Finite Group Databasebeta

← #13170744

Subgroups — #13170744

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#11723685C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723494C211yesmaximal, characteristic, complemented
6#11723486C211yesmaximal, characteristic, complemented
7C3×#63895C211yesmaximal, characteristic, complemented
8C3×#63890C211yesmaximal, characteristic, complemented
9C3×#63878C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722961C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14#11722937C211yesmaximal, characteristic, complemented
15#11722937C211yesmaximal, characteristic, complemented
16#10594627—31nomaximal
17#10594615—31nomaximal
18#10594079—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6292C2211yescharacteristic
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic, complemented
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic, complemented
31C2×C3×#627C2211yescharacteristic, complemented
32C2×C3×#626C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88962—24no—
37D3×#624—24no—
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic, complemented
40C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×C4⋊Dic3C2211yescharacteristic, complemented
43C32×Dic3⋊C4C2211yescharacteristic, complemented
44#88815C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic, complemented
48#88804C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic, complemented
56C22×#624—31no—
57C2×#3804—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64104—31no—
63#64102—31no—
64#64091—31no—
65C3×#897—31no—
66C3×#896—31no—
67C3×#894—31no—
68C3×#892—31no—
69C3×#886—31no—
70C3×#877—31no—
71#63981—31no—
72#63966—31no—
73#63923—31no—
74#63923—31no—
75#63923—31no—
76#63923—61no—
77#63922—31no—
78#63910—31no—
79#63910—31no—
80#63910—31no—
81#63910—61no—
82#63909—31no—
83#63906—31no—
84#63902—31no—
85#63895—31no—
86#63895D311yescharacteristic, complemented
87#63894—31no—
88#63894—31no—
89#63894—31no—
90#63894—31no—
91#63894—61no—
92#63890—31no—
93#63890D311yescharacteristic, complemented
94#63888—31no—
95#63881—31no—
96#63881—31no—
97#63880—31no—
98#63880—31no—
99#63880—31no—
100#63880—31no—
101#63878D311yescharacteristic, complemented
102#63871—31no—
103#63850—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊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×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6295—22no—
124#6294—22no—
125#6294—22no—
126#6292—22no—
127#6292—22no—
128#6292—22no—
129#6291—22no—
130#6289—22no—
131#6289—22no—
132#6289—22no—
133C3×#627—22no—
134C3×#626—22no—
135C3×#624—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3D414yescomplemented
138#5656—91no—
139#5627—91no—
140#5524—91no—
141C23×C3⋊D3—31no—
142C22×D32—31no—
143C22×D32—31no—
144C22×D32—61no—
145C2×#638—31no—
146C2×C4⋊(C3⋊D3)—31no—
147C2×C4⋊(C3⋊D3)—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—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C2×C3×D12—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×Dic6—31no—
168C2×C3×Dic6—31no—
169C2×#627C2×D311yescharacteristic, complemented
170C2×#626—31no—
171C2×#626—31no—
172C2×#626—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626—31no—
180C2×#626—61no—
181C2×#626—61no—
182C2×#626—61no—
183C2×#626—61no—
184C2×#626C2×D311yescharacteristic
