Finite Group Databasebeta

← #13172842

Subgroups — #13172842

Order 1728.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#627C211yesmaximal, characteristic, complemented
2C2×#88962C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723635C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723618C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×Dic3×#67C211yesmaximal, characteristic, complemented
9#11723005C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11723001C211yesmaximal, characteristic, complemented
12#11722979C211yesmaximal, characteristic, complemented
13#11722973C211yesmaximal, characteristic, complemented
14#11722969C211yesmaximal, characteristic, complemented
15#11722940C211yesmaximal, characteristic, complemented
16#10595141—31nomaximal
17#10594902—31nomaximal
18#10594900—31nomaximal
19C2×#6312C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6289C2211yescharacteristic
29C2×C3×#627—24no—
30C2×C3×#627C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic
32C2×C3×#627C2211yescharacteristic
33C2×C3×#627C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88962—24no—
37C3×#3757C2211yescharacteristic
38#88815C2211yescharacteristic
39#88814C2211yescharacteristic
40#88813C2211yescharacteristic
41#88807C2211yescharacteristic
42#88806C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88803C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49Dic3×C3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×#3722C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C22×C3×Dic6—31no—
57C22×C3×Dic6—31no—
58C22×#627D311yescharacteristic, complemented
59C2×#3804—31no—
60C2×#3799—31no—
61C2×#3796—31no—
62#64148—31no—
63#64139—31no—
64C4×#638—31no—
65C3×#939—31no—
66C3×D4×Dic3—31no—
67C3×#930—31no—
68C3×C4×#67—31no—
69#63978—31no—
70#63978—31no—
71#63978—31no—
72#63978—31no—
73#63978—61no—
74#63978—61no—
75#63978D311yescharacteristic, complemented
76#67⋊Dic3—31no—
77Dic3×#67—31no—
78Dic3×#67D311yescharacteristic, complemented
79#63964—31no—
80#63959—31no—
81#63953—31no—
82#63952—31no—
83#63952—31no—
84#63952—31no—
85#63952—61no—
86#63907—31no—
87#63907—31no—
88#63907—31no—
89#63907—31no—
90#63899—31no—
91#63895—31no—
92#63888—31no—
93#63888—31no—
94#63887—31no—
95#63887—31no—
96#63871—31no—
97#63864—31no—
98#63863—31no—
99#63856—31no—
100#63852—31no—
101#63843—31no—
102Dic3×Dic6—31no—
103#63837—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108#6312—22no—
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C3×#638—22no—
111C2×C3×C3⋊Dic3—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C2×C32×Dic3—22no—
119C2×C32×Dic3—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6294—22no—
126#6292—22no—
127#6291—22no—
128#6289—22no—
129C3×#627—22no—
130C3×#627—22no—
131C3×#627—22no—
132C3×#627D414yescomplemented
133C3×#626—22no—
134C3×D3×Dic3—22no—
135#5817—91no—
136#5598—91no—
137#5552—91no—
138C2×C32×D4—31no—
139C22×C32×C4—31no—
140C22×C32×C4—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—61no—
