—121no—
834C22×D3—122no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—361no—
842C22×D3—361no—
843C22×D3—361no—
844C3×Q8—182no—
845C3×D4—182no—
846C3×D4—182no—
847C3×D4—182no—
848C3×D4—182no—
849C3×D4—361no—
850C2×C3×C4—21no—
851C2×C3×C4—21no—
852C2×C3×C4—21no—
853C2×C3×C4—21no—
854C2×C3×C4—21no—
855C2×C3×C4—21no—
856C2×C3×C4—41no—
857C2×C3×C4—41no—
858C2×C3×C4—91no—
859C2×C3×C4—91no—
860C2×C3×C4—91no—
861C2×C3×C4—91no—
862C2×C3×C4—91no—
863C2×C3×C4—91no—
864C2×C3×C4—91no—
865C2×C3×C4—182no—
866C2×C3×C4C2×D3211yescharacteristic
867C2×C3×C4C2×D3211yescharacteristic
868C2×C3×C4C2×D3211yescharacteristic
869C2×C3×C4C2×D3211yescharacteristic
870C2×C3×C4C2×D3211yescharacteristic
871C2×C3×C4C2×D3211yescharacteristic
872#67—62no—
873#67—62no—
874#67—62no—
875#67—62no—
876#67—94no—
877#67—94no—
878#67—122no—
879#67—122no—
880#67—121no—
881#67—121no—
882#67—122no—
883#67—182no—
884#67—182no—
885#67—182no—
886#67—182no—
887#67—361no—
888#67—361no—
889C2×Dic3—31no—
890C2×Dic3—31no—
891C2×Dic3—31no—
892C2×Dic3—31no—
893C2×Dic3—31no—
894C2×Dic3—31no—
895C2×Dic3—31no—
896C2×Dic3—31no—
897C2×Dic3—31no—
898C2×Dic3—31no—
899C2×Dic3—31no—
900C2×Dic3—31no—
901C2×Dic3—31no—
902C2×Dic3—31no—
903C2×Dic3—61no—
904C2×Dic3—61no—
905C2×Dic3—61no—
906C2×Dic3—61no—
907C2×Dic3—61no—
908C2×Dic3—61no—
909C2×Dic3—61no—
910C2×Dic3—182no—
911C2×Dic3—182no—
912C2×Dic3—182no—
913C2×Dic3—361no—
914C2×Dic3—361no—
915D12—62no—
916D12—62no—
917D12—62no—
918D12—62no—
919D12—94no—
920D12—122no—
921D12—122no—
922D12—182no—
923D12—182no—
924D12—361no—
925C4×D3—62no—
926C4×D3—62no—
927C4×D3—122no—
928C4×D3—182no—
929C4×D3—182no—
930C4×D3—182no—
931C4×D3—182no—
932C4×D3—182no—
933C4×D3—182no—
934C4×D3—361no—
935C4×D3—361no—
936C4×D3—361no—
937C4×D3—361no—
938Dic6—62no—
939Dic6—62no—
940Dic6—122no—
941C2×C32—21no—
942C2×C32—21no—
943C2×C32—21no—
944C2×C32—21no—
945C2×C32—21no—
946C2×C32—21no—
947C2×C32—21no—
948C2×C32—21no—
949C2×C32—21no—
950C2×C32—41no—
951C2×C32—41no—
952C2×C32—41no—
953C2×C32—41no—
954C2×C32—42no—
955C2×C32—41no—
956C2×C32—41no—
957C2×C32—81no—
958C2×C32—81no—
959C2×C32—82no—
960C2×C32C2×D3×D411yescharacteristic
961C2×C32C2×D3×D411yescharacteristic
962C2×C32C2×D3×D411yescharacteristic
963C2×C32C2×#23711yescharacteristic
964C2×C32#100411yescharacteristic
965C2×C32D3×#4111yescharacteristic
966C2×C32D3×#4111yescharacteristic
967C2×C32#100911yescharacteristic
968C2×C32#100911yescharacteristic
969C3⋊D3—22no—
970C3⋊D3—22no—
971C3⋊D3—22no—
972C3⋊D3—41no—
973C3⋊D3—41no—
974C3×D3—62no—
975C3×D3—62no—
976C3×D3—62no—
977C3×D3—62no—
978C3×D3—62no—
979C3×D3—62no—
980C3×D3—122no—
981C3×D3—122no—
982C3×D3—122no—
