Finite Group Databasebeta

← #13172090

Subgroups — #13172090

Order 1728.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723726C211yesmaximal, characteristic, complemented
2#11723609C211yesmaximal, characteristic, complemented
3#11723603C211yesmaximal, characteristic, complemented
4C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63964C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723022C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11723001C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13#11722927C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595187—31nomaximal
17#10594965—31nomaximal
18#10594216—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88814C2211yescharacteristic
32#88813C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35Dic3⋊(C3⋊Dic3)C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37#88803C2211yescharacteristic
38#88803C2211yescharacteristic
39(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64144—31no—
55C2×C4×C3⋊Dic3—31no—
56#64095—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#930—31no—
60C3×#924—31no—
61C3×#67⋊C4—31no—
62C3×#878—31no—
63#63978D311yescharacteristic
64#67⋊Dic3—31no—
65#67⋊Dic3D311yescharacteristic, complemented
66Dic3×#67—31no—
67Dic3×#67—31no—
68#63964D311yescharacteristic, complemented
69#63962—31no—
70#63962—31no—
71#63962—31no—
72#63962—31no—
73#63962—61no—
74#63962—61no—
75#63959—31no—
76#63956—31no—
77#63955—31no—
78C2×Dic32—31no—
79C2×Dic32—31no—
80C2×Dic32—61no—
81#63952—31no—
82#63907—31no—
83#63904—31no—
84#63898—31no—
85#63878—31no—
86#63878—31no—
87#63877—31no—
88#63872—31no—
89#63863—31no—
90#63862—31no—
91#63862—31no—
92#63861—31no—
93#63858—31no—
94#63848—31no—
95#63846—31no—
96#63845—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63841—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)—22no—
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C2×C32×Dic3—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6294—22no—
123C3×#627—22no—
124C3×#626—22no—
125C3×D3×Dic3—22no—
126#5624—91no—
127#5600—91no—
128#5538—91no—
129C2×C32×D4—31no—
130C22×C32×C4—31no—
131C2×#638C2×D311yescharacteristic
132C22×C3⋊Dic3—31no—
133C22×C3⋊Dic3—31no—
134C22×C3⋊Dic3—31no—
135C22×C3⋊Dic3—61no—
136C22×C3⋊Dic3—61no—
137C22×C3⋊Dic3—61no—
138C22×C3⋊Dic3—121no—
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×C3×#67—21no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—61no—
145C2×C3×#67C2×D311yescharacteristic
146C2×C3×#67C2×D311yescharacteristic
147C22×C3×Dic3—21no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—61no—
152C22×C3×Dic3C2×D311yescharacteristic
153C22×C3×Dic3C2×D311yescharacteristic
154C2×C3×D12—31no—
155C2×C3×C4×D3—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6—31no—
158C2×#627C2×D311yescharacteristic
159C2×#626C2×D311yescharacteristic
160C2×#624—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3C2×D311yescharacteristic
164C32×C22⋊C4—31no—
165#3757—31no—
166#3757—31no—
167#3757C2×D311yescharacteristic
168#3752—31no—
169#3752—31no—
170C4⋊(C3⋊Dic3)—31no—
171C4⋊(C3⋊Dic3)—31no—
172#3750—31no—
173#3750—31no—
174C4×C3⋊Dic3—31no—
175C4×C3⋊Dic3—31no—
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—31no—
178C3×#217—21no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—61no—
184C3×#217C2×D311yescharacteristic
185C3×#217C2×D311yescharacteristic
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202#3724—31no—
203#3724C2×D311yescharacteristic
204Dic3⋊Dic3—31no—
205Dic3⋊Dic3—31no—
206Dic3⋊Dic3—31no—
207Dic3⋊Dic3—31no—
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—61no—
215Dic3⋊Dic3—61no—
216Dic3⋊Dic3—61no—
217Dic3⋊Dic3—61no—
218Dic3⋊Dic3C2×D311yescharacteristic
219Dic3⋊Dic3C2×D311yescharacteristic
220Dic3⋊Dic3C2×D311yescharacteristic
221Dic3⋊Dic3C2×D311yescharacteristic
222#3722—31no—
223#3722C2×D311yescharacteristic
224(C2×D3)⋊Dic3—31no—
225(C2×D3)⋊Dic3—31no—
226(C2×D3)⋊Dic3—31no—
227(C2×D3)⋊Dic3—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—61no—
235(C2×D3)⋊Dic3—61no—
236(C2×D3)⋊Dic3—61no—
237(C2×D3)⋊Dic3—61no—
