Finite Group Databasebeta

← #13171911

Subgroups — #13171911

Order 1728.

1112 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723718C211yesmaximal, characteristic, complemented
2#11723605C211yesmaximal, characteristic, complemented
3#11723600C211yesmaximal, characteristic, complemented
4#11723597C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C211yesmaximal, characteristic, complemented
6C3×#63964C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic
8#11723035C211yesmaximal, characteristic, complemented
9#11723026C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722986C211yesmaximal, characteristic, complemented
12#11722978C211yesmaximal, characteristic, complemented
13#11722972C211yesmaximal, characteristic, complemented
14#11722943C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595124—31nomaximal
17#10594837—31nomaximal
18#10594149—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6293C2211yescharacteristic
24C2×C3×#627C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#624C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88864C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88814C2211yescharacteristic
33#88814C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38#88806C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64145—31no—
55#64138—31no—
56#64088—31no—
57C3×#938—31no—
58C3×D4×Dic3—31no—
59C3×C4×#67—31no—
60C3×#924—31no—
61C3×#884—31no—
62C3×#878—31no—
63Dic3×#67D311yescharacteristic, complemented
64#63964—31no—
65#63964D311yescharacteristic, complemented
66#63961—31no—
67#63961—31no—
68#63961—31no—
69#63961—61no—
70#63959—31no—
71#63959—31no—
72#63959—31no—
73#63959—31no—
74#63959—31no—
75#63959—61no—
76#63958D311yescharacteristic
77#63956—31no—
78#63956—31no—
79#63956—31no—
80#63956—61no—
81#63953—31no—
82#63919—31no—
83#63907—31no—
84#63899—31no—
85#63895—31no—
86#63884—31no—
87#63863—31no—
88#63861—31no—
89#63858—31no—
90#63857—31no—
91#63855—31no—
92#63851—31no—
93#63851—31no—
94#63850—31no—
95#63844—31no—
96#63841—31no—
97#63839—31no—
98#63839—31no—
99#63838—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638—41no—
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×Dic3—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120#6296—41no—
121#6293—22no—
122C3×#627—41no—
123C3×#626—41no—
124C3×#624—22no—
125C3×D3×Dic3—41no—
126#5640—91no—
127#5603—91no—
128#5561—91no—
129C2×C32×D4—31no—
130C22×C32×C4—31no—
131C2×#638C2×D311yescharacteristic
132C2×#634—31no—
133C2×C3×#67—21no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—61no—
138C2×C3×#67C2×D311yescharacteristic
139C2×C3×#67C2×D311yescharacteristic
140C22×C3×Dic3—21no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3C2×D311yescharacteristic
143C22×C3×Dic3C2×D311yescharacteristic
144C2×C3×D12—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#627—31no—
153C2×#627—31no—
154C2×#627—31no—
155C2×#627—61no—
156C2×#627C2×D311yescharacteristic
157C2×#626C2×D311yescharacteristic
158C2×#624C2×D311yescharacteristic
159C2×D3×Dic3C2×D311yescharacteristic
160C32×C22⋊C4—31no—
161#3757—31no—
162#3757—31no—
163#3757—31no—
164#3757—31no—
165#3757—31no—
166#3757—61no—
167#3757—61no—
168#3757—61no—
169#3757—121no—
170#3757C2×D311yescharacteristic
171#3757C2×D311yescharacteristic
172#3752—31no—
173#3752—31no—
174C4⋊(C3⋊Dic3)—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—31no—
181C3×#217—21no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—61no—
189C3×#217—61no—
190C3×#217C2×D311yescharacteristic
191C3×#217C2×D311yescharacteristic
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×Dic3⋊C4—31no—
199C3×Dic3⋊C4—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—61no—
213#3724—61no—
214#3724—61no—
215#3724C2×D311yescharacteristic
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—61no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3C2×D311yescharacteristic
223Dic3⋊Dic3C2×D311yescharacteristic
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226#3722—31no—
227#3722—31no—
228(C2×D3)⋊Dic3—31no—
229(C2×D3)⋊Dic3—31no—
230(C2×D3)⋊Dic3—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