983C3×D3—121no—
984C3×D3—121no—
985C3×D3—121no—
986C3×D3—121no—
987C3×D3—241no—
988C3×D3—241no—
989C24—91no—
990C24—271no—
991#41—544no—
992C2×Q8—91no—
993C2×D4—91no—
994C2×D4—91no—
995C2×D4—91no—
996C2×D4—91no—
997C2×D4—91no—
998C2×D4—271no—
999C2×D4—271no—
1000C2×D4—271no—
1001C2×D4—271no—
1002C2×D4—544no—
1003C22×C4—91no—
1004C22×C4—271no—
1005C22×C4—271no—
1006C22×C4—271no—
1007C22×C4—271no—
1008C22×C4—271no—
1009C4⋊C4—91no—
1010C4⋊C4—91no—
1011C4⋊C4—271no—
1012C4⋊C4—271no—
1013C22⋊C4—91no—
1014C22⋊C4—91no—
1015C22⋊C4—91no—
1016C22⋊C4—91no—
1017C22⋊C4—91no—
1018C22⋊C4—91no—
1019C22⋊C4—91no—
1020C22⋊C4—271no—
1021C22⋊C4—271no—
1022C22⋊C4—271no—
1023C22⋊C4—271no—
1024C22⋊C4#111311yescharacteristic, complemented
1025C42—91no—
1026C22×C3—22no—
1027C22×C3—21no—
1028C22×C3—21no—
1029C22×C3—21no—
1030C22×C3—21no—
1031C22×C3—21no—
1032C22×C3—21no—
1033C22×C3—21no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—21no—
1038C22×C3—21no—
1039C22×C3—41no—
1040C22×C3—41no—
1041C22×C3—41no—
1042C22×C3—41no—
1043C22×C3—41no—
1044C22×C3—41no—
1045C22×C3—41no—
1046C22×C3—41no—
1047C22×C3—42no—
1048C22×C3—41no—
1049C22×C3—81no—
1050C22×C3—81no—
1051C22×C3—92no—
1052C22×C3—92no—
1053C22×C3—92no—
1054C22×C3—181no—
1055C22×C3—181no—
1056C22×C3—181no—
1057C22×C3—181no—
1058C22×C3—181no—
1059C22×C3—181no—
1060C22×C3—181no—
1061C22×C3—181no—
1062C22×C3—181no—
1063C22×C3—181no—
1064C22×C3—181no—
1065C22×C3—181no—
1066C22×C3—364no—
1067C22×C3C22×D3211yescharacteristic
1068C22×C3C22×D3211yescharacteristic
1069C22×C3C22×D3211yescharacteristic
1070C2×D3—32no—
1071C2×D3—32no—
1072C2×D3—32no—
1073C2×D3—32no—
1074C2×D3—32no—
1075C2×D3—32no—
1076C2×D3—62no—
1077C2×D3—62no—
1078C2×D3—62no—
1079C2×D3—61no—
1080C2×D3—61no—
1081C2×D3—61no—
1082C2×D3—61no—
1083C2×D3—61no—
1084C2×D3—61no—
1085C2×D3—61no—
1086C2×D3—61no—
1087C2×D3—61no—
1088C2×D3—61no—
1089C2×D3—61no—
1090C2×D3—61no—
1091C2×D3—61no—
1092C2×D3—61no—
1093C2×D3—61no—
1094C2×D3—61no—
1095C2×D3—61no—
1096C2×D3—61no—
1097C2×D3—61no—
1098C2×D3—61no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—121no—
1104C2×D3—121no—
1105C2×D3—121no—
1106C2×D3—121no—
1107C2×D3—121no—
1108C2×D3—121no—
1109C2×D3—121no—
1110C2×D3—121no—
1111C2×D3—121no—
1112C2×D3—121no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—124no—
1116C2×D3—124no—
1117C2×D3—128no—
1118C2×D3—364no—
1119C2×D3—364no—
1120C2×D3—364no—
1121C3×C4—21no—
1122C3×C4—21no—
1123C3×C4—21no—
1124C3×C4—21no—
1125C3×C4—21no—
1126C3×C4—21no—
1127C3×C4—41no—
1128C3×C4—41no—
1129C3×C4—41no—
1130C3×C4—41no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—81no—
1134C3×C4—81no—
1135C3×C4—92no—
1136C3×C4—181no—
