Finite Group Databasebeta

← #13168352

Subgroups — #13168352

Order 1728.

1036 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723692C211yesmaximal, characteristic
2#11723502C211yesmaximal, characteristic
3#11723444C211yesmaximal, characteristic, complemented
4#11723401C211yesmaximal, characteristic, complemented
5C3×#63918C211yesmaximal, characteristic, complemented
6C3×#63846C211yesmaximal, characteristic, complemented
7C3×#63836C211yesmaximal, characteristic
8#11723036C211yesmaximal, characteristic, complemented
9#11723035C211yesmaximal, characteristic, complemented
10#11723033C211yesmaximal, characteristic, complemented
11#11723012C211yesmaximal, characteristic, complemented
12#11722979C211yesmaximal, characteristic
13#11722974C211yesmaximal, characteristic
14#11722915C211yesmaximal, characteristic
15#11722908C211yesmaximal, characteristic
16#10594505—31nomaximal
17#10594400—31nomaximal
18#10593954—31nomaximal
19C2×#6296C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×#3750C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32C32×C4×Dic3C2211yescharacteristic
33#88815C2211yescharacteristic
34#88814C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88803C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64105—31no—
55#64099—31no—
56#64079—31no—
57C3×#892—31no—
58C3×#890—31no—
59C3×#889—31no—
60C3×#888—31no—
61C3×#872—31no—
62C3×#869—31no—
63#63919—31no—
64#63918—31no—
65#63918—31no—
66#63918—31no—
67#63918D311yescharacteristic, complemented
68#63899—31no—
69#63899—31no—
70#63899—31no—
71#63899—31no—
72#63899—61no—
73#63895—31no—
74#63893—31no—
75#63893—31no—
76D3×C4⋊Dic3—31no—
77D3×C4⋊Dic3—31no—
78#63888—31no—
79#63887—31no—
80#63887—31no—
81#63883—31no—
82#63871—31no—
83#63869—31no—
84#63867—31no—
85#63867—31no—
86#63867—31no—
87#63867—61no—
88#63866—31no—
89#63855—31no—
90#63846—31no—
91#63846—31no—
92#63846—31no—
93#63846—61no—
94#63846D311yescharacteristic, complemented
95#63841—31no—
96#63840—31no—
97#63839—31no—
98#63839—31no—
99#63839—31no—
100#63836—31no—
101#63836D311yescharacteristic
102C22×C3×C3⋊D3C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
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×C32×Dic3C2311yescharacteristic
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6296—41no—
118#6294—41no—
119#6293—41no—
120Dic3×C3⋊D3—41no—
121C3×#627—41no—
122C3×#627—41no—
123C3×#624Q814yescomplemented
124#5729—91no—
125#5689—91no—
126#5519—91no—
127C2×C4×C3⋊D3—31no—
128C2×#634—31no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×Dic6—31no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×#627—31no—
136C2×#627—31no—
137C2×#627—31no—
138C2×#627—31no—
139C2×#627—31no—
140C2×#627—61no—
141C2×#627C2×D311yescharacteristic
142C2×#627C2×D311yescharacteristic
143C2×#624—31no—
144C2×#624C2×D311yescharacteristic
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—61no—
150C32×C4⋊C4—31no—
151C32×C4⋊C4—31no—
152C32×C42—31no—
153#3752—31no—
154#3752C2×D311yescharacteristic
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159C4⋊(C3⋊Dic3)C2×D311yescharacteristic
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—31no—
165#3750—31no—
166#3750—31no—
167#3750—61no—
168#3750—61no—
169#3750—61no—
170#3750—121no—
171#3750C2×D311yescharacteristic
172C4×C3⋊Dic3—31no—
173C3×(C2×D3)⋊C4—31no—
174C3×(C2×D3)⋊C4—31no—