146C2×#638—61no—
147C2×#638—61no—
148C2×#638—121no—
149C2×#638C2×D311yescharacteristic
150C22×C3⋊Dic3C2×D311yescharacteristic
151C2×C4⋊(C3⋊D3)—31no—
152C2×C4×C3⋊D3—31no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—61no—
158C2×C3×#67C2×D311yescharacteristic
159C2×C3×#67C2×D311yescharacteristic
160C22×C3×Dic3—21no—
161C22×C3×Dic3—21no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—61no—
166C22×C3×Dic3C2×D311yescharacteristic
167C22×C3×Dic3C2×D311yescharacteristic
168C22×C3×Dic3C2×D311yescharacteristic
169C22×C3×Dic3C2×D311yescharacteristic
170C2×C3×D12—31no—
171C2×C3×C4×D3—31no—
172C2×C3×Dic6—31no—
173C2×C3×Dic6—31no—
174C2×C3×Dic6—31no—
175C2×C3×Dic6—31no—
176C2×C3×Dic6—31no—
177C2×C3×Dic6—31no—
178C2×C3×Dic6—31no—
179C2×C3×Dic6—31no—
180C2×C3×Dic6—64no—
181C2×C3×Dic6—64no—
182C2×#627—24no—
183C2×#627C2×D311yescharacteristic
184C2×#627C2×D311yescharacteristic
185C2×#627C2×D311yescharacteristic
186C2×#627C2×D311yescharacteristic
187C2×#626—31no—
188C2×#626—31no—
189C2×#626—31no—
190C2×#626—31no—
191C2×#626—61no—
192C2×#626—61no—
193C2×#626C2×D311yescharacteristic
194C2×#624—31no—
195C2×#624—31no—
196C2×#624—31no—
197C2×#624—61no—
198#3804—64no—
199C2×D3×Dic3—31no—
200C2×D3×Dic3—31no—
201C2×D3×Dic3C2×D311yescharacteristic
202#3799—64no—
203#3796—64no—
204#3757—31no—
205#3757C2×D311yescharacteristic
206#3752—31no—
207#3752—31no—
208#3752—31no—
209#3752—31no—
210C4⋊(C3⋊Dic3)—31no—
211#3750—31no—
212#3750—31no—
213C4×C3⋊Dic3—31no—
214C3×#217—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—61no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×Dic3⋊C4—31no—
226C3×Dic3⋊C4—31no—
227C3×C4×Dic3—31no—
228C3×C4×Dic3—31no—
229#3724—31no—
230#3724—31no—
231#3724—31no—
232#3724—61no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—61no—
240Dic3⋊Dic3—61no—
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243#3722—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—61no—
251#3722—61no—
252#3722—61no—
253#3722C2×D311yescharacteristic
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—61no—
261(C2×D3)⋊Dic3—61no—
262(C2×D3)⋊Dic3C2×D311yescharacteristic
263(C2×D3)⋊Dic3C2×D311yescharacteristic
264Dic32—31no—
265Dic32—31no—
266Dic32—31no—
267Dic32—31no—
268Dic32—31no—
269Dic32—61no—
270Dic32C2×D311yescharacteristic
271C22×C33—21no—
272C22×C33—21no—
273C22×C33#4112yescomplemented
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—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C3⋊(C3⋊Dic3)—21no—
285C3×C3⋊Dic3—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3C2×D412yes—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3C2×D412yes—
294C32×Dic3C2×D412yes—
295C22×C3×Q8—91no—
296C2×#239—91no—
297C2×#237—91no—
298C2×#235—91no—
299C22×Dic6—31no—
300C22×Dic6—31no—
301C3×#121—91no—
302C3×C4×D4—91no—
303#947—91no—
304#947—91no—
305#947—91no—
306#946—91no—
307#946—91no—
308#946—91no—
309Q8×Dic3—91no—
310#939—31no—
311#939—91no—
312#939—91no—
313#939—91no—
314#939—181no—