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—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3C2×D311yescharacteristic
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—61no—
254Dic32—61no—
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33—21no—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3—21no—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×C22⋊Q8—91no—
279C3×#121—91no—
280C3×C4×D4—91no—
281#947—91no—
282#944—91no—
283#938—31no—
284#936—91no—
285#936—91no—
286#936—91no—
287#936—91no—
288#936—181no—
289#935—91no—
290#935—91no—
291D4×Dic3—31no—
292#929—91no—
293#929—91no—
294#929—91no—
295#929—181no—
296C4×#67—31no—
297#926—91no—
298#924—31no—
299#924—91no—
300#924—91no—
301#898—91no—
302#897—91no—
303#896—91no—
304#896—91no—
305#894—91no—
306#892—91no—
307#888—91no—
308#888—91no—
309#887—91no—
310#887—91no—
311#885—91no—
312#885—91no—
313#885—91no—
314#885—91no—
315#884—31no—
316#879—91no—
317#879—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#879—181no—
322#878—31no—
323#878—91no—
324#872—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—31no—
330C23×C32—41no—
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C23×C32C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—61no—
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C32×D4—62no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—121no—
348#638—41no—
349C2×C3⋊Dic3—31no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—61no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368#634—62no—
369C3×#67—22no—
370C3×#67—22no—
371C3×#67—42no—
372C3×#67—121no—
373C3×#67—121no—
374C3×#67—121no—
375C3×#67—122no—
376C2×C3×Dic3—21no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
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—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—41no—
392C2×C3×Dic3—41no—
393C2×C3×Dic3—42no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—121no—
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C3×D12—121no—
411C3×C4×D3—62no—
412C3×C4×D3—62no—
413C3×C4×D3—121no—
414C3×Dic6—121no—
415C3×Dic6—121no—
416#627—41no—
417#627—62no—
418#627—62no—
419#627—122no—
420#627—121no—
421#627—121no—
422#627—121no—
423#626—41no—
424#624—22no—
425D3×Dic3—41no—
426#542—271noSylow
427C2×C33—41no—
428C2×C33C2×#4111yescharacteristic
429C2×C33H(5,𝔽2)11yescharacteristic
430C2×C332−1+411yescharacteristic
431C3×C3⋊D3—41no—
432C32×D3—41no—
433C2×C3×Q8—91no—
434C2×C3×D4—31no—
435C2×C3×D4—31no—
436C2×C3×D4—61no—
437C2×C3×D4—91no—
438C2×C3×D4—91no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—61no—
442C22×C3×C4—91no—
443C22×C3×C4—91no—
444C2×#67—31no—
445C2×#67—31no—
446C2×#67—31no—
447C2×#67—61no—
448C2×#67D3211yescharacteristic
449C22×Dic3—31no—
450C22×Dic3D3211yescharacteristic
451C2×D12—31no—
452C2×C4×D3—31no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×Dic6—31no—
456C2×Dic6—31no—
457C2×Dic6—91no—
458C2×Dic6—91no—
459C2×Dic6—91no—
460C2×Dic6—91no—
461C2×Dic6—91no—
462C2×Dic6—91no—
463C2×Dic6—181no—
464C3×C4⋊C4—91no—
465C3×C4⋊C4—91no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C22⋊C4—31no—
470C3×C22⋊C4—31no—
471C3×C22⋊C4—61no—
472C3×C22⋊C4—91no—
473C3×C22⋊C4—91no—
474C3×C22⋊C4—91no—
475C3×C22⋊C4—91no—
476C3×C42—91no—
477#217—31no—
478#217—31no—
479#217—31no—
480#217—31no—
481#217—31no—
482#217—31no—
483#217—61no—
484#217—61no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496#217—181no—
497#217—181no—
498#217—181no—
499#217—181no—
500#217—181no—
501#217—361no—
502#217D3211yescharacteristic
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—91no—
506(C2×D3)⋊C4—91no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515(C2×D3)⋊C4—181no—
516(C2×D3)⋊C4—181no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—181no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—91no—
532Dic3⋊C4—91no—
533Dic3⋊C4—91no—
534Dic3⋊C4—91no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—181no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546Dic3⋊C4—181no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—181no—
559C4×Dic3—181no—
560C22×C32—21no—
561C22×C32—22no—
