Finite Group Databasebeta

← #13170807

Subgroups — #13170807

Order 1728.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88962C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic, complemented
3#11723683C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723525C211yesmaximal, characteristic, complemented
6#11723494C211yesmaximal, characteristic, complemented
7C3×#63902C211yesmaximal, characteristic, complemented
8C3×#63899C211yesmaximal, characteristic, complemented
9C3×#63854C211yesmaximal, characteristic, complemented
10#11722993C211yesmaximal, characteristic, complemented
11#11722977C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722935C211yesmaximal, characteristic, complemented
15#11722935C211yesmaximal, characteristic, complemented
16#10594615—31nomaximal
17#10594266—31nomaximal
18#10594066—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6292C2211yescharacteristic
23C2×#6291C2211yescharacteristic
24C2×#6291C2211yescharacteristic
25C2×#6291C2211yescharacteristic, complemented
26C2×#6289C2211yescharacteristic
27C2×#6289C2211yescharacteristic
28C2×#6289C2211yescharacteristic, complemented
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×#626C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic, complemented
36#88962—24no—
37D3×#624—24no—
38C3×#3752C2211yescharacteristic
39C3×#3750C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C32×C4⋊Dic3C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88814C2211yescharacteristic
46#88813C2211yescharacteristic, complemented
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×#3724C2211yescharacteristic, complemented
53C3×#3724C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64102—31no—
63#64093—31no—
64#64091—31no—
65C3×#896—31no—
66C3×#894—31no—
67C3×#883—31no—
68C3×#67⋊C4—31no—
69C3×#67⋊C4—31no—
70C3×#878—31no—
71#63983—31no—
72#63981—31no—
73#63978—31no—
74#63971—31no—
75#63952—31no—
76#63952—31no—
77#63923—31no—
78#63923—31no—
79#63923—61no—
80#63922—31no—
81#63910—31no—
82#63910—31no—
83#63910—61no—
84#63906—31no—
85#63904—31no—
86#63904—31no—
87#63902D311yescharacteristic, complemented
88#63899D311yescharacteristic, complemented
89#63897—31no—
90#63894—31no—
91#63894—31no—
92#63894—61no—
93#63888—31no—
94#63888—31no—
95#63881—31no—
96#63881—31no—
97#63878—31no—
98#63877—31no—
99#63865—31no—
100#63854D311yescharacteristic, complemented
101#63850—31no—
102#63850—31no—
103#63836—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×D3×C3⋊D3—22no—
110C2×D3×C3⋊D3—22no—
111C2×D3×C3⋊D3—22no—
112C2×C33×C4C2311yescharacteristic
113C4⋊(C3⋊(C3⋊D3))—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294D414yescomplemented
124#6292—22no—
125#6291—22no—
126#6291—22no—
127#6291—22no—
128#6289—22no—
129#6289—22no—
130#6289—22no—
131C3×#627—22no—
132C3×#626—22no—
133C3×#625—22no—
134C3×#624—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138#5656—91no—
139#5627—91no—
140#5547—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×#638—31no—
147C2×#638—31no—