315#936—91no—
316D4×Dic3—31no—
317D4×Dic3—91no—
318#930—31no—
319#930—91no—
320#930—91no—
321#930—91no—
322#930—181no—
323C4×#67—31no—
324C4×#67—91no—
325C4×#67—91no—
326C4×#67—91no—
327C4×#67—181no—
328#924—91no—
329#897—91no—
330#896—91no—
331#896—91no—
332#887—91no—
333#885—91no—
334#885—91no—
335#885—91no—
336#885—91no—
337#67⋊C4—91no—
338#67⋊C4—91no—
339#878—91no—
340#878—91no—
341#875—91no—
342C4×Dic6—91no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—31no—
347C23×C32—41no—
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C22×C3⋊D3—31no—
352C22×C3⋊D3—31no—
353C22×C3⋊D3—31no—
354C22×C3⋊D3—61no—
355C22×C3⋊D3—61no—
356C22×C3⋊D3—61no—
357C22×C3⋊D3—121no—
358C22×C3⋊D3C22×D311yescharacteristic
359C22×C3×D3—21no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C32×D4—62no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—62no—
372C2×C32×C4—62no—
373#638—22no—
374#638—62no—
375#638—64no—
376#638—62no—
377#638—62no—
378#638—62no—
379#638—122no—
380#638—122no—
381#638—124no—
382C2×C3⋊Dic3—22no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—121no—
390C2×C3⋊Dic3C22×D311yescharacteristic
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C4⋊(C3⋊D3)—62no—
396C4×C3⋊D3—62no—
397C3×#67—22no—
398C3×#67—22no—
399C3×#67—42no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—62no—
403C3×#67—122no—
404C2×C3×Dic3—22no—
405C2×C3×Dic3—22no—
406C2×C3×Dic3—22no—
407C2×C3×Dic3—22no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—42no—
424C2×C3×Dic3—42no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3—122no—
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
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
444C3×D12—62no—
445C3×C4×D3—62no—
446C3×Dic6—34no—
447C3×Dic6—34no—
448C3×Dic6—62no—
449C3×Dic6—62no—
450C3×Dic6—62no—
451C3×Dic6—62no—
452C3×Dic6—62no—
453C3×Dic6—62no—
454#627—22no—
455#627—22no—
456#627—22no—
457#627#6714yescomplemented
458#626—22no—
459#626—62no—
460#626—62no—
461#626—62no—
462#626—62no—
463#626—122no—
464#626—122no—
465#624—62no—
466#624—62no—
467#624—62no—
468#624—122no—
469D3×Dic3—22no—
470D3×Dic3—62no—
471D3×Dic3—62no—
472#548—271noSylow
473C2×C33—22no—
474C2×C33C22×D411yescharacteristic
475C2×C33C2×#4111yescharacteristic
476C2×C332−1+411yescharacteristic
477C3⋊(C3⋊D3)—41no—
478C3×C3⋊D3—41no—
479C32×D3—41no—
480C2×C3×Q8—91no—
481C2×C3×Q8—91no—
482C2×C3×Q8—91no—
483C2×C3×Q8—91no—
484C2×C3×Q8—184no—
485C2×C3×D4—31no—
486C2×C3×D4—31no—
487C2×C3×D4—61no—
488C2×C3×D4—91no—
489C2×C3×D4—91no—
490C22×C3×C4—31no—
491C22×C3×C4—31no—
492C22×C3×C4—31no—
493C22×C3×C4—31no—
494C22×C3×C4—61no—
495C22×C3×C4—61no—
496C22×C3×C4—91no—
497C22×C3×C4—91no—
498C2×#67—31no—
499C2×#67—31no—
500C2×#67—31no—
501C2×#67—61no—
502C2×#67—91no—
503C2×#67—91no—
504C2×#67—91no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—91no—
508C2×#67—181no—
509C2×#67—181no—
510C2×#67—181no—
511C2×#67—181no—
512C2×#67—361no—
513C2×#67D3211yescharacteristic
514C22×Dic3—31no—
515C22×Dic3—31no—
516C22×Dic3—31no—
