Finite Group Databasebeta

← #13168256

Subgroups — #13168256

Order 1728.

1104 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723669C211yesmaximal, characteristic, complemented
2#11723479C211yesmaximal, characteristic
3#11723468C211yesmaximal, characteristic, complemented
4#11723411C211yesmaximal, characteristic, complemented
5C3×#63899C211yesmaximal, characteristic, complemented
6C3×#63877C211yesmaximal, characteristic, complemented
7C3×#63869C211yesmaximal, characteristic, complemented
8#11723021C211yesmaximal, characteristic, complemented
9#11723018C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic
11#11722977C211yesmaximal, characteristic, complemented
12#11722940C211yesmaximal, characteristic, complemented
13#11722935C211yesmaximal, characteristic
14#11722917C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594449—31nomaximal
17#10594045—31nomaximal
18#10593918—31nomaximal
19C2×#6291C2211yescharacteristic
20C2×#6289C2211yescharacteristic
21C2×D3×C3⋊Dic3C2211yescharacteristic
22C2×C3×#627C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25#88859C2211yescharacteristic
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×#3750C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×C4×Dic3C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88815C2211yescharacteristic
35#88813C2211yescharacteristic
36#88807C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64107—31no—
55#64095—31no—
56#64081—31no—
57C3×#896—31no—
58C3×#890—31no—
59C3×#878—31no—
60C3×#877—31no—
61C3×#872—31no—
62C3×#870—31no—
63#63966—31no—
64C2×Dic3⋊Dic3—31no—
65#63957—31no—
66#63952—31no—
67#63904—31no—
68#63899D311yescharacteristic, complemented
69#63890—31no—
70#63890—31no—
71#63890—31no—
72#63890—61no—
73D3×C4⋊Dic3—31no—
74#63888—31no—
75#63888—31no—
76#63881—31no—
77#63878—31no—
78#63878—31no—
79#63877D311yescharacteristic, complemented
80D3×Dic3⋊C4—31no—
81#63870—31no—
82#63869D311yescharacteristic, complemented
83#63868—31no—
84#63868—31no—
85#63865—31no—
86#63850—31no—
87#63848—31no—
88#63848—31no—
89#63848—31no—
90#63848—61no—
91#63847—31no—
92#63846—31no—
93#63845—31no—
94#63845—31no—
95#63845—31no—
96#63843—31no—
97Dic3×Dic6—31no—
98#63837—31no—
99#63836—31no—
100#63836—31no—
101#63836—61no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6291—22no—
118#6289—22no—
119D3×C3⋊Dic3—22no—
120C3×#627—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123#5693—91no—
124#5642—91no—
125#5531—91no—
126C2×#638—31no—
127C22×C3⋊Dic3—31no—
128C2×C4×C3⋊D3—31no—
129C22×C3×Dic3—31no—
130C22×C3×Dic3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×#627C2×D311yescharacteristic
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—61no—
139C2×#624—31no—
140C2×#624—31no—
141C2×#624—61no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—61no—
145C2×D3×Dic3C2×D311yescharacteristic
146C2×D3×Dic3C2×D311yescharacteristic
147C32×C4⋊C4—31no—
148C32×C22⋊C4—31no—
149C32×C42—31no—
150#3752—31no—
151#3752—31no—
152#3752—31no—
153#3752—31no—
154#3752—31no—
155#3752—31no—
156#3752—31no—
157#3752—61no—
158#3752—61no—
159#3752—61no—
160#3752—121no—
161C4⋊(C3⋊Dic3)—31no—
162C4⋊(C3⋊Dic3)—31no—
163C4⋊(C3⋊Dic3)C2×D311yescharacteristic
164#3750—31no—
165#3750C2×D311yescharacteristic
166#3750C2×D311yescharacteristic
167C4×C3⋊Dic3—31no—
168C4×C3⋊Dic3—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×(C2×D3)⋊C4—21no—