148C2×C4⋊(C3⋊D3)—31no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4⋊(C3⋊D3)—61no—
153C2×C4⋊(C3⋊D3)—61no—
154C2×C4⋊(C3⋊D3)—61no—
155C2×C4⋊(C3⋊D3)—121no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—31no—
158C2×C4×C3⋊D3—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C2×C3×D12—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×Dic6—31no—
172C2×C3×Dic6—31no—
173C2×#627C2×D311yescharacteristic, complemented
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—31no—
181C2×#626—31no—
182C2×#626—61no—
183C2×#626—61no—
184C2×#626—61no—
185C2×#626—61no—
186C2×#626C2×D311yescharacteristic
187C2×#625C2×D311yescharacteristic
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—31no—
195C2×#624—64no—
196C2×#624—61no—
197C2×#624—61no—
198C2×#624—61no—
199C2×#624C2×D311yescharacteristic
200#3804—64no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3C2×D311yescharacteristic
204C2×D3×Dic3C2×D311yescharacteristic
205C2×D3×Dic3C2×D311yescharacteristic, complemented
206C4×D32—64no—
207C4×D32—64no—
208#3799—64no—
209#3796—64no—
210C32×C4⋊C4—31no—
211C32×C22⋊C4—31no—
212C32×C22⋊C4—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—31no—
217#3752C2×D311yescharacteristic
218#3750C2×D311yescharacteristic, complemented
219C4×C3⋊Dic3C2×D311yescharacteristic, complemented
220C3×#217—31no—
221C3×#217—31no—
222C3×(C2×D3)⋊C4—21no—
223C3×(C2×D3)⋊C4—21no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—61no—
229C3×(C2×D3)⋊C4C2×D311yescharacteristic
230C3×(C2×D3)⋊C4C2×D311yescharacteristic
231C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
232C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
233C3×C4⋊Dic3—21no—
234C3×C4⋊Dic3C2×D311yescharacteristic, complemented
235C3×C4⋊Dic3C2×D311yescharacteristic, complemented
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—31no—
240C3×Dic3⋊C4—31no—
241C3×Dic3⋊C4—31no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—61no—
245C3×C4×Dic3—31no—
246C3×C4×Dic3—31no—
247C3×C4×Dic3—61no—
248#3724—31no—
249#3724C2×D311yescharacteristic, complemented
250#3724C2×D311yescharacteristic, complemented
251#3724C2×D311yescharacteristic, complemented
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722—61no—
265#3722—61no—
266#3722—61no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3C2×D311yescharacteristic
270(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
271Dic32—31no—
272Dic32—31no—
273Dic32—31no—
274C22×C33C2411yescharacteristic
275C2×C3⋊(C3⋊D3)—21no—
276C2×C3⋊(C3⋊D3)—21no—
277C2×C3⋊(C3⋊D3)—21no—
278C2×C3⋊(C3⋊D3)—21no—
279C2×C3⋊(C3⋊D3)—21no—
280C2×C3⋊(C3⋊D3)#4112yescomplemented
281C2×C3×C3⋊D3—21no—
282C2×C3×C3⋊D3—21no—
283C2×C3×C3⋊D3C2×D412yes—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3—21no—
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3#4112yescomplemented
290D3×C3⋊D3—28no—
291C33×C4—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3C2×D412yes—
296C3×C3⋊Dic3C2×D412yes—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C2×#239—91no—
302C2×#237—91no—
303C2×#235—91no—