517C22×Dic3—61no—
518C22×Dic3—91no—
519C22×Dic3D3211yescharacteristic
520C22×Dic3D3211yescharacteristic
521#239—184no—
522#237—184no—
523#235—184no—
524C2×D12—31no—
525C2×D12—91no—
526C2×D12—91no—
527C2×D12—91no—
528C2×D12—181no—
529C2×C4×D3—31no—
530C2×C4×D3—91no—
531C2×C4×D3—91no—
532C2×C4×D3—91no—
533C2×C4×D3—91no—
534C2×C4×D3—91no—
535C2×C4×D3—181no—
536C2×Dic6—31no—
537C2×Dic6—31no—
538C2×Dic6—31no—
539C2×Dic6—31no—
540C2×Dic6—31no—
541C2×Dic6—31no—
542C2×Dic6—31no—
543C2×Dic6—31no—
544C2×Dic6—64no—
545C2×Dic6—64no—
546C3×C4⋊C4—91no—
547C3×C4⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552C3×C42—91no—
553#217—31no—
554#217—31no—
555#217—31no—
556#217—31no—
557#217—61no—
558#217—91no—
559#217—91no—
560#217—91no—
561#217—91no—
562#217—181no—
563(C2×D3)⋊C4—31no—
564(C2×D3)⋊C4—31no—
565(C2×D3)⋊C4—31no—
566(C2×D3)⋊C4—31no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—91no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—181no—
582(C2×D3)⋊C4—181no—
583(C2×D3)⋊C4—181no—
584(C2×D3)⋊C4—181no—
585C4⋊Dic3—31no—
586C4⋊Dic3—31no—
587C4⋊Dic3—91no—
588C4⋊Dic3—91no—
589C4⋊Dic3—91no—
590C4⋊Dic3—91no—
591C4⋊Dic3—181no—
592Dic3⋊C4—31no—
593Dic3⋊C4—31no—
594Dic3⋊C4—91no—
595Dic3⋊C4—91no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—91no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—181no—
603Dic3⋊C4—181no—
604C4×Dic3—31no—
605C4×Dic3—31no—
606C4×Dic3—91no—
607C4×Dic3—91no—
608C4×Dic3—91no—
609C4×Dic3—91no—
610C4×Dic3—91no—
611C4×Dic3—91no—
612C4×Dic3—181no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—22no—
623C22×C32—22no—
624C22×C32—22no—
625C22×C32—41no—
626C22×C32—42no—
627C22×C32—41no—
628C22×C32—41no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—81no—
637C22×C32—81no—
638C22×C32#23512yescomplemented
639C22×C32#23712yescomplemented
640C22×C32#23912yescomplemented
641C22×C32C23×D311yescharacteristic
642C22×C32C23×D311yescharacteristic
643C22×C32C23×D311yescharacteristic
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3—21no—
647C2×C3⋊D3—61no—
648C2×C3⋊D3—62no—
649C2×C3⋊D3—61no—
650C2×C3⋊D3—61no—
651C2×C3⋊D3—61no—
652C2×C3⋊D3—61no—
653C2×C3⋊D3—61no—
654C2×C3⋊D3—61no—
655C2×C3⋊D3—61no—
656C2×C3⋊D3—61no—
657C2×C3⋊D3—121no—
658C2×C3⋊D3—121no—
659C2×C3⋊D3—122no—
660C2×C3⋊D3—121no—
661C2×C3⋊D3—121no—
662C2×C3⋊D3—121no—
663C2×C3⋊D3—121no—
664C2×C3⋊D3—121no—
665C2×C3⋊D3—121no—
666C2×C3⋊D3—241no—
667C2×C3⋊D3—241no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C32×C4—32no—
687C32×C4—32no—
688C32×C4—61no—
689C32×C4—61no—
690C32×C4—61no—
691C3⋊Dic3—21no—
692C3⋊Dic3—21no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—61no—
696C3⋊Dic3—62no—
697C3⋊Dic3—61no—
698C3⋊Dic3—61no—
699C3⋊Dic3—121no—
700C3⋊Dic3—121no—
701C3⋊Dic3—122no—
702C3⋊Dic3C2×#6712yes—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—22no—
710C3×Dic3—22no—
711C3×Dic3—32no—
712C3×Dic3—32no—
713C3×Dic3—41no—
714C3×Dic3—41no—
715C3×Dic3—41no—
716C3×Dic3—62no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—121no—
