Finite Group Databasebeta

← #13168513

Subgroups — #13168513

Order 1728.

1332 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723675C211yesmaximal, characteristic, complemented
2#11723539C211yesmaximal, characteristic, complemented
3#11723420C211yesmaximal, characteristic, complemented
4#11723413C211yesmaximal, characteristic, complemented
5C3×#63899C211yesmaximal, characteristic, complemented
6C3×#63891C211yesmaximal, characteristic, complemented
7C3×#63890C211yesmaximal, characteristic, complemented
8#11723027C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722973C211yesmaximal, characteristic, complemented
11#11722949C211yesmaximal, characteristic
12#11722935C211yesmaximal, characteristic, complemented
13Dic3×#625C211yesmaximal, characteristic, complemented
14#11722914C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10594653—31nomaximal
17#10594304—31nomaximal
18#10594164—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×#6291C2211yescharacteristic
22C2×#6289C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic, complemented
24C2×C3×#626C2211yescharacteristic
25C2×C3×#625C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic, complemented
29C3×#3752C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×#3750C2211yescharacteristic, complemented
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C32×C4⋊Dic3C2211yescharacteristic, complemented
35#88815C2211yescharacteristic, complemented
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88813C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47Dic3×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#3724C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64101—31no—
55#64092—31no—
56C22⋊C4×C3⋊D3—31no—
57C3×#896—31no—
58C3×#894—31no—
59C3×#886—31no—
60C3×#886—31no—
61C3×#883—31no—
62C3×#878—31no—
63#63983—31no—
64#63981—31no—
65Dic3×#67—31no—
66Dic3×#67—31no—
67C2×#3722—31no—
68#63959—31no—
69#63955—31no—
70#63952—31no—
71#63922—31no—
72#63921—31no—
73#63921—31no—
74#63921—61no—
75D3×(C2×D3)⋊C4—31no—
76D3×(C2×D3)⋊C4—31no—
77#63907—31no—
78#63904—31no—
79C4×#625—31no—
80#63899D311yescharacteristic, complemented
81#63895—31no—
82#63891D311yescharacteristic, complemented
83#63890D311yescharacteristic, complemented
84#63888—31no—
85#63881—31no—
86#63878—31no—
87#63871—31no—
88#63863—31no—
89#63862—31no—
90#63861—31no—
91#63861—31no—
92#63858—31no—
93#63853—31no—
94#63853—31no—
95#63853—61no—
96#63849—31no—
97#63849—31no—
98#63849—61no—
99#63848—31no—
100#63848—31no—
101#63841—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×D3×C3⋊D3—22no—
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×C33×C4C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C4×C3⋊(C3⋊D3)—22no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6291—22no—
122#6289—41no—
123C3×#627—41no—
124C3×#626—41no—
125C3×#625—22no—
126C3×D3×Dic3—22no—
127C3×D3×Dic3—41no—
128C3×D3×Dic3—41no—
129#5659—91no—
130#5658—91no—
131#5637—91no—
132C23×C3⋊D3—31no—
133C22×D32—31no—
134C22×D32—31no—
135C22×D32—61no—
136C2×#638—31no—
137C2×C4×C3⋊D3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—61no—
142C2×C4×C3⋊D3—61no—
143C2×C4×C3⋊D3—61no—
144C2×C4×C3⋊D3—121no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C2×C3×D12—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—31no—