185C2×#625—31no—
186C2×#624—31no—
187C2×#624—31no—
188C2×#624—31no—
189C2×#624—31no—
190C2×#624—31no—
191C2×#624—31no—
192C2×#624—31no—
193C2×#624—31no—
194C2×#624—64no—
195C2×#624—61no—
196C2×#624—61no—
197C2×#624—61no—
198C2×#624C2×D311yescharacteristic
199#3804—64no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3C2×D311yescharacteristic
205C2×D3×Dic3C2×D311yescharacteristic
206C4×D32—64no—
207C4×D32—64no—
208#3799—64no—
209#3796—64no—
210C32×C4⋊C4—31no—
211C32×C4⋊C4—31no—
212C32×C22⋊C4—31no—
213#3752—31no—
214#3752—31no—
215#3752—31no—
216#3752—31no—
217#3752C2×D311yescharacteristic
218#3752C2×D311yescharacteristic, complemented
219C4×C3⋊Dic3C2×D311yescharacteristic, complemented
220C3×#217—31no—
221C3×(C2×D3)⋊C4—21no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—61no—
232C3×(C2×D3)⋊C4—61no—
233C3×(C2×D3)⋊C4C2×D311yescharacteristic
234C3×(C2×D3)⋊C4C2×D311yescharacteristic
235C3×C4⋊Dic3—21no—
236C3×C4⋊Dic3—31no—
237C3×C4⋊Dic3—31no—
238C3×C4⋊Dic3—31no—
239C3×C4⋊Dic3C2×D311yescharacteristic, complemented
240C3×C4⋊Dic3C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4—21no—
242C3×Dic3⋊C4—31no—
243C3×Dic3⋊C4—31no—
244C3×Dic3⋊C4—31no—
245C3×Dic3⋊C4C2×D311yescharacteristic, complemented
246C3×Dic3⋊C4C2×D311yescharacteristic, complemented
247C3×C4×Dic3—31no—
248C3×C4×Dic3—31no—
249C3×C4×Dic3—31no—
250C3×C4×Dic3—31no—
251C3×C4×Dic3—61no—
252#3724—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256Dic3⋊Dic3C2×D311yescharacteristic, complemented
257Dic3⋊Dic3C2×D311yescharacteristic, complemented
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—31no—
264#3722—31no—
265#3722—31no—
266#3722—61no—
267#3722—61no—
268#3722—61no—
269#3722—61no—
270#3722C2×D311yescharacteristic
271#3722C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273Dic32C2×D311yescharacteristic, complemented
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⋊D3—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3#4112yescomplemented
287C2×C32×D3—21no—
288C2×C32×D3—21no—
289C2×C32×D3C2×D412yes—
290D3×C3⋊D3—28no—
291C33×C4—21no—
292C3×C3⋊Dic3—21no—
293C3×C3⋊Dic3—21no—
294C3×C3⋊Dic3—21no—
295C3×C3⋊Dic3C2×D412yes—
296C32×Dic3—21no—
297C32×Dic3—21no—
298C32×Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3C2×D412yes—
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×#117—91no—
310#946—91no—
311#937—91no—
312#930—91no—
313#929—91no—
314#897—31no—
315#897—91no—
316#896—31no—
317#896—91no—
318#895—91no—
319#895—91no—
320#895—91no—
321#895—181no—
322#894—31no—
323#894—91no—
324#893—91no—
325#893—91no—
326#893—91no—
327#893—91no—
328#893—181no—
329#892—31no—
330#886—31no—
331#886—91no—
332#884—91no—
333#884—91no—
334#882—91no—
335#882—91no—
336#882—91no—
337#882—91no—
338#882—91no—
339#882—181no—
340#67⋊C4—91no—
341#67⋊C4—91no—
342#67⋊C4—91no—
343#67⋊C4—91no—
344#877—31no—
345C4×D12—91no—
346C4×D12—91no—
347C4×D12—91no—
348C4×D12—91no—
349C23×C32—31no—
350C22×C3⋊D3—31no—
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—31no—
355C22×C3⋊D3—31no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—61no—
358C22×C3⋊D3—61no—
359C22×C3⋊D3—61no—
360C22×C3⋊D3—61no—
361C22×C3⋊D3—61no—
362C22×C3⋊D3—62no—
363C22×C3⋊D3—62no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—121no—
366C22×C3⋊D3—121no—
367C22×C3⋊D3C22×D311yescharacteristic