175C3×(C2×D3)⋊C4—31no—
176C3×(C2×D3)⋊C4—31no—
177C3×(C2×D3)⋊C4—61no—
178C3×C4⋊Dic3—21no—
179C3×C4⋊Dic3—31no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—31no—
183C3×C4⋊Dic3—31no—
184C3×C4⋊Dic3—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—61no—
188C3×C4⋊Dic3C2×D311yescharacteristic
189C3×C4⋊Dic3C2×D311yescharacteristic
190C3×Dic3⋊C4—21no—
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—31no—
199C3×Dic3⋊C4—61no—
200C3×Dic3⋊C4C2×D311yescharacteristic
201C3×Dic3⋊C4C2×D311yescharacteristic
202C3×C4×Dic3—21no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3C2×D311yescharacteristic
208C3×C4×Dic3C2×D311yescharacteristic
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—61no—
215#3724—61no—
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—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3—61no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3C2×D311yescharacteristic
237Dic3⋊Dic3C2×D311yescharacteristic
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242#3722—31no—
243#3722C2×D311yescharacteristic
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—61no—
249Dic32—31no—
250Dic32—31no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254C22×C33C2411yescharacteristic
255C2×C3×C3⋊D3—21no—
256C2×C3×C3⋊D3—21no—
257C2×C3×C3⋊D3C2×Q812yes—
258C33×C4—21no—
259C3⋊(C3⋊Dic3)—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—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3C2×Q812yes—
271C32×Dic3C2×Q812yes—
272C3×C4⋊Q8—91no—
273C3×#125—91no—
274C3×#117—91no—
275#946—91no—
276#946—91no—
277#944—91no—
278#944—91no—
279#926—91no—
280C2×C4⋊Dic3—91no—
281#897—91no—
282#897—91no—
283#896—91no—
284#896—91no—
285#896—91no—
286#896—91no—
287#896—181no—
288#892—31no—
289#892—91no—
290D3×C4⋊C4—91no—
291D3×C4⋊C4—91no—
292#890—31no—
293#890—91no—
294#890—91no—
295#890—91no—
296#890—181no—
297#889—31no—
298#889—91no—
299#889—91no—
300#889—91no—
301#888—31no—
302#888—91no—
303#888—91no—
304#888—91no—
305#888—91no—
306#888—91no—
307#878—91no—
308#878—91no—
309#878—91no—
310#878—91no—
311#872—31no—
312#872—91no—
313#870—91no—
314#870—91no—
315#870—91no—
316#870—181no—
317#869—31no—
318#869—91no—
319#869—91no—
320C22×C3⋊D3C22×D311yescharacteristic
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—61no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—31no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—41no—
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C3⋊Dic3—31no—
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—61no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—121no—
350C2×C3⋊Dic3—121no—
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C4×C3⋊D3—121no—
357#634—121no—
358C2×C3×Dic3—21no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—21no—
362C2×C3×Dic3—21no—
363C2×C3×Dic3—21no—
364C2×C3×Dic3—31no—
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—61no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3C22×D311yescharacteristic
380C2×C3×Dic3C22×D311yescharacteristic
381C2×C3×Dic3C22×D311yescharacteristic
382C2×C3×Dic3C22×D311yescharacteristic
383C2×C3×Dic3C22×D311yescharacteristic
384C2×C3×Dic3C22×D311yescharacteristic
385C2×C3×Dic3C22×D311yescharacteristic
386C2×C3×Dic3C22×D311yescharacteristic
387C2×C3×Dic3C22×D311yescharacteristic
388C2×C3×Dic3C22×D311yescharacteristic
