Finite Group Databasebeta

← #13171923

Subgroups — #13171923

Order 1728.

1154 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723716C211yesmaximal, characteristic, complemented
2#11723642C211yesmaximal, characteristic, complemented
3#67⋊(C3⋊Dic3)C211yesmaximal, characteristic
4#11723598C211yesmaximal, characteristic, complemented
5C3×#63969C211yesmaximal, characteristic
6C3×#63969C211yesmaximal, characteristic
7C3×#63956C211yesmaximal, characteristic, complemented
8#11723018C211yesmaximal, characteristic, complemented
9#11723016C211yesmaximal, characteristic, complemented
10#11723013C211yesmaximal, characteristic, complemented
11#11722980C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722914C211yesmaximal, characteristic, complemented
14#11722913C211yesmaximal, characteristic, complemented
15D3×#3724C211yesmaximal, characteristic, complemented
16#10595120—31nomaximal
17#10594120—31nomaximal
18#10594116—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×#6293C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×D3×Dic3C2211yescharacteristic
24C2×C3×D3×Dic3C2211yescharacteristic
25C3×#3757C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C32×#217C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88813C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×#3724C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54D4×C3⋊Dic3—31no—
55#64087—31no—
56#64086—31no—
57C3×#935—31no—
58C3×#935—31no—
59C3×#883—31no—
60C3×#883—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63982—31no—
64#63982—31no—
65#63982—31no—
66#63982—61no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—61no—
70#63969D311yescharacteristic
71#63969D311yescharacteristic
72C2×#3724—31no—
73#63957—31no—
74#63957—31no—
75#63957—61no—
76#63956—31no—
77#63956—31no—
78#63956—31no—
79#63956D311yescharacteristic, complemented
80#63955—31no—
81#63955—31no—
82#63899—31no—
83#63896—31no—
84#63878—31no—
85#63877—31no—
86D3×Dic3⋊C4—31no—
87D3×Dic3⋊C4—31no—
88#63872—31no—
89#63870—31no—
90#63870—31no—
91#63855—31no—
92#63847—31no—
93#63847—31no—
94#63846—31no—
95#63845—31no—
96#63845—31no—
97#63845—31no—
98#63844—31no—
99#63841—31no—
100#63838—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)—22no—
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C32×#67—22no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119#6293—22no—
120D3×C3⋊Dic3—22no—
121C3×D3×Dic3—22no—
122C3×D3×Dic3—22no—
123#5708—91no—
124#5650—91no—
125#5650—91no—
126C2×C32×D4—31no—
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—31no—
131C22×C3⋊Dic3—61no—
132C22×C3⋊Dic3—61no—
133C22×C3⋊Dic3—61no—
134C22×C3⋊Dic3—121no—
135C2×#634—31no—
136C2×C3×#67—21no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C2×C3×C4×D3—31no—
142C2×C3×C4×D3—31no—
143C2×#627—31no—
144C2×#627—31no—
145C2×#627—61no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C2×D3×Dic3—61no—
149C2×D3×Dic3C2×D311yescharacteristic
150C2×D3×Dic3C2×D311yescharacteristic
151C32×C22⋊C4—31no—
152C32×C22⋊C4—31no—
153#3757—31no—
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic
156#3757C2×D311yescharacteristic
157C4⋊(C3⋊Dic3)—31no—
158C4⋊(C3⋊Dic3)—31no—
159#3750—31no—
160#3750—31no—
161#3750—31no—
162#3750—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—31no—
165C4×C3⋊Dic3—31no—
166C3×#217—21no—