368C22×C3⋊D3C22×D311yescharacteristic
369C22×C3×D3—21no—
370C22×C3×D3—31no—
371C22×C3×D3—31no—
372C22×C3×D3—31no—
373C22×C3×D3—31no—
374C22×C3×D3—61no—
375C22×C3×D3—61no—
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—31no—
395C2×C32×C4—41no—
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398C2×C32×C4C22×D311yescharacteristic
399#638—62no—
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403C2×C3⋊Dic3C22×D311yescharacteristic
404C4⋊(C3⋊D3)—62no—
405C4⋊(C3⋊D3)—62no—
406C4⋊(C3⋊D3)—62no—
407C4⋊(C3⋊D3)—64no—
408C4⋊(C3⋊D3)—62no—
409C4⋊(C3⋊D3)—62no—
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—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—34no—
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—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—62no—
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C3×D12—62no—
448C3×C4×D3—34no—
449C3×C4×D3—62no—
450C3×C4×D3—62no—
451C3×C4×D3—62no—
452C3×Dic6—62no—
453C3×Dic6—62no—
454#627—22no—
455#626—22no—
456#626—62no—
457#626—62no—
458#626—62no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—62no—
464#626—62no—
465#626—62no—
466#626—122no—
467#626—122no—
468#626—122no—
469#626—122no—
470#625—62no—
471#624—22no—
472#624—62no—
473#624—62no—
474#624—62no—
475#624—62no—
476#624—62no—
477#624—62no—
478#624—62no—
479#624—62no—
480#624—122no—
481#624—122no—
482#624—122no—
483D3×Dic3—22no—
484D3×Dic3—62no—
485D3×Dic3—62no—
486D3×Dic3—62no—
487D3×Dic3—62no—
488D3×Dic3D1214yescomplemented
489#525—271noSylow
490C2×C33C22×D411yescharacteristic
491C2×C33C2×#4111yescharacteristic
492C2×C33C2×#4111yescharacteristic
493C3⋊(C3⋊D3)—22no—
494C3⋊(C3⋊D3)—41no—
495C3×C3⋊D3—22no—
496C3×C3⋊D3—41no—
497C32×D3—22no—
498C23×D3—91no—
499C23×D3—91no—
500C23×D3—91no—
501C23×D3—181no—
502C2×C3×Q8—91no—
503C2×C3×D4—91no—
504C22×C3×C4—91no—
505C22×C3×C4—91no—
506C22×C3×C4—91no—
507C2×#67—31no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—181no—
516C22×Dic3—31no—
517C22×Dic3—31no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520#239—184no—
521#237—184no—
522#235—184no—
523C2×D12—31no—
524C2×D12—91no—
525C2×D12—91no—
526C2×D12—91no—
527C2×D12—91no—
528C2×D12—91no—
529C2×D12—91no—
530C2×D12—91no—
531C2×D12—91no—
532C2×D12—91no—
533C2×D12—91no—
534C2×D12—91no—
535C2×D12—181no—
536C2×D12—181no—
537C2×D12—181no—
538C2×D12—181no—
539C2×D12—181no—
540C2×D12—181no—
541C2×D12—361no—
542C2×C4×D3—31no—
543C2×C4×D3—31no—
544C2×C4×D3—31no—
545C2×C4×D3—31no—
546C2×C4×D3—91no—
547C2×C4×D3—91no—
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—31no—
570C3×C4⋊C4—31no—
571C3×C4⋊C4—61no—
572C3×C4⋊C4—61no—
573C3×C4⋊C4—91no—
574C3×C4⋊C4—91no—
575C3×C4⋊C4—91no—
576C3×C22⋊C4—31no—
577C3×C22⋊C4—31no—
578C3×C22⋊C4—61no—
579C3×C22⋊C4—91no—
580C3×C22⋊C4—91no—
581C3×C22⋊C4—91no—
582C3×C22⋊C4—91no—
583C3×C22⋊C4—91no—
584C3×C42—91no—
585C3×C42—91no—
586#217—31no—
587(C2×D3)⋊C4—31no—
588(C2×D3)⋊C4—31no—
589(C2×D3)⋊C4—31no—
590(C2×D3)⋊C4—31no—
591(C2×D3)⋊C4—31no—
592(C2×D3)⋊C4—31no—
593(C2×D3)⋊C4—31no—
594(C2×D3)⋊C4—31no—
595(C2×D3)⋊C4—31no—
596(C2×D3)⋊C4—61no—
597(C2×D3)⋊C4—61no—
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—91no—
607(C2×D3)⋊C4—91no—
608(C2×D3)⋊C4—91no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—181no—
611(C2×D3)⋊C4—181no—
612(C2×D3)⋊C4—181no—
613(C2×D3)⋊C4—181no—
614(C2×D3)⋊C4D3211yescharacteristic