154C2×C3×C4×D3—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×#627C2×D311yescharacteristic, complemented
158C2×#626—31no—
159C2×#626—31no—
160C2×#626—61no—
161C2×#626C2×D311yescharacteristic
162C2×#625C2×D311yescharacteristic
163C2×#624—31no—
164C2×#624—31no—
165C2×#624—61no—
166C2×D3×Dic3C2×D311yescharacteristic
167C2×D3×Dic3C2×D311yescharacteristic
168C2×D3×Dic3C2×D311yescharacteristic, complemented
169C32×C4⋊C4—31no—
170C32×C22⋊C4—31no—
171C32×C22⋊C4—31no—
172#3757—31no—
173#3757—31no—
174#3752—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752C2×D311yescharacteristic
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
181#3750C2×D311yescharacteristic, complemented
182C4×C3⋊Dic3—31no—
183C4×C3⋊Dic3—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×(C2×D3)⋊C4—21no—
187C3×(C2×D3)⋊C4—21no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—61no—
195C3×(C2×D3)⋊C4C2×D311yescharacteristic
196C3×(C2×D3)⋊C4C2×D311yescharacteristic
197C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
198C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
199C3×C4⋊Dic3—21no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—31no—
203C3×C4⋊Dic3—31no—
204C3×C4⋊Dic3—61no—
205C3×C4⋊Dic3C2×D311yescharacteristic, complemented
206C3×C4⋊Dic3C2×D311yescharacteristic, complemented
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—61no—
214#3724—31no—
215#3724C2×D311yescharacteristic, complemented
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3C2×D311yescharacteristic, complemented
222Dic3⋊Dic3C2×D311yescharacteristic, complemented
223#3722—31no—
224#3722—31no—
225#3722—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—61no—
232#3722—61no—
233#3722—61no—
234#3722C2×D311yescharacteristic
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—31no—
257Dic32—61no—
258Dic32—61no—
259C22×C33C2411yescharacteristic
260C2×C3⋊(C3⋊D3)—21no—
261C2×C3⋊(C3⋊D3)—21no—
262C2×C3⋊(C3⋊D3)#4112yes—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3#4112yes—
272D3×C3⋊D3—44no—
273C33×C4—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3—21no—
284C3×#123—91no—
285C3×#123—91no—
286C3×C22⋊Q8—91no—
287#947—91no—
288#946—91no—
289#937—91no—
290#937—91no—
291#936—91no—
292D4×Dic3—91no—
293C4×#67—91no—
294C4×#67—91no—
295C4×#67—91no—
296C2×(C2×D3)⋊C4—91no—
297C2×(C2×D3)⋊C4—91no—
298#926—91no—
299#898—91no—
300#898—91no—
301#898—91no—
302#898—91no—
303#897—91no—
304#896—31no—
305#896—91no—
306#894—31no—
307#894—91no—
308#893—91no—
309#892—91no—
310#892—91no—
311#892—91no—
312#892—91no—
313#892—181no—
314#886—31no—
315#886—31no—
316#885—91no—
317#883—31no—
318#883—91no—
319#883—91no—
320#883—181no—
321#882—91no—
322#67⋊C4—91no—
323D3×C22⋊C4—91no—
324D3×C22⋊C4—91no—
325D3×C22⋊C4—91no—
326D3×C22⋊C4—91no—
327D3×C22⋊C4—181no—
328#879—91no—
329#879—91no—
330#878—31no—
331#877—91no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3—31no—
335C22×C3⋊D3—31no—
336C22×C3⋊D3—31no—
337C22×C3⋊D3—61no—
338C22×C3⋊D3—61no—
339C22×C3⋊D3—61no—
340C22×C3⋊D3—62no—
341C22×C3⋊D3—62no—
342C22×C3⋊D3—121no—
343C22×C3⋊D3—121no—
344C22×C3⋊D3C22×D311yescharacteristic
345C22×C3×D3—21no—
346C22×C3×D3—21no—
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—61no—
350C22×C3×D3C22×D311yescharacteristic
351C22×C3×D3C22×D311yescharacteristic
352C22×C3×D3C22×D311yescharacteristic