167C3×#217—21no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—61no—
177C3×#217—61no—
178C3×#217—61no—
179C3×#217C2×D311yescharacteristic
180C3×#217C2×D311yescharacteristic
181C3×#217C2×D311yescharacteristic
182C3×#217C2×D311yescharacteristic
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×C4⋊Dic3—31no—
186C3×C4⋊Dic3—31no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—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—31no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201#3724—31no—
202#3724—31no—
203#3724—31no—
204#3724—31no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—61no—
211#3724—61no—
212#3724—61no—
213#3724C2×D311yescharacteristic
214#3724C2×D311yescharacteristic
215#3724C2×D311yescharacteristic
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—61no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic
232Dic3⋊Dic3C2×D311yescharacteristic
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—61no—
238(C2×D3)⋊Dic3C2×D311yescharacteristic
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—61no—
250Dic32—61no—
251Dic32—61no—
252Dic32C2×D311yescharacteristic
253C22×C33—21no—
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2411yescharacteristic
257C2×C32×D3—21no—
258C2×C32×D3—21no—
259C2×C32×D3#4112yes—
260C3⋊(C3⋊Dic3)—21no—
261C3⋊(C3⋊Dic3)#4112yes—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C32×Dic3—21no—
269C32×Dic3—21no—
270C32×Dic3—21no—
271C32×Dic3—21no—
272C32×Dic3—21no—
273C3×#126—91no—
274C3×#123—91no—
275C3×#123—91no—
276#935—31no—
277#935—31no—
278D4×Dic3—91no—
279D4×Dic3—91no—
280D4×Dic3—181no—
281#926—91no—
282#926—91no—
283C2×Dic3⋊C4—91no—
284C2×Dic3⋊C4—91no—
285#896—91no—
286#892—91no—
287D3×C4⋊C4—91no—
288#890—91no—
289#890—91no—
290#890—91no—
291#889—91no—
292#889—91no—
293#889—91no—
294#889—91no—
295#889—91no—
296#889—91no—
297#887—91no—
298#887—91no—
299#883—31no—
300#883—31no—
301#67⋊C4—91no—
302#879—31no—
303#879—31no—
304#879—91no—
305#879—91no—
306#879—91no—
307#878—91no—
308#878—91no—
309#878—91no—
310#878—91no—
311#878—91no—
312#878—181no—
313#877—91no—
314#877—91no—
315#877—91no—
316#877—91no—
317#877—91no—
318#877—181no—
319#872—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—31no—
325C23×C32—41no—
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C23×C32C22×D311yescharacteristic
329C22×C3×D3—21no—
330C22×C3×D3C22×D311yescharacteristic
331C22×C3×D3C22×D311yescharacteristic
332C32×D4—62no—
333C2×C32×C4—31no—
334C2×C32×C4—31no—
335C2×C32×C4—31no—
336C2×C32×C4—31no—
337C2×C32×C4—31no—
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—62no—
351C2×C3⋊Dic3—62no—
352C2×C3⋊Dic3—62no—
353C2×C3⋊Dic3—62no—
354C2×C3⋊Dic3—64no—
355C2×C3⋊Dic3—121no—
356C2×C3⋊Dic3—121no—
357C2×C3⋊Dic3—122no—
358C2×C3⋊Dic3—122no—
359C2×C3⋊Dic3—124no—
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366#634—62no—
367C3×#67—24no—
368C3×#67—22no—
369C3×#67—22no—
370C2×C3×Dic3—21no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
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—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—62no—
394C2×C3×Dic3—62no—
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
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C3×C4×D3—62no—
406C3×C4×D3—62no—
407#627—62no—
408#627—62no—
409#627—122no—
410D3×Dic3—22no—
411D3×Dic3—22no—
412D3×Dic3—62no—
413D3×Dic3—62no—
