Finite Group Databasebeta

← #13168262

Subgroups — #13168262

Order 1728.

1188 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723668C211yesmaximal, characteristic, complemented
2#11723489C211yesmaximal, characteristic, complemented
3#11723485C211yesmaximal, characteristic, complemented
4#11723461C211yesmaximal, characteristic
5C3×#63896C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×#63870C211yesmaximal, characteristic, complemented
8#11723034C211yesmaximal, characteristic, complemented
9#11723017C211yesmaximal, characteristic, complemented
10#11722980C211yesmaximal, characteristic, complemented
11#11722973C211yesmaximal, characteristic, complemented
12#11722935C211yesmaximal, characteristic
13#11722935C211yesmaximal, characteristic
14#11722912C211yesmaximal, characteristic, complemented
15D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
16#10594396—31nomaximal
17#10594395—31nomaximal
18#10594141—31nomaximal
19C2×C3×#634C2211yescharacteristic
20C2×#6293C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24C2×#6289C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29#88859C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×Dic3⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88813C2211yescharacteristic
38#88813C2211yescharacteristic
39#88807C2211yescharacteristic
40#88807C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54#64106—31no—
55#64105—31no—
56#64090—31no—
57C3×#897—31no—
58C3×#896—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#878—31no—
62C3×#878—31no—
63#63982—31no—
64C2×Dic3⋊Dic3—31no—
65#63952—31no—
66#63952—31no—
67#63904—31no—
68#63904—31no—
69#63900—31no—
70#63899—31no—
71#63896—31no—
72#63896D311yescharacteristic, complemented
73#63895—31no—
74#63895—31no—
75#63895—31no—
76#63895—61no—
77#63893D311yescharacteristic, complemented
78D3×C4⋊Dic3—31no—
79#63888—31no—
80#63888—31no—
81#63888—31no—
82#63888—61no—
83#63883—31no—
84#63883—31no—
85#63881—31no—
86#63881—31no—
87#63880—31no—
88#63880—31no—
89#63880—61no—
90D3×Dic3⋊C4—31no—
91#63871—31no—
92#63870D311yescharacteristic, complemented
93#63847—31no—
94#63846—31no—
95#63845—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63840—31no—
100#63839—31no—
101#63839—31no—
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
112C3×#634—22no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118#6293—41no—
119#6291Q814yescomplemented
120#6289—22no—
121#6289—41no—
122#6289—41no—
123D3×C3⋊Dic3—41no—
124C3×#627—41no—
125C3×D3×Dic3—22no—
126C3×D3×Dic3—41no—
127#5690—91no—
128#5636—91no—
129#5635—91no—
130C2×#638—31no—
131C22×C3⋊Dic3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×#634—31no—
136C2×#634C2×D311yescharacteristic
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×C3×Dic6—31no—
144C2×C3×Dic6—31no—
145C2×C3×Dic6—61no—
146C2×#627—31no—
147C2×#627—31no—
148C2×#627—61no—
149C2×#627C2×D311yescharacteristic
150C2×#626—31no—
151C2×#626—31no—
152C2×#626—61no—
153C2×#624—31no—
154C2×#624—31no—
155C2×#624—31no—
156C2×#624—31no—
157C2×#624—31no—
158C2×#624—31no—
159C2×#624—61no—
160C2×#624—61no—
161C2×#624—61no—
162C2×D3×Dic3—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—61no—
165C2×D3×Dic3C2×D311yescharacteristic
166C2×D3×Dic3C2×D311yescharacteristic
167C32×C4⋊C4—31no—
168C32×C4⋊C4—31no—
169C32×C22⋊C4—31no—
170#3752—31no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—61no—
176#3752—61no—
177#3752—61no—