353C22×C3×D3C22×D311yescharacteristic
354C2×D32—62no—
355C2×D32—62no—
356C2×D32—64no—
357C2×D32—62no—
358C2×D32—62no—
359C2×D32—122no—
360C2×D32—121no—
361C2×D32—121no—
362C2×D32—122no—
363C2×C32×C4—21no—
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—41no—
371C2×C32×C4C22×D311yescharacteristic
372C2×C32×C4C22×D311yescharacteristic
373C2×C32×C4C22×D311yescharacteristic
374#638—62no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4×C3⋊D3—62no—
388C4×C3⋊D3—62no—
389C4×C3⋊D3—62no—
390C4×C3⋊D3—64no—
391C4×C3⋊D3—122no—
392C4×C3⋊D3—122no—
393C4×C3⋊D3—124no—
394C4×C3⋊D3—121no—
395C3×#67—62no—
396C3×#67—62no—
397C3×#67—121no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—62no—
418C2×C3×Dic3—121no—
419C2×C3×Dic3—121no—
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C3×D12—121no—
429C3×C4×D3—62no—
430C3×C4×D3—121no—
431C3×C4×D3—121no—
432C3×Dic6—121no—
433C3×Dic6—121no—
434#627—41no—
435#626—41no—
436#626—62no—
437#626—62no—
438#626—122no—
439#625—22no—
440#624—121no—
441#624—121no—
442#624—122no—
443D3×Dic3—22no—
444D3×Dic3—41no—
445D3×Dic3—41no—
446#551—271noSylow
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3⋊(C3⋊D3)—22no—
451C3×C3⋊D3—41no—
452C32×D3—22no—
453C32×D3—41no—
454C23×D3—91no—
455C23×D3—91no—
456C23×D3—91no—
457C23×D3—181no—
458C2×C3×Q8—91no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C22×C3×C4—91no—
462C22×C3×C4—91no—
463C22×C3×C4—91no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—181no—
470C22×Dic3—31no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C2×D12—31no—
474C2×D12—91no—
475C2×C4×D3—31no—
476C2×C4×D3—31no—
477C2×C4×D3—31no—
478C2×C4×D3—91no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—181no—
485C2×C4×D3—181no—
486C2×C4×D3—181no—
487C2×C4×D3—181no—
488C2×C4×D3—361no—
489C2×Dic6—31no—
490C2×Dic6—31no—
491C3×C4⋊C4—31no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—61no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
502C3×C22⋊C4—31no—
503C3×C22⋊C4—61no—
504C3×C22⋊C4—61no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509#217—31no—
510#217—31no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—181no—
519#217—181no—
520(C2×D3)⋊C4—31no—
521(C2×D3)⋊C4—31no—
522(C2×D3)⋊C4—31no—
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—61no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—181no—
545(C2×D3)⋊C4—181no—
546(C2×D3)⋊C4—181no—
547(C2×D3)⋊C4—181no—
548(C2×D3)⋊C4D3211yescharacteristic
549(C2×D3)⋊C4D3211yescharacteristic, complemented
550C4⋊Dic3—31no—
551C4⋊Dic3—31no—
552C4⋊Dic3—31no—
553C4⋊Dic3—31no—
554C4⋊Dic3—61no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—91no—
558C4⋊Dic3—181no—
559C4⋊Dic3D3211yescharacteristic, complemented
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—31no—
565Dic3⋊C4—31no—
566Dic3⋊C4—61no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—181no—
580C4×Dic3—181no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—32no—
585C22×C32—41no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3⋊D3—32no—
598C2×C3⋊D3—32no—
599C2×C3⋊D3—32no—
600C2×C3⋊D3—62no—
601C2×C3⋊D3—62no—
602C2×C3⋊D3—62no—
603C2×C3⋊D3—61no—
604C2×C3⋊D3—61no—
605C2×C3⋊D3—62no—
606C2×C3⋊D3—62no—
607C2×C3⋊D3—61no—
608C2×C3⋊D3—61no—
609C2×C3⋊D3—61no—
610C2×C3⋊D3—61no—
611C2×C3⋊D3—122no—
612C2×C3⋊D3—121no—
613C2×C3⋊D3—121no—
614C2×C3⋊D3—121no—
615C2×C3⋊D3—121no—