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—61no—
252Dic32—61no—
253Dic32—61no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3#4112yes—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×C22⋊Q8—91no—
279C3×#121—91no—
280C3×C4×D4—91no—
281#947—91no—
282Q8×Dic3—91no—
283#939—31no—
284#936—91no—
285#935—91no—
286#935—91no—
287#935—91no—
288#935—181no—
289D4×Dic3—31no—
290D4×Dic3—91no—
291D4×Dic3—91no—
292#930—31no—
293C4×#67—91no—
294C4×#67—91no—
295#926—91no—
296#924—31no—
297C2×C4×Dic3—91no—
298C2×C4×Dic3—91no—
299C2×C4×Dic3—91no—
300C2×C4×Dic3—181no—
301#898—91no—
302#898—91no—
303#898—91no—
304#893—91no—
305#892—91no—
306#892—91no—
307#890—91no—
308#890—91no—
309#889—91no—
310#887—91no—
311#886—91no—
312#886—91no—
313#886—91no—
314#886—181no—
315#885—91no—
316#67⋊C4—31no—
317#67⋊C4—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#878—31no—
322#877—91no—
323#877—91no—
324#872—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—31no—
330C23×C32—41no—
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C23×C32C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—61no—
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C32×D4—62no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—62no—
348#638—22no—
349C2×C3⋊Dic3—22no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—62no—
363C2×C3⋊Dic3—64no—
364C2×C3⋊Dic3—62no—
365C2×C3⋊Dic3—62no—
366C2×C3⋊Dic3—121no—
367C2×C3⋊Dic3—121no—
368C2×C3⋊Dic3—122no—
369C2×C3⋊Dic3—122no—
370C2×C3⋊Dic3—124no—
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C3×#67—22no—
377C3×#67—22no—
378C3×#67—42no—
379C3×#67—62no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—122no—
383C2×C3×Dic3—24no—
384C2×C3×Dic3—22no—
385C2×C3×Dic3—22no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—21no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—62no—
407C2×C3×Dic3—62no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—64no—
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C3×D12—62no—
421C3×C4×D3—62no—
422C3×Dic6—62no—
423C3×Dic6—62no—
424#627—22no—
425#626—22no—
426#624—62no—
427D3×Dic3—22no—
428D3×Dic3—62no—
429D3×Dic3—62no—
430#529—271noSylow
431C2×C33—22no—
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C2×C33C2×#4111yescharacteristic
435C3×C3⋊D3—41no—
436C32×D3—41no—
437C2×C3×Q8—91no—
438C2×C3×D4—31no—
439C2×C3×D4—31no—
440C2×C3×D4—61no—
441C2×C3×D4—91no—
442C2×C3×D4—91no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—61no—
446C22×C3×C4—91no—
447C22×C3×C4—91no—
448C2×#67—31no—
449C2×#67—31no—
450C2×#67—31no—
451C2×#67—61no—
452C2×#67D3211yescharacteristic
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—61no—
457C22×Dic3—91no—
458C22×Dic3—91no—
459C22×Dic3—91no—
460C22×Dic3—91no—
461C22×Dic3—181no—
462C22×Dic3—181no—
463C22×Dic3—181no—
464C22×Dic3—361no—
465C22×Dic3D3211yescharacteristic
466C2×D12—31no—
467C2×C4×D3—31no—
468C2×C4×D3—91no—
469C2×C4×D3—91no—
470C2×Dic6—31no—
471C2×Dic6—31no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C22⋊C4—31no—
478C3×C22⋊C4—31no—
479C3×C22⋊C4—61no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C42—91no—
485#217—31no—
486#217—31no—
487#217—31no—
488#217—31no—
489#217—61no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217—91no—
497#217—181no—
498#217—181no—
499#217D3211yescharacteristic
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—181no—
513(C2×D3)⋊C4—181no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—181no—
526C4⋊Dic3—181no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—181no—
542Dic3⋊C4—181no—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—91no—
546C4×Dic3—91no—
547C4×Dic3—91no—
548C4×Dic3—91no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—181no—
561C4×Dic3—181no—
562C4×Dic3—181no—
563C4×Dic3—181no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—22no—
567C22×C32—22no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—22no—
576C22×C32—22no—
577C22×C32—22no—
578C22×C32—42no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—42no—
585C22×C32—42no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32#23512yes—