178#3752—121no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)C2×D311yescharacteristic
181#3750—31no—
182#3750—31no—
183#3750—31no—
184C4×C3⋊Dic3C2×D311yescharacteristic
185C3×#217—31no—
186C3×#217—31no—
187C3×(C2×D3)⋊C4—21no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×C4⋊Dic3—31no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—61no—
199C3×Dic3⋊C4—21no—
200C3×Dic3⋊C4—21no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4C2×D311yescharacteristic
212C3×Dic3⋊C4C2×D311yescharacteristic
213C3×Dic3⋊C4C2×D311yescharacteristic
214C3×Dic3⋊C4C2×D311yescharacteristic
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—61no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—61no—
223#3724C2×D311yescharacteristic
224#3724C2×D311yescharacteristic
225#3724C2×D311yescharacteristic
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242Dic3⋊Dic3C2×D311yescharacteristic
243#3722—31no—
244#3722—31no—
245#3722—31no—
246#3722—31no—
247#3722—61no—
248#3722—61no—
249(C2×D3)⋊Dic3C2×D311yescharacteristic
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257C22×C33C2411yescharacteristic
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C3⋊(C3⋊D3)C2×Q812yes—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3C2×Q812yes—
264C33×C4—21no—
265C3⋊(C3⋊Dic3)—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3C2×Q812yes—
271C3×C3⋊Dic3#4112yes—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C3×#125—91no—
278C3×C22⋊Q8—91no—
279C3×C22⋊Q8—91no—
280#946—91no—
281#946—91no—
282Q8×Dic3—91no—
283#944—91no—
284C4×#67—91no—
285C4×#67—91no—
286C2×C4⋊Dic3—91no—
287C2×Dic3⋊C4—91no—
288#897—31no—
289#897—91no—
290#897—91no—
291#897—91no—
292#897—181no—
293#896—31no—
294#896—91no—
295#896—91no—
296#896—91no—
297#896—91no—
298#896—91no—
299#896—181no—
300#893—91no—
301#893—91no—
302D3×C4⋊C4—91no—
303D3×C4⋊C4—91no—
304D3×C4⋊C4—91no—
305D3×C4⋊C4—91no—
306#890—91no—
307#889—31no—
308#889—31no—
309#889—91no—
310#889—91no—
311#888—91no—
312#888—91no—
313#887—91no—
314#67⋊C4—91no—
315#67⋊C4—91no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#67⋊C4—181no—
319#878—31no—
320#878—31no—
321#878—91no—
322#878—91no—
323C4×D12—91no—
324C4×Dic6—91no—
325C23×C32—31no—
326C22×C3⋊D3—31no—
327C22×C3⋊D3—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—61no—
330C22×C3⋊D3—61no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—121no—
333C22×C3×D3—21no—
334C22×C3×D3C22×D311yescharacteristic
335C22×C3×D3C22×D311yescharacteristic
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—21no—
339C2×C32×C4—31no—
340C2×C32×C4—31no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—41no—
345C2×C32×C4C22×D311yescharacteristic
346C2×C32×C4C22×D311yescharacteristic
347C2×C32×C4C22×D311yescharacteristic
348#638—34no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—61no—
353C2×C3⋊Dic3—61no—
354C2×C3⋊Dic3—61no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C4×C3⋊D3—62no—
364C4×C3⋊D3—121no—
365C4×C3⋊D3—121no—
366#634—22no—
367#634—121no—
368C2×C3×Dic3—21no—
369C2×C3×Dic3—21no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
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—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—62no—
392C2×C3×Dic3—121no—
393C2×C3×Dic3C22×D311yescharacteristic
394C2×C3×Dic3C22×D311yescharacteristic
395C2×C3×Dic3C22×D311yescharacteristic
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C3×C4×D3—62no—
404C3×C4×D3—121no—
405C3×Dic6—62no—
406C3×Dic6—62no—
407C3×Dic6—122no—
408C3×Dic6—121no—