414D3×Dic3—122no—
415#552—271noSylow
416C2×C33—41no—
417C2×C33C2×#4111yescharacteristic
418C2×C33C2×#4111yescharacteristic
419C2×C332−1+411yescharacteristic
420C32×D3—22no—
421C2×C3×D4—31no—
422C2×C3×D4—31no—
423C2×C3×D4—61no—
424C22×C3×C4—91no—
425C22×C3×C4—91no—
426C2×#67D3211yescharacteristic
427C22×Dic3—31no—
428C22×Dic3—31no—
429C22×Dic3—91no—
430C22×Dic3—91no—
431C22×Dic3—91no—
432C22×Dic3—91no—
433C22×Dic3—91no—
434C22×Dic3—181no—
435C22×Dic3—181no—
436C22×Dic3—181no—
437C22×Dic3—181no—
438C22×Dic3—361no—
439C2×C4×D3—31no—
440C2×C4×D3—31no—
441C2×C4×D3—91no—
442C2×Dic6—91no—
443C2×Dic6—91no—
444C2×Dic6—91no—
445C2×Dic6—181no—
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×C22⋊C4—31no—
454C3×C22⋊C4—31no—
455C3×C22⋊C4—31no—
456C3×C22⋊C4—31no—
457C3×C22⋊C4—61no—
458C3×C22⋊C4—61no—
459C3×C22⋊C4—91no—
460C3×C22⋊C4—91no—
461C3×C22⋊C4—91no—
462C3×C22⋊C4—91no—
463C3×C22⋊C4—91no—
464C3×C42—91no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—31no—
469#217—31no—
470#217—31no—
471#217—31no—
472#217—31no—
473#217—61no—
474#217—61no—
475#217—61no—
476#217—91no—
477#217—91no—
478#217—181no—
479#217D3211yescharacteristic
480#217D3211yescharacteristic
481(C2×D3)⋊C4—31no—
482(C2×D3)⋊C4—31no—
483(C2×D3)⋊C4—91no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—91no—
489C4⋊Dic3—91no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—181no—
497C4⋊Dic3—181no—
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—31no—
507Dic3⋊C4—31no—
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—91no—
527Dic3⋊C4—181no—
528Dic3⋊C4—181no—
529Dic3⋊C4—181no—
530Dic3⋊C4—181no—
531C4×Dic3—31no—
532C4×Dic3—31no—
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—91no—
543C4×Dic3—91no—
544C4×Dic3—91no—
545C4×Dic3—181no—
546C4×Dic3—181no—
547C4×Dic3—181no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—22no—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—21no—
558C22×C32—21no—
559C22×C32—21no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—32no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—41no—
568C22×C32—41no—
569C22×C32—41no—
570C22×C32—41no—
571C22×C32—42no—
572C22×C32—42no—
573C22×C32—42no—
574C22×C32—61no—
575C22×C32—61no—
576C22×C32C23×D311yescharacteristic
577C22×C32C23×D311yescharacteristic
578C22×C32C23×D311yescharacteristic
579C2×C3×D3—21no—
580C2×C3×D3—21no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—22no—
584C2×C3×D3—41no—
585C2×C3×D3—41no—
586C2×C3×D3#23712yes—
587C2×C3×D3#23712yes—
588C32×C4—61no—
589C32×C4—61no—
590C32×C4—61no—
591C32×C4—61no—
592C32×C4—61no—
593C3⋊Dic3—21no—
594C3⋊Dic3—21no—
595C3⋊Dic3—21no—
596C3⋊Dic3—21no—
597C3⋊Dic3—21no—
598C3⋊Dic3—21no—
599C3⋊Dic3—32no—
600C3⋊Dic3—32no—
601C3⋊Dic3—32no—
602C3⋊Dic3—62no—
603C3⋊Dic3—62no—
604C3⋊Dic3—62no—
605C3⋊Dic3—61no—
606C3⋊Dic3—62no—
607C3⋊Dic3—61no—
608C3⋊Dic3—61no—
609C3⋊Dic3—122no—
610C3⋊Dic3—121no—
611C3⋊Dic3—121no—
612C3⋊Dic3—122no—
613C3×Dic3—22no—
614C3×Dic3—21no—
615C3×Dic3—21no—
616C3×Dic3—21no—
617C3×Dic3—21no—
618C3×Dic3—21no—
619C3×Dic3—21no—
620C3×Dic3—21no—
621C3×Dic3—21no—
622C3×Dic3—21no—
623C3×Dic3—21no—
624C3×Dic3—41no—
625C3×Dic3—41no—
626C3×Dic3—41no—
627C3×Dic3—41no—
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—61no—
638C3×Dic3—61no—
639C3×Dic3—61no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C3×Dic3—121no—