304C22×C4×D3—91no—
305C22×C4×D3—91no—
306C22×C4×D3—91no—
307C3×#123—91no—
308C3×C22⋊Q8—91no—
309C3×C4×D4—91no—
310#946—91no—
311#939—91no—
312#937—91no—
313#937—91no—
314#930—91no—
315#929—91no—
316C4×#67—91no—
317C4×#67—91no—
318#896—31no—
319#896—91no—
320#896—91no—
321#895—91no—
322#894—31no—
323#894—91no—
324#894—91no—
325#893—91no—
326#893—91no—
327#893—91no—
328#893—91no—
329#893—181no—
330#892—91no—
331#884—91no—
332#884—91no—
333#884—91no—
334#884—181no—
335#883—31no—
336#882—91no—
337#882—91no—
338#882—91no—
339#882—91no—
340#882—181no—
341#67⋊C4—31no—
342#67⋊C4—31no—
343#67⋊C4—91no—
344#67⋊C4—91no—
345#878—31no—
346#877—91no—
347C4×D12—91no—
348#872—91no—
349C23×C32—31no—
350C23×C32—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—31no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—61no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—62no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3—121no—
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3×D3—21no—
370C22×C3×D3—21no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—61no—
374C22×C3×D3C22×D311yescharacteristic
375C22×C3×D3C22×D311yescharacteristic
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C2×D32—62no—
379C2×D32—62no—
380C2×D32—62no—
381C2×D32—62no—
382C2×D32—62no—
383C2×D32—62no—
384C2×D32—122no—
385C2×D32—122no—
386C2×D32—122no—
387C2×C32×C4—21no—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—31no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—41no—
395C2×C32×C4C22×D311yescharacteristic
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398#638—62no—
399#638—62no—
400#638—62no—
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—62no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—64no—
410C4⋊(C3⋊D3)—62no—
411C4⋊(C3⋊D3)—122no—
412C4⋊(C3⋊D3)—122no—
413C4⋊(C3⋊D3)—124no—
414C4×C3⋊D3—62no—
415C4×C3⋊D3—62no—
416C4×C3⋊D3—62no—
417C3×#67—62no—
418C3×#67—62no—
419C3×#67—62no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—21no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C3×D12—62no—
451C3×C4×D3—62no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455C3×C4×D3—62no—
456C3×Dic6—62no—
457C3×Dic6—62no—
458#627—22no—
459#626—22no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—62no—
466#626—62no—
467#626—62no—
468#626—122no—
469#626—122no—
470#626—122no—
471#626—122no—
472#625—22no—
473#624—22no—
474#624—34no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—62no—
480#624—62no—
481#624—122no—
482#624—122no—
483#624—122no—
484D3×Dic3—22no—
485D3×Dic3—22no—
486D3×Dic3—22no—
487D3×Dic3—34no—
488D3×Dic3—34no—
489#525—271noSylow
490C2×C33C22×D411yescharacteristic
491C2×C33C2×#4111yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C3⋊(C3⋊D3)—22no—
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C32×D3—22no—
497C32×D3—41no—
498C23×D3—91no—
499C23×D3—91no—
500C23×D3—91no—
501C23×D3—181no—
502C2×C3×Q8—91no—
503C2×C3×D4—91no—
504C2×C3×D4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C22×C3×C4—91no—
