Finite Group Databasebeta

← #13169350

Subgroups — #13169350

Order 1728.

1114 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723683C211yesmaximal, characteristic
2#11723476C211yesmaximal, characteristic
3#11723412C211yesmaximal, characteristic, complemented
4#11723390C211yesmaximal, characteristic, complemented
5C3×#63895C211yesmaximal, characteristic
6C3×#63843C211yesmaximal, characteristic, complemented
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723033C211yesmaximal, characteristic, complemented
9#11723015C211yesmaximal, characteristic, complemented
10#11722974C211yesmaximal, characteristic
11#11722972C211yesmaximal, characteristic
12#11722940C211yesmaximal, characteristic, complemented
13#11722940C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic
15Dic3×#624C211yesmaximal, characteristic
16#10595374—31nomaximal
17#10594387—31nomaximal
18#10594386—31nomaximal
19C2×C32×Dic6C2211yescharacteristic
20C2×#6294C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×Dic3×C3⋊D3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#624C2211yescharacteristic
26#88857C2211yescharacteristic
27C3×#3752C2211yescharacteristic
28C3×#3750C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30C32×C4⋊Dic3C2211yescharacteristic
31C32×Dic3⋊C4C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88807C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64155—31no—
55#64098—31no—
56#64096—31no—
57C3×Q8×Dic3—31no—
58C3×#944—31no—
59C3×#897—31no—
60C3×#896—31no—
61C3×#888—31no—
62C3×#887—31no—
63#63918—31no—
64#63895—31no—
65#63895D311yescharacteristic
66#63893—31no—
67#63887—31no—
68#63887—31no—
69#63887—31no—
70#63887—61no—
71C4×#624—31no—
72#63878—31no—
73#63878—31no—
74#63877—31no—
75#63877—31no—
76C4×D3×Dic3—31no—
77C4×D3×Dic3—31no—
78#63871—31no—
79#63870—31no—
80#63866—31no—
81#63857—31no—
82#63851—31no—
83#63846—31no—
84#63846—31no—
85#63846—31no—
86#63846—31no—
87#63846—61no—
88#63843—31no—
89#63843—31no—
90#63843D311yescharacteristic, complemented
91Dic3×Dic6—31no—
92Dic3×Dic6—31no—
93#63839—31no—
94#63839D311yescharacteristic, complemented
95#63837—31no—
96#63837—31no—
97#63837—31no—
98#63837—31no—
99#63837—61no—
100#63836—31no—
101#63836—31no—
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
117C32×Dic6—22no—
118#6294Q814yescomplemented
119#6293—22no—
120Dic3×C3⋊D3—22no—
121C3×#627—22no—
122C3×#627—22no—
123C3×#624—22no—
124#5728—91no—
125#5622—91no—
126#5578—91no—
127C2×C32×Q8—31no—
128C2×C4×C3⋊D3—31no—
129C2×#634—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—31no—
132C2×C3×Dic6—21no—
133C2×C3×Dic6—31no—
134C2×C3×Dic6—31no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6C2×D311yescharacteristic
138C2×C3×Dic6C2×D311yescharacteristic
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—61no—
142C2×#627C2×D311yescharacteristic
143C2×#627C2×D311yescharacteristic
144C2×#624—31no—
145C2×#624C2×D311yescharacteristic
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150C2×D3×Dic3—61no—
151C32×C4⋊C4—31no—
152C32×C4⋊C4—31no—
153#3752—31no—
154#3752C2×D311yescharacteristic
155C4⋊(C3⋊Dic3)—31no—
156C4⋊(C3⋊Dic3)—31no—
157#3750—31no—
158#3750—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163#3750—31no—
164#3750—61no—
