Finite Group Databasebeta

← #13171905

Subgroups — #13171905

Order 1728.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic
2#11723641C211yesmaximal, characteristic, complemented
3Dic3×#638C211yesmaximal, characteristic, complemented
4#11723605C211yesmaximal, characteristic, complemented
5C3×#63966C211yesmaximal, characteristic, complemented
6C2×C3×Dic32C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723024C211yesmaximal, characteristic, complemented
9#11723023C211yesmaximal, characteristic, complemented
10#11723014C211yesmaximal, characteristic, complemented
11#11723010C211yesmaximal, characteristic, complemented
12#11722942C211yesmaximal, characteristic, complemented
13#11722934C211yesmaximal, characteristic, complemented
14#11722919C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10594948—31nomaximal
17#10594839—31nomaximal
18#10594131—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88864C2211yescharacteristic
29C32×#217C2211yescharacteristic
30#88815C2211yescharacteristic
31#88814C2211yescharacteristic
32#88814C2211yescharacteristic
33#88807C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×Dic3⋊Dic3C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×#3722C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×Dic32C2211yescharacteristic
50C3×Dic32C2211yescharacteristic
51C3×Dic32C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64138—31no—
55C4×#638—31no—
56#64087—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C2×C3×C4×Dic3—31no—
60C2×C3×C4×Dic3—31no—
61C3×#886—31no—
62C3×#67⋊C4—31no—
63#63980—31no—
64#63978—31no—
65#63978—31no—
66Dic3×#67—31no—
67Dic3×#67—31no—
68Dic3×#67—61no—
69#63966D311yescharacteristic, complemented
70#63964—31no—
71#63964—31no—
72#63964—61no—
73#63961—31no—
74#63961—31no—
75#63961—61no—
76C2×Dic32D311yescharacteristic, complemented
77#63952D311yescharacteristic, complemented
78C4×#627—31no—
79#63913—31no—
80C4×#626—31no—
81#63880—31no—
82#63879—31no—
83#63877—31no—
84#63877—31no—
85#63874—31no—
86#63868—31no—
87#63868—31no—
88#63867—31no—
89#63867—31no—
90#63861—31no—
91#63859—31no—
92#63859—31no—
93#63858—31no—
94#63855—31no—
95#63852—31no—
96#63852—31no—
97#63847—31no—
98#63844—31no—
99#63841—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638—22no—
108C3×#638—22no—
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3—22no—
115C2×C32×Dic3—22no—
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6295—22no—
123#6293—22no—
124Dic3×C3⋊D3—22no—
125C3×#624—22no—
126#5649—91no—
127#5538—91no—
128#5479—91no—
129C22×C32×C4—31no—
130C22×C32×C4—31no—
131C2×#638C2×D311yescharacteristic
132C2×#638C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic
134C2×C4×C3⋊D3—31no—
135C2×#634—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C2×C3×#67—61no—
142C22×C3×Dic3—21no—
143C22×C3×Dic3—21no—
144C22×C3×Dic3—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—61no—
147C22×C3×Dic3C2×D311yescharacteristic
148C22×C3×Dic3C2×D311yescharacteristic
149C22×C3×Dic3C2×D311yescharacteristic
150C22×C3×Dic3C2×D311yescharacteristic
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×#627—31no—
154C2×#627—31no—
155C2×#627—61no—
156C2×#626—31no—
157C2×#626—31no—
158C2×#625—31no—
159C2×#624C2×D311yescharacteristic
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—61no—
163C32×C22⋊C4—31no—
164#3757—31no—
165#3757—31no—
166#3757—31no—
167#3757—61no—
168#3757—61no—
169#3757—61no—
170#3757—121no—
171#3752—31no—
172#3752—31no—
173#3752—31no—
174C4⋊(C3⋊Dic3)—31no—
175#3750—31no—
176#3750—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180C4×C3⋊Dic3—31no—
181C3×#217—21no—
182C3×#217C2×D311yescharacteristic
183C3×#217C2×D311yescharacteristic
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×C4⋊Dic3—31no—
191C3×C4⋊Dic3—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×C4×Dic3—31no—
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—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—61no—
214#3724—61no—
215#3724—61no—
216#3724C2×D311yescharacteristic
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—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230#3722—31no—