508C22×C3×C4—91no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—91no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—181no—
520C2×#67—181no—
521C2×#67—181no—
522C22×Dic3—31no—
523C22×Dic3—31no—
524C22×Dic3—31no—
525C22×Dic3—91no—
526#239—184no—
527#237—184no—
528#235—184no—
529C2×D12—31no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—91no—
536C2×D12—91no—
537C2×D12—91no—
538C2×D12—181no—
539C2×D12—181no—
540C2×D12—181no—
541C2×D12—181no—
542C2×D12—361no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C2×C4×D3—31no—
546C2×C4×D3—31no—
547C2×C4×D3—31no—
548C2×C4×D3—91no—
549C2×C4×D3—91no—
550C2×C4×D3—91no—
551C2×C4×D3—91no—
552C2×C4×D3—91no—
553C2×C4×D3—91no—
554C2×C4×D3—91no—
555C2×C4×D3—91no—
556C2×C4×D3—91no—
557C2×C4×D3—91no—
558C2×C4×D3—91no—
559C2×C4×D3—181no—
560C2×C4×D3—181no—
561C2×C4×D3—181no—
562C2×C4×D3—184no—
563C2×C4×D3—184no—
564C2×C4×D3—184no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C3×C4⋊C4—31no—
568C3×C4⋊C4—31no—
569C3×C4⋊C4—61no—
570C3×C4⋊C4—91no—
571C3×C4⋊C4—91no—
572C3×C4⋊C4—91no—
573C3×C4⋊C4—91no—
574C3×C22⋊C4—31no—
575C3×C22⋊C4—31no—
576C3×C22⋊C4—31no—
577C3×C22⋊C4—31no—
578C3×C22⋊C4—61no—
579C3×C22⋊C4—61no—
580C3×C22⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C42—91no—
584#217—31no—
585#217—31no—
586#217—91no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—61no—
592(C2×D3)⋊C4—91no—
593(C2×D3)⋊C4—91no—
594(C2×D3)⋊C4—91no—
595(C2×D3)⋊C4—91no—
596(C2×D3)⋊C4—91no—
597(C2×D3)⋊C4—91no—
598(C2×D3)⋊C4—91no—
599(C2×D3)⋊C4—91no—
600(C2×D3)⋊C4—91no—
601(C2×D3)⋊C4—91no—
602(C2×D3)⋊C4—91no—
603(C2×D3)⋊C4—91no—
604(C2×D3)⋊C4—91no—
605(C2×D3)⋊C4—91no—
606(C2×D3)⋊C4—181no—
607(C2×D3)⋊C4—181no—
608(C2×D3)⋊C4—181no—
609(C2×D3)⋊C4—181no—
610(C2×D3)⋊C4D3211yescharacteristic
611(C2×D3)⋊C4D3211yescharacteristic, complemented
612C4⋊Dic3—91no—
613C4⋊Dic3D3211yescharacteristic, complemented
614Dic3⋊C4—31no—
615Dic3⋊C4—31no—
616Dic3⋊C4—31no—
617Dic3⋊C4—31no—
618Dic3⋊C4—31no—
619Dic3⋊C4—31no—
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—61no—
623Dic3⋊C4—91no—
624Dic3⋊C4—91no—
625C4×Dic3—31no—
626C4×Dic3—31no—
627C4×Dic3—61no—
628C4×Dic3—91no—
629C4×Dic3—91no—
630C4×Dic3—91no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—32no—
635C22×C32—41no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32C23×D311yescharacteristic
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—32no—
647C2×C3⋊D3—32no—
648C2×C3⋊D3—32no—
649C2×C3⋊D3—62no—
650C2×C3⋊D3—62no—
651C2×C3⋊D3—62no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—68no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—61no—
658C2×C3⋊D3—61no—
659C2×C3⋊D3—61no—
660C2×C3⋊D3—62no—
661C2×C3⋊D3—61no—
662C2×C3⋊D3—61no—
663C2×C3⋊D3—61no—
664C2×C3⋊D3—61no—
665C2×C3⋊D3—61no—
666C2×C3⋊D3—61no—
667C2×C3⋊D3—61no—
668C2×C3⋊D3—61no—
669C2×C3⋊D3—122no—
670C2×C3⋊D3—121no—
671C2×C3⋊D3—121no—
672C2×C3⋊D3—122no—
673C2×C3⋊D3—121no—
674C2×C3⋊D3—121no—
675C2×C3⋊D3—121no—
676C2×C3⋊D3—121no—
677C2×C3⋊D3—121no—
678C2×C3⋊D3—121no—
679C2×C3⋊D3—121no—
680C2×C3⋊D3—121no—
681C2×C3⋊D3—121no—
