Finite Group Databasebeta

← #13172221

Subgroups — #13172221

Order 1728.

1160 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723715C211yesmaximal, characteristic, complemented
2#11723618C211yesmaximal, characteristic
3#11723612C211yesmaximal, characteristic
4#11723608C211yesmaximal, characteristic
5C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63955C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723017C211yesmaximal, characteristic, complemented
11#11723013C211yesmaximal, characteristic, complemented
12#11723012C211yesmaximal, characteristic, complemented
13#11722973C211yesmaximal, characteristic, complemented
14#11722940C211yesmaximal, characteristic, complemented
15#11722920C211yesmaximal, characteristic, complemented
16#10594825—31nomaximal
17#10594807—31nomaximal
18#10594045—31nomaximal
19C2×#6312C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C3×#3757C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C32×#217C2211yescharacteristic
28#88815C2211yescharacteristic
29#88815C2211yescharacteristic
30#88813C2211yescharacteristic
31#88813C2211yescharacteristic
32#88807C2211yescharacteristic
33#88807C2211yescharacteristic
34#88806C2211yescharacteristic
35Dic3⋊(C3⋊Dic3)C2211yescharacteristic
36Dic3⋊(C3⋊Dic3)C2211yescharacteristic
37#88804C2211yescharacteristic
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64138—31no—
55C4×#638—31no—
56#64095—31no—
57C3×#926—31no—
58C2×C3×C4⋊Dic3—31no—
59C3×#924—31no—
60C2×C3×Dic3⋊C4—31no—
61C3×#878—31no—
62C3×#877—31no—
63#63966—31no—
64#63966—31no—
65#63966—31no—
66#63966—31no—
67#63966—61no—
68#63966—61no—
69C2×Dic3⋊Dic3D311yescharacteristic, complemented
70#63964D311yescharacteristic, complemented
71#63957—31no—
72#63955—31no—
73#63955—31no—
74#63955D311yescharacteristic, complemented
75#63952—31no—
76#63952—31no—
77#63952—61no—
78#63895—31no—
79#63888—31no—
80#63872—31no—
81#63871—31no—
82#63869—31no—
83#63868—31no—
84#63868—31no—
85#63867—31no—
86#63849—31no—
87#63848—31no—
88#63848—31no—
89#63848—31no—
90#63848—31no—
91#63847—31no—
92#63846—31no—
93#63846—31no—
94#63846—31no—
95#63845—31no—
96#63845—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63837—31no—
100#63836—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104#6312—22no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3—22no—
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3—22no—
114C2×C32×Dic3—22no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6289—22no—
122C3×#627—22no—
123#5642—91no—
124#5531—91no—
125#5513—91no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×#638—31no—
131C2×#638—61no—
132C2×#638—61no—
133C2×#638—61no—
134C2×#638—121no—
135C22×C3⋊Dic3C2×D311yescharacteristic
136C2×C4×C3⋊D3—31no—
137C22×C3×Dic3—21no—
138C22×C3×Dic3—21no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—61no—
142C22×C3×Dic3C2×D311yescharacteristic
143C22×C3×Dic3C2×D311yescharacteristic
144C22×C3×Dic3C2×D311yescharacteristic
145C22×C3×Dic3C2×D311yescharacteristic
146C2×C3×Dic6—31no—
147C2×C3×Dic6—31no—
148C2×#627C2×D311yescharacteristic
149C2×#624—31no—
150C2×#624—31no—
151C2×#624—61no—
152C32×C22⋊C4—31no—
153#3757C2×D311yescharacteristic
154#3757C2×D311yescharacteristic
155#3752—31no—
156#3752—31no—
157#3752—31no—
158#3752—31no—
159#3752—31no—
160C4⋊(C3⋊Dic3)—31no—
161C4⋊(C3⋊Dic3)—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165C4×C3⋊Dic3—31no—
166C3×#217—21no—