389C2×C3×Dic3C22×D311yescharacteristic
390C2×C3×Dic3C22×D311yescharacteristic
391C3×C4×D3—34no—
392C3×C4×D3—34no—
393C3×Dic6—121no—
394C3×Dic6—121no—
395C3×Dic6—121no—
396C3×Dic6—121no—
397#627—41no—
398#627—41no—
399#627—121no—
400#627—121no—
401#627—122no—
402#627—121no—
403#627—121no—
404#627—121no—
405#624—121no—
406#624Dic614yescomplemented
407D3×Dic3—121no—
408D3×Dic3—121no—
409D3×Dic3—122no—
410D3×Dic3—121no—
411D3×Dic3—121no—
412#544—271noSylow
413C2×C33C22×Q811yescharacteristic
414C2×C33H(5,𝔽2)11yescharacteristic
415C2×C332−1+411yescharacteristic
416C3×C3⋊D3—22no—
417C2×C3×Q8—91no—
418C2×C3×Q8—91no—
419C22×C3×C4—91no—
420C22×Dic3—91no—
421C22×Dic3—91no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—91no—
425C2×C4×D3—91no—
426C2×C4×D3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—181no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—181no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—61no—
445C3×C4⋊C4—61no—
446C3×C4⋊C4—91no—
447C3×C4⋊C4—91no—
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×C22⋊C4—91no—
455C3×C22⋊C4—91no—
456C3×C42—31no—
457C3×C42—31no—
458C3×C42—61no—
459C3×C42—91no—
460C3×C42—91no—
461#217—91no—
462#217—91no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—61no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—91no—
472(C2×D3)⋊C4—181no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—31no—
480C4⋊Dic3—31no—
481C4⋊Dic3—61no—
482C4⋊Dic3—91no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—91no—
486C4⋊Dic3—91no—
487C4⋊Dic3—91no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—181no—
494C4⋊Dic3—181no—
495C4⋊Dic3—181no—
496C4⋊Dic3—181no—
497C4⋊Dic3D3211yescharacteristic
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—31no—
506Dic3⋊C4—61no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523Dic3⋊C4—91no—
524Dic3⋊C4—91no—
525Dic3⋊C4—91no—
526Dic3⋊C4—181no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—181no—
531Dic3⋊C4—181no—
532Dic3⋊C4—181no—
533Dic3⋊C4—361no—
534Dic3⋊C4D3211yescharacteristic
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—181no—
543C4×Dic3D3211yescharacteristic
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32C23×D311yescharacteristic
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C2×C3⋊D3—21no—
552C2×C3⋊D3—21no—
553C2×C3⋊D3C2×Dic612yes—
554C2×C3×D3—32no—
555C2×C3×D3—32no—
556C2×C3×D3—62no—
557C2×C3×D3—61no—
558C2×C3×D3—61no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—121no—
562C2×C3×D3—121no—
563C32×C4—21no—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—32no—
567C32×C4—32no—
568C32×C4—41no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—61no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—81no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—21no—
581C3⋊Dic3—61no—
582C3⋊Dic3—62no—
583C3⋊Dic3—61no—
584C3⋊Dic3—61no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—61no—
588C3⋊Dic3—121no—
589C3⋊Dic3—121no—
590C3⋊Dic3—122no—
591C3⋊Dic3—121no—
592C3⋊Dic3—121no—
593C3⋊Dic3—121no—
594C3⋊Dic3—241no—
595C3×Dic3—21no—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—22no—
604C3×Dic3—22no—
605C3×Dic3—41no—
606C3×Dic3—41no—
607C3×Dic3—41no—
608C3×Dic3—41no—
609C3×Dic3—61no—
610C3×Dic3—61no—
611C3×Dic3—61no—
612C3×Dic3—61no—
613C3×Dic3—61no—
614C3×Dic3—61no—