1137C3×C4—181no—
1138C3×C4—181no—
1139C3×C4—181no—
1140C3×C4—181no—
1141C3×C4—181no—
1142Dic3—32no—
1143Dic3—32no—
1144Dic3—62no—
1145Dic3—61no—
1146Dic3—61no—
1147Dic3—61no—
1148Dic3—61no—
1149Dic3—61no—
1150Dic3—61no—
1151Dic3—61no—
1152Dic3—61no—
1153Dic3—61no—
1154Dic3—61no—
1155Dic3—61no—
1156Dic3—61no—
1157Dic3—121no—
1158Dic3—121no—
1159Dic3—121no—
1160Dic3—121no—
1161Dic3—121no—
1162Dic3—121no—
1163C32—21no—
1164C32—21no—
1165C32—21no—
1166C32—41no—
1167C32#559111yescharacteristic, complemented
1168C32#565411yescharacteristic, complemented
1169C32#567611yescharacteristic, complemented
1170C23—91no—
1171C23—91no—
1172C23—91no—
1173C23—91no—
1174C23—91no—
1175C23—182no—
1176C23—182no—
1177C23—361no—
1178C23—542no—
1179C23—542no—
1180C23—1081no—
1181C23C2×#111311yescharacteristic
1182Q8—182no—
1183D4—182no—
1184D4—182no—
1185D4—182no—
1186D4—182no—
1187D4—274no—
1188D4—361no—
1189D4—542no—
1190D4—542no—
1191D4—1081no—
1192C2×C4—91no—
1193C2×C4—91no—
1194C2×C4—91no—
1195C2×C4—91no—
1196C2×C4—91no—
1197C2×C4—91no—
1198C2×C4—91no—
1199C2×C4—182no—
1200C2×C4—542no—
1201C2×C4—542no—
1202C2×C4—542no—
1203C2×C4—1081no—
1204C2×C4—1081no—
1205C2×C4C2×#111311yescharacteristic
1206C2×C4C2×#111311yescharacteristic
1207C2×C3—21no—
1208C2×C3—21no—
1209C2×C3—21no—
1210C2×C3—21no—
1211C2×C3—21no—
1212C2×C3—21no—
1213C2×C3—21no—
1214C2×C3—21no—
1215C2×C3—21no—
1216C2×C3—42no—
1217C2×C3—41no—
1218C2×C3—41no—
1219C2×C3—41no—
1220C2×C3—41no—
1221C2×C3—41no—
1222C2×C3—41no—
1223C2×C3—81no—
1224C2×C3—81no—
1225C2×C3—82no—
1226C2×C3—182no—
1227C2×C3—182no—
1228C2×C3—182no—
1229C2×C3—361no—
1230C2×C3—361no—
1231C2×C3#6430711yescharacteristic
1232C2×C3#6430711yescharacteristic
1233C2×C3#6430811yescharacteristic
1234C2×C3D32×D411yescharacteristic
1235C2×C3D32×D411yescharacteristic
1236C2×C3D32×D411yescharacteristic
1237C2×C3D3×#23711yescharacteristic
1238C2×C3D3×#23711yescharacteristic
1239C2×C3#6431211yescharacteristic
1240D3—62no—
1241D3—62no—
1242D3—62no—
1243D3—62no—
1244D3—62no—
1245D3—62no—
1246D3—122no—
1247D3—122no—
1248D3—122no—
1249D3—121no—
1250D3—121no—
1251D3—121no—
1252D3—121no—
1253D3—241no—
1254D3—241no—
1255C22—21no—
1256C22—21no—
1257C22—21no—
1258C22—92no—
1259C22—92no—
1260C22—92no—
1261C22—181no—
1262C22—181no—
1263C22—181no—
1264C22—181no—
1265C22—181no—
1266C22—181no—
1267C22—181no—
1268C22—181no—
1269C22—181no—
1270C22—181no—
1271C22—181no—
1272C22—181no—
1273C22—364no—
1274C22—1084no—
1275C22C22×#111311yescharacteristic
1276C4—21no—
1277C4—21no—
1278C4—92no—
1279C4—181no—
1280C4—181no—
1281C4—181no—
1282C4—181no—
1283C4—181no—
1284C4—181no—
1285C3—21no—
1286C3—21no—
1287C3—21no—