682C2×C3⋊D3—121no—
683C2×C3⋊D3—121no—
684C2×C3⋊D3—121no—
685C2×C3⋊D3—241no—
686C2×C3⋊D3—241no—
687C2×C3⋊D3—241no—
688C2×C3⋊D3—241no—
689C2×C3⋊D3D3×D412yes—
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—21no—
695C2×C3×D3—21no—
696C2×C3×D3—21no—
697C2×C3×D3—21no—
698C2×C3×D3—21no—
699C2×C3×D3—21no—
700C2×C3×D3—22no—
701C2×C3×D3—32no—
702C2×C3×D3—32no—
703C2×C3×D3—41no—
704C2×C3×D3—41no—
705C2×C3×D3—41no—
706C2×C3×D3—41no—
707C2×C3×D3—41no—
708C2×C3×D3—62no—
709C2×C3×D3—61no—
710C2×C3×D3—61no—
711C2×C3×D3—61no—
712C2×C3×D3—61no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715C2×C3×D3#23512yescomplemented
716C2×C3×D3#23912yescomplemented
717D32—68no—
718D32—68no—
719D32—128no—
720C32×C4—21no—
721C32×C4—22no—
722C32×C4—21no—
723C32×C4—21no—
724C32×C4—41no—
725C32×C4—41no—
726C32×C4—42no—
727C32×C4—61no—
728C32×C4—61no—
729C32×C4—61no—
730C32×C4—61no—
731C3⋊Dic3—21no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3D3×D412yes—
735C3⋊Dic3D3×D412yes—
736C3×Dic3—21no—
737C3×Dic3—21no—
738C3×Dic3—21no—
739C3×Dic3—21no—
740C3×Dic3—21no—
741C3×Dic3—21no—
742C3×Dic3—21no—
743C3×Dic3—21no—
744C3×Dic3—32no—
745C3×Dic3—32no—
746C3×Dic3—32no—
747C3×Dic3—32no—
748C3×Dic3—41no—
749C3×Dic3—41no—
750C3×Dic3—41no—
751C3×Dic3—41no—
752C3×Dic3—62no—
753C3×Dic3—62no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—61no—
758C3×Dic3—61no—
759C3×Dic3—61no—
760C3×Dic3—121no—
761C3×Dic3—121no—
762C3×Dic3—121no—
763C2×#41—271no—
764C23×C4—271no—
765#123—91no—
766#123—271no—
767C22⋊Q8—91no—
768C22⋊Q8—271no—
769#121—271no—
770#121—271no—
771#120—271no—
772#120—271no—
773C4×D4—91no—
774C4×D4—271no—
775C4×D4—271no—
776C4×D4—271no—
777#117—271no—
778C33#52511yescharacteristic, complemented, Sylow
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—31no—
782C23×C3—31no—
783C23×C3—61no—
784C23×C3—61no—
785C23×C3—91no—
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—61no—
789C22×D3—91no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—91no—
793C22×D3—91no—
794C22×D3—91no—
795C22×D3—181no—
796C22×D3—181no—
797C22×D3—181no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—182no—
802C22×D3—182no—
803C22×D3—182no—
804C22×D3—182no—
805C22×D3—182no—
806C22×D3—182no—
807C22×D3—182no—
808C22×D3—182no—
809C22×D3—182no—
810C22×D3—361no—
811C22×D3—361no—
812C22×D3—362no—
813C22×D3—362no—
814C22×D3—362no—
815C22×D3C2×D3211yescharacteristic
816C22×D3C2×D3211yescharacteristic
817C3×Q8—182no—
818C3×D4—182no—
819C3×D4—182no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—21no—
823C2×C3×C4—31no—
824C2×C3×C4—31no—
825C2×C3×C4—31no—
826C2×C3×C4—31no—
827C2×C3×C4—31no—
828C2×C3×C4—31no—
829C2×C3×C4—31no—
830C2×C3×C4—31no—
831C2×C3×C4—41no—
832C2×C3×C4—61no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—91no—
837C2×C3×C4—91no—
838C2×C3×C4—91no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—182no—
842C2×C3×C4—182no—
843C2×C3×C4—182no—
844C2×C3×C4—182no—
845C2×C3×C4C2×D3211yescharacteristic
846C2×C3×C4C2×D3211yescharacteristic
847C2×C3×C4C2×D3211yescharacteristic
