Finite Group Databasebeta

← #13168553

Subgroups — #13168553

Order 1728.

1202 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723687C211yesmaximal, characteristic, complemented
2#11723466C211yesmaximal, characteristic, complemented
3#11723460C211yesmaximal, characteristic, complemented
4#11723436C211yesmaximal, characteristic, complemented
5C3×#63910C211yesmaximal, characteristic, complemented
6C3×#63907C211yesmaximal, characteristic, complemented
7C3×#63839C211yesmaximal, characteristic, complemented
8#11723007C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722962C211yesmaximal, characteristic, complemented
11#11722955C211yesmaximal, characteristic, complemented
12#11722934C211yesmaximal, characteristic, complemented
13#11722928C211yesmaximal, characteristic, complemented
14#11722922C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595385—31nomaximal
17#10594463—31nomaximal
18#10594136—31nomaximal
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C2×#6295C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36#88814C2211yescharacteristic
37#88807C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64156—31no—
55#64101—31no—
56#64086—31no—
57C3×#947—31no—
58C3×#944—31no—
59C3×#895—31no—
60C3×#888—31no—
61C3×#885—31no—
62C3×#884—31no—
63#63980—31no—
64#67⋊Dic3—31no—
65#63970—31no—
66#63959—31no—
67#63916—31no—
68#63915—31no—
69#63910—31no—
70#63910D311yescharacteristic, complemented
71#63907—31no—
72#63907—31no—
73#63907—31no—
74#63907D311yescharacteristic, complemented
75C4×#626—31no—
76Dic3×D12—31no—
77#63886—31no—
78#63886—31no—
79#63886—31no—
80#63886—31no—
81#63885—31no—
82#63880—31no—
83#63880—31no—
84#63879—31no—
85#63878—31no—
86#63878—31no—
87#63878—31no—
88#63878—31no—
89#63878—31no—
90#63878—61no—
91#63878—61no—
92#63877—31no—
93#63863—31no—
94#63863—31no—
95#63863—31no—
96#63863—61no—
97#63855—31no—
98#63841—31no—
99#63839D311yescharacteristic, complemented
100#63836—31no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4⋊(C3⋊D3)—41no—
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×Dic6—41no—
119#6295—22no—
120#6295—41no—
121#6294—22no—
122Dic3×C3⋊D3—22no—
123D3×C3⋊Dic3—22no—
124C3×#627—41no—
125C3×#626—22no—
126C3×#626—41no—
127C3×#626—41no—
128C3×#624—22no—
129#5734—91no—
130#5670—91no—
131#5616—91no—
132C2×C32×Q8—31no—
133C22×C3⋊Dic3—31no—
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
135C2×C4×C3⋊D3—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×D12—31no—
140C2×C3×D12—31no—
141C2×C3×D12—31no—
142C2×C3×D12—31no—
143C2×C3×D12—31no—
144C2×C3×D12—61no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×Dic6—21no—
148C2×C3×Dic6—31no—
149C2×C3×Dic6—31no—
150C2×C3×Dic6C2×D311yescharacteristic
151C2×C3×Dic6C2×D311yescharacteristic
152C2×#627C2×D311yescharacteristic
153C2×#626—31no—
154C2×#626—31no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626C2×D311yescharacteristic
158C2×#626C2×D311yescharacteristic
159C2×#626C2×D311yescharacteristic
160C2×#625—31no—
161C2×#625—31no—
162C2×#624—31no—
163C2×#624C2×D311yescharacteristic
164C2×D3×Dic3—31no—
165C2×D3×Dic3—31no—
166C2×D3×Dic3—31no—
167C2×D3×Dic3—31no—
168C2×D3×Dic3—31no—
169C2×D3×Dic3—31no—
170C2×D3×Dic3—61no—
171C2×D3×Dic3—61no—
172C32×C4⋊C4—31no—
173C32×C22⋊C4—31no—
174#3757—31no—
175#3752—31no—
176#3752—31no—
177#3752—31no—
178#3752—31no—
179#3752—31no—
180#3752C2×D311yescharacteristic
181C4⋊(C3⋊Dic3)—31no—
182#3750—31no—
183#3750C2×D311yescharacteristic