172C3×(C2×D3)⋊C4—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4C2×D311yescharacteristic
175C3×(C2×D3)⋊C4C2×D311yescharacteristic
176C3×C4⋊Dic3—21no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—31no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—61no—
182C3×C4⋊Dic3C2×D311yescharacteristic
183C3×C4⋊Dic3C2×D311yescharacteristic
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×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4—61no—
200C3×C4×Dic3—21no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3C2×D311yescharacteristic
204C3×C4×Dic3C2×D311yescharacteristic
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724C2×D311yescharacteristic
209#3724C2×D311yescharacteristic
210#3724C2×D311yescharacteristic
211#3724C2×D311yescharacteristic
212Dic3⋊Dic3—31no—
213Dic3⋊Dic3—31no—
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
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(C2×D3)⋊Dic3C2×D311yescharacteristic
242(C2×D3)⋊Dic3C2×D311yescharacteristic
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33C2411yescharacteristic
254C2×C3⋊(C3⋊D3)—21no—
255C2×C3⋊(C3⋊D3)—21no—
256C2×C3⋊(C3⋊D3)—21no—
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3#4112yes—
260C33×C4—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—
267C3×C3⋊Dic3#4112yes—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#125—91no—
274C3×C22⋊Q8—91no—
275C3×#117—91no—
276#946—91no—
277Q8×Dic3—91no—
278#929—91no—
279C4×#67—91no—
280C2×C4⋊Dic3—91no—
281C2×Dic3⋊C4—91no—
282#898—91no—
283#898—91no—
284#898—91no—
285#898—91no—
286#898—91no—
287#898—181no—
288#896—31no—
289#896—91no—
290#896—91no—
291#894—91no—
292#894—91no—
293#893—91no—
294#892—91no—
295#892—91no—
296D3×C4⋊C4—91no—
297#890—31no—
298#890—91no—
299#890—91no—
300#889—91no—
301#889—91no—
302#889—91no—
303#889—91no—
304#887—91no—
305#886—91no—
306#886—91no—
307#886—91no—
308#886—181no—
309#67⋊C4—91no—
310#878—31no—
311#877—31no—
312#877—91no—
313#877—91no—
314#876—91no—
315#872—31no—
316#872—91no—
317#872—91no—
318#872—181no—
319#870—31no—
320C4×Dic6—91no—
321C23×C32—31no—
322C22×C3⋊D3—31no—
323C22×C3⋊D3—31no—
324C22×C3⋊D3—31no—
325C22×C3⋊D3—61no—
326C22×C3⋊D3—61no—
327C22×C3⋊D3—61no—
328C22×C3⋊D3—121no—
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
338C2×C32×C4—31no—
339C2×C32×C4—31no—
340C2×C32×C4—41no—
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344#638—62no—
345C2×C3⋊Dic3—31no—
346C2×C3⋊Dic3—31no—
347C2×C3⋊Dic3—31no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—61no—
351C2×C3⋊Dic3—62no—
352C2×C3⋊Dic3—121no—
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C4×C3⋊D3—62no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—21no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—62no—
384C2×C3×Dic3—62no—
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C2×C3×Dic3C22×D311yescharacteristic
392C2×C3×Dic3C22×D311yescharacteristic
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C3×C4×D3—62no—
396C3×C4×D3—62no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399#627—22no—
400#626—62no—
401#626—62no—
402#626—122no—
403#624—62no—
404#624—62no—
405#624—64no—
406D3×Dic3—22no—
407D3×Dic3—22no—
408D3×Dic3—62no—
409D3×Dic3—62no—
410D3×Dic3—122no—
411#552—271noSylow
412C2×C33C2×#4111yescharacteristic
413C2×C33C2×#4111yescharacteristic
414C2×C332−1+411yescharacteristic
415C3⋊(C3⋊D3)—41no—
416C32×D3—22no—
417C2×C3×Q8—91no—
418C22×C3×C4—91no—
419C22×C3×C4—91no—