1288C3—41no—
1289C3#1059427411yescharacteristic, complemented
1290C3#1059428111yescharacteristic, complemented
1291C3#1059428211yescharacteristic, complemented
1292C2—41no—
1293C2—182no—
1294C2—182no—
1295C2—182no—
1296C2—361no—
1297C2—361no—
1298C2#1172461911yescharacteristic
1299C2D4×#111311yescharacteristic
1300C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
hypercenterC22⋊C4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#89049C2semidirect
2. C2×#89041C2semidirect
3. C3×#64094C2semidirect
4. C3×#64092C2semidirect
5. C3×#64091C2semidirect
6. #11723725C2semidirect
7. #11723725C2semidirect
8. #11723723C2semidirect
9. #11723701C2semidirect
10. #11723700C2semidirect
11. #11723691C2semidirect
12. #11723690C2semidirect
13. #11723688C2semidirect
14. #11723687C2semidirect
15. #11723685C2semidirect
23. C2×C3×#638C22semidirect
25. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×#634C22semidirect
31. C2×#6295C22semidirect
32. C2×#6295C22semidirect
34. C2×#6294C22semidirect
35. C2×#6294C22semidirect
36. C2×#6294C22semidirect
37. C2×#6294C22semidirect
39. C33×C22⋊C4C22semidirect
40. C3×#3757C22semidirect
41. C3×#3757C22semidirect
43. C3×#3752C22semidirect
44. C3×#3752C22semidirect
45. C3×#3752C22semidirect
46. C3×#3752C22semidirect
47. C3×C4⋊(C3⋊Dic3)C22semidirect
48. C3×#3750C22semidirect
49. C3×C4×C3⋊Dic3C22semidirect
50. #88815C22semidirect
51. #88815C22semidirect
54. #88814C22semidirect
55. #88814C22semidirect
62. #64094D3semidirect
63. #64092D3semidirect
64. #64091D3semidirect
135. #6295D4semidirect
153. C2×#638C2×D3semidirect
155. C2×C4⋊(C3⋊D3)C2×D3semidirect
156. C2×C4×C3⋊D3C2×D3semidirect
157. C2×#634C2×D3semidirect
216. C32×C22⋊C4C2×D3semidirect
217. C32×C22⋊C4C2×D3semidirect
218. C32×C22⋊C4C2×D3semidirect
219. #3757C2×D3semidirect
220. #3757C2×D3semidirect
222. #3752C2×D3semidirect
223. #3752C2×D3semidirect
224. #3752C2×D3semidirect
225. #3752C2×D3semidirect
226. C4⋊(C3⋊Dic3)C2×D3semidirect
227. #3750C2×D3semidirect
228. C4×C3⋊Dic3C2×D3semidirect
296. C2×C3×C3⋊D3#41semidirect
591. C3×C22⋊C4D32semidirect
592. C3×C22⋊C4D32semidirect
593. C3×C22⋊C4D32semidirect
686. C2×C3⋊D3#237semidirect
795. C33#546semidirect
1024. C22⋊C4#1113semidirect
1167. C32#5591semidirect
1168. C32#5654semidirect
1169. C32#5676semidirect
1289. C3#10594274semidirect
1290. C3#10594281semidirect
1291. C3#10594282semidirect

Maximal subgroups

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

subgroupindex
C2×#890492
C2×#890412
C3×#640942
C3×#640922
C3×#640912
#117237252
#117237232
#117237012
#117237002
#117236912
#117236902
#117236882
#117236872
#117236852
#105942823
#105942813
#105942743