643C3×Dic3—121no—
644C3×Dic3—121no—
645C3×Dic3—121no—
646#126—91no—
647#126—271no—
648#125—271no—
649#125—271no—
650#125—271no—
651#123—91no—
652#123—91no—
653C22⋊Q8—271no—
654C22⋊Q8—271no—
655C4×Q8—271no—
656C4×D4—271no—
657#117—271no—
658#117—271no—
659#117—271no—
660C2×C4⋊C4—271no—
661C33#55211yescharacteristic, complemented, Sylow
662C23×C3—21no—
663C23×C3—21no—
664C23×C3—21no—
665C23×C3—31no—
666C23×C3—31no—
667C23×C3—41no—
668C23×C3—61no—
669C23×C3C2×D3211yescharacteristic
670C23×C3C2×D3211yescharacteristic
671C23×C3C2×D3211yescharacteristic
672C22×D3C2×D3211yescharacteristic
673C3×D4—62no—
674C3×D4—62no—
675C3×D4—64no—
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—31no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—91no—
692C2×C3×C4—91no—
693C2×C3×C4—91no—
694C2×C3×C4—91no—
695C2×C3×C4—91no—
696C2×C3×C4—91no—
697C2×C3×C4—182no—
698C2×C3×C4—182no—
699#67—22no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
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—61no—
713C2×Dic3—61no—
714C2×Dic3—61no—
715C2×Dic3—61no—
716C2×Dic3—61no—
717C2×Dic3—61no—
718C2×Dic3—62no—
719C2×Dic3—62no—
720C2×Dic3—91no—
721C2×Dic3—91no—
722C2×Dic3—91no—
723C2×Dic3—91no—
724C2×Dic3—91no—
725C2×Dic3—91no—
726C2×Dic3—181no—
727C2×Dic3—181no—
728C2×Dic3—181no—
729C2×Dic3—181no—
730C2×Dic3—181no—
731C2×Dic3—181no—
732C2×Dic3—182no—
733C2×Dic3—182no—
734C2×Dic3—182no—
735C2×Dic3—182no—
736C2×Dic3—182no—
737C2×Dic3—184no—
738C2×Dic3—361no—
739C2×Dic3—361no—
740C2×Dic3—362no—
741C2×Dic3—362no—
742C2×Dic3—362no—
743C2×Dic3—364no—
744C2×Dic3C2×D3211yescharacteristic
745C2×Dic3C2×D3211yescharacteristic
746C2×Dic3C2×D3211yescharacteristic
747C2×Dic3C2×D3211yescharacteristic
748C2×Dic3C2×D3211yescharacteristic
749C4×D3—62no—
750C4×D3—62no—
751C4×D3—182no—
752Dic6—182no—
753Dic6—182no—
754Dic6—182no—
755Dic6—362no—
756C2×C32—21no—
757C2×C32—21no—
758C2×C32—21no—
759C2×C32—21no—
760C2×C32—21no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—41no—
766C2×C32—41no—
767C2×C32—41no—
768C2×C32—42no—
769C2×C32—42no—
770C2×C32—42no—
771C2×C32—44no—
772C2×C32—41no—
773C2×C32—41no—
774C2×C32—41no—
775C2×C32—62no—
776C2×C32C2×#23711yescharacteristic
777C2×C32C2×#23711yescharacteristic
778C2×C32D3×#4111yescharacteristic
779C2×C32D3×#4111yescharacteristic
780C2×C32D3×#4111yescharacteristic
781C2×C32D3×#4111yescharacteristic
782C2×C32#101011yescharacteristic
783C2×C32#101011yescharacteristic
784C2×C32#101011yescharacteristic
785C3×D3—22no—
786C3×D3—22no—
787C3×D3—42no—
788C2×Q8—271no—
789C2×D4—31no—
790C22×C4—91no—
791C22×C4—91no—
792C22×C4—271no—
793C22×C4—271no—
794C4⋊C4—91no—
795C4⋊C4—91no—
796C4⋊C4—91no—
797C4⋊C4—91no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C4⋊C4—91no—
801C4⋊C4—271no—
802C4⋊C4—271no—
803C4⋊C4—271no—
804C4⋊C4—271no—
805C4⋊C4—271no—
806C4⋊C4—271no—
807C4⋊C4—271no—
808C4⋊C4—271no—
809C4⋊C4—271no—
810C22⋊C4—31no—
811C22⋊C4—31no—
812C22⋊C4—91no—
813C22⋊C4—91no—
814C22⋊C4—91no—
815C22⋊C4—91no—
816C22⋊C4—91no—
817C22⋊C4—271no—
818C42—91no—
819C42—271no—
820C42—271no—
821C42—271no—
822C42—271no—
823C22×C3—22no—
824C22×C3—22no—
825C22×C3—22no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—32no—
839C22×C3—32no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—41no—
850C22×C3—62no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—121no—