420C2×#67—91no—
421C2×#67—91no—
422C2×#67—181no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—91no—
426C22×Dic3—91no—
427C22×Dic3—181no—
428C2×D12—91no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—91no—
432C2×C4×D3—91no—
433C2×C4×D3—91no—
434C2×C4×D3—91no—
435C2×C4×D3—181no—
436C2×Dic6—31no—
437C2×Dic6—31no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—31no—
440C3×C4⋊C4—61no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C4⋊C4—91no—
444C3×C4⋊C4—91no—
445C3×C4⋊C4—91no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
448C3×C4⋊C4—91no—
449C3×C4⋊C4—91no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—31no—
452C3×C22⋊C4—61no—
453C3×C22⋊C4—91no—
454C3×C22⋊C4—91no—
455C3×C42—31no—
456C3×C42—31no—
457C3×C42—61no—
458C3×C42—91no—
459#217—31no—
460#217—31no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—91no—
464(C2×D3)⋊C4—91no—
465(C2×D3)⋊C4—91no—
466(C2×D3)⋊C4—91no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
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—181no—
479(C2×D3)⋊C4—181no—
480(C2×D3)⋊C4—181no—
481(C2×D3)⋊C4—181no—
482(C2×D3)⋊C4—181no—
483(C2×D3)⋊C4—181no—
484(C2×D3)⋊C4—181no—
485(C2×D3)⋊C4—361no—
486(C2×D3)⋊C4D3211yescharacteristic
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—31no—
491C4⋊Dic3—61no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497C4⋊Dic3—91no—
498C4⋊Dic3—91no—
499C4⋊Dic3—91no—
500C4⋊Dic3—181no—
501C4⋊Dic3—181no—
502C4⋊Dic3D3211yescharacteristic
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—31no—
507Dic3⋊C4—31no—
508Dic3⋊C4—31no—
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—61no—
518Dic3⋊C4—61no—
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—181no—
530C4×Dic3—31no—
531C4×Dic3—31no—
532C4×Dic3—91no—
533C4×Dic3—91no—
534C4×Dic3—91no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—181no—
542C4×Dic3—181no—
543C4×Dic3D3211yescharacteristic
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—32no—
548C22×C32—41no—
549C22×C32—61no—
550C22×C32—61no—
551C22×C32C23×D311yescharacteristic
552C22×C32C23×D311yescharacteristic
553C22×C32C23×D311yescharacteristic
554C2×C3⋊D3—61no—
555C2×C3⋊D3—62no—
556C2×C3⋊D3—61no—
557C2×C3⋊D3—61no—
558C2×C3⋊D3—61no—
559C2×C3⋊D3—61no—
560C2×C3⋊D3—61no—
561C2×C3⋊D3—61no—
562C2×C3⋊D3—61no—
563C2×C3⋊D3—61no—
564C2×C3⋊D3—121no—
565C2×C3⋊D3—121no—
566C2×C3⋊D3—122no—
567C2×C3⋊D3—121no—
568C2×C3⋊D3—121no—
569C2×C3⋊D3—121no—
570C2×C3⋊D3—121no—
571C2×C3⋊D3—121no—
572C2×C3⋊D3—121no—
573C2×C3⋊D3—241no—
574C2×C3⋊D3—241no—
575C2×C3×D3—21no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—21no—
579C2×C3×D3—22no—
580C2×C3×D3—41no—
581C2×C3×D3—41no—
582C2×C3×D3#23512yes—
583C2×C3×D3#23912yes—
584C32×C4—21no—
585C32×C4—21no—
586C32×C4—21no—
587C32×C4—41no—
588C32×C4—41no—
589C32×C4—41no—
590C32×C4—61no—
591C32×C4—61no—
592C32×C4—61no—
593C32×C4—61no—
594C32×C4—61no—
595C32×C4—81no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—61no—
602C3⋊Dic3—61no—
603C3⋊Dic3—61no—
604C3⋊Dic3—121no—
605C3⋊Dic3—121no—
606C3⋊Dic3—121no—
607C3⋊Dic3—241no—
608C3⋊Dic3#23712yes—
609C3×Dic3—22no—
610C3×Dic3—21no—
611C3×Dic3—21no—
612C3×Dic3—21no—
613C3×Dic3—21no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—32no—
621C3×Dic3—32no—
622C3×Dic3—41no—
623C3×Dic3—41no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—62no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—61no—
635C3×Dic3—61no—
636C3×Dic3—61no—