848#67—62no—
849#67—62no—
850#67—62no—
851#67—182no—
852#67—182no—
853#67—182no—
854#67—182no—
855#67—182no—
856#67—182no—
857#67—182no—
858#67—362no—
859#67—362no—
860#67—362no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—31no—
867C2×Dic3—31no—
868C2×Dic3—31no—
869C2×Dic3—31no—
870C2×Dic3—31no—
871C2×Dic3—61no—
872C2×Dic3—61no—
873C2×Dic3—61no—
874C2×Dic3—61no—
875C2×Dic3—61no—
876C2×Dic3—62no—
877C2×Dic3—62no—
878C2×Dic3—62no—
879C2×Dic3—94no—
880C2×Dic3C2×D3211yescharacteristic
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883C2×Dic3C2×D3211yescharacteristic
884D12—62no—
885D12—182no—
886D12—182no—
887D12—182no—
888D12—184no—
889D12—182no—
890D12—182no—
891D12—182no—
892D12—182no—
893D12—182no—
894D12—362no—
895D12—362no—
896D12—364no—
897D12—362no—
898C4×D3—62no—
899C4×D3—62no—
900C4×D3—62no—
901C4×D3—62no—
902C4×D3—62no—
903C4×D3—94no—
904C4×D3—94no—
905C4×D3—182no—
906C4×D3—182no—
907C4×D3—182no—
908C4×D3—182no—
909C4×D3—182no—
910C4×D3—182no—
911C4×D3—182no—
912C4×D3—182no—
913C4×D3—182no—
914C4×D3—362no—
915C4×D3—362no—
916C4×D3—362no—
917Dic6—62no—
918Dic6—62no—
919C2×C32—21no—
920C2×C32—21no—
921C2×C32—21no—
922C2×C32—21no—
923C2×C32—21no—
924C2×C32—21no—
925C2×C32—21no—
926C2×C32—21no—
927C2×C32—21no—
928C2×C32—41no—
929C2×C32—41no—
930C2×C32—41no—
931C2×C32—62no—
932C2×C32—121no—
933C2×C32C2×#23511yescharacteristic
934C2×C32C2×D3×D411yescharacteristic
935C2×C32C2×D3×D411yescharacteristic
936C2×C32C2×D3×D411yescharacteristic
937C2×C32C2×#23911yescharacteristic
938C2×C32D3×#4111yescharacteristic
939C2×C32D3×#4111yescharacteristic
940C2×C32D3×#4111yescharacteristic
941C2×C32D3×#4111yescharacteristic
942C3⋊D3—22no—
943C3⋊D3—62no—
944C3⋊D3—62no—
945C3⋊D3—62no—
946C3⋊D3—122no—
947C3⋊D3—122no—
948C3⋊D3—122no—
949C3⋊D3—121no—
950C3⋊D3—122no—
951C3⋊D3—121no—
952C3⋊D3—121no—
953C3⋊D3—242no—
954C3⋊D3—241no—
955C3⋊D3—241no—
956C3⋊D3—242no—
957C3×D3—22no—
958C3×D3—22no—
959C3×D3—42no—
960C3×D3—41no—
961C3×D3—41no—
962C3×D3—62no—
963C3×D3—62no—
964C3×D3—81no—
965C3×D3—122no—
966C24—271no—
967#41—544no—
968C2×Q8—91no—
969C2×D4—91no—
970C2×D4—91no—
971C2×D4—271no—
972C2×D4—271no—
973C2×D4—271no—
974C2×D4—271no—
975C2×D4—271no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—91no—
980C22×C4—271no—
981C22×C4—271no—
982C22×C4—271no—
983C22×C4—271no—
984C22×C4—544no—
985C4⋊C4—31no—
986C4⋊C4—91no—
987C4⋊C4—91no—
988C4⋊C4—91no—
989C4⋊C4—91no—
990C4⋊C4—271no—
991C22⋊C4—31no—
992C22⋊C4—31no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22⋊C4—271no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C22⋊C4—271no—
1001C42—91no—
1002C42—271no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—32no—
1007C22×C3—32no—
1008C22×C3—41no—
1009C22×C3—62no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—61no—
1020C22×C3—92no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—181no—
1027C22×C3—181no—
1028C22×C3C22×D3211yescharacteristic
1029C22×C3C22×D3211yescharacteristic
1030C22×C3C22×D3211yescharacteristic
1031C2×D3—21no—