616C2×C3⋊D3—122no—
617C2×C3⋊D3—122no—
618C2×C3⋊D3—124no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—22no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—62no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C2×C3×D3#23712yes—
645C2×C3×D3#23912yes—
646D32—124no—
647D32—124no—
648D32—128no—
649C32×C4—21no—
650C32×C4—22no—
651C32×C4—21no—
652C32×C4—21no—
653C32×C4—41no—
654C32×C4—41no—
655C32×C4—42no—
656C32×C4—61no—
657C32×C4—61no—
658C32×C4—61no—
659C32×C4—61no—
660C3⋊Dic3—21no—
661C3⋊Dic3—21no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—61no—
666C3⋊Dic3—62no—
667C3⋊Dic3—61no—
668C3⋊Dic3—61no—
669C3⋊Dic3—121no—
670C3⋊Dic3—121no—
671C3⋊Dic3—122no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—21no—
679C3×Dic3—21no—
680C3×Dic3—41no—
681C3×Dic3—41no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—61no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699#126—271no—
700#126—271no—
701#124—271no—
702#123—91no—
703#123—91no—
704#123—271no—
705C22⋊Q8—91no—
706C22⋊Q8—271no—
707#120—271no—
708C4×D4—271no—
709C4×D4—271no—
710#117—271no—
711#117—271no—
712C2×C22⋊C4—271no—
713C2×C22⋊C4—271no—
714C33#55111yescharacteristic, complemented, Sylow
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—31no—
718C23×C3—31no—
719C23×C3—61no—
720C23×C3—61no—
721C23×C3—91no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3—91no—
726C22×D3—91no—
727C22×D3—91no—
728C22×D3—181no—
729C22×D3—181no—
730C22×D3—181no—
731C22×D3—182no—
732C22×D3—182no—
733C22×D3—182no—
734C22×D3—182no—
735C22×D3—182no—
736C22×D3—184no—
737C22×D3—182no—
738C22×D3—361no—
739C22×D3—362no—
740C22×D3—361no—
741C22×D3—361no—
742C22×D3—361no—
743C22×D3—362no—
744C22×D3C2×D3211yescharacteristic
745C22×D3C2×D3211yescharacteristic
746C3×Q8—361no—
747C3×D4—182no—
748C3×D4—361no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—31no—
753C2×C3×C4—31no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—41no—
761C2×C3×C4—61no—
762C2×C3×C4—61no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—91no—
766C2×C3×C4—91no—
767C2×C3×C4—91no—
768C2×C3×C4—91no—
769C2×C3×C4—91no—
770C2×C3×C4—182no—
771C2×C3×C4—361no—
772C2×C3×C4—361no—
773C2×C3×C4C2×D3211yescharacteristic
774C2×C3×C4C2×D3211yescharacteristic
775C2×C3×C4C2×D3211yescharacteristic
776#67—62no—
777#67—62no—
778#67—121no—
779#67—182no—
780#67—182no—
781#67—362no—
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—31no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—61no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—62no—
798C2×Dic3—91no—
799C2×Dic3—91no—
800C2×Dic3—91no—
801C2×Dic3—121no—
802C2×Dic3—121no—
803C2×Dic3—181no—
804C2×Dic3—181no—
805C2×Dic3—181no—
806C2×Dic3—361no—
807C2×Dic3C2×D3211yescharacteristic
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811D12—121no—
812D12—182no—
813C4×D3—62no—
814C4×D3—121no—
815C4×D3—121no—
816C4×D3—182no—
817C4×D3—182no—
818C4×D3—182no—
819C4×D3—184no—
820C4×D3—362no—
821C4×D3—362no—
822C4×D3—364no—
823C4×D3—361no—
824C4×D3—361no—
825C4×D3—361no—
826C4×D3—362no—
827Dic6—121no—
828Dic6—121no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—41no—
839C2×C32—41no—
840C2×C32—41no—
841C2×C32—62no—
842C2×C32—121no—
843C2×C32C2×#23711yescharacteristic
844C2×C32#100411yescharacteristic
845C2×C32#100411yescharacteristic