615C4⋊Dic3—31no—
616C4⋊Dic3—31no—
617C4⋊Dic3—31no—
618C4⋊Dic3—91no—
619C4⋊Dic3D3211yescharacteristic, complemented
620Dic3⋊C4—31no—
621Dic3⋊C4—31no—
622Dic3⋊C4—31no—
623Dic3⋊C4—91no—
624Dic3⋊C4—91no—
625Dic3⋊C4D3211yescharacteristic, complemented
626C4×Dic3—31no—
627C4×Dic3—31no—
628C4×Dic3—31no—
629C4×Dic3—31no—
630C4×Dic3—61no—
631C22×C32—21no—
632C22×C32—21no—
633C22×C32—21no—
634C22×C32—32no—
635C22×C32—41no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32C23×D311yescharacteristic
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
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⋊D3#23912yescomplemented
690C2×C3×D3—21no—
691C2×C3×D3—21no—
692C2×C3×D3—21no—
693C2×C3×D3—21no—
694C2×C3×D3—22no—
695C2×C3×D3—32no—
696C2×C3×D3—32no—
697C2×C3×D3—41no—
698C2×C3×D3—41no—
699C2×C3×D3—62no—
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—121no—
711C2×C3×D3—121no—
712C2×C3×D3—121no—
713C2×C3×D3—121no—
714C2×C3×D3—121no—
715C2×C3×D3C2×D1212yes—
716C2×C3×D3D3×D412yes—
717D32—68no—
718D32—68no—
719D32—128no—
720C32×C4—21no—
721C32×C4—22no—
722C32×C4—21no—
723C32×C4—21no—
724C32×C4—32no—
725C32×C4—41no—
726C32×C4—41no—
727C32×C4—42no—
728C32×C4—61no—
729C32×C4—61no—
730C32×C4—61no—
731C32×C4—61no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3—21no—
735C3⋊Dic3C2×D1212yes—
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—22no—
745C3×Dic3—32no—
746C3×Dic3—32no—
747C3×Dic3—41no—
748C3×Dic3—41no—
749C3×Dic3—41no—
750C3×Dic3—41no—
751C3×Dic3—62no—
752C3×Dic3—61no—
753C3×Dic3—61no—
754C3×Dic3—61no—
755C3×Dic3—61no—
756C3×Dic3—61no—
757C3×Dic3—61no—
758C3×Dic3—121no—
759C3×Dic3—121no—
760C3×Dic3—121no—
761C3×Dic3C2×D1212yes—
762C3×Dic3D3×D412yes—
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—271no—
774C4×D4—271no—
775C4×D4—271no—
776C4×D4—271no—
777#117—91no—
778C33#52511yescharacteristic, complemented, Sylow
779C23×C3—31no—
780C23×C3—31no—
781C23×C3—61no—
782C23×C3—91no—
783C23×C3—91no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—31no—
787C22×D3—31no—
788C22×D3—61no—
789C22×D3—61no—
790C22×D3—91no—
791C22×D3—91no—
792C22×D3—91no—
793C22×D3—91no—
794C22×D3—91no—
795C22×D3—91no—
796C22×D3—181no—
797C22×D3—181no—
798C22×D3—181no—
799C22×D3—181no—
800C22×D3—181no—
801C22×D3—181no—
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—182no—
811C22×D3—361no—
812C22×D3—361no—
813C22×D3—362no—
814C22×D3—362no—
815C22×D3—362no—
816C22×D3C2×D3211yescharacteristic
817C3×Q8—182no—
818C3×D4—182no—
819C2×C3×C4—21no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—31no—
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—31no—
832C2×C3×C4—41no—
833C2×C3×C4—61no—
834C2×C3×C4—61no—
835C2×C3×C4—61no—
836C2×C3×C4—61no—
837C2×C3×C4—61no—
838C2×C3×C4—94no—
839C2×C3×C4—91no—
840C2×C3×C4—91no—
841C2×C3×C4—91no—
842C2×C3×C4—91no—
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—182no—
850#67—182no—
851#67—182no—
852#67—182no—
853#67—182no—
854#67—182no—
855#67—182no—
856#67—362no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—34no—
860C2×Dic3—31no—
861C2×Dic3—31no—
862C2×Dic3—31no—
863C2×Dic3—31no—
864C2×Dic3—31no—
865C2×Dic3—31no—
866C2×Dic3—61no—
867C2×Dic3—61no—
868C2×Dic3—61no—
869C2×Dic3—61no—
870C2×Dic3—62no—
871C2×Dic3—182no—
872C2×Dic3—182no—
873C2×Dic3C2×D3211yescharacteristic