184C4×C3⋊Dic3—31no—
185C4×C3⋊Dic3—31no—
186C4×C3⋊Dic3—31no—
187C4×C3⋊Dic3—31no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3—61no—
190C4×C3⋊Dic3—61no—
191C4×C3⋊Dic3—61no—
192C4×C3⋊Dic3—121no—
193C3×#217—31no—
194C3×(C2×D3)⋊C4—21no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
202C3×(C2×D3)⋊C4—61no—
203C3×(C2×D3)⋊C4C2×D311yescharacteristic
204C3×(C2×D3)⋊C4C2×D311yescharacteristic
205C3×C4⋊Dic3—31no—
206C3×Dic3⋊C4—21no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4C2×D311yescharacteristic
214C3×Dic3⋊C4C2×D311yescharacteristic
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219#3724C2×D311yescharacteristic
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722C2×D311yescharacteristic
229#3722C2×D311yescharacteristic
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—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3—61no—
247(C2×D3)⋊Dic3—61no—
248(C2×D3)⋊Dic3—61no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3C2×D311yescharacteristic
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32—61no—
257Dic32C2×D311yescharacteristic
258Dic32C2×D311yescharacteristic
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—
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C33×C4—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3⋊(C3⋊Dic3)—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3#4112yes—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×C4⋊Q8—91no—
284C3×#124—91no—
285C3×#121—91no—
286#947—31no—
287#947—91no—
288#947—91no—
289#947—91no—
290#947—91no—
291#947—181no—
292#944—31no—
293#939—91no—
294#939—91no—
295#939—91no—
296#939—91no—
297#938—91no—
298#936—91no—
299#936—91no—
300D4×Dic3—91no—
301C4×#67—91no—
302#926—91no—
303#895—31no—
304#895—91no—
305#895—91no—
306#895—91no—
307#892—91no—
308#892—91no—
309#892—91no—
310#892—91no—
311#892—91no—
312#892—181no—
313#888—31no—
314#885—31no—
315#885—91no—
316#885—91no—
317#885—91no—
318#884—31no—
319#884—91no—
320#67⋊C4—91no—
321#67⋊C4—91no—
322#877—91no—
323#877—91no—
324#877—91no—
325#877—91no—
326#877—181no—
327C4×D12—91no—
328C4×D12—91no—
329#872—91no—
330#872—91no—
331C23×C32—31no—
332C22×C3⋊D3C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—31no—
341C22×C3×D3—31no—
342C22×C3×D3—61no—
343C22×C3×D3—61no—
344C22×C3×D3—61no—
345C22×C3×D3C22×D311yescharacteristic
346C22×C3×D3C22×D311yescharacteristic
347C32×Q8—121no—
348C2×C32×C4—21no—
349C2×C32×C4—21no—
350C2×C32×C4—21no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—41no—
357C2×C32×C4C22×D311yescharacteristic
358C2×C32×C4C22×D311yescharacteristic
359C2×C32×C4C22×D311yescharacteristic
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—62no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C4⋊(C3⋊D3)—41no—
379C4×C3⋊D3—62no—
380C3×#67—62no—
381C3×#67—121no—
382C3×#67—121no—
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—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
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
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C3×D12—62no—
408C3×D12—121no—
409C3×D12—121no—
410C3×D12—122no—
411C3×D12—121no—
412C3×D12—121no—
413C3×C4×D3—62no—
414C3×C4×D3—62no—
415C3×Dic6—41no—
416C3×Dic6—41no—
417C3×Dic6—42no—
418C3×Dic6—121no—
419C3×Dic6—121no—
420#627—41no—
421#626—22no—
422#626—41no—
423#626—41no—
424#626—62no—
425#626—62no—
426#626—121no—
427#626—121no—
428#625—62no—
429#625—121no—
430#624—22no—
431#624—62no—
432D3×Dic3—64no—