1032C2×D3—21no—
1033C2×D3—21no—
1034C2×D3—21no—
1035C2×D3—21no—
1036C2×D3—32no—
1037C2×D3—32no—
1038C2×D3—62no—
1039C2×D3—61no—
1040C2×D3—61no—
1041C2×D3—61no—
1042C2×D3—61no—
1043C2×D3—92no—
1044C2×D3—92no—
1045C2×D3—92no—
1046C2×D3—121no—
1047C2×D3—121no—
1048C2×D3—182no—
1049C2×D3—182no—
1050C2×D3—182no—
1051C2×D3—188no—
1052C2×D3—188no—
1053C2×D3—188no—
1054C2×D3—181no—
1055C2×D3—181no—
1056C2×D3—181no—
1057C2×D3—181no—
1058C2×D3—181no—
1059C2×D3—181no—
1060C2×D3—182no—
1061C2×D3—181no—
1062C2×D3—181no—
1063C2×D3—181no—
1064C2×D3—181no—
1065C2×D3—181no—
1066C2×D3—181no—
1067C2×D3—181no—
1068C2×D3—181no—
1069C2×D3—181no—
1070C2×D3—362no—
1071C2×D3—368no—
1072C2×D3—361no—
1073C2×D3—361no—
1074C2×D3—361no—
1075C2×D3—361no—
1076C2×D3—361no—
1077C2×D3—361no—
1078C2×D3—361no—
1079C2×D3—361no—
1080C2×D3—361no—
1081C2×D3—361no—
1082C2×D3—361no—
1083C2×D3—361no—
1084C2×D3—361no—
1085C2×D3—361no—
1086C2×D3—362no—
1087C2×D3—721no—
1088C2×D3—721no—
1089C2×D3—721no—
1090C2×D3—721no—
1091C2×D3#379912yescomplemented
1092C3×C4—22no—
1093C3×C4—21no—
1094C3×C4—21no—
1095C3×C4—21no—
1096C3×C4—41no—
1097C3×C4—41no—
1098C3×C4—42no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—92no—
1108C3×C4—92no—
1109C3×C4—121no—
1110C3×C4—121no—
1111C3×C4—121no—
1112C3×C4—121no—
1113C3×C4—181no—
1114C3×C4—181no—
1115C3×C4—181no—
1116Dic3—21no—
1117Dic3—21no—
1118Dic3—21no—
1119Dic3—21no—
1120Dic3—32no—
1121Dic3—32no—
1122Dic3—32no—
1123Dic3—32no—
1124Dic3—62no—
1125Dic3—62no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—61no—
1129Dic3—61no—
1130Dic3—61no—
1131Dic3—61no—
1132Dic3—121no—
1133Dic3—121no—
1134Dic3—121no—
1135C32—21no—
1136C32—21no—
1137C32—21no—
1138C32—41no—
1139C32#554711yescharacteristic, complemented
1140C32#562711yescharacteristic, complemented
1141C32#565611yescharacteristic, complemented
1142C23—31no—
1143C23—31no—
1144C23—91no—
1145C23—271no—
1146C23—271no—
1147C23—542no—
1148C23—542no—
1149C23—542no—
1150Q8—182no—
1151D4—182no—
1152D4—182no—
1153D4—542no—
1154D4—542no—
1155D4—542no—
1156D4—542no—
1157D4—542no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—91no—
1163C2×C4—91no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—182no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—182no—
1171C2×C4—274no—
1172C2×C4—542no—
1173C2×C4—542no—
1174C2×C4—542no—
1175C2×C4D3311yescharacteristic
1176C2×C3—21no—
1177C2×C3—21no—
1178C2×C3—21no—
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—21no—
1183C2×C3—21no—
1184C2×C3—21no—
1185C2×C3—41no—
1186C2×C3—41no—
1187C2×C3—41no—
1188C2×C3—62no—
1189C2×C3—62no—
1190C2×C3—122no—
1191C2×C3—121no—
1192C2×C3—121no—
1193C2×C3—182no—
1194C2×C3—241no—
1195C2×C3C2×#379911yescharacteristic
1196C2×C3D3×#23511yescharacteristic
1197C2×C3#6430611yescharacteristic
1198C2×C3D32×D411yescharacteristic
1199C2×C3D32×D411yescharacteristic
1200C2×C3D32×D411yescharacteristic
1201C2×C3#6431211yescharacteristic
1202C2×C3#6431211yescharacteristic
1203C2×C3D3×#23911yescharacteristic
1204D3—22no—
1205D3—41no—
1206D3—62no—