726C3×Dic3—121no—
727C3×Dic3—121no—
728C3×Dic3—121no—
729C3×Dic3D3×D412yes—
730C3×Dic3D3×D412yes—
731C3×Dic3C2×#6712yes—
732C3×Dic3C2×#6712yes—
733C2×#41—271no—
734C22×Q8—91no—
735#124—271no—
736#124—271no—
737#124—271no—
738C22⋊Q8—271no—
739C22⋊Q8—271no—
740C22⋊Q8—271no—
741#121—91no—
742#121—271no—
743#121—271no—
744C4×Q8—271no—
745C4×D4—91no—
746C4×D4—271no—
747C4×D4—271no—
748C33#54811yescharacteristic, complemented, Sylow
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—21no—
752C23×C3—31no—
753C23×C3—31no—
754C23×C3—41no—
755C23×C3—61no—
756C23×C3—91no—
757C23×C3C2×D3211yescharacteristic
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—61no—
763C22×D3—91no—
764C22×D3—91no—
765C22×D3—91no—
766C22×D3—181no—
767C22×D3—181no—
768C22×D3—181no—
769C22×D3—361no—
770C22×D3C2×D3211yescharacteristic
771C3×Q8—94no—
772C3×Q8—182no—
773C3×Q8—182no—
774C3×Q8—182no—
775C3×D4—62no—
776C3×D4—62no—
777C3×D4—122no—
778C3×D4—182no—
779C3×D4—182no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—31no—
789C2×C3×C4—31no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—61no—
794C2×C3×C4—61no—
795C2×C3×C4—62no—
796C2×C3×C4—62no—
797C2×C3×C4—62no—
798C2×C3×C4—62no—
799C2×C3×C4—91no—
800C2×C3×C4—91no—
801C2×C3×C4—91no—
802C2×C3×C4—91no—
803C2×C3×C4—91no—
804C2×C3×C4—122no—
805C2×C3×C4—122no—
806C2×C3×C4—182no—
807C2×C3×C4—182no—
808#67—22no—
809#67—62no—
810#67—62no—
811#67—62no—
812#67—122no—
813#67—182no—
814#67—182no—
815#67—184no—
816#67—182no—
817#67—182no—
818#67—182no—
819#67—182no—
820#67—362no—
821#67—362no—
822#67—362no—
823#67—364no—
824C2×Dic3—22no—
825C2×Dic3—22no—
826C2×Dic3—31no—
827C2×Dic3—31no—
828C2×Dic3—31no—
829C2×Dic3—31no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—61no—
840C2×Dic3—61no—
841C2×Dic3—62no—
842C2×Dic3—62no—
843C2×Dic3—62no—
844C2×Dic3—91no—
845C2×Dic3—91no—
846C2×Dic3—91no—
847C2×Dic3—122no—
848C2×Dic3—181no—
849C2×Dic3—181no—
850C2×Dic3—181no—
851C2×Dic3—182no—
852C2×Dic3—361no—
853C2×Dic3C2×D3211yescharacteristic
854C2×Dic3C2×D3211yescharacteristic
855C2×Dic3C2×D3211yescharacteristic
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858D12—62no—
859D12—182no—
860D12—182no—
861D12—182no—
862D12—362no—
863C4×D3—62no—
864C4×D3—182no—
865C4×D3—182no—
866C4×D3—182no—
867C4×D3—182no—
868C4×D3—182no—
869C4×D3—362no—
870Dic6—34no—
871Dic6—34no—
872Dic6—62no—
873Dic6—62no—
874Dic6—62no—
875Dic6—62no—
876Dic6—62no—
877Dic6—62no—
878C2×C32—22no—
879C2×C32—22no—
880C2×C32—22no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—21no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—21no—
890C2×C32—41no—
891C2×C32—41no—
892C2×C32—41no—
893C2×C32—42no—
894C2×C32—42no—
895C2×C32—42no—
896C2×C32—82no—
897C2×C32—121no—
898C2×C32C2×#23511yescharacteristic
899C2×C32C2×D3×D411yescharacteristic
900C2×C32C2×D3×D411yescharacteristic
901C2×C32C2×#23711yescharacteristic
902C2×C32C2×#23911yescharacteristic
903C2×C32#100711yescharacteristic
904C2×C32#101011yescharacteristic