846C2×C32C2×#23911yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32D3×#4111yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32#100911yescharacteristic
852C3⋊D3—41no—
853C3⋊D3—62no—
854C3⋊D3—64no—
855C3⋊D3—62no—
856C3⋊D3—62no—
857C3⋊D3—122no—
858C3⋊D3—122no—
859C3⋊D3—124no—
860C3×D3—22no—
861C3×D3—22no—
862C3×D3—42no—
863C3×D3—41no—
864C3×D3—41no—
865C3×D3—81no—
866C3×D3—122no—
867C3×D3—121no—
868C3×D3—121no—
869C24—271no—
870C2×Q8—91no—
871C2×D4—91no—
872C2×D4—91no—
873C2×D4—271no—
874C22×C4—91no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—31no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—91no—
883C4⋊C4—91no—
884C4⋊C4—91no—
885C4⋊C4—271no—
886C4⋊C4—271no—
887C22⋊C4—31no—
888C22⋊C4—31no—
889C22⋊C4—91no—
890C22⋊C4—91no—
891C22⋊C4—91no—
892C22⋊C4—91no—
893C22⋊C4—271no—
894C22⋊C4—271no—
895C22⋊C4—271no—
896C22⋊C4—271no—
897C22⋊C4—271no—
898C22⋊C4—271no—
899C22⋊C4—271no—
900C22⋊C4—271no—
901C42—271no—
902C42—271no—
903C42—271no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—32no—
908C22×C3—32no—
909C22×C3—41no—
910C22×C3—62no—
911C22×C3—61no—
912C22×C3—61no—
913C22×C3—61no—
914C22×C3—61no—
915C22×C3—61no—
916C22×C3—61no—
917C22×C3—61no—
918C22×C3—61no—
919C22×C3—61no—
920C22×C3—61no—
921C22×C3—121no—
922C22×C3—121no—
923C22×C3—121no—
924C22×C3—121no—
925C22×C3—121no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3C22×D3211yescharacteristic
930C22×C3C22×D3211yescharacteristic
931C22×C3C22×D3211yescharacteristic
932C2×D3—21no—
933C2×D3—21no—
934C2×D3—21no—
935C2×D3—21no—
936C2×D3—21no—
937C2×D3—62no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—92no—
945C2×D3—92no—
946C2×D3—92no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—182no—
950C2×D3—182no—
951C2×D3—182no—
952C2×D3—182no—
953C2×D3—182no—
954C2×D3—181no—
955C2×D3—181no—
956C2×D3—181no—
957C2×D3—181no—
958C2×D3—181no—
959C2×D3—181no—
960C2×D3—362no—
961C2×D3—361no—
962C2×D3—361no—
963C2×D3—361no—
964C2×D3—361no—
965C2×D3—362no—
966C2×D3—362no—
967C2×D3—364no—
968C2×D3—364no—
969C2×D3—364no—
970C2×D3—368no—
971C2×D3#379612yes—
972C3×C4—22no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4—42no—
979C3×C4—61no—
980C3×C4—61no—
981C3×C4—61no—
982C3×C4—61no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—121no—
988C3×C4—121no—
989C3×C4—121no—
990C3×C4—121no—
991C3×C4—181no—
992C3×C4—181no—
993C3×C4—181no—
994C3×C4—181no—
995C3×C4—181no—
996Dic3—21no—
997Dic3—21no—
998Dic3—21no—
999Dic3—21no—
1000Dic3—61no—
1001Dic3—61no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—121no—
1011Dic3—121no—
1012Dic3—121no—
1013Dic3—121no—
1014Dic3—121no—
1015Dic3—182no—
1016Dic3—181no—
1017Dic3—181no—
1018Dic3—181no—
1019Dic3—361no—
1020Dic3—361no—
1021Dic3—362no—
1022C32—21no—
1023C32—21no—
1024C32—21no—
1025C32—41no—
1026C32#563711yescharacteristic, complemented
1027C32#565811yescharacteristic, complemented
1028C32#565911yescharacteristic, complemented
1029C23—31no—
1030C23—31no—
1031C23—91no—
1032C23—271no—
1033C23—542no—
1034C23—542no—
1035C23—1081no—
1036Q8—361no—
1037D4—182no—
1038D4—361no—
1039D4—542no—
1040C2×C4—31no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—31no—
1044C2×C4—91no—
1045C2×C4—91no—
1046C2×C4—91no—
1047C2×C4—91no—
1048C2×C4—91no—
1049C2×C4—182no—
1050C2×C4—271no—
1051C2×C4—361no—
1052C2×C4—361no—
1053C2×C4—542no—
1054C2×C4—1081no—