874C2×Dic3C2×D3211yescharacteristic
875C2×Dic3C2×D3211yescharacteristic
876C2×Dic3C2×D3211yescharacteristic
877C2×Dic3C2×D3211yescharacteristic
878D12—62no—
879D12—182no—
880D12—182no—
881D12—182no—
882D12—184no—
883D12—182no—
884D12—182no—
885D12—182no—
886D12—182no—
887D12—182no—
888D12—182no—
889D12—182no—
890D12—182no—
891D12—362no—
892D12—362no—
893D12—364no—
894D12—362no—
895D12—362no—
896D12—362no—
897C4×D3—34no—
898C4×D3—62no—
899C4×D3—62no—
900C4×D3—62no—
901C4×D3—182no—
902C4×D3—182no—
903C4×D3—182no—
904C4×D3—182no—
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×C32C22×D1211yescharacteristic
933C2×C32C2×D3×D411yescharacteristic
934C2×C32C2×D3×D411yescharacteristic
935C2×C32C2×#23911yescharacteristic
936C2×C32D3×#4111yescharacteristic
937C2×C32D3×#4111yescharacteristic
938C2×C32D3×#4111yescharacteristic
939C2×C32D3×#4111yescharacteristic
940C2×C32D3×#4111yescharacteristic
941C3⋊D3—22no—
942C3⋊D3—41no—
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—62no—
961C3×D3—62no—
962C3×D3—122no—
963C3×D3—121no—
964C3×D3—121no—
965C3×D3—241no—
966C24—271no—
967#41—544no—
968C2×Q8—91no—
969C2×D4—91no—
970C2×D4—271no—
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—271no—
980C22×C4—271no—
981C22×C4—271no—
982C22×C4—271no—
983C22×C4—271no—
984C22×C4—544no—
985C4⋊C4—31no—
986C4⋊C4—31no—
987C4⋊C4—91no—
988C4⋊C4—91no—
989C4⋊C4—91no—
990C4⋊C4—271no—
991C22⋊C4—31no—
992C22⋊C4—91no—
993C22⋊C4—91no—
994C22⋊C4—91no—
995C22⋊C4—91no—
996C22⋊C4—91no—
997C22⋊C4—271no—
998C22⋊C4—271no—
999C22⋊C4—271no—
1000C22⋊C4—271no—
1001C42—91no—
1002C42—91no—
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—92no—
1015C22×C3—121no—
1016C22×C3—121no—
1017C22×C3—181no—
1018C22×C3—181no—
1019C22×C3—181no—
1020C22×C3—181no—
1021C22×C3—181no—
1022C22×C3C22×D3211yescharacteristic
1023C22×C3C22×D3211yescharacteristic
1024C22×C3C22×D3211yescharacteristic
1025C2×D3—21no—
1026C2×D3—21no—
1027C2×D3—32no—
1028C2×D3—32no—
1029C2×D3—62no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—61no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—92no—
1041C2×D3—92no—
1042C2×D3—92no—
1043C2×D3—121no—
1044C2×D3—121no—
1045C2×D3—121no—
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×D3D3×D1212yes—
1092C3×C4—22no—
1093C3×C4—21no—
1094C3×C4—21no—
1095C3×C4—21no—
1096C3×C4—32no—
1097C3×C4—32no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—42no—
1101C3×C4—62no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—61no—
1105C3×C4—61no—
1106C3×C4—61no—
1107C3×C4—61no—
1108C3×C4—61no—
1109C3×C4—61no—
1110C3×C4—92no—
1111C3×C4—121no—
1112C3×C4—121no—
1113C3×C4—121no—
1114C3×C4—121no—
1115C3×C4—181no—
1116C3×C4—181no—
1117C3×C4—181no—
1118Dic3—21no—
1119Dic3—21no—
1120Dic3—21no—
1121Dic3—21no—
1122Dic3—32no—
1123Dic3—32no—
1124Dic3—62no—
1125Dic3—61no—
1126Dic3—61no—
1127Dic3—61no—
1128Dic3—61no—
1129Dic3—61no—
1130Dic3—61no—
1131Dic3—121no—
1132Dic3—121no—
1133Dic3—121no—
1134Dic3D3×D1212yes—
1135C32—21no—
1136C32—21no—
1137C32—21no—
1138C32—41no—
1139C32#552411yescharacteristic, complemented
1140C32#562711yescharacteristic, complemented
1141C32#565611yescharacteristic, complemented
1142C23—31no—
1143C23—91no—
1144C23—91no—
1145C23—271no—
1146C23—271no—
1147C23—542no—
1148C23—542no—
1149C23—542no—
1150Q8—182no—
1151D4—182no—
1152D4—542no—
1153D4—542no—
1154D4—542no—