231#3722—31no—
232#3722C2×D311yescharacteristic
233#3722C2×D311yescharacteristic
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—
248Dic32—31no—
249Dic32—31no—
250Dic32—61no—
251Dic32C2×D311yescharacteristic
252Dic32C2×D311yescharacteristic
253Dic32C2×D311yescharacteristic
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33#4112yes—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊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#4112yes—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3#4112yes—
278C3×#123—91no—
279C3×C4×D4—91no—
280C2×C3×C42—91no—
281#939—91no—
282#939—91no—
283#935—91no—
284D4×Dic3—91no—
285#930—91no—
286#929—31no—
287#929—91no—
288#929—91no—
289#929—181no—
290C4×#67—31no—
291C4×#67—91no—
292C4×#67—91no—
293C4×#67—91no—
294C4×#67—181no—
295#926—91no—
296#924—91no—
297C2×C4×Dic3—31no—
298C2×C4×Dic3—31no—
299#898—91no—
300#898—91no—
301#892—91no—
302#889—91no—
303#889—91no—
304#887—91no—
305#886—31no—
306#885—91no—
307#885—91no—
308#67⋊C4—31no—
309#67⋊C4—91no—
310#879—91no—
311#879—91no—
312#878—91no—
313#878—91no—
314#878—181no—
315#877—91no—
316#876—91no—
317#876—91no—
318#875—91no—
319C4×D12—91no—
320#872—91no—
321#872—91no—
322#872—91no—
323#870—91no—
324C4×Dic6—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—41no—
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—61no—
340C22×C3×D3—61no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—62no—
348C2×C32×C4—62no—
349#638—22no—
350#638—22no—
351C2×C3⋊Dic3—22no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—61no—
363C2×C3⋊Dic3—61no—
364C2×C3⋊Dic3—121no—
365C2×C3⋊Dic3—121no—
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C4×C3⋊D3—62no—
371#634—62no—
372C3×#67—64no—
373C3×#67—62no—
374C3×#67—62no—
375C3×#67—62no—
376C3×#67—62no—
377C3×#67—122no—
378C2×C3×Dic3—22no—
379C2×C3×Dic3—22no—
380C2×C3×Dic3—22no—
381C2×C3×Dic3—22no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—21no—
384C2×C3×Dic3—21no—
385C2×C3×Dic3—21no—
386C2×C3×Dic3—21no—
387C2×C3×Dic3—21no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—42no—
397C2×C3×Dic3—42no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—62no—
403C2×C3×Dic3—62no—
404C2×C3×Dic3—122no—
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C3×C4×D3—62no—
418C3×C4×D3—62no—
419#627—62no—
420#627—62no—
421#627—122no—
422#626—62no—
423#626—62no—
424#625—62no—
425#624—22no—
426D3×Dic3—62no—
427D3×Dic3—62no—
428D3×Dic3—122no—
429#529—271noSylow
430C2×C33—22no—
431C2×C33C2×#4111yescharacteristic
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C3×C3⋊D3—41no—
435C3×C3⋊D3—41no—
436C2×C3×D4—91no—
437C2×C3×D4—91no—
438C22×C3×C4—31no—
439C22×C3×C4—31no—
440C22×C3×C4—31no—
441C22×C3×C4—31no—
442C22×C3×C4—61no—
443C22×C3×C4—61no—
444C22×C3×C4—91no—
445C22×C3×C4—91no—
446C2×#67—31no—
447C2×#67—31no—
448C2×#67—31no—
449C2×#67—31no—
450C2×#67—61no—
451C2×#67—61no—
452C2×#67—91no—
453C2×#67—91no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—61no—
457C22×Dic3—91no—
458C22×Dic3D3211yescharacteristic
459C22×Dic3D3211yescharacteristic
460C2×D12—91no—
461C2×C4×D3—31no—
462C2×C4×D3—31no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×C4×D3—181no—
466C2×Dic6—91no—
467C2×Dic6—91no—
468C2×Dic6—91no—
469C2×Dic6—181no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C22⋊C4—31no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—61no—
476C3×C22⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C42—91no—
480C3×C42—91no—
481C3×C42—91no—
482C3×C42—91no—
483C3×C42—91no—
484#217—91no—
485#217—91no—
486#217—91no—
487#217—91no—
488#217—91no—
489#217—91no—
490#217—91no—
491#217—91no—
492#217—181no—
493#217—181no—
494#217—181no—
495#217—361no—
496#217D3211yescharacteristic
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
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—181no—
514(C2×D3)⋊C4—181no—
515(C2×D3)⋊C4—181no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—91no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—181no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—91no—
529Dic3⋊C4—91no—
530Dic3⋊C4—91no—
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—91no—