167C3×#217—31no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—61no—
172C3×#217—61no—
173C3×#217C2×D311yescharacteristic
174C3×#217C2×D311yescharacteristic
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×C4×Dic3—31no—
194C3×C4×Dic3—31no—
195C3×C4×Dic3—31no—
196C3×C4×Dic3—31no—
197#3724—31no—
198#3724—31no—
199#3724—31no—
200#3724—31no—
201#3724—61no—
202#3724C2×D311yescharacteristic
203Dic3⋊Dic3—31no—
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—31no—
215Dic3⋊Dic3—61no—
216Dic3⋊Dic3—61no—
217Dic3⋊Dic3—61no—
218Dic3⋊Dic3—61no—
219Dic3⋊Dic3C2×D311yescharacteristic
220Dic3⋊Dic3C2×D311yescharacteristic
221Dic3⋊Dic3C2×D311yescharacteristic
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238#3722—61no—
239#3722—61no—
240#3722—61no—
241#3722—61no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253C22×C33—21no—
254C22×C33—21no—
255C22×C33#4112yes—
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C3⋊(C3⋊Dic3)—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3#4112yes—
273C3×C22⋊Q8—91no—
274C3×#117—91no—
275C2×C3×C4⋊C4—91no—
276#946—91no—
277Q8×Dic3—91no—
278#929—91no—
279#929—91no—
280#929—91no—
281#929—181no—
282C4×#67—91no—
283C4×#67—91no—
284C4×#67—181no—
285#926—31no—
286#926—91no—
287C2×C4⋊Dic3—31no—
288#924—31no—
289C2×Dic3⋊C4—31no—
290#898—91no—
291#898—91no—
292#898—91no—
293#898—91no—
294#898—91no—
295#897—91no—
296#896—91no—
297#892—91no—
298#892—91no—
299#890—91no—
300#890—91no—
301#890—91no—
302#890—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#889—91no—
307#887—91no—
308#886—91no—
309#886—91no—
310#886—91no—
311#886—181no—
312#67⋊C4—91no—
313#878—31no—
314#877—31no—
315#877—91no—
316#877—91no—
317#876—91no—
318#872—91no—
319#870—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—41no—
325C23×C32C22×D311yescharacteristic
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—31no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—61no—
334C22×C3⋊D3—121no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—62no—
342C2×C32×C4—62no—
343#638—62no—
344#638—64no—
345#638—62no—
346#638—62no—
347#638—122no—
348#638—122no—
349#638—124no—
350C2×C3⋊Dic3—22no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—121no—
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C4×C3⋊D3—62no—
365C2×C3×Dic3—22no—
366C2×C3×Dic3—22no—
367C2×C3×Dic3—22no—
368C2×C3×Dic3—22no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—42no—
388C2×C3×Dic3—42no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—62no—
396C2×C3×Dic3—62no—
397C2×C3×Dic3—122no—
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C3×Dic6—62no—
411C3×Dic6—62no—
412#627—22no—
413#624—62no—
414#624—62no—
415#624—122no—
416#552—271noSylow
417C2×C33—22no—
418C2×C33C2×#4111yescharacteristic
419C2×C33C2×#4111yescharacteristic
420C2×C332−1+411yescharacteristic
421C3⋊(C3⋊D3)—41no—
422C2×C3×Q8—91no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—31no—
427C22×C3×C4—61no—
428C22×C3×C4—61no—
429C22×C3×C4—91no—
430C2×#67—91no—
431C2×#67—91no—
432C2×#67—91no—
433C2×#67—181no—
434C2×#67—181no—
435C2×#67—181no—
436C2×#67—361no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—61no—
440C22×Dic3D3211yescharacteristic
441C22×Dic3D3211yescharacteristic
442C2×C4×D3—91no—
443C2×C4×D3—91no—
444C2×C4×D3—91no—
445C2×C4×D3—181no—
446C2×Dic6—31no—
447C2×Dic6—31no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C4⋊C4—91no—
451C3×C4⋊C4—91no—
452C3×C4⋊C4—91no—
453C3×C4⋊C4—91no—