433D3×Dic3—62no—
434D3×Dic3—62no—
435D3×Dic3—62no—
436D3×Dic3—64no—
437D3×Dic3—62no—
438D3×Dic3—62no—
439D3×Dic3—62no—
440#555—271noSylow
441C2×C33C2×#4111yescharacteristic
442C2×C33C2×#4111yescharacteristic
443C2×C33H(5,𝔽2)11yescharacteristic
444C3×C3⋊D3—41no—
445C3×C3⋊D3—41no—
446C3×C3⋊D3—41no—
447C32×D3—41no—
448C2×C3×Q8—31no—
449C2×C3×Q8—31no—
450C2×C3×Q8—61no—
451C2×C3×Q8—91no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C2×C3×D4—91no—
456C22×C3×C4—91no—
457C2×#67—31no—
458C2×#67—31no—
459C2×#67—31no—
460C2×#67—91no—
461C2×#67—91no—
462C2×#67—91no—
463C2×#67—91no—
464C22×Dic3—91no—
465C22×Dic3—91no—
466C22×Dic3—91no—
467C22×Dic3—91no—
468C22×Dic3—181no—
469C2×D12—31no—
470C2×D12—31no—
471C2×D12—31no—
472C2×D12—31no—
473C2×D12—31no—
474C2×D12—61no—
475C2×D12—91no—
476C2×D12—91no—
477C2×C4×D3—31no—
478C2×C4×D3—31no—
479C2×C4×D3—91no—
480C2×C4×D3—91no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—181no—
485C2×Dic6—31no—
486C2×Dic6—31no—
487C2×Dic6D3211yescharacteristic
488C3×C4⋊C4—31no—
489C3×C4⋊C4—31no—
490C3×C4⋊C4—61no—
491C3×C4⋊C4—91no—
492C3×C4⋊C4—91no—
493C3×C4⋊C4—91no—
494C3×C22⋊C4—31no—
495C3×C22⋊C4—31no—
496C3×C22⋊C4—61no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C42—91no—
502C3×C42—91no—
503#217—31no—
504#217—91no—
505#217—91no—
506#217—91no—
507#217—91no—
508#217—91no—
509#217—91no—
510#217—91no—
511#217—91no—
512#217—181no—
513(C2×D3)⋊C4—31no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—31no—
517(C2×D3)⋊C4—31no—
518(C2×D3)⋊C4—31no—
519(C2×D3)⋊C4—31no—
520(C2×D3)⋊C4—61no—
521(C2×D3)⋊C4—91no—
522(C2×D3)⋊C4—91no—
523(C2×D3)⋊C4—91no—
524(C2×D3)⋊C4—91no—
525(C2×D3)⋊C4—91no—
526(C2×D3)⋊C4—91no—
527(C2×D3)⋊C4—91no—
528(C2×D3)⋊C4—91no—
529(C2×D3)⋊C4—91no—
530(C2×D3)⋊C4—91no—
531(C2×D3)⋊C4—91no—
532(C2×D3)⋊C4—91no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—181no—
535(C2×D3)⋊C4—181no—
536(C2×D3)⋊C4—181no—
537(C2×D3)⋊C4—181no—
538(C2×D3)⋊C4—181no—
539(C2×D3)⋊C4D3211yescharacteristic
540C4⋊Dic3—31no—
541C4⋊Dic3—91no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—181no—
545Dic3⋊C4—31no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—61no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—181no—
555Dic3⋊C4D3211yescharacteristic
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—91no—
566C4×Dic3—91no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—181no—
570C4×Dic3—181no—
571C4×Dic3—181no—
572C4×Dic3—181no—
573C4×Dic3—181no—
574C4×Dic3—361no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—41no—
579C22×C32—61no—
580C22×C32—61no—
581C22×C32—61no—
582C22×C32C23×D311yescharacteristic
583C22×C32C23×D311yescharacteristic
584C22×C32C23×D311yescharacteristic
585C2×C3⋊D3—21no—
586C2×C3⋊D3—21no—
587C2×C3⋊D3—21no—
588C2×C3⋊D3—21no—
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3×D3—22no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—41no—
602C2×C3×D3—41no—
603C2×C3×D3—62no—
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—61no—
611C2×C3×D3—61no—
612C2×C3×D3—61no—
613C2×C3×D3—61no—
614C2×C3×D3—61no—
615C2×C3×D3—61no—
616C2×C3×D3—61no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—121no—
623C2×C3×D3—121no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C2×C3×D3—121no—
627C2×C3×D3—121no—
628C2×C3×D3—121no—
629C2×C3×D3—121no—
630C32×C4—21no—
631C32×C4—22no—
632C32×C4—21no—
633C32×C4—21no—
634C32×C4—32no—
635C32×C4—41no—
636C32×C4—41no—
637C32×C4—42no—
638C32×C4—61no—
639C32×C4—61no—
640C32×C4—61no—