409C3×Dic6—121no—
410#627—41no—
411#627—121no—
412#627—121no—
413#627—122no—
414#626—34no—
415#626—34no—
416#626—64no—
417#624—62no—
418#624—62no—
419#624—122no—
420#624—121no—
421#624—121no—
422#624—121no—
423#624—121no—
424#624—122no—
425#624—122no—
426D3×Dic3—22no—
427D3×Dic3—41no—
428D3×Dic3—121no—
429D3×Dic3—121no—
430D3×Dic3—122no—
431#554—271noSylow
432C2×C33C22×Q811yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C2×C33H(5,𝔽2)11yescharacteristic
435C3⋊(C3⋊D3)—22no—
436C32×D3—22no—
437C2×C3×Q8—91no—
438C2×C3×Q8—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—181no—
444C22×Dic3—31no—
445C22×Dic3—31no—
446C22×Dic3—91no—
447C22×Dic3—91no—
448C22×Dic3—181no—
449C2×D12—91no—
450C2×C4×D3—31no—
451C2×C4×D3—31no—
452C2×C4×D3—91no—
453C2×C4×D3—91no—
454C2×C4×D3—91no—
455C2×C4×D3—91no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—181no—
463C2×C4×D3—181no—
464C2×C4×D3—181no—
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6—61no—
470C2×Dic6—91no—
471C2×Dic6—91no—
472C2×Dic6—91no—
473C2×Dic6—181no—
474C3×C4⋊C4—31no—
475C3×C4⋊C4—31no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4—61no—
480C3×C4⋊C4—91no—
481C3×C4⋊C4—91no—
482C3×C4⋊C4—91no—
483C3×C4⋊C4—91no—
484C3×C4⋊C4—91no—
485C3×C4⋊C4—91no—
486C3×C4⋊C4—91no—
487C3×C4⋊C4—91no—
488C3×C22⋊C4—31no—
489C3×C22⋊C4—31no—
490C3×C22⋊C4—61no—
491C3×C22⋊C4—91no—
492C3×C22⋊C4—91no—
493C3×C42—91no—
494#217—31no—
495#217—31no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—181no—
508(C2×D3)⋊C4—181no—
509(C2×D3)⋊C4—181no—
510(C2×D3)⋊C4—181no—
511(C2×D3)⋊C4—181no—
512(C2×D3)⋊C4—361no—
513(C2×D3)⋊C4D3211yescharacteristic
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—61no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—181no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—181no—
551Dic3⋊C4—181no—
552Dic3⋊C4—181no—
553Dic3⋊C4D3211yescharacteristic
554Dic3⋊C4D3211yescharacteristic
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—61no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—32no—
568C22×C32—41no—
569C22×C32—61no—
570C22×C32—61no—
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C22×C32C23×D311yescharacteristic
574C2×C3⋊D3—32no—
575C2×C3⋊D3—32no—
576C2×C3⋊D3—32no—
577C2×C3⋊D3—62no—
578C2×C3⋊D3—62no—
579C2×C3⋊D3—62no—
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—122no—
587C2×C3⋊D3—121no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—121no—
593C2×C3⋊D3—241no—
594C2×C3⋊D3—241no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—22no—
600C2×C3×D3—41no—
601C2×C3×D3—41no—
602C2×C3×D3D3×Q812yes—
603C2×C3×D3D3×Q812yes—
604C32×C4—21no—
605C32×C4—21no—
606C32×C4—21no—
607C32×C4—41no—
608C32×C4—41no—
609C32×C4—41no—
610C32×C4—61no—
611C32×C4—61no—
612C32×C4—61no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—81no—
616C3⋊Dic3—21no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—61no—
621C3⋊Dic3—61no—
622C3⋊Dic3—61no—
623C3⋊Dic3—121no—
624C3⋊Dic3—121no—
625C3⋊Dic3—121no—
626C3⋊Dic3—241no—
627C3⋊Dic3#23712yes—
628C3⋊Dic3D3×Q812yes—
629C3×Dic3—22no—
630C3×Dic3—21no—
631C3×Dic3—21no—
632C3×Dic3—21no—
633C3×Dic3—21no—
634C3×Dic3—21no—
635C3×Dic3—21no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—32no—
641C3×Dic3—32no—
642C3×Dic3—32no—
643C3×Dic3—32no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—62no—
649C3×Dic3—62no—
650C3×Dic3—62no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C4⋊Q8—271no—
663#125—91no—
664#125—271no—
665C22⋊Q8—91no—
666C22⋊Q8—91no—