1155D4—542no—
1156D4—542no—
1157D4—542no—
1158C2×C4—31no—
1159C2×C4—31no—
1160C2×C4—31no—
1161C2×C4—31no—
1162C2×C4—31no—
1163C2×C4—94no—
1164C2×C4—91no—
1165C2×C4—91no—
1166C2×C4—91no—
1167C2×C4—91no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—542no—
1171C2×C4—542no—
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—182no—
1192C2×C3—361no—
1193C2×C3C2×D3×D1211yescharacteristic
1194C2×C3C2×D3×D1211yescharacteristic
1195C2×C3#6430611yescharacteristic
1196C2×C3D32×D411yescharacteristic
1197C2×C3#6431211yescharacteristic
1198C2×C3#6431211yescharacteristic
1199C2×C3#6431211yescharacteristic
1200C2×C3D3×#23911yescharacteristic
1201C2×C3D3×#23911yescharacteristic
1202D3—22no—
1203D3—62no—
1204D3—62no—
1205D3—122no—
1206D3—121no—
1207D3—121no—
1208D3—182no—
1209D3—182no—
1210D3—182no—
1211D3—241no—
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—92no—
1227C22—181no—
1228C22—181no—
1229C22—181no—
1230C22—181no—
1231C22—181no—
1232C22—272no—
1233C22—548no—
1234C22—541no—
1235C22—541no—
1236C22—541no—
1237C22—541no—
1238C22—541no—
1239C22C2×D3311yescharacteristic
1240C4—21no—
1241C4—32no—
1242C4—61no—
1243C4—61no—
1244C4—61no—
1245C4—61no—
1246C4—92no—
1247C4—181no—
1248C4—181no—
1249C4—181no—
1250C3—21no—
1251C3—21no—
1252C3—21no—
1253C3—41no—
1254C3#1059407911yescharacteristic, complemented
1255C3#1059461511yescharacteristic, complemented
1256C3#1059462711yescharacteristic, complemented
1257C2—62no—
1258C2—182no—
1259C2—361no—
1260C2—542no—
1261C2—1081no—
1262C2#1172437711yescharacteristic
1263C2D32×D1211yescharacteristic
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. #11723685C2semidirect
4. #11723542C2semidirect
5. #11723494C2semidirect
6. #11723486C2semidirect
7. C3×#63895C2semidirect
8. C3×#63890C2semidirect
9. C3×#63878C2semidirect
10. #11722987C2semidirect
11. #11722973C2semidirect
12. #11722961C2semidirect
13. #11722950C2semidirect
14. #11722937C2semidirect
15. #11722937C2semidirect
23. C2×#6294C22semidirect
26. C2×#6292C22semidirect
30. C2×#6289C22semidirect
31. C2×C3×#627C22semidirect
39. C3×#3752C22semidirect
40. C3×C4×C3⋊Dic3C22semidirect
42. C32×C4⋊Dic3C22semidirect
43. C32×Dic3⋊C4C22semidirect
44. #88815C22semidirect
47. #88804C22semidirect
48. #88804C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
86. #63895D3semidirect
93. #63890D3semidirect
101. #63878D3semidirect
137. C3×D3×Dic3D4semidirect
169. C2×#627C2×D3semidirect
218. #3752C2×D3semidirect
219. C4×C3⋊Dic3C2×D3semidirect
239. C3×C4⋊Dic3C2×D3semidirect
240. C3×C4⋊Dic3C2×D3semidirect
245. C3×Dic3⋊C4C2×D3semidirect
246. C3×Dic3⋊C4C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
256. Dic3⋊Dic3C2×D3semidirect
257. Dic3⋊Dic3C2×D3semidirect
271. #3722C2×D3semidirect
273. Dic32C2×D3semidirect
280. C2×C3⋊(C3⋊D3)#41semidirect
286. C2×C3×C3⋊D3#41semidirect
488. D3×Dic3D12semidirect
619. C4⋊Dic3D32semidirect
625. Dic3⋊C4D32semidirect
689. C2×C3⋊D3#239semidirect
778. C33#525semidirect
1139. C32#5524semidirect
1140. C32#5627semidirect
1141. C32#5656semidirect
1254. C3#10594079semidirect
1255. C3#10594615semidirect
1256. C3#10594627semidirect

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
#117236852
#117235422
#117234942
#117234862
C3×#638952
C3×#638902
C3×#638782
#117229872
#117229732
#117229612
#117229502
#117229372
#105946273
#105946153
#105940793