637C3×Dic3—121no—
638C3×Dic3—121no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642#126—271no—
643#126—271no—
644#125—91no—
645#125—271no—
646#125—271no—
647#123—271no—
648#123—271no—
649C22⋊Q8—91no—
650C22⋊Q8—271no—
651C4×Q8—271no—
652C4×D4—271no—
653#117—91no—
654#117—271no—
655#117—271no—
656C2×C4⋊C4—271no—
657C33#55211yescharacteristic, complemented, Sylow
658C23×C3—31no—
659C23×C3—31no—
660C23×C3—61no—
661C22×D3—91no—
662C22×D3—91no—
663C22×D3—91no—
664C22×D3—181no—
665C22×D3—181no—
666C22×D3—181no—
667C22×D3—361no—
668C22×D3C2×D3211yescharacteristic
669C3×Q8—182no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—31no—
674C2×C3×C4—31no—
675C2×C3×C4—31no—
676C2×C3×C4—31no—
677C2×C3×C4—31no—
678C2×C3×C4—31no—
679C2×C3×C4—31no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—31no—
683C2×C3×C4—41no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—91no—
690C2×C3×C4—91no—
691C2×C3×C4—91no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—182no—
696C2×C3×C4—182no—
697C2×C3×C4C2×D3211yescharacteristic
698C2×C3×C4C2×D3211yescharacteristic
699C2×C3×C4C2×D3211yescharacteristic
700#67—182no—
701#67—182no—
702#67—362no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—61no—
719C2×Dic3—61no—
720C2×Dic3—61no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—91no—
724C2×Dic3—91no—
725C2×Dic3—91no—
726C2×Dic3—181no—
727C2×Dic3—181no—
728C2×Dic3—181no—
729C2×Dic3—182no—
730C2×Dic3—182no—
731C2×Dic3—361no—
732C2×Dic3—362no—
733C2×Dic3C2×D3211yescharacteristic
734C2×Dic3C2×D3211yescharacteristic
735C2×Dic3C2×D3211yescharacteristic
736C2×Dic3C2×D3211yescharacteristic
737C2×Dic3C2×D3211yescharacteristic
738D12—182no—
739C4×D3—62no—
740C4×D3—62no—
741C4×D3—182no—
742C4×D3—182no—
743C4×D3—182no—
744C4×D3—184no—
745C4×D3—182no—
746Dic6—62no—
747Dic6—62no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—62no—
761C2×C32C2×#23511yescharacteristic
762C2×C32C2×#23711yescharacteristic
763C2×C32C2×#23911yescharacteristic
764C2×C32#100711yescharacteristic
765C2×C32D3×#4111yescharacteristic
766C2×C32D3×#4111yescharacteristic
767C2×C32D3×#4111yescharacteristic
768C2×C32#101011yescharacteristic
769C2×C32#101011yescharacteristic
770C3⋊D3—121no—
771C3⋊D3—122no—
772C3⋊D3—121no—
773C3⋊D3—121no—
774C3⋊D3—241no—
775C3⋊D3—241no—
776C3⋊D3—242no—
777C3×D3—22no—
778C3×D3—22no—
779C3×D3—42no—
780C2×Q8—91no—
781C2×D4—271no—
782C22×C4—91no—
783C22×C4—91no—
784C22×C4—271no—
785C22×C4—271no—
786C4⋊C4—31no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—91no—
792C4⋊C4—91no—
793C4⋊C4—91no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C4⋊C4—271no—
799C4⋊C4—271no—
800C4⋊C4—271no—
801C4⋊C4—271no—
802C22⋊C4—31no—
803C22⋊C4—91no—
804C22⋊C4—91no—
805C22⋊C4—271no—
806C22⋊C4—271no—
807C22⋊C4—271no—
808C22⋊C4—271no—
809C22⋊C4—271no—
810C42—31no—
811C42—91no—
812C42—271no—
813C42—271no—
814C42—271no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—32no—
819C22×C3—32no—
820C22×C3—41no—
821C22×C3—62no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—61no—
825C22×C3—61no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3C22×D3211yescharacteristic
829C22×C3C22×D3211yescharacteristic
830C22×C3C22×D3211yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—182no—
834C2×D3—181no—
835C2×D3—181no—
836C2×D3—181no—
837C2×D3—181no—
838C2×D3—181no—
839C2×D3—181no—
840C2×D3—181no—
841C2×D3—181no—
842C2×D3—181no—
843C2×D3—361no—