667C22⋊Q8—271no—
668C22⋊Q8—271no—
669C22⋊Q8—271no—
670C22⋊Q8—271no—
671C4×Q8—271no—
672C4×D4—271no—
673C4×D4—271no—
674C4×D4—271no—
675C2×C4⋊C4—271no—
676C2×C4⋊C4—271no—
677C33#55411yescharacteristic, complemented, Sylow
678C23×C3—31no—
679C23×C3—31no—
680C23×C3—61no—
681C22×D3—91no—
682C22×D3—91no—
683C22×D3—91no—
684C22×D3—181no—
685C22×D3—181no—
686C22×D3—181no—
687C22×D3—361no—
688C22×D3C2×D3211yescharacteristic
689C3×Q8—182no—
690C3×Q8—361no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—31no—
695C2×C3×C4—31no—
696C2×C3×C4—31no—
697C2×C3×C4—31no—
698C2×C3×C4—31no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—41no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—182no—
717C2×C3×C4—361no—
718C2×C3×C4C2×D3211yescharacteristic
719C2×C3×C4C2×D3211yescharacteristic
720C2×C3×C4C2×D3211yescharacteristic
721#67—94no—
722#67—94no—
723#67—184no—
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—91no—
744C2×Dic3—91no—
745C2×Dic3—91no—
746C2×Dic3—121no—
747C2×Dic3—181no—
748C2×Dic3—181no—
749C2×Dic3—181no—
750C2×Dic3—361no—
751C2×Dic3—361no—
752C2×Dic3—361no—
753C2×Dic3—362no—
754C2×Dic3C2×D3211yescharacteristic
755C2×Dic3C2×D3211yescharacteristic
756C2×Dic3C2×D3211yescharacteristic
757C2×Dic3C2×D3211yescharacteristic
758C2×Dic3C2×D3211yescharacteristic
759D12—94no—
760C4×D3—62no—
761C4×D3—121no—
762C4×D3—182no—
763C4×D3—182no—
764C4×D3—182no—
765C4×D3—362no—
766C4×D3—361no—
767C4×D3—361no—
768C4×D3—361no—
769C4×D3—361no—
770C4×D3—361no—
771C4×D3—361no—
772C4×D3—362no—
773C4×D3—362no—
774C4×D3—361no—
775Dic6—62no—
776Dic6—62no—
777Dic6—122no—
778Dic6—121no—
779Dic6—121no—
780Dic6—361no—
781Dic6—361no—
782Dic6—361no—
783Dic6—362no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—41no—
794C2×C32—41no—
795C2×C32—41no—
796C2×C32—62no—
797C2×C32C2×#23711yescharacteristic
798C2×C32#100411yescharacteristic
799C2×C32C2×D3×Q811yescharacteristic
800C2×C32C2×D3×Q811yescharacteristic
801C2×C32C2×D3×Q811yescharacteristic
802C2×C32D3×#4111yescharacteristic
803C2×C32D3×#4111yescharacteristic
804C2×C32#100911yescharacteristic
805C2×C32#100911yescharacteristic
806C3⋊D3—62no—
807C3⋊D3—62no—
808C3⋊D3—62no—
809C3⋊D3—122no—
810C3⋊D3—122no—
811C3⋊D3—122no—
812C3⋊D3—242no—
813C3×D3—22no—
814C3×D3—22no—
815C3×D3—42no—
816C2×Q8—91no—
817C2×Q8—91no—
818C2×Q8—271no—
819C2×D4—271no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—271no—
823C22×C4—271no—
824C22×C4—271no—
825C22×C4—271no—
826C4⋊C4—31no—
827C4⋊C4—31no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C22⋊C4—31no—
843C22⋊C4—91no—
844C22⋊C4—91no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C42—91no—
849C42—271no—
850C42—271no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—32no—
855C22×C3—32no—
856C22×C3—41no—
857C22×C3—62no—
858C22×C3—61no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3C22×D3211yescharacteristic
865C22×C3C22×D3211yescharacteristic
866C22×C3C22×D3211yescharacteristic
867C2×D3—21no—
868C2×D3—21no—
869C2×D3—92no—
870C2×D3—92no—
871C2×D3—92no—
872C2×D3—182no—
873C2×D3—182no—
874C2×D3—182no—
875C2×D3—181no—
876C2×D3—181no—
877C2×D3—181no—
878C2×D3—181no—
879C2×D3—181no—
880C2×D3—181no—
881C2×D3—362no—
882C2×D3—361no—
883C2×D3—361no—
884C2×D3—361no—
885C2×D3—361no—
886C2×D3—361no—
887C2×D3—361no—
888C2×D3—721no—
889C2×D3—721no—
890C2×D3#379712yes—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—21no—
894C3×C4—41no—
895C3×C4—41no—
896C3×C4—41no—
897C3×C4—62no—
898C3×C4—61no—