590C22×C32#23712yes—
591C22×C32#23912yes—
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C22×C32C23×D311yescharacteristic
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—41no—
605C2×C3×D3—41no—
606C2×C3×D3—41no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—121no—
614C2×C3×D3—121no—
615C2×C3×D3—121no—
616C32×C4—32no—
617C32×C4—61no—
618C32×C4—61no—
619C32×C4—61no—
620C32×C4—61no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—62no—
628C3⋊Dic3—62no—
629C3⋊Dic3—61no—
630C3⋊Dic3—61no—
631C3⋊Dic3—61no—
632C3⋊Dic3—61no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—121no—
636C3⋊Dic3—121no—
637C3⋊Dic3—122no—
638C3⋊Dic3—122no—
639C3⋊Dic3#23712yes—
640C3×Dic3—22no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—22no—
650C3×Dic3—32no—
651C3×Dic3—32no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—62no—
656C3×Dic3—62no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3#23712yes—
669C3×Dic3#23712yes—
670#126—271no—
671#126—271no—
672#125—271no—
673#124—271no—
674#123—271no—
675#123—271no—
676C22⋊Q8—91no—
677#121—91no—
678C4×Q8—271no—
679C4×D4—91no—
680C4×D4—271no—
681C4×D4—271no—
682#117—271no—
683#117—271no—
684C2×C42—271no—
685C33#52911yescharacteristic, complemented, Sylow
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—21no—
689C23×C3—31no—
690C23×C3—31no—
691C23×C3—41no—
692C23×C3—61no—
693C23×C3—91no—
694C23×C3C2×D3211yescharacteristic
695C23×C3C2×D3211yescharacteristic
696C23×C3C2×D3211yescharacteristic
697C22×D3—31no—
698C22×D3—31no—
699C22×D3—61no—
700C22×D3C2×D3211yescharacteristic
701C3×Q8—182no—
702C3×D4—62no—
703C3×D4—62no—
704C3×D4—122no—
705C3×D4—182no—
706C3×D4—182no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—31no—
714C2×C3×C4—31no—
715C2×C3×C4—31no—
716C2×C3×C4—31no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—61no—
721C2×C3×C4—61no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—64no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—91no—
730C2×C3×C4—182no—
731C2×C3×C4—182no—
732#67—22no—
733#67—62no—
734#67—62no—
735#67—62no—
736#67—122no—
737C2×Dic3—22no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—64no—
757C2×Dic3—91no—
758C2×Dic3—91no—
759C2×Dic3—91no—
760C2×Dic3—91no—
761C2×Dic3—91no—
762C2×Dic3—91no—
763C2×Dic3—181no—
764C2×Dic3—181no—
765C2×Dic3—181no—
766C2×Dic3—181no—
767C2×Dic3—181no—
768C2×Dic3—181no—
769C2×Dic3—182no—
770C2×Dic3—184no—
771C2×Dic3—182no—
772C2×Dic3—182no—
773C2×Dic3—182no—
774C2×Dic3—361no—
775C2×Dic3—361no—
776C2×Dic3—362no—
777C2×Dic3—362no—
778C2×Dic3—364no—
779C2×Dic3C2×D3211yescharacteristic
780C2×Dic3C2×D3211yescharacteristic
781C2×Dic3C2×D3211yescharacteristic
782C2×Dic3C2×D3211yescharacteristic
783C2×Dic3C2×D3211yescharacteristic
784D12—62no—
785C4×D3—62no—
786C4×D3—182no—
787C4×D3—182no—
788Dic6—62no—
789Dic6—62no—
790C2×C32—22no—
791C2×C32—24no—
792C2×C32—22no—
793C2×C32—22no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—41no—
804C2×C32—41no—
805C2×C32—41no—
806C2×C32—42no—
807C2×C32—42no—
808C2×C32—44no—
809C2×C32—121no—
810C2×C32C2×#23511yescharacteristic
811C2×C32C2×#23711yescharacteristic
812C2×C32C2×#23711yescharacteristic
813C2×C32C2×#23711yescharacteristic
814C2×C32C2×#23711yescharacteristic
815C2×C32C2×#23911yescharacteristic
816C2×C32D3×#4111yescharacteristic
817C2×C32D3×#4111yescharacteristic
818C2×C32D3×#4111yescharacteristic
819C3⋊D3—41no—
820C3×D3—41no—
821C3×D3—41no—
822C3×D3—81no—
823C3×D3—121no—
824C3×D3—121no—
825C3×D3—241no—
826C2×Q8—91no—
827C2×D4—31no—
828C2×D4—91no—
829C2×D4—91no—
830C22×C4—31no—
831C22×C4—91no—
832C22×C4—91no—
833C22×C4—271no—
834C22×C4—271no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—91no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—31no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—271no—
857C42—271no—
858C42—271no—
859C42—271no—
860C42—271no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—41no—
879C22×C3—42no—
880C22×C3—42no—
881C22×C3—41no—
882C22×C3—42no—
883C22×C3—61no—
884C22×C3—61no—
885C22×C3—61no—
886C22×C3—61no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—121no—