615C3×Dic3—61no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—121no—
620C3×Dic3—121no—
621C3×Dic3—121no—
622C3×Dic3—121no—
623C3×Dic3—121no—
624C3×Dic3C2×Dic612yes—
625C3×Dic3C2×Dic612yes—
626C3×Dic3D3×Q812yes—
627C3×Dic3D3×Q812yes—
628C4⋊Q8—91no—
629C4⋊Q8—271no—
630C4⋊Q8—271no—
631C4⋊Q8—271no—
632#125—91no—
633#125—271no—
634#125—271no—
635#125—271no—
636C22⋊Q8—271no—
637C22⋊Q8—271no—
638C22⋊Q8—271no—
639C22⋊Q8—271no—
640#117—91no—
641#117—271no—
642C2×C4⋊C4—271no—
643C33#54411yescharacteristic, complemented, Sylow
644C23×C3—91no—
645C22×D3—31no—
646C22×D3—31no—
647C22×D3—61no—
648C3×Q8—361no—
649C3×Q8—361no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—31no—
654C2×C3×C4—31no—
655C2×C3×C4—31no—
656C2×C3×C4—31no—
657C2×C3×C4—31no—
658C2×C3×C4—31no—
659C2×C3×C4—31no—
660C2×C3×C4—31no—
661C2×C3×C4—31no—
662C2×C3×C4—31no—
663C2×C3×C4—31no—
664C2×C3×C4—31no—
665C2×C3×C4—41no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—94no—
673C2×C3×C4—91no—
674C2×C3×C4—91no—
675C2×C3×C4—91no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4C2×D3211yescharacteristic
679C2×C3×C4C2×D3211yescharacteristic
680C2×C3×C4C2×D3211yescharacteristic
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—61no—
692C2×Dic3—61no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—91no—
697C2×Dic3—91no—
698C2×Dic3—91no—
699C2×Dic3—91no—
700C2×Dic3—91no—
701C2×Dic3—91no—
702C2×Dic3—181no—
703C2×Dic3—181no—
704C2×Dic3—181no—
705C2×Dic3—181no—
706C2×Dic3—181no—
707C2×Dic3—181no—
708C2×Dic3—361no—
709C2×Dic3—361no—
710C2×Dic3—361no—
711C2×Dic3—361no—
712C2×Dic3C2×D3211yescharacteristic
713C2×Dic3C2×D3211yescharacteristic
714C2×Dic3C2×D3211yescharacteristic
715C2×Dic3C2×D3211yescharacteristic
716C2×Dic3C2×D3211yescharacteristic
717C2×Dic3C2×D3211yescharacteristic
718C4×D3—34no—
719C4×D3—34no—
720C4×D3—361no—
721C4×D3—361no—
722C4×D3—361no—
723C4×D3—361no—
724C4×D3—362no—
725Dic6—121no—
726Dic6—121no—
727Dic6—121no—
728Dic6—121no—
729Dic6—361no—
730Dic6—361no—
731Dic6—361no—
732Dic6—361no—
733Dic6—361no—
734Dic6—361no—
735Dic6—362no—
736C2×C32—21no—
737C2×C32—21no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—41no—
746C2×C32—41no—
747C2×C32—41no—
748C2×C32C22×Dic611yescharacteristic
749C2×C32#100411yescharacteristic
750C2×C32C2×D3×Q811yescharacteristic
751C2×C32C2×D3×Q811yescharacteristic
752C2×C32#100711yescharacteristic
753C2×C32#100911yescharacteristic
754C2×C32#100911yescharacteristic
755C2×C32#101011yescharacteristic
756C2×C32#101011yescharacteristic
757C3⋊D3—22no—
758C3×D3—62no—
759C3×D3—62no—
760C3×D3—122no—
761C2×Q8—91no—
762C2×Q8—91no—
763C2×Q8—271no—
764C2×Q8—271no—
765C22×C4—91no—
766C22×C4—271no—
767C22×C4—271no—
768C4⋊C4—31no—
769C4⋊C4—31no—
770C4⋊C4—91no—
771C4⋊C4—91no—
772C4⋊C4—91no—
773C4⋊C4—91no—
774C4⋊C4—91no—
775C4⋊C4—91no—
776C4⋊C4—91no—
777C4⋊C4—91no—
778C4⋊C4—271no—
779C4⋊C4—271no—
780C4⋊C4—271no—
781C4⋊C4—271no—
782C4⋊C4—271no—
783C4⋊C4—271no—
784C4⋊C4—271no—
785C4⋊C4—271no—
786C4⋊C4—271no—
787C4⋊C4—271no—
788C22⋊C4—91no—
789C22⋊C4—91no—
790C22⋊C4—271no—
791C22⋊C4—271no—
792C42—31no—
793C42—91no—
794C42—91no—
795C42—271no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—41no—
800C22×C3—92no—
801C22×C3—181no—
802C22×C3—181no—
803C22×C3C22×D3211yescharacteristic
804C22×C3C22×D3211yescharacteristic
805C22×C3C22×D3211yescharacteristic
806C2×D3—32no—