905C2×C32#101011yescharacteristic
906C2×C32C22×#6711yescharacteristic
907C3⋊D3—41no—
908C3⋊D3—121no—
909C3⋊D3—122no—
910C3⋊D3—121no—
911C3⋊D3—121no—
912C3⋊D3—241no—
913C3⋊D3—241no—
914C3⋊D3—242no—
915C3×D3—41no—
916C3×D3—41no—
917C3×D3—81no—
918C3×D3—121no—
919C3×D3—121no—
920C3×D3—241no—
921#41—544no—
922C2×Q8—91no—
923C2×Q8—91no—
924C2×Q8—91no—
925C2×Q8—91no—
926C2×Q8—184no—
927C2×D4—31no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—271no—
931C2×D4—271no—
932C2×D4—271no—
933C22×C4—31no—
934C22×C4—31no—
935C22×C4—91no—
936C22×C4—91no—
937C22×C4—271no—
938C22×C4—271no—
939C4⋊C4—91no—
940C4⋊C4—91no—
941C4⋊C4—271no—
942C4⋊C4—271no—
943C4⋊C4—271no—
944C4⋊C4—271no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—91no—
956C42—271no—
957C42—271no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—22no—
968C22×C3—22no—
969C22×C3—22no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—42no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—81no—
985C22×C3—81no—
986C22×C3—121no—
987C22×C3—121no—
988C22×C3—121no—
989C22×C3—181no—
990C22×C3—181no—
991C22×C3—181no—
992C22×C3#379612yescomplemented
993C22×C3#379912yescomplemented
994C22×C3#380412yescomplemented
995C22×C3C22×D3211yescharacteristic
996C22×C3C22×D3211yescharacteristic
997C22×C3C22×D3211yescharacteristic
998C2×D3—21no—
999C2×D3—21no—
1000C2×D3—21no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—121no—
1008C2×D3—121no—
1009C2×D3—121no—
1010C2×D3—182no—
1011C2×D3—181no—
1012C2×D3—181no—
1013C2×D3—181no—
1014C2×D3—181no—
1015C2×D3—181no—
1016C2×D3—181no—
1017C2×D3—181no—
1018C2×D3—181no—
1019C2×D3—181no—
1020C2×D3—361no—
1021C2×D3—361no—
1022C2×D3—361no—
1023C2×D3—361no—
1024C2×D3—361no—
1025C2×D3—361no—
1026C2×D3—361no—
1027C2×D3—361no—
1028C2×D3—362no—
1029C2×D3—721no—
1030C2×D3—721no—
1031C3×C4—32no—
1032C3×C4—32no—
1033C3×C4—32no—
1034C3×C4—32no—
1035C3×C4—62no—
1036C3×C4—62no—
1037C3×C4—61no—
1038C3×C4—61no—
1039C3×C4—61no—
1040C3×C4—61no—
1041C3×C4—61no—
1042C3×C4—61no—
1043C3×C4—92no—
1044C3×C4—121no—
1045C3×C4—121no—
1046C3×C4—121no—
1047C3×C4—181no—
1048C3×C4—181no—
1049C3×C4—181no—
1050C3×C4—181no—
1051Dic3—21no—
1052Dic3—21no—
1053Dic3—21no—
1054Dic3—32no—
1055Dic3—32no—
1056Dic3—62no—
1057Dic3—61no—
1058Dic3—61no—
1059Dic3—61no—
1060Dic3—61no—
1061Dic3—61no—
1062Dic3—61no—
1063Dic3—61no—
1064Dic3—61no—
1065Dic3—121no—
1066Dic3—121no—
1067Dic3—121no—
1068Dic3—121no—
1069Dic3—182no—
1070Dic3—181no—
1071Dic3—181no—
1072Dic3—181no—
1073Dic3—361no—
1074Dic3—361no—
1075Dic3—362no—
1076Dic3D3×#6712yes—
1077Dic3D3×#6712yes—
1078C32—21no—
1079C32—21no—
1080C32—21no—
1081C32—41no—
1082C32#555211yescharacteristic, complemented
1083C32#559811yescharacteristic, complemented
1084C32#581711yescharacteristic, complemented
1085C23—31no—
1086C23—91no—
1087C23—271no—
1088C23D3311yescharacteristic
1089Q8—94no—
1090Q8—182no—
1091Q8—182no—
1092Q8—182no—
1093D4—62no—
1094D4—182no—
1095D4—182no—
1096D4—542no—
1097D4—542no—
1098D4—542no—
1099C2×C4—31no—