899C3×C4—61no—
900C3×C4—61no—
901C3×C4—61no—
902C3×C4—61no—
903C3×C4—61no—
904C3×C4—61no—
905C3×C4—61no—
906C3×C4—61no—
907C3×C4—61no—
908C3×C4—81no—
909C3×C4—92no—
910C3×C4—92no—
911C3×C4—121no—
912C3×C4—121no—
913C3×C4—121no—
914C3×C4—121no—
915C3×C4—181no—
916C3×C4—181no—
917C3×C4—181no—
918C3×C4—181no—
919Dic3—21no—
920Dic3—21no—
921Dic3—21no—
922Dic3—21no—
923Dic3—21no—
924Dic3—32no—
925Dic3—32no—
926Dic3—32no—
927Dic3—32no—
928Dic3—62no—
929Dic3—62no—
930Dic3—62no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—121no—
940Dic3—121no—
941Dic3—121no—
942Dic3—181no—
943Dic3—181no—
944Dic3—181no—
945Dic3—361no—
946Dic3—361no—
947Dic3—361no—
948Dic3—721no—
949C32—21no—
950C32—21no—
951C32—21no—
952C32—41no—
953C32#563511yescharacteristic, complemented
954C32#563611yescharacteristic, complemented
955C32#569011yescharacteristic, complemented
956C23—31no—
957C23—271no—
958Q8—182no—
959Q8—361no—
960Q8—1081no—
961D4—274no—
962C2×C4—31no—
963C2×C4—31no—
964C2×C4—31no—
965C2×C4—31no—
966C2×C4—31no—
967C2×C4—91no—
968C2×C4—91no—
969C2×C4—91no—
970C2×C4—91no—
971C2×C4—91no—
972C2×C4—91no—
973C2×C4—182no—
974C2×C4—271no—
975C2×C4—361no—
976C2×C4—542no—
977C2×C4—1081no—
978C2×C4—1081no—
979C2×C4—1081no—
980C2×C4D3311yescharacteristic
981C2×C3—21no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—41no—
991C2×C3—41no—
992C2×C3—41no—
993C2×C3—62no—
994C2×C3—62no—
995C2×C3—122no—
996C2×C3C2×#379711yescharacteristic
997C2×C3#6430711yescharacteristic
998C2×C3#6430811yescharacteristic
999C2×C3D3×#23711yescharacteristic
1000C2×C3D3×#23711yescharacteristic
1001C2×C3#6431211yescharacteristic
1002C2×C3#6431411yescharacteristic
1003C2×C3D32×Q811yescharacteristic
1004C2×C3D32×Q811yescharacteristic
1005D3—22no—
1006D3—182no—
1007D3—182no—
1008D3—182no—
1009D3—362no—
1010D3—362no—
1011D3—362no—
1012D3—722no—
1013C22—32no—
1014C22—61no—
1015C22—61no—
1016C22—272no—
1017C22—541no—
1018C22—541no—
1019C22C2×D3311yescharacteristic
1020C4—21no—
1021C4—61no—
1022C4—61no—
1023C4—61no—
1024C4—61no—
1025C4—61no—
1026C4—92no—
1027C4—92no—
1028C4—181no—
1029C4—181no—
1030C4—181no—
1031C4—181no—
1032C4—541no—
1033C3—21no—
1034C3—21no—
1035C3—21no—
1036C3—41no—
1037C3#1059414111yescharacteristic, complemented
1038C3#1059439511yescharacteristic, complemented
1039C3#1059439611yescharacteristic, complemented
1040C2—62no—
1041C2—542no—
1042C2D3×#379711yescharacteristic
1043C2#1172438411yescharacteristic
1044C2#1172440811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×#6291C22
hypercenterC2×C4D33
hypocenterC33#554
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723668C2semidirect
2. #11723489C2semidirect
3. #11723485C2semidirect
5. C3×#63896C2semidirect
6. C3×#63893C2semidirect
7. C3×#63870C2semidirect
8. #11723034C2semidirect
9. #11723017C2semidirect
10. #11722980C2semidirect
11. #11722973C2semidirect
14. #11722912C2semidirect
15. D3×Dic3⋊Dic3C2semidirect
72. #63896D3semidirect
77. #63893D3semidirect
92. #63870D3semidirect
119. #6291Q8semidirect
677. C33#554semidirect
953. C32#5635semidirect
954. C32#5636semidirect
955. C32#5690semidirect
1037. C3#10594141semidirect
1038. C3#10594395semidirect
1039. C3#10594396semidirect

Maximal subgroups

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

subgroupindex
#117236682
#117234892
#117234852
#117234612
C3×#638962
C3×#638932
C3×#638702
#117230342
#117230172
#117229802
#117229732
#117229352
#117229122
D3×Dic3⋊Dic32
#105943963
#105943953
#105941413