890C22×C3—121no—
891C22×C3—121no—
892C22×C3—181no—
893C22×C3—181no—
894C22×C3—181no—
895C22×C3#379612yes—
896C22×C3#379912yes—
897C22×C3#380412yes—
898C22×C3C22×D3211yescharacteristic
899C22×C3C22×D3211yescharacteristic
900C22×C3C22×D3211yescharacteristic
901C2×D3—21no—
902C2×D3—21no—
903C2×D3—21no—
904C2×D3—61no—
905C2×D3—61no—
906C2×D3—61no—
907C2×D3—61no—
908C2×D3—61no—
909C2×D3—61no—
910C2×D3—121no—
911C2×D3—121no—
912C2×D3—121no—
913C3×C4—32no—
914C3×C4—32no—
915C3×C4—62no—
916C3×C4—62no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—61no—
925C3×C4—92no—
926C3×C4—121no—
927C3×C4—121no—
928C3×C4—121no—
929C3×C4—181no—
930C3×C4—181no—
931C3×C4—181no—
932C3×C4—181no—
933Dic3—21no—
934Dic3—21no—
935Dic3—21no—
936Dic3—21no—
937Dic3—32no—
938Dic3—32no—
939Dic3—62no—
940Dic3—62no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—121no—
950Dic3—121no—
951Dic3—121no—
952Dic3—182no—
953Dic3—182no—
954Dic3—181no—
955Dic3—181no—
956Dic3—181no—
957Dic3—181no—
958Dic3—181no—
959Dic3—181no—
960Dic3—361no—
961Dic3—361no—
962Dic3—361no—
963Dic3—361no—
964Dic3—362no—
965Dic3—362no—
966Dic3#380512yes—
967C32—21no—
968C32—21no—
969C32—21no—
970C32—41no—
971C32#553811yescharacteristic, complemented
972C32#560011yescharacteristic, complemented
973C32#562411yescharacteristic, complemented
974C23—31no—
975C23—91no—
976C23D3311yescharacteristic
977Q8—182no—
978D4—62no—
979D4—182no—
980D4—182no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—31no—
986C2×C4—62no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—91no—
992C2×C4—182no—
993C2×C4—182no—
994C2×C4—271no—
995C2×C4—271no—
996C2×C4—542no—
997C2×C4—542no—
998C2×C3—24no—
999C2×C3—22no—
1000C2×C3—22no—
1001C2×C3—22no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—21no—
1009C2×C3—21no—
1010C2×C3—21no—
1011C2×C3—42no—
1012C2×C3—42no—
1013C2×C3—44no—
1014C2×C3—41no—
1015C2×C3—41no—
1016C2×C3—41no—
1017C2×C3—121no—
1018C2×C3—121no—
1019C2×C3—241no—
1020C2×C3—361no—
1021C2×C3C2×#379611yescharacteristic
1022C2×C3C2×#379911yescharacteristic
1023C2×C3#6430611yescharacteristic
1024C2×C3D3×#23711yescharacteristic
1025C2×C3D3×#23711yescharacteristic
1026C2×C3D3×#23711yescharacteristic
1027C2×C3D3×#23711yescharacteristic
1028C2×C3C2×#380411yescharacteristic
1029C2×C3C2×#380511yescharacteristic
1030D3—41no—
1031D3—121no—
1032D3—121no—
1033D3—241no—
1034C22—21no—
1035C22—21no—
1036C22—61no—
1037C22—61no—
1038C22—61no—
1039C22—181no—
1040C22—181no—
1041C22—181no—
1042C22#8896212yes—
1043C22C2×D3311yescharacteristic
1044C4—32no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—61no—
1049C4—92no—
1050C4—181no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C4—541no—
1055C4—541no—
1056C3—21no—
1057C3—21no—
1058C3—21no—
1059C3—41no—
1060C3#1059421611yescharacteristic, complemented
1061C3#1059496511yescharacteristic, complemented
1062C3#1059518711yescharacteristic, complemented
1063C2—22no—
1064C2—121no—
1065C2—361no—
1066C2D3×#380511yescharacteristic
1067C2#1172440711yescharacteristic
1068C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63978C2
hypercenterC23D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723726C2semidirect
2. #11723609C2semidirect
3. #11723603C2semidirect
4. C2×Dic3×C3⋊Dic3C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63964C2semidirect
8. #11723025C2semidirect
9. #11723022C2semidirect
10. #11723013C2semidirect
11. #11723001C2semidirect
12. #11722940C2semidirect
13. #11722927C2semidirect
14. #11722922C2semidirect
15. #11722914C2semidirect
65. #67⋊Dic3D3semidirect
68. #63964D3semidirect
685. C33#529semidirect
971. C32#5538semidirect
972. C32#5600semidirect
973. C32#5624semidirect
1060. C3#10594216semidirect
1061. C3#10594965semidirect
1062. C3#10595187semidirect

Maximal subgroups

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

subgroupindex
#117237262
#117236092
#117236032
C2×Dic3×C3⋊Dic32
C3×#639782
C3×#67⋊Dic32
C3×#639642
#117230252
#117230222
#117230132
#117230012
#117229402
#117229272
#117229222
#117229142
#105951873
#105949653
#105942163