165#3750—61no—
166#3750—61no—
167#3750—121no—
168#3750C2×D311yescharacteristic
169C4×C3⋊Dic3—31no—
170C4×C3⋊Dic3—31no—
171C4×C3⋊Dic3—31no—
172C4×C3⋊Dic3C2×D311yescharacteristic
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⋊Dic3C2×D311yescharacteristic
184C3×C4⋊Dic3C2×D311yescharacteristic
185C3×Dic3⋊C4—21no—
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—61no—
195C3×Dic3⋊C4C2×D311yescharacteristic
196C3×Dic3⋊C4C2×D311yescharacteristic
197C3×C4×Dic3—31no—
198C3×C4×Dic3—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—61no—
206#3724—31no—
207#3724C2×D311yescharacteristic
208Dic3⋊Dic3—31no—
209Dic3⋊Dic3—31no—
210Dic3⋊Dic3—31no—
211Dic3⋊Dic3—31no—
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—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231Dic3⋊Dic3C2×D311yescharacteristic
232#3722—31no—
233#3722C2×D311yescharacteristic
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—61no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—61no—
249Dic32—61no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
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⋊Dic3C2×Q812yes—
265C3×C3⋊Dic3C2×Q812yes—
266C32×Dic3—21no—
267C32×Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3#4112yes—
271C32×Dic3#4112yes—
272C3×C4⋊Q8—91no—
273C3×C22⋊Q8—91no—
274C3×C4×Q8—91no—
275#946—91no—
276#946—91no—
277#946—91no—
278#946—181no—
279Q8×Dic3—31no—
280Q8×Dic3—91no—
281Q8×Dic3—91no—
282#944—31no—
283#944—91no—
284#924—91no—
285C2×C4×Dic3—91no—
286#897—31no—
287#897—91no—
288#897—91no—
289#896—31no—
290#896—91no—
291#892—91no—
292#892—91no—
293#890—91no—
294#890—91no—
295#889—91no—
296#889—91no—
297#889—91no—
298#889—91no—
299#889—181no—
300#888—31no—
301#888—91no—
302#887—31no—
303#887—91no—
304#887—91no—
305#887—91no—
306#887—91no—
307#887—181no—
308#878—91no—
309#878—91no—
310#877—91no—
311#877—91no—
312#872—91no—
313#872—91no—
314C42×D3—91no—
315C42×D3—91no—
316#869—91no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C22×C3⋊D3C22×D311yescharacteristic
321C22×C3×D3—31no—
322C22×C3×D3—31no—
323C22×C3×D3—61no—
324C32×Q8—62no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—31no—
329C2×C32×C4—31no—
330C2×C32×C4—31no—
331C2×C32×C4—31no—
332C2×C32×C4—31no—
333C2×C32×C4—31no—
334C2×C32×C4—41no—
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C32×C4C22×D311yescharacteristic
338C2×C3⋊Dic3—31no—
339C2×C3⋊Dic3—31no—
340C2×C3⋊Dic3—31no—
341C2×C3⋊Dic3—31no—
342C2×C3⋊Dic3—31no—
343C2×C3⋊Dic3—31no—
344C2×C3⋊Dic3—61no—
345C2×C3⋊Dic3—61no—
346C2×C3⋊Dic3—61no—
347C2×C3⋊Dic3—61no—
348C2×C3⋊Dic3—61no—
349C2×C3⋊Dic3—61no—
350C2×C3⋊Dic3—121no—
351C2×C3⋊Dic3—121no—
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C4×C3⋊D3—62no—
358#634—62no—
359C2×C3×Dic3—21no—
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—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
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
391C2×C3×Dic3C22×D311yescharacteristic
392C3×C4×D3—62no—
393C3×C4×D3—62no—
394C3×Dic6—22no—
395C3×Dic6—22no—
396C3×Dic6—42no—
397C3×Dic6—62no—
398C3×Dic6—62no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401#627—22no—
402#627—22no—
403#627—64no—
404#627—62no—
405#627—62no—
406#624—22no—
407#624—34no—
408D3×Dic3—34no—