1100C2×C4—31no—
1101C2×C4—31no—
1102C2×C4—31no—
1103C2×C4—31no—
1104C2×C4—62no—
1105C2×C4—62no—
1106C2×C4—91no—
1107C2×C4—91no—
1108C2×C4—91no—
1109C2×C4—91no—
1110C2×C4—91no—
1111C2×C4—182no—
1112C2×C4—182no—
1113C2×C4—271no—
1114C2×C4—542no—
1115C2×C4—542no—
1116C2×C3—22no—
1117C2×C3—22no—
1118C2×C3—22no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—21no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—42no—
1129C2×C3—42no—
1130C2×C3—42no—
1131C2×C3—41no—
1132C2×C3—41no—
1133C2×C3—41no—
1134C2×C3—82no—
1135C2×C3—121no—
1136C2×C3—121no—
1137C2×C3—241no—
1138C2×C3—361no—
1139C2×C3C2×#379611yescharacteristic
1140C2×C3#6429711yescharacteristic
1141C2×C3#6429711yescharacteristic
1142C2×C3C2×#379911yescharacteristic
1143C2×C3#6430911yescharacteristic
1144C2×C3D32×D411yescharacteristic
1145C2×C3C2×#380411yescharacteristic
1146C2×C3C2×D3×#6711yescharacteristic
1147C2×C3C2×D3×#6711yescharacteristic
1148D3—41no—
1149D3—121no—
1150D3—121no—
1151D3—241no—
1152D3—362no—
1153D3—361no—
1154D3—361no—
1155D3—361no—
1156D3—721no—
1157D3—721no—
1158D3—722no—
1159C22—21no—
1160C22—21no—
1161C22—61no—
1162C22—61no—
1163C22—61no—
1164C22—181no—
1165C22—181no—
1166C22—181no—
1167C22—541no—
1168C22—541no—
1169C22—541no—
1170C22#8896212yescomplemented
1171C22C2×D3311yescharacteristic
1172C4—32no—
1173C4—32no—
1174C4—61no—
1175C4—61no—
1176C4—61no—
1177C4—92no—
1178C4—181no—
1179C4—181no—
1180C4—181no—
1181C4—181no—
1182C4—541no—
1183C3—21no—
1184C3—21no—
1185C3—21no—
1186C3—41no—
1187C3#1059490011yescharacteristic, complemented
1188C3#1059490211yescharacteristic, complemented
1189C3#1059514111yescharacteristic, complemented
1190C2—22no—
1191C2—121no—
1192C2—361no—
1193C2—1081no—
1194C2#1172442611yescharacteristic
1195C2C2×#8896211yescharacteristic
1196C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×C3×#627C2semidirect
2. C2×#88962C2semidirect
3. #11723726C2semidirect
4. #11723635C2semidirect
5. #11723632C2semidirect
6. #11723618C2semidirect
7. C3×#63978C2semidirect
8. C3×Dic3×#67C2semidirect
9. #11723005C2semidirect
10. #11723003C2semidirect
11. #11723001C2semidirect
12. #11722979C2semidirect
13. #11722973C2semidirect
14. #11722969C2semidirect
15. #11722940C2semidirect
58. C22×#627D3semidirect
75. #63978D3semidirect
78. Dic3×#67D3semidirect
132. C3×#627D4semidirect
273. C22×C33#41semidirect
457. #627#67semidirect
638. C22×C32#235semidirect
639. C22×C32#237semidirect
640. C22×C32#239semidirect
748. C33#548semidirect
992. C22×C3#3796semidirect
993. C22×C3#3799semidirect
994. C22×C3#3804semidirect
1082. C32#5552semidirect
1083. C32#5598semidirect
1084. C32#5817semidirect
1170. C22#88962semidirect
1187. C3#10594900semidirect
1188. C3#10594902semidirect
1189. C3#10595141semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6272
C2×#889622
#117237262
#117236352
#117236322
#117236182
C3×#639782
C3×Dic3×#672
#117230052
#117230032
#117230012
#117229792
#117229732
#117229692
#117229402
#105951413
#105949023
#105949003