544Dic3⋊C4—181no—
545Dic3⋊C4—181no—
546Dic3⋊C4—181no—
547Dic3⋊C4—181no—
548Dic3⋊C4—181no—
549C4×Dic3—31no—
550C4×Dic3—31no—
551C4×Dic3—31no—
552C4×Dic3—31no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—181no—
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—22no—
573C22×C32—22no—
574C22×C32—22no—
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—81no—
584C22×C32—81no—
585C22×C32#23512yes—
586C22×C32#23512yes—
587C22×C32#23712yes—
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—62no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
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—61no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C2×C3×D3—121no—
615C32×C4—32no—
616C32×C4—61no—
617C32×C4—61no—
618C32×C4—61no—
619C32×C4—61no—
620C32×C4—61no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—61no—
629C3⋊Dic3—61no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—121no—
636C3⋊Dic3—241no—
637C3⋊Dic3—241no—
638C3⋊Dic3#23512yes—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—22no—
650C3×Dic3—32no—
651C3×Dic3—32no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—41no—
657C3×Dic3—62no—
658C3×Dic3—62no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3#23512yes—
668C3×Dic3#23712yes—
669#126—271no—
670#126—271no—
671#125—271no—
672#124—271no—
673#123—91no—
674#123—271no—
675C22⋊Q8—271no—
676#121—271no—
677C4×Q8—271no—
678C4×D4—91no—
679C4×D4—271no—
680C4×D4—271no—
681#117—271no—
682#117—271no—
683C2×C42—91no—
684C33#52911yescharacteristic, complemented, Sylow
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—41no—
689C23×C3—91no—
690C23×C3—91no—
691C23×C3C2×D3211yescharacteristic
692C23×C3C2×D3211yescharacteristic
693C23×C3C2×D3211yescharacteristic
694C22×D3—31no—
695C22×D3—31no—
696C22×D3—31no—
697C22×D3—31no—
698C22×D3—61no—
699C22×D3—61no—
700C3×D4—182no—
701C3×D4—182no—
702C2×C3×C4—31no—
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—31no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—62no—
721C2×C3×C4—62no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—91no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—122no—
729C2×C3×C4—122no—
730C2×C3×C4—182no—
731C2×C3×C4—182no—
732#67—64no—
733#67—62no—
734#67—62no—
735#67—62no—
736#67—62no—
737#67—122no—
738#67—182no—
739#67—182no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—31no—
743C2×Dic3—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—91no—
757C2×Dic3—91no—
758C2×Dic3—91no—
759C2×Dic3—91no—
760C2×Dic3—91no—
761C2×Dic3—91no—
762C2×Dic3—122no—
763C2×Dic3—181no—
764C2×Dic3—181no—
765C2×Dic3—181no—
766C2×Dic3—181no—
767C2×Dic3—181no—
768C2×Dic3—181no—
769C2×Dic3—182no—
770C2×Dic3—361no—
771C2×Dic3—361no—
772C2×Dic3C2×D3211yescharacteristic
773C2×Dic3C2×D3211yescharacteristic
774C2×Dic3C2×D3211yescharacteristic
775C2×Dic3C2×D3211yescharacteristic
776C2×Dic3C2×D3211yescharacteristic
777C2×Dic3C2×D3211yescharacteristic
778D12—182no—
779C4×D3—62no—
780C4×D3—62no—
781C4×D3—182no—
782C4×D3—182no—
783C4×D3—362no—
784Dic6—182no—
785Dic6—182no—
786Dic6—182no—
787Dic6—362no—
788C2×C32—22no—
789C2×C32—22no—
790C2×C32—22no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—41no—
803C2×C32—42no—
804C2×C32—42no—
805C2×C32—42no—
806C2×C32—82no—
807C2×C32C2×#23511yescharacteristic
808C2×C32C2×#23511yescharacteristic
809C2×C32C2×#23511yescharacteristic
810C2×C32C2×#23511yescharacteristic
811C2×C32C2×#23711yescharacteristic
812C2×C32C2×#23711yescharacteristic
813C2×C32D3×#4111yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32D3×#4111yescharacteristic
816C3⋊D3—41no—
817C3⋊D3—41no—
818C3×D3—122no—
819C3×D3—121no—
820C3×D3—121no—
821C3×D3—121no—
822C3×D3—121no—
823C3×D3—241no—
824C2×Q8—271no—
825C2×D4—91no—
826C2×D4—91no—
827C2×D4—271no—
828C22×C4—31no—
829C22×C4—31no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—271no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C22⋊C4—31no—
844C22⋊C4—91no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—271no—
848C22⋊C4—271no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C42—91no—
854C42—91no—
855C42—91no—
856C42—91no—
857C42—91no—