562C22×C32—21no—
563C22×C32—21no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—41no—
574C22×C32—41no—
575C22×C32—41no—
576C22×C32—42no—
577C22×C32—41no—
578C22×C32—41no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—81no—
587C22×C32—81no—
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—41no—
601C2×C3×D3—41no—
602C2×C3×D3—41no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—121no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C32×C4—32no—
613C32×C4—61no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C3⋊Dic3—21no—
618C3⋊Dic3—21no—
619C3⋊Dic3—21no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—61no—
623C3⋊Dic3—61no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—121no—
629C3⋊Dic3—121no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—241no—
635C3⋊Dic3—241no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—22no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—41no—
649C3×Dic3—61no—
650C3×Dic3—61no—
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—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C3×Dic3#23512yes—
665C3×Dic3#23712yes—
666C4⋊Q8—271no—
667#126—271no—
668#126—271no—
669#124—271no—
670#124—271no—
671#124—271no—
672#123—271no—
673#123—271no—
674C22⋊Q8—91no—
675C22⋊Q8—271no—
676C22⋊Q8—271no—
677#121—91no—
678C4×Q8—271no—
679C4×D4—91no—
680#117—271no—
681C33#54211yescharacteristic, complemented, Sylow
682C23×C3—21no—
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—31no—
686C23×C3—31no—
687C23×C3—41no—
688C23×C3—61no—
689C23×C3—91no—
690C23×C3C2×D3211yescharacteristic
691C23×C3C2×D3211yescharacteristic
692C23×C3C2×D3211yescharacteristic
693C22×D3—31no—
694C22×D3—31no—
695C22×D3—61no—
696C22×D3C2×D3211yescharacteristic
697C3×Q8—361no—
698C3×D4—62no—
699C3×D4—62no—
700C3×D4—122no—
701C3×D4—361no—
702C3×D4—361no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—121no—
724C2×C3×C4—121no—
725C2×C3×C4—122no—
726C2×C3×C4—182no—
727C2×C3×C4—361no—
728#67—22no—
729#67—121no—
730#67—121no—
731#67—121no—
732#67—122no—
733C2×Dic3—31no—
734C2×Dic3—31no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—41no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—91no—
752C2×Dic3—91no—
753C2×Dic3—91no—
754C2×Dic3—91no—
755C2×Dic3—121no—
756C2×Dic3—181no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—181no—
760C2×Dic3—181no—
761C2×Dic3—181no—
762C2×Dic3—361no—
763C2×Dic3—361no—
764C2×Dic3C2×D3211yescharacteristic
765C2×Dic3C2×D3211yescharacteristic
766C2×Dic3C2×D3211yescharacteristic
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769D12—121no—
770C4×D3—62no—
771C4×D3—62no—
772C4×D3—121no—
773Dic6—121no—
774Dic6—121no—
775Dic6—182no—
776Dic6—182no—
777Dic6—182no—
778Dic6—362no—
779Dic6—361no—
780Dic6—361no—
781Dic6—361no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32—41no—
795C2×C32—42no—
796C2×C32—41no—
797C2×C32—41no—
798C2×C32—81no—
799C2×C32—81no—
800C2×C32—82no—
801C2×C32—121no—
802C2×C32C2×#23511yescharacteristic
803C2×C32C2×#23711yescharacteristic
804C2×C32#100411yescharacteristic
805C2×C32#100411yescharacteristic
806C2×C32#100411yescharacteristic
807C2×C32#100711yescharacteristic
808C2×C32D3×#4111yescharacteristic
809C2×C32#101011yescharacteristic
810C2×C32#101011yescharacteristic
811C3⋊D3—41no—
812C3×D3—41no—
813C3×D3—41no—
814C3×D3—81no—
815C3×D3—121no—
816C3×D3—121no—
817C3×D3—241no—
818C2×Q8—91no—
819C2×Q8—271no—
820C2×Q8—271no—
821C2×D4—31no—
822C2×D4—91no—
823C2×D4—91no—
824C22×C4—31no—
825C22×C4—91no—
826C22×C4—91no—
827C4⋊C4—91no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—271no—
833C4⋊C4—271no—
834C4⋊C4—271no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C22⋊C4—31no—
838C22⋊C4—91no—
839C22⋊C4—91no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C22⋊C4—271no—
843C22⋊C4—271no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C22⋊C4—271no—
849C42—91no—
850C42—271no—
851C42—271no—
852C42—271no—
853C22×C3—22no—
854C22×C3—21no—
855C22×C3—21no—
856C22×C3—21no—
857C22×C3—21no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—41no—
867C22×C3—41no—
868C22×C3—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—42no—