454C3×C4⋊C4—91no—
455C3×C4⋊C4—91no—
456C3×C4⋊C4—91no—
457C3×C22⋊C4—31no—
458C3×C22⋊C4—31no—
459C3×C22⋊C4—61no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C42—91no—
463C3×C42—91no—
464#217—31no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—61no—
469#217—61no—
470#217D3211yescharacteristic
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—91no—
473(C2×D3)⋊C4—91no—
474(C2×D3)⋊C4—91no—
475(C2×D3)⋊C4—91no—
476(C2×D3)⋊C4—91no—
477(C2×D3)⋊C4—91no—
478(C2×D3)⋊C4—91no—
479(C2×D3)⋊C4—91no—
480(C2×D3)⋊C4—91no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—181no—
487(C2×D3)⋊C4—181no—
488(C2×D3)⋊C4—181no—
489(C2×D3)⋊C4—181no—
490(C2×D3)⋊C4—181no—
491C4⋊Dic3—31no—
492C4⋊Dic3—31no—
493C4⋊Dic3—31no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—91no—
500C4⋊Dic3—91no—
501C4⋊Dic3—91no—
502C4⋊Dic3—91no—
503C4⋊Dic3—91no—
504C4⋊Dic3—91no—
505C4⋊Dic3—91no—
506C4⋊Dic3—91no—
507C4⋊Dic3—181no—
508C4⋊Dic3—181no—
509Dic3⋊C4—31no—
510Dic3⋊C4—31no—
511Dic3⋊C4—31no—
512Dic3⋊C4—31no—
513Dic3⋊C4—31no—
514Dic3⋊C4—31no—
515Dic3⋊C4—31no—
516Dic3⋊C4—31no—
517Dic3⋊C4—31no—
518Dic3⋊C4—31no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—91no—
527Dic3⋊C4—91no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
531Dic3⋊C4—91no—
532Dic3⋊C4—181no—
533Dic3⋊C4—181no—
534Dic3⋊C4—181no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—91no—
546C4×Dic3—91no—
547C4×Dic3—91no—
548C4×Dic3—181no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—21no—
558C22×C32—22no—
559C22×C32—22no—
560C22×C32—22no—
561C22×C32—41no—
562C22×C32—42no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—41no—
569C22×C32—81no—
570C22×C32—81no—
571C22×C32#23512yes—
572C22×C32#23712yes—
573C22×C32#23912yes—
574C22×C32C23×D311yescharacteristic
575C22×C32C23×D311yescharacteristic
576C22×C32C23×D311yescharacteristic
577C2×C3⋊D3—61no—
578C2×C3⋊D3—62no—
579C2×C3⋊D3—61no—
580C2×C3⋊D3—61no—
581C2×C3⋊D3—61no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—61no—
584C2×C3⋊D3—61no—
585C2×C3⋊D3—61no—
586C2×C3⋊D3—61no—
587C2×C3⋊D3—121no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—122no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—121no—
594C2×C3⋊D3—121no—
595C2×C3⋊D3—121no—
596C2×C3⋊D3—241no—
597C2×C3⋊D3—241no—
598C32×C4—32no—
599C32×C4—61no—
600C32×C4—61no—
601C32×C4—61no—
602C32×C4—61no—
603C32×C4—61no—
604C3⋊Dic3—21no—
605C3⋊Dic3—21no—
606C3⋊Dic3—21no—
607C3⋊Dic3—21no—
608C3⋊Dic3—21no—
609C3⋊Dic3—21no—
610C3⋊Dic3—61no—
611C3⋊Dic3—62no—
612C3⋊Dic3—61no—
613C3⋊Dic3—61no—
614C3⋊Dic3—121no—
615C3⋊Dic3—121no—
616C3⋊Dic3—122no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—21no—
622C3×Dic3—21no—
623C3×Dic3—21no—
624C3×Dic3—21no—
625C3×Dic3—21no—
626C3×Dic3—21no—
627C3×Dic3—22no—
628C3×Dic3—41no—
629C3×Dic3—41no—
630C3×Dic3—41no—
631C3×Dic3—41no—
632C3×Dic3—41no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—121no—
646C3×Dic3—121no—
647C3×Dic3—121no—
648C3×Dic3—121no—
649C3×Dic3—121no—
650C3×Dic3—121no—
651C3×Dic3#23512yes—
652C3×Dic3#23712yes—
653#126—271no—
654#126—271no—
655#125—271no—
656#125—271no—
657#125—271no—
658#123—271no—
659#123—271no—
660C22⋊Q8—91no—
661C22⋊Q8—271no—
662C4×Q8—271no—
663C4×D4—271no—
664#117—91no—
665#117—271no—
666#117—271no—
667C2×C4⋊C4—91no—
668C33#55211yescharacteristic, complemented, Sylow
669C23×C3—21no—
670C23×C3—21no—
671C23×C3—21no—
672C23×C3—41no—
673C23×C3C2×D3211yescharacteristic
674C23×C3C2×D3211yescharacteristic