856C22×C3—121no—
857C22×C3C22×D3211yescharacteristic
858C22×C3C22×D3211yescharacteristic
859C22×C3C22×D3211yescharacteristic
860C2×D3—21no—
861C2×D3—21no—
862C2×D3#380512yes—
863C3×C4—62no—
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—61no—
873C3×C4—61no—
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—
883C3×C4—181no—
884Dic3—21no—
885Dic3—21no—
886Dic3—21no—
887Dic3—21no—
888Dic3—21no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—92no—
902Dic3—92no—
903Dic3—92no—
904Dic3—121no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—182no—
911Dic3—182no—
912Dic3—182no—
913Dic3—182no—
914Dic3—181no—
915Dic3—181no—
916Dic3—181no—
917Dic3—362no—
918Dic3—361no—
919Dic3—361no—
920Dic3—362no—
921C32—21no—
922C32—21no—
923C32—21no—
924C32—41no—
925C32#565011yescharacteristic, complemented
926C32#565011yescharacteristic, complemented
927C32#570811yescharacteristic, complemented
928C23—31no—
929C23D3311yescharacteristic
930Q8—542no—
931D4—62no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—31no—
937C2×C4—91no—
938C2×C4—91no—
939C2×C4—91no—
940C2×C4—91no—
941C2×C4—91no—
942C2×C4—91no—
943C2×C4—182no—
944C2×C4—182no—
945C2×C4—271no—
946C2×C4—271no—
947C2×C4—542no—
948C2×C4—542no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—42no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—44no—
962C2×C3—41no—
963C2×C3—41no—
964C2×C3—41no—
965C2×C3—41no—
966C2×C3—41no—
967C2×C3—41no—
968C2×C3—62no—
969C2×C3—62no—
970C2×C3—122no—
971C2×C3#6429811yescharacteristic
972C2×C3#6430611yescharacteristic
973C2×C3#6430911yescharacteristic
974C2×C3#6430911yescharacteristic
975C2×C3D3×#23711yescharacteristic
976C2×C3D3×#23711yescharacteristic
977C2×C3#6431211yescharacteristic
978C2×C3#6431211yescharacteristic
979C2×C3C2×#380511yescharacteristic
980D3—22no—
981C22—21no—
982C22—21no—
983C22—21no—
984C22—32no—
985C22—61no—
986C22—61no—
987C22C2×D3311yescharacteristic
988C4—61no—
989C4—61no—
990C4—61no—
991C4—61no—
992C4—61no—
993C4—181no—
994C4—181no—
995C4—181no—
996C4—181no—
997C4—181no—
998C4—181no—
999C4—272no—
1000C4—541no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059411611yescharacteristic, complemented
1006C3#1059412011yescharacteristic, complemented
1007C3#1059512011yescharacteristic, complemented
1008C2—41no—
1009C2—62no—
1010C2D3×#380511yescharacteristic
1011C2#1172441111yescharacteristic
1012C2#1172442711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC2×C32×#67C22
hypercenterC23D33
hypocenterC33#552
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723716C2semidirect
2. #11723642C2semidirect
4. #11723598C2semidirect
7. C3×#63956C2semidirect
8. #11723018C2semidirect
9. #11723016C2semidirect
10. #11723013C2semidirect
11. #11722980C2semidirect
12. #11722943C2semidirect
13. #11722914C2semidirect
14. #11722913C2semidirect
15. D3×#3724C2semidirect
79. #63956D3semidirect
661. C33#552semidirect
925. C32#5650semidirect
926. C32#5650semidirect
927. C32#5708semidirect
1005. C3#10594116semidirect
1006. C3#10594120semidirect
1007. C3#10595120semidirect

Maximal subgroups

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

subgroupindex
#117237162
#117236422
#67⋊(C3⋊Dic3)2
#117235982
C3×#639692
C3×#639562
#117230182
#117230162
#117230132
#117229802
#117229432
#117229142
#117229132
D3×#37242
#105951203
#105941203
#105941163