409D3×Dic3—34no—
410D3×Dic3—62no—
411D3×Dic3—62no—
412D3×Dic3—122no—
413#533—271noSylow
414C2×C33C22×Q811yescharacteristic
415C2×C33C2×#4111yescharacteristic
416C2×C33C2×#4111yescharacteristic
417C3×C3⋊D3—22no—
418C2×C3×Q8—31no—
419C2×C3×Q8—31no—
420C2×C3×Q8—61no—
421C2×C3×Q8—91no—
422C2×C3×Q8—91no—
423C22×C3×C4—91no—
424C22×Dic3—91no—
425C22×Dic3—91no—
426C2×C4×D3—31no—
427C2×C4×D3—31no—
428C2×C4×D3—91no—
429C2×C4×D3—91no—
430C2×C4×D3—91no—
431C2×C4×D3—91no—
432C2×C4×D3—181no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—31no—
436C2×Dic6—31no—
437C2×Dic6—91no—
438C2×Dic6—91no—
439C2×Dic6—91no—
440C2×Dic6—181no—
441C2×Dic6D3211yescharacteristic
442C3×C4⋊C4—31no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—61no—
447C3×C4⋊C4—61no—
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—91no—
457C3×C42—91no—
458C3×C42—91no—
459C3×C42—91no—
460#217—91no—
461#217—91no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—31no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—61no—
467(C2×D3)⋊C4—91no—
468(C2×D3)⋊C4—91no—
469(C2×D3)⋊C4—91no—
470(C2×D3)⋊C4—91no—
471(C2×D3)⋊C4—181no—
472C4⋊Dic3—31no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—31no—
476C4⋊Dic3—91no—
477C4⋊Dic3—91no—
478C4⋊Dic3—91no—
479C4⋊Dic3—91no—
480C4⋊Dic3—91no—
481C4⋊Dic3—91no—
482C4⋊Dic3—91no—
483C4⋊Dic3—91no—
484C4⋊Dic3—91no—
485C4⋊Dic3—181no—
486C4⋊Dic3—181no—
487C4⋊Dic3D3211yescharacteristic
488Dic3⋊C4—31no—
489Dic3⋊C4—31no—
490Dic3⋊C4—31no—
491Dic3⋊C4—31no—
492Dic3⋊C4—31no—
493Dic3⋊C4—31no—
494Dic3⋊C4—31no—
495Dic3⋊C4—31no—
496Dic3⋊C4—61no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—181no—
513Dic3⋊C4—181no—
514Dic3⋊C4—181no—
515Dic3⋊C4—181no—
516Dic3⋊C4—181no—
517Dic3⋊C4—181no—
518Dic3⋊C4—181no—
519Dic3⋊C4—361no—
520Dic3⋊C4D3211yescharacteristic
521C4×Dic3—31no—
522C4×Dic3—31no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—61no—
530C4×Dic3—91no—
531C4×Dic3—91no—
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—91no—
542C4×Dic3—181no—
543C4×Dic3—181no—
544C4×Dic3—181no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—41no—
549C22×C32C23×D311yescharacteristic
550C22×C32C23×D311yescharacteristic
551C22×C32C23×D311yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3D3×Q812yes—
555C2×C3×D3—32no—
556C2×C3×D3—32no—
557C2×C3×D3—62no—
558C2×C3×D3—61no—
559C2×C3×D3—61no—
560C2×C3×D3—61no—
561C2×C3×D3—61no—
562C2×C3×D3—121no—
563C2×C3×D3—121no—
564C32×C4—21no—
565C32×C4—21no—
566C32×C4—21no—
567C32×C4—32no—
568C32×C4—32no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—41no—
572C32×C4—61no—
573C32×C4—61no—
574C32×C4—61no—
575C32×C4—61no—
576C32×C4—81no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—61no—
581C3⋊Dic3—62no—
582C3⋊Dic3—61no—
583C3⋊Dic3—61no—
584C3⋊Dic3—61no—
585C3⋊Dic3—61no—
586C3⋊Dic3—61no—
587C3⋊Dic3—121no—
588C3⋊Dic3—121no—
589C3⋊Dic3—122no—
590C3⋊Dic3—121no—
591C3⋊Dic3—121no—
592C3⋊Dic3—121no—
593C3⋊Dic3—241no—
594C3⋊Dic3D3×Q812yes—
595C3⋊Dic3D3×Q812yes—
596C3×Dic3—21no—
597C3×Dic3—21no—
598C3×Dic3—21no—
599C3×Dic3—21no—
600C3×Dic3—21no—
601C3×Dic3—21no—
602C3×Dic3—21no—
603C3×Dic3—21no—
604C3×Dic3—22no—
605C3×Dic3—22no—
606C3×Dic3—32no—
607C3×Dic3—32no—
608C3×Dic3—32no—
609C3×Dic3—32no—
610C3×Dic3—41no—