675C23×C3C2×D3211yescharacteristic
676C22×D3—91no—
677C22×D3—91no—
678C22×D3—91no—
679C22×D3—181no—
680C22×D3—181no—
681C22×D3—181no—
682C22×D3—361no—
683C3×Q8—182no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—31no—
687C2×C3×C4—31no—
688C2×C3×C4—31no—
689C2×C3×C4—31no—
690C2×C3×C4—31no—
691C2×C3×C4—31no—
692C2×C3×C4—31no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—62no—
703C2×C3×C4—62no—
704C2×C3×C4—62no—
705C2×C3×C4—62no—
706C2×C3×C4—91no—
707C2×C3×C4—91no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—122no—
713C2×C3×C4—122no—
714C2×C3×C4—182no—
715#67—184no—
716#67—182no—
717#67—182no—
718#67—182no—
719#67—362no—
720#67—362no—
721#67—364no—
722C2×Dic3—22no—
723C2×Dic3—22no—
724C2×Dic3—31no—
725C2×Dic3—31no—
726C2×Dic3—31no—
727C2×Dic3—31no—
728C2×Dic3—31no—
729C2×Dic3—31no—
730C2×Dic3—31no—
731C2×Dic3—31no—
732C2×Dic3—31no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—62no—
743C2×Dic3—62no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—91no—
747C2×Dic3—122no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—181no—
751C2×Dic3—361no—
752C2×Dic3C2×D3211yescharacteristic
753C2×Dic3C2×D3211yescharacteristic
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C4×D3—182no—
759C4×D3—182no—
760C4×D3—182no—
761C4×D3—362no—
762Dic6—62no—
763Dic6—62no—
764C2×C32—22no—
765C2×C32—22no—
766C2×C32—22no—
767C2×C32—21no—
768C2×C32—21no—
769C2×C32—21no—
770C2×C32—21no—
771C2×C32—21no—
772C2×C32—21no—
773C2×C32—21no—
774C2×C32—21no—
775C2×C32—21no—
776C2×C32—41no—
777C2×C32—41no—
778C2×C32—41no—
779C2×C32—42no—
780C2×C32—42no—
781C2×C32—42no—
782C2×C32—82no—
783C2×C32C2×#23511yescharacteristic
784C2×C32C2×#23511yescharacteristic
785C2×C32C2×#23711yescharacteristic
786C2×C32C2×#23711yescharacteristic
787C2×C32C2×#23911yescharacteristic
788C2×C32#100711yescharacteristic
789C2×C32D3×#4111yescharacteristic
790C2×C32#101011yescharacteristic
791C2×C32#101011yescharacteristic
792C3⋊D3—121no—
793C3⋊D3—122no—
794C3⋊D3—121no—
795C3⋊D3—121no—
796C3⋊D3—241no—
797C3⋊D3—241no—
798C3⋊D3—242no—
799C2×Q8—91no—
800C2×D4—271no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—91no—
804C22×C4—271no—
805C4⋊C4—91no—
806C4⋊C4—91no—
807C4⋊C4—91no—
808C4⋊C4—91no—
809C4⋊C4—91no—
810C4⋊C4—91no—
811C4⋊C4—91no—
812C4⋊C4—91no—
813C4⋊C4—91no—
814C4⋊C4—271no—
815C4⋊C4—271no—
816C4⋊C4—271no—
817C4⋊C4—271no—
818C4⋊C4—271no—
819C4⋊C4—271no—
820C4⋊C4—271no—
821C22⋊C4—31no—
822C22⋊C4—91no—
823C22⋊C4—91no—
824C22⋊C4—271no—
825C22⋊C4—271no—
826C22⋊C4—271no—
827C22⋊C4—271no—
828C22⋊C4—271no—
829C42—91no—
830C42—91no—
831C42—271no—
832C42—271no—
833C42—271no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—22no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—42no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3#379612yes—
857C22×C3#379912yes—
858C22×C3#380412yes—
859C22×C3C22×D3211yescharacteristic
860C22×C3C22×D3211yescharacteristic
861C22×C3C22×D3211yescharacteristic
862C2×D3—182no—
863C2×D3—181no—
864C2×D3—181no—
865C2×D3—181no—
866C2×D3—181no—
867C2×D3—181no—
868C2×D3—181no—
869C2×D3—181no—
870C2×D3—181no—
871C2×D3—181no—
872C2×D3—361no—
873C2×D3—361no—
874C2×D3—361no—
875C2×D3—361no—
876C2×D3—361no—
877C2×D3—361no—
878C2×D3—361no—
879C2×D3—361no—
880C2×D3—362no—
881C2×D3—721no—
882C2×D3—721no—
883C3×C4—32no—
884C3×C4—32no—
885C3×C4—62no—
886C3×C4—61no—
887C3×C4—61no—
888C3×C4—61no—
889C3×C4—61no—
890C3×C4—61no—
891C3×C4—61no—