875C22×C3—41no—
876C22×C3—61no—
877C22×C3—61no—
878C22×C3—61no—
879C22×C3—61no—
880C22×C3—61no—
881C22×C3—61no—
882C22×C3—81no—
883C22×C3—81no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—181no—
888C22×C3—181no—
889C22×C3—181no—
890C22×C3C22×D3211yescharacteristic
891C22×C3C22×D3211yescharacteristic
892C22×C3C22×D3211yescharacteristic
893C2×D3—21no—
894C2×D3—21no—
895C2×D3—21no—
896C2×D3—61no—
897C2×D3—61no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—121no—
903C2×D3—121no—
904C2×D3—121no—
905C3×C4—32no—
906C3×C4—32no—
907C3×C4—62no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—61no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—121no—
917C3×C4—121no—
918C3×C4—121no—
919C3×C4—121no—
920C3×C4—181no—
921C3×C4—181no—
922C3×C4—181no—
923C3×C4—181no—
924C3×C4—181no—
925Dic3—21no—
926Dic3—21no—
927Dic3—21no—
928Dic3—21no—
929Dic3—61no—
930Dic3—61no—
931Dic3—61no—
932Dic3—61no—
933Dic3—61no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—121no—
940Dic3—121no—
941Dic3—121no—
942Dic3—121no—
943Dic3—121no—
944Dic3—181no—
945Dic3—181no—
946Dic3—181no—
947Dic3—181no—
948Dic3—181no—
949Dic3—181no—
950Dic3—361no—
951Dic3—361no—
952Dic3—361no—
953Dic3—361no—
954Dic3—361no—
955Dic3—361no—
956Dic3—721no—
957Dic3—721no—
958Dic3#380412yes—
959C32—21no—
960C32—21no—
961C32—21no—
962C32—41no—
963C32#556111yescharacteristic, complemented
964C32#560311yescharacteristic, complemented
965C32#564011yescharacteristic, complemented
966C23—31no—
967C23—91no—
968C23D3311yescharacteristic
969Q8—361no—
970Q8—542no—
971Q8—1081no—
972D4—62no—
973D4—361no—
974D4—361no—
975C2×C4—31no—
976C2×C4—31no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—91no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—121no—
986C2×C4—182no—
987C2×C4—271no—
988C2×C4—271no—
989C2×C4—361no—
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—42no—
1000C2×C3—41no—
1001C2×C3—41no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—81no—
1007C2×C3—81no—
1008C2×C3—82no—
1009C2×C3—121no—
1010C2×C3—121no—
1011C2×C3—241no—
1012C2×C3—361no—
1013C2×C3#6429711yescharacteristic
1014C2×C3#6429711yescharacteristic
1015C2×C3D3×#23511yescharacteristic
1016C2×C3#6430911yescharacteristic
1017C2×C3D3×#23711yescharacteristic
1018C2×C3#6431311yescharacteristic
1019C2×C3#6431311yescharacteristic
1020C2×C3C2×#380411yescharacteristic
1021C2×C3#6433011yescharacteristic
1022D3—41no—
1023D3—121no—
1024D3—121no—
1025D3—241no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—61no—
1030C22—61no—
1031C22—61no—
1032C22—181no—
1033C22—181no—
1034C22—181no—
1035C22C2×D3311yescharacteristic
1036C4—32no—
1037C4—61no—
1038C4—61no—
1039C4—61no—
1040C4—61no—
1041C4—181no—
1042C4—181no—
1043C4—181no—
1044C4—181no—
1045C4—181no—
1046C4—541no—
1047C4—541no—
1048C3—21no—
1049C3—21no—
1050C3—21no—
1051C3—41no—
1052C3#1059414911yescharacteristic, complemented
1053C3#1059483711yescharacteristic, complemented
1054C3#1059512411yescharacteristic, complemented
1055C2—41no—
1056C2—121no—
1057C2—361no—
1058C2D3×#380411yescharacteristic
1059C2#1172441511yescharacteristic
1060C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63958C2
hypercenterC23D33
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723718C2semidirect
2. #11723605C2semidirect
3. #11723600C2semidirect
4. #11723597C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63964C2semidirect
8. #11723035C2semidirect
9. #11723026C2semidirect
10. #11723001C2semidirect
11. #11722986C2semidirect
12. #11722978C2semidirect
13. #11722972C2semidirect
14. #11722943C2semidirect
15. #11722915C2semidirect
63. Dic3×#67D3semidirect
65. #63964D3semidirect
681. C33#542semidirect
963. C32#5561semidirect
964. C32#5603semidirect
965. C32#5640semidirect
1052. C3#10594149semidirect
1053. C3#10594837semidirect
1054. C3#10595124semidirect

Maximal subgroups

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

subgroupindex
#117237182
#117236052
#117236002
#117235972
C3×Dic3×#672
C3×#639642
C3×#639582
#117230352
#117230262
#117230012
#117229862
#117229782
#117229722
#117229432
#117229152
#105951243
#105948373
#105941493