611C3×Dic3—41no—
612C3×Dic3—41no—
613C3×Dic3—41no—
614C3×Dic3—62no—
615C3×Dic3—62no—
616C3×Dic3—62no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—121no—
624C3×Dic3—121no—
625C3×Dic3#23512yes—
626C3×Dic3#23712yes—
627C3×Dic3#23712yes—
628C3×Dic3#23912yes—
629C4⋊Q8—91no—
630C4⋊Q8—271no—
631#125—271no—
632#125—271no—
633C22⋊Q8—91no—
634C22⋊Q8—271no—
635C22⋊Q8—271no—
636C22⋊Q8—271no—
637C4×Q8—91no—
638C4×Q8—271no—
639C4×Q8—271no—
640C4×Q8—271no—
641#117—271no—
642#117—271no—
643C2×C42—271no—
644C33#53311yescharacteristic, complemented, Sylow
645C23×C3—91no—
646C22×D3—31no—
647C22×D3—31no—
648C22×D3—61no—
649C3×Q8—62no—
650C3×Q8—62no—
651C3×Q8—122no—
652C3×Q8—182no—
653C3×Q8—182no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
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—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—41no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4—61no—
674C2×C3×C4—61no—
675C2×C3×C4—61no—
676C2×C3×C4—91no—
677C2×C3×C4—91no—
678C2×C3×C4—91no—
679C2×C3×C4—91no—
680C2×C3×C4—91no—
681C2×C3×C4—182no—
682C2×C3×C4C2×D3211yescharacteristic
683C2×C3×C4C2×D3211yescharacteristic
684C2×C3×C4C2×D3211yescharacteristic
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—94no—
701C2×Dic3—91no—
702C2×Dic3—91no—
703C2×Dic3—91no—
704C2×Dic3—91no—
705C2×Dic3—91no—
706C2×Dic3—91no—
707C2×Dic3—181no—
708C2×Dic3—181no—
709C2×Dic3—181no—
710C2×Dic3—181no—
711C2×Dic3—181no—
712C2×Dic3—181no—
713C2×Dic3—182no—
714C2×Dic3—361no—
715C2×Dic3—361no—
716C2×Dic3C2×D3211yescharacteristic
717C2×Dic3C2×D3211yescharacteristic
718C2×Dic3C2×D3211yescharacteristic
719C2×Dic3C2×D3211yescharacteristic
720C2×Dic3C2×D3211yescharacteristic
721C2×Dic3C2×D3211yescharacteristic
722C4×D3—62no—
723C4×D3—62no—
724C4×D3—94no—
725C4×D3—94no—
726C4×D3—182no—
727C4×D3—182no—
728C4×D3—362no—
729Dic6—22no—
730Dic6—62no—
731Dic6—62no—
732Dic6—62no—
733Dic6—62no—
734Dic6—182no—
735Dic6—182no—
736Dic6—184no—
737Dic6—182no—
738C2×C32—21no—
739C2×C32—21no—
740C2×C32—21no—
741C2×C32—21no—
742C2×C32—21no—
743C2×C32—21no—
744C2×C32—21no—
745C2×C32—21no—
746C2×C32—21no—
747C2×C32—41no—
748C2×C32—41no—
749C2×C32—41no—
750C2×C32C2×#23511yescharacteristic
751C2×C32C2×#23711yescharacteristic
752C2×C32C2×#23711yescharacteristic
753C2×C32C2×D3×Q811yescharacteristic
754C2×C32C2×D3×Q811yescharacteristic
755C2×C32C2×D3×Q811yescharacteristic
756C2×C32C2×#23911yescharacteristic
757C2×C32D3×#4111yescharacteristic
758C2×C32D3×#4111yescharacteristic
759C3⋊D3—22no—
760C3×D3—62no—
761C3×D3—62no—
762C3×D3—122no—
763C2×Q8—31no—
764C2×Q8—91no—
765C2×Q8—91no—
766C2×Q8—271no—
767C22×C4—91no—
768C22×C4—271no—
769C22×C4—271no—
770C4⋊C4—31no—
771C4⋊C4—31no—
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—
786C22⋊C4—91no—
787C22⋊C4—91no—
788C22⋊C4—271no—
789C22⋊C4—271no—
790C42—91no—
791C42—91no—
792C42—91no—
793C42—91no—
794C42—271no—
795C42—271no—
796C42—271no—
797C42—271no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—41no—
802C22×C3—92no—
803C22×C3—181no—
804C22×C3—181no—
805C22×C3C22×D3211yescharacteristic
806C22×C3C22×D3211yescharacteristic
807C22×C3C22×D3211yescharacteristic
808C2×D3—32no—
809C2×D3—32no—
810C2×D3—62no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—61no—