807C2×D3—32no—
808C2×D3—62no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—121no—
814C2×D3—121no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—32no—
819C3×C4—32no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—41no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—61no—
828C3×C4—61no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—81no—
836C3×C4—121no—
837C3×C4—121no—
838C3×C4—121no—
839C3×C4—121no—
840C3×C4—181no—
841C3×C4—181no—
842C3×C4—181no—
843C3×C4—181no—
844C3×C4—181no—
845Dic3—21no—
846Dic3—21no—
847Dic3—21no—
848Dic3—21no—
849Dic3—61no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—61no—
859Dic3—121no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—121no—
864Dic3—182no—
865Dic3—181no—
866Dic3—181no—
867Dic3—181no—
868Dic3—181no—
869Dic3—181no—
870Dic3—181no—
871Dic3—361no—
872Dic3—361no—
873Dic3—361no—
874Dic3—361no—
875Dic3—361no—
876Dic3—362no—
877Dic3—721no—
878Dic3D3×Dic612yes—
879Dic3D3×Dic612yes—
880C32—21no—
881C32—21no—
882C32—21no—
883C32—41no—
884C32#551911yescharacteristic, complemented
885C32#568911yescharacteristic, complemented
886C32#572911yescharacteristic, complemented
887C23—91no—
888Q8—361no—
889Q8—361no—
890Q8—1081no—
891Q8—1081no—
892C2×C4—31no—
893C2×C4—31no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—94no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—271no—
905C2×C4—271no—
906C2×C4—1081no—
907C2×C4—1081no—
908C2×C4D3311yescharacteristic
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—41no—
919C2×C3—41no—
920C2×C3—41no—
921C2×C3—182no—
922C2×C3C2×D3×Dic611yescharacteristic
923C2×C3C2×D3×Dic611yescharacteristic
924C2×C3#6429711yescharacteristic
925C2×C3#6429711yescharacteristic
926C2×C3#6430711yescharacteristic
927C2×C3#6430911yescharacteristic
928C2×C3#6431411yescharacteristic
929C2×C3D32×Q811yescharacteristic
930C2×C3#6432011yescharacteristic
931D3—62no—
932D3—62no—
933D3—122no—
934C22—92no—
935C22—181no—
936C22—181no—
937C22C2×D3311yescharacteristic
938C4—21no—
939C4—32no—
940C4—32no—
941C4—61no—
942C4—61no—
943C4—61no—
944C4—61no—
945C4—181no—
946C4—181no—
947C4—181no—
948C4—181no—
949C4—181no—
950C4—541no—
951C4—541no—
952C3—21no—
953C3—21no—
954C3—21no—
955C3—41no—
956C3#1059395411yescharacteristic, complemented
957C3#1059440011yescharacteristic, complemented
958C3#1059450511yescharacteristic, complemented
959C2—182no—
960C2D32×Dic611yescharacteristic
961C2#1172438511yescharacteristic
962C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#544
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723444C2semidirect
4. #11723401C2semidirect
5. C3×#63918C2semidirect
6. C3×#63846C2semidirect
8. #11723036C2semidirect
9. #11723035C2semidirect
10. #11723033C2semidirect
11. #11723012C2semidirect
67. #63918D3semidirect
94. #63846D3semidirect
123. C3×#624Q8semidirect
406. #624Dic6semidirect
643. C33#544semidirect
884. C32#5519semidirect
885. C32#5689semidirect
886. C32#5729semidirect
956. C3#10593954semidirect
957. C3#10594400semidirect
958. C3#10594505semidirect

Maximal subgroups

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

subgroupindex
#117236922
#117235022
#117234442
#117234012
C3×#639182
C3×#638462
C3×#638362
#117230362
#117230352
#117230332
#117230122
#117229792
#117229742
#117229152
#117229082
#105945053
#105944003
#105939543