1055C2×C4D3311yescharacteristic
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—41no—
1068C2×C3—62no—
1069C2×C3—62no—
1070C2×C3—122no—
1071C2×C3—121no—
1072C2×C3—121no—
1073C2×C3—241no—
1074C2×C3—361no—
1075C2×C3C2×#379611yescharacteristic
1076C2×C3#6430611yescharacteristic
1077C2×C3#6430711yescharacteristic
1078C2×C3D3×#23711yescharacteristic
1079C2×C3#6431211yescharacteristic
1080C2×C3#6431211yescharacteristic
1081C2×C3#6431311yescharacteristic
1082C2×C3#6431411yescharacteristic
1083C2×C3D3×#23911yescharacteristic
1084D3—22no—
1085D3—41no—
1086D3—122no—
1087D3—121no—
1088D3—121no—
1089D3—184no—
1090D3—182no—
1091D3—182no—
1092D3—182no—
1093D3—362no—
1094D3—362no—
1095D3—364no—
1096C22—32no—
1097C22—61no—
1098C22—61no—
1099C22—61no—
1100C22—61no—
1101C22—61no—
1102C22—181no—
1103C22—181no—
1104C22—181no—
1105C22—272no—
1106C22—541no—
1107C22—541no—
1108C22—1084no—
1109C22C2×D3311yescharacteristic
1110C4—21no—
1111C4—61no—
1112C4—61no—
1113C4—61no—
1114C4—61no—
1115C4—181no—
1116C4—181no—
1117C4—181no—
1118C4—181no—
1119C4—181no—
1120C4—541no—
1121C3—21no—
1122C3—21no—
1123C3—21no—
1124C3—41no—
1125C3#1059416411yescharacteristic, complemented
1126C3#1059430411yescharacteristic, complemented
1127C3#1059465311yescharacteristic, complemented
1128C2—62no—
1129C2—121no—
1130C2—361no—
1131C2—542no—
1132C2D3×#379611yescharacteristic
1133C2#1172438111yescharacteristic
1134C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722949C2
hypercenterC2×C4D33
hypocenterC33#551
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723675C2semidirect
2. #11723539C2semidirect
3. #11723420C2semidirect
4. #11723413C2semidirect
5. C3×#63899C2semidirect
6. C3×#63891C2semidirect
7. C3×#63890C2semidirect
8. #11723027C2semidirect
9. #11723001C2semidirect
10. #11722973C2semidirect
12. #11722935C2semidirect
13. Dic3×#625C2semidirect
14. #11722914C2semidirect
15. D3×#3722C2semidirect
23. C2×C3×#627C22semidirect
28. C2×C3×D3×Dic3C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×#3750C22semidirect
33. C32×(C2×D3)⋊C4C22semidirect
34. C32×C4⋊Dic3C22semidirect
35. #88815C22semidirect
38. #88813C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
45. (C2×D3)⋊(C3⋊Dic3)C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. Dic3×C3⋊Dic3C22semidirect
48. C3×#3724C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
80. #63899D3semidirect
82. #63891D3semidirect
83. #63890D3semidirect
157. C2×#627C2×D3semidirect
168. C2×D3×Dic3C2×D3semidirect
180. C4⋊(C3⋊Dic3)C2×D3semidirect
181. #3750C2×D3semidirect
197. C3×(C2×D3)⋊C4C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
205. C3×C4⋊Dic3C2×D3semidirect
206. C3×C4⋊Dic3C2×D3semidirect
215. #3724C2×D3semidirect
221. Dic3⋊Dic3C2×D3semidirect
222. Dic3⋊Dic3C2×D3semidirect
249. (C2×D3)⋊Dic3C2×D3semidirect
549. (C2×D3)⋊C4D32semidirect
559. C4⋊Dic3D32semidirect
714. C33#551semidirect
1026. C32#5637semidirect
1027. C32#5658semidirect
1028. C32#5659semidirect
1125. C3#10594164semidirect
1126. C3#10594304semidirect
1127. C3#10594653semidirect

Maximal subgroups

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

subgroupindex
#117236752
#117235392
#117234202
#117234132
C3×#638992
C3×#638912
C3×#638902
#117230272
#117230012
#117229732
#117229492
#117229352
Dic3×#6252
#117229142
D3×#37222
#105946533
#105943043
#105941643