815C2×D3—121no—
816C2×D3—121no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—32no—
821C3×C4—32no—
822C3×C4—32no—
823C3×C4—32no—
824C3×C4—41no—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—61no—
832C3×C4—61no—
833C3×C4—61no—
834C3×C4—61no—
835C3×C4—61no—
836C3×C4—61no—
837C3×C4—81no—
838C3×C4—92no—
839C3×C4—92no—
840C3×C4—121no—
841C3×C4—121no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4—181no—
845C3×C4—181no—
846C3×C4—181no—
847Dic3—21no—
848Dic3—21no—
849Dic3—21no—
850Dic3—21no—
851Dic3—32no—
852Dic3—32no—
853Dic3—32no—
854Dic3—32no—
855Dic3—62no—
856Dic3—62no—
857Dic3—62no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—121no—
865Dic3—121no—
866Dic3—182no—
867Dic3—181no—
868Dic3—181no—
869Dic3—181no—
870Dic3—181no—
871Dic3—181no—
872Dic3—181no—
873Dic3—361no—
874Dic3—361no—
875Dic3—361no—
876Dic3—361no—
877Dic3—361no—
878Dic3—362no—
879Dic3—721no—
880Dic3#379612yes—
881Dic3#380412yes—
882C32—21no—
883C32—21no—
884C32—21no—
885C32—41no—
886C32#557811yescharacteristic, complemented
887C32#562211yescharacteristic, complemented
888C32#572811yescharacteristic, complemented
889C23—91no—
890Q8—62no—
891Q8—182no—
892Q8—182no—
893Q8—542no—
894C2×C4—31no—
895C2×C4—31no—
896C2×C4—31no—
897C2×C4—31no—
898C2×C4—31no—
899C2×C4—31no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—91no—
905C2×C4—182no—
906C2×C4—274no—
907C2×C4—271no—
908C2×C4—271no—
909C2×C4—542no—
910C2×C4D3311yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—41no—
921C2×C3—41no—
922C2×C3—41no—
923C2×C3—182no—
924C2×C3C2×#379611yescharacteristic
925C2×C3D3×#23511yescharacteristic
926C2×C3D3×#23711yescharacteristic
927C2×C3D3×#23711yescharacteristic
928C2×C3D32×Q811yescharacteristic
929C2×C3D32×Q811yescharacteristic
930C2×C3D32×Q811yescharacteristic
931C2×C3D3×#23911yescharacteristic
932C2×C3C2×#380411yescharacteristic
933D3—62no—
934D3—62no—
935D3—122no—
936C22—92no—
937C22—181no—
938C22—181no—
939C22C2×D3311yescharacteristic
940C4—21no—
941C4—32no—
942C4—32no—
943C4—61no—
944C4—61no—
945C4—61no—
946C4—61no—
947C4—92no—
948C4—92no—
949C4—181no—
950C4—181no—
951C4—181no—
952C4—541no—
953C4—541no—
954C3—21no—
955C3—21no—
956C3—21no—
957C3—41no—
958C3#1059438611yescharacteristic, complemented
959C3#1059438711yescharacteristic, complemented
960C3#1059537411yescharacteristic, complemented
961C2—182no—
962C2D3×#379611yescharacteristic
963C2#1172437811yescharacteristic
964C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×C4D33
hypocenterC33#533
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
3. #11723412C2semidirect
4. #11723390C2semidirect
6. C3×#63843C2semidirect
7. C3×#63839C2semidirect
8. #11723033C2semidirect
9. #11723015C2semidirect
12. #11722940C2semidirect
13. #11722940C2semidirect
90. #63843D3semidirect
94. #63839D3semidirect
118. #6294Q8semidirect
644. C33#533semidirect
886. C32#5578semidirect
887. C32#5622semidirect
888. C32#5728semidirect
958. C3#10594386semidirect
959. C3#10594387semidirect
960. C3#10595374semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117234762
#117234122
#117233902
C3×#638952
C3×#638432
C3×#638392
#117230332
#117230152
#117229742
#117229722
#117229402
#117229222
Dic3×#6242
#105953743
#105943873
#105943863