1207D3—62no—
1208D3—122no—
1209D3—182no—
1210D3—182no—
1211D3—182no—
1212D3—362no—
1213D3—362no—
1214D3—362no—
1215D3—362no—
1216D3—361no—
1217D3—361no—
1218D3—361no—
1219D3—722no—
1220D3—721no—
1221D3—721no—
1222D3—722no—
1223C22—32no—
1224C22—61no—
1225C22—61no—
1226C22—61no—
1227C22—61no—
1228C22—61no—
1229C22—92no—
1230C22—181no—
1231C22—181no—
1232C22—272no—
1233C22—548no—
1234C22—541no—
1235C22—541no—
1236C22—541no—
1237C22—541no—
1238C22—541no—
1239C22C2×D3311yescharacteristic
1240C4—21no—
1241C4—61no—
1242C4—61no—
1243C4—61no—
1244C4—61no—
1245C4—92no—
1246C4—92no—
1247C4—181no—
1248C4—181no—
1249C4—181no—
1250C3—21no—
1251C3—21no—
1252C3—21no—
1253C3—41no—
1254C3#1059406611yescharacteristic, complemented
1255C3#1059426611yescharacteristic, complemented
1256C3#1059461511yescharacteristic, complemented
1257C2—62no—
1258C2—121no—
1259C2—182no—
1260C2—542no—
1261C2—1081no—
1262C2D3×#379911yescharacteristic
1263C2#1172440311yescharacteristic
1264C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#525
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88962C2semidirect
2. C2×D3×#624C2semidirect
3. #11723683C2semidirect
4. #11723542C2semidirect
5. #11723525C2semidirect
6. #11723494C2semidirect
7. C3×#63902C2semidirect
8. C3×#63899C2semidirect
9. C3×#63854C2semidirect
10. #11722993C2semidirect
11. #11722977C2semidirect
12. #11722958C2semidirect
13. #11722949C2semidirect
14. #11722935C2semidirect
15. #11722935C2semidirect
25. C2×#6291C22semidirect
28. C2×#6289C22semidirect
29. C2×C3×#627C22semidirect
35. C2×C3×D3×Dic3C22semidirect
39. C3×#3750C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
42. C32×(C2×D3)⋊C4C22semidirect
43. C32×C4⋊Dic3C22semidirect
44. #88815C22semidirect
46. #88813C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. C3×#3724C22semidirect
52. C3×#3724C22semidirect
53. C3×#3724C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
87. #63902D3semidirect
88. #63899D3semidirect
100. #63854D3semidirect
123. #6294D4semidirect
173. C2×#627C2×D3semidirect
205. C2×D3×Dic3C2×D3semidirect
218. #3750C2×D3semidirect
219. C4×C3⋊Dic3C2×D3semidirect
231. C3×(C2×D3)⋊C4C2×D3semidirect
232. C3×(C2×D3)⋊C4C2×D3semidirect
234. C3×C4⋊Dic3C2×D3semidirect
235. C3×C4⋊Dic3C2×D3semidirect
249. #3724C2×D3semidirect
250. #3724C2×D3semidirect
251. #3724C2×D3semidirect
270. (C2×D3)⋊Dic3C2×D3semidirect
280. C2×C3⋊(C3⋊D3)#41semidirect
289. C2×C32×D3#41semidirect
611. (C2×D3)⋊C4D32semidirect
613. C4⋊Dic3D32semidirect
715. C2×C3×D3#235semidirect
716. C2×C3×D3#239semidirect
778. C33#525semidirect
1091. C2×D3#3799semidirect
1139. C32#5547semidirect
1140. C32#5627semidirect
1141. C32#5656semidirect
1254. C3#10594066semidirect
1255. C3#10594266semidirect
1256. C3#10594615semidirect

Maximal subgroups

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

subgroupindex
C2×#889622
C2×D3×#6242
#117236832
#117235422
#117235252
#117234942
C3×#639022
C3×#638992
C3×#638542
#117229932
#117229772
#117229582
#117229492
#117229352
#105946153
#105942663
#105940663