892C3×C4—61no—
893C3×C4—61no—
894C3×C4—61no—
895C3×C4—61no—
896C3×C4—121no—
897C3×C4—121no—
898C3×C4—121no—
899C3×C4—121no—
900C3×C4—121no—
901C3×C4—181no—
902C3×C4—181no—
903C3×C4—181no—
904C3×C4—181no—
905C3×C4—181no—
906C3×C4—181no—
907Dic3—21no—
908Dic3—21no—
909Dic3—21no—
910Dic3—21no—
911Dic3—21no—
912Dic3—61no—
913Dic3—61no—
914Dic3—61no—
915Dic3—61no—
916Dic3—61no—
917Dic3—61no—
918Dic3—61no—
919Dic3—61no—
920Dic3—61no—
921Dic3—61no—
922Dic3—61no—
923Dic3—61no—
924Dic3—121no—
925Dic3—121no—
926Dic3—121no—
927Dic3—121no—
928Dic3—121no—
929Dic3—121no—
930Dic3—182no—
931Dic3—181no—
932Dic3—181no—
933Dic3—181no—
934Dic3—361no—
935Dic3—361no—
936Dic3—362no—
937Dic3#380412yes—
938C32—21no—
939C32—21no—
940C32—21no—
941C32—41no—
942C32#551311yescharacteristic, complemented
943C32#553111yescharacteristic, complemented
944C32#564211yescharacteristic, complemented
945C23—271no—
946C23D3311yescharacteristic
947Q8—182no—
948D4—542no—
949C2×C4—31no—
950C2×C4—31no—
951C2×C4—31no—
952C2×C4—31no—
953C2×C4—31no—
954C2×C4—31no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—91no—
961C2×C4—91no—
962C2×C4—91no—
963C2×C4—182no—
964C2×C4—271no—
965C2×C4—542no—
966C2×C3—22no—
967C2×C3—22no—
968C2×C3—22no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—21no—
977C2×C3—21no—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—41no—
982C2×C3—41no—
983C2×C3—41no—
984C2×C3—82no—
985C2×C3C2×#379611yescharacteristic
986C2×C3#6429711yescharacteristic
987C2×C3#6429711yescharacteristic
988C2×C3C2×#379911yescharacteristic
989C2×C3D3×#23511yescharacteristic
990C2×C3#6430911yescharacteristic
991C2×C3D3×#23711yescharacteristic
992C2×C3C2×#380411yescharacteristic
993C2×C3C2×#380411yescharacteristic
994D3—362no—
995D3—361no—
996D3—361no—
997D3—361no—
998D3—721no—
999D3—721no—
1000D3—722no—
1001C22—21no—
1002C22—21no—
1003C22—541no—
1004C22—541no—
1005C22—541no—
1006C22#8896212yes—
1007C22C2×D3311yescharacteristic
1008C4—32no—
1009C4—61no—
1010C4—61no—
1011C4—61no—
1012C4—61no—
1013C4—61no—
1014C4—181no—
1015C4—181no—
1016C4—181no—
1017C4—181no—
1018C4—181no—
1019C4—181no—
1020C4—541no—
1021C3—21no—
1022C3—21no—
1023C3—21no—
1024C3—41no—
1025C3#1059404511yescharacteristic, complemented
1026C3#1059480711yescharacteristic, complemented
1027C3#1059482511yescharacteristic, complemented
1028C2—22no—
1029C2—1081no—
1030C2D3×#380411yescharacteristic
1031C2#1172442611yescharacteristic
1032C2C2×#8896211yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×#6312C22
hypercenterC23D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723715C2semidirect
5. C2×C3×Dic3⋊Dic3C2semidirect
6. C3×#63964C2semidirect
7. C3×#63955C2semidirect
8. #11723028C2semidirect
9. #11723021C2semidirect
10. #11723017C2semidirect
11. #11723013C2semidirect
12. #11723012C2semidirect
13. #11722973C2semidirect
14. #11722940C2semidirect
15. #11722920C2semidirect
69. C2×Dic3⋊Dic3D3semidirect
70. #63964D3semidirect
74. #63955D3semidirect
668. C33#552semidirect
942. C32#5513semidirect
943. C32#5531semidirect
944. C32#5642semidirect
1025. C3#10594045semidirect
1026. C3#10594807semidirect
1027. C3#10594825semidirect

Maximal subgroups

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

subgroupindex
#117237152
#117236182
#117236122
#117236082
C2×C3×Dic3⋊Dic32
C3×#639642
C3×#639552
#117230282
#117230212
#117230172
#117230132
#117230122
#117229732
#117229402
#117229202
#105948253
#105948073
#105940453