858C42—271no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—42no—
879C22×C3—81no—
880C22×C3—81no—
881C22×C3—181no—
882C22×C3—181no—
883C22×C3—181no—
884C22×C3—181no—
885C22×C3—181no—
886C22×C3—181no—
887C22×C3#379512yes—
888C22×C3#379812yes—
889C22×C3#380412yes—
890C22×C3C22×D3211yescharacteristic
891C22×C3C22×D3211yescharacteristic
892C22×C3C22×D3211yescharacteristic
893C2×D3—62no—
894C2×D3—61no—
895C2×D3—61no—
896C2×D3—61no—
897C2×D3—61no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—61no—
904C2×D3—61no—
905C2×D3—61no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—121no—
910C2×D3—121no—
911C3×C4—32no—
912C3×C4—32no—
913C3×C4—62no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—61no—
923C3×C4—61no—
924C3×C4—92no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—121no—
928C3×C4—121no—
929C3×C4—121no—
930C3×C4—181no—
931C3×C4—181no—
932C3×C4—181no—
933Dic3—21no—
934Dic3—21no—
935Dic3—21no—
936Dic3—21no—
937Dic3—21no—
938Dic3—32no—
939Dic3—32no—
940Dic3—62no—
941Dic3—62no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—61no—
947Dic3—61no—
948Dic3—121no—
949Dic3—121no—
950Dic3—181no—
951Dic3—181no—
952Dic3—181no—
953Dic3—181no—
954Dic3—181no—
955Dic3—181no—
956Dic3—361no—
957Dic3—361no—
958Dic3—361no—
959Dic3—361no—
960Dic3—361no—
961Dic3—361no—
962Dic3—721no—
963Dic3—721no—
964Dic3#380412yes—
965C32—21no—
966C32—21no—
967C32—21no—
968C32—41no—
969C32#547911yescharacteristic, complemented
970C32#553811yescharacteristic, complemented
971C32#564911yescharacteristic, complemented
972C23—91no—
973C23—91no—
974C23D3311yescharacteristic
975Q8—542no—
976D4—182no—
977D4—182no—
978D4—542no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—31no—
984C2×C4—31no—
985C2×C4—62no—
986C2×C4—62no—
987C2×C4—91no—
988C2×C4—91no—
989C2×C4—91no—
990C2×C4—91no—
991C2×C4—182no—
992C2×C4—182no—
993C2×C4—271no—
994C2×C4—271no—
995C2×C4—542no—
996C2×C3—22no—
997C2×C3—22no—
998C2×C3—22no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—41no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—82no—
1015C2×C3—361no—
1016C2×C3—361no—
1017C2×C3C2×#379511yescharacteristic
1018C2×C3C2×#379811yescharacteristic
1019C2×C3D3×#23511yescharacteristic
1020C2×C3D3×#23511yescharacteristic
1021C2×C3D3×#23511yescharacteristic
1022C2×C3D3×#23711yescharacteristic
1023C2×C3#6431211yescharacteristic
1024C2×C3C2×#380411yescharacteristic
1025C2×C3C2×#380411yescharacteristic
1026D3—122no—
1027D3—121no—
1028D3—121no—
1029D3—121no—
1030D3—121no—
1031D3—241no—
1032C22—21no—
1033C22—21no—
1034C22—181no—
1035C22—181no—
1036C22—181no—
1037C22—181no—
1038C22—181no—
1039C22—181no—
1040C22#8896012yes—
1041C22C2×D3311yescharacteristic
1042C4—32no—
1043C4—61no—
1044C4—61no—
1045C4—61no—
1046C4—61no—
1047C4—61no—
1048C4—92no—
1049C4—181no—
1050C4—181no—
1051C4—181no—
1052C4—541no—
1053C4—541no—
1054C3—21no—
1055C3—21no—
1056C3—21no—
1057C3—41no—
1058C3#1059413111yescharacteristic, complemented
1059C3#1059483911yescharacteristic, complemented
1060C3#1059494811yescharacteristic, complemented
1061C2—22no—
1062C2—361no—
1063C2—361no—
1064C2D3×#380411yescharacteristic
1065C2#1172441011yescharacteristic
1066C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723717C2
hypercenterC23D33
hypocenterC33#529
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723641C2semidirect
3. Dic3×#638C2semidirect
4. #11723605C2semidirect
5. C3×#63966C2semidirect
6. C2×C3×Dic32C2semidirect
7. C3×#63952C2semidirect
8. #11723024C2semidirect
9. #11723023C2semidirect
10. #11723014C2semidirect
11. #11723010C2semidirect
12. #11722942C2semidirect
13. #11722934C2semidirect
14. #11722919C2semidirect
15. #11722915C2semidirect
69. #63966D3semidirect
76. C2×Dic32D3semidirect
77. #63952D3semidirect
684. C33#529semidirect
969. C32#5479semidirect
970. C32#5538semidirect
971. C32#5649semidirect
1058. C3#10594131semidirect
1059. C3#10594839semidirect
1060. C3#10594948semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236412
Dic3×#6382
#117236052
C3×#639662
C2×C3×Dic322
C3×#639522
#117230242
#117230232
#117230142
#117230102
#117229422
#117229342
#117229192
#117229152
#105949483
#105948393
#105941313