844C2×D3—361no—
845C2×D3—361no—
846C2×D3—361no—
847C2×D3—361no—
848C2×D3—361no—
849C2×D3—361no—
850C2×D3—361no—
851C2×D3—362no—
852C2×D3—721no—
853C2×D3—721no—
854C2×D3#379912yes—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—41no—
859C3×C4—41no—
860C3×C4—41no—
861C3×C4—62no—
862C3×C4—61no—
863C3×C4—61no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4—61no—
867C3×C4—61no—
868C3×C4—61no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—81no—
873C3×C4—92no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4—121no—
877C3×C4—121no—
878C3×C4—181no—
879C3×C4—181no—
880C3×C4—181no—
881C3×C4—181no—
882C3×C4—181no—
883Dic3—21no—
884Dic3—21no—
885Dic3—21no—
886Dic3—21no—
887Dic3—21no—
888Dic3—32no—
889Dic3—32no—
890Dic3—62no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—121no—
906Dic3—181no—
907Dic3—181no—
908Dic3—181no—
909Dic3—361no—
910Dic3—361no—
911Dic3—361no—
912Dic3—721no—
913C32—21no—
914C32—21no—
915C32—21no—
916C32—41no—
917C32#553111yescharacteristic, complemented
918C32#564211yescharacteristic, complemented
919C32#569311yescharacteristic, complemented
920C23—31no—
921C23—271no—
922Q8—182no—
923D4—542no—
924C2×C4—31no—
925C2×C4—31no—
926C2×C4—31no—
927C2×C4—31no—
928C2×C4—31no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—182no—
936C2×C4—182no—
937C2×C4—271no—
938C2×C4—542no—
939C2×C4—542no—
940C2×C4D3311yescharacteristic
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—41no—
951C2×C3—41no—
952C2×C3—41no—
953C2×C3—62no—
954C2×C3—62no—
955C2×C3—122no—
956C2×C3#6429711yescharacteristic
957C2×C3#6429711yescharacteristic
958C2×C3C2×#379911yescharacteristic
959C2×C3D3×#23511yescharacteristic
960C2×C3#6430611yescharacteristic
961C2×C3#6430911yescharacteristic
962C2×C3D3×#23711yescharacteristic
963C2×C3D3×#23711yescharacteristic
964C2×C3D3×#23911yescharacteristic
965D3—22no—
966D3—362no—
967D3—361no—
968D3—361no—
969D3—361no—
970D3—721no—
971D3—721no—
972D3—722no—
973C22—32no—
974C22—61no—
975C22—61no—
976C22—541no—
977C22—541no—
978C22—541no—
979C22C2×D3311yescharacteristic
980C4—21no—
981C4—61no—
982C4—61no—
983C4—61no—
984C4—61no—
985C4—61no—
986C4—92no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—181no—
992C4—541no—
993C3—21no—
994C3—21no—
995C3—21no—
996C3—41no—
997C3#1059391811yescharacteristic, complemented
998C3#1059404511yescharacteristic, complemented
999C3#1059444911yescharacteristic, complemented
1000C2—62no—
1001C2—1081no—
1002C2#1172437311yescharacteristic
1003C2D3×#379911yescharacteristic
1004C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723669C2semidirect
3. #11723468C2semidirect
4. #11723411C2semidirect
5. C3×#63899C2semidirect
6. C3×#63877C2semidirect
7. C3×#63869C2semidirect
8. #11723021C2semidirect
9. #11723018C2semidirect
11. #11722977C2semidirect
12. #11722940C2semidirect
14. #11722917C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
68. #63899D3semidirect
79. #63877D3semidirect
82. #63869D3semidirect
657. C33#552semidirect
917. C32#5531semidirect
918. C32#5642semidirect
919. C32#5693semidirect
997. C3#10593918semidirect
998. C3#10594045semidirect
999. C3#10594449semidirect

Maximal subgroups

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

subgroupindex
#117236692
#117234792
#117234682
#117234112
C3×#638992
C3×#638772
C3×#638692
#117230212
#117230182
#117229872
#117229772
#117229402
#117229352
#117229172
D3×Dic3⋊Dic32
#105944493
#105940453
#105939183