641C32×C4—61no—
642C3⋊Dic3—21no—
643C3⋊Dic3—21no—
644C3⋊Dic3—61no—
645C3⋊Dic3—61no—
646C3⋊Dic3—62no—
647C3⋊Dic3—62no—
648C3⋊Dic3—61no—
649C3⋊Dic3—61no—
650C3⋊Dic3—61no—
651C3⋊Dic3—61no—
652C3⋊Dic3—121no—
653C3⋊Dic3—121no—
654C3⋊Dic3—121no—
655C3⋊Dic3—121no—
656C3⋊Dic3—122no—
657C3⋊Dic3—122no—
658C3⋊Dic3#23912yes—
659C3×Dic3—21no—
660C3×Dic3—21no—
661C3×Dic3—21no—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—22no—
668C3×Dic3—32no—
669C3×Dic3—32no—
670C3×Dic3—41no—
671C3×Dic3—41no—
672C3×Dic3—41no—
673C3×Dic3—41no—
674C3×Dic3—62no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—121no—
680C3×Dic3—121no—
681C3×Dic3#23712yes—
682C3×Dic3#23912yes—
683C4⋊Q8—91no—
684#124—91no—
685#124—271no—
686#124—271no—
687#124—271no—
688#121—91no—
689#121—271no—
690#121—271no—
691#121—271no—
692C4×D4—271no—
693C4×D4—271no—
694#117—271no—
695#117—271no—
696#117—271no—
697#117—271no—
698C33#55511yescharacteristic, complemented, Sylow
699C23×C3—31no—
700C23×C3—31no—
701C23×C3—61no—
702C23×C3—91no—
703C23×C3—91no—
704C23×C3—91no—
705C22×D3—31no—
706C22×D3—31no—
707C22×D3—31no—
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—31no—
711C22×D3—61no—
712C22×D3—61no—
713C22×D3—61no—
714C22×D3C2×D3211yescharacteristic
715C3×Q8—121no—
716C3×Q8—121no—
717C3×Q8—122no—
718C3×Q8—361no—
719C3×D4—182no—
720C3×D4—361no—
721C3×D4—361no—
722C3×D4—361no—
723C2×C3×C4—21no—
724C2×C3×C4—21no—
725C2×C3×C4—21no—
726C2×C3×C4—31no—
727C2×C3×C4—31no—
728C2×C3×C4—31no—
729C2×C3×C4—31no—
730C2×C3×C4—31no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—41no—
737C2×C3×C4—61no—
738C2×C3×C4—61no—
739C2×C3×C4—61no—
740C2×C3×C4—61no—
741C2×C3×C4—61no—
742C2×C3×C4—91no—
743C2×C3×C4—91no—
744C2×C3×C4—91no—
745C2×C3×C4—182no—
746C2×C3×C4C2×D3211yescharacteristic
747C2×C3×C4C2×D3211yescharacteristic
748C2×C3×C4C2×D3211yescharacteristic
749#67—62no—
750#67—121no—
751#67—121no—
752#67—182no—
753#67—182no—
754#67—361no—
755#67—361no—
756C2×Dic3—31no—
757C2×Dic3—31no—
758C2×Dic3—31no—
759C2×Dic3—31no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—61no—
763C2×Dic3—61no—
764C2×Dic3—61no—
765C2×Dic3—91no—
766C2×Dic3—91no—
767C2×Dic3—91no—
768C2×Dic3—91no—
769C2×Dic3—91no—
770C2×Dic3—91no—
771C2×Dic3—181no—
772C2×Dic3—181no—
773C2×Dic3—181no—
774C2×Dic3—181no—
775C2×Dic3—181no—
776C2×Dic3—181no—
777C2×Dic3—182no—
778C2×Dic3—182no—
779C2×Dic3—182no—
780C2×Dic3—184no—
781C2×Dic3—182no—
782C2×Dic3—361no—
783C2×Dic3—361no—
784C2×Dic3C2×D3211yescharacteristic
785C2×Dic3C2×D3211yescharacteristic
786C2×Dic3C2×D3211yescharacteristic
787C2×Dic3C2×D3211yescharacteristic
788C2×Dic3C2×D3211yescharacteristic
789D12—62no—
790D12—121no—
791D12—121no—
792D12—122no—
793D12—121no—
794D12—121no—
795D12—182no—
796D12—361no—
797C4×D3—62no—
798C4×D3—62no—
799C4×D3—182no—
800C4×D3—182no—
801C4×D3—182no—
802C4×D3—182no—
803C4×D3—184no—
804C4×D3—182no—
805Dic6—41no—
806Dic6—121no—
807Dic6—121no—
808C2×C32—21no—
809C2×C32—21no—
810C2×C32—21no—
811C2×C32—21no—
812C2×C32—21no—
813C2×C32—21no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—41no—
818C2×C32—41no—
819C2×C32—41no—
820C2×C32—121no—
821C2×C32C2×#23711yescharacteristic
822C2×C32#100411yescharacteristic
823C2×C32#100411yescharacteristic
824C2×C32#100411yescharacteristic
825C2×C32C2×#23911yescharacteristic
826C2×C32C2×#23911yescharacteristic
827C2×C32D3×#4111yescharacteristic
828C2×C32D3×#4111yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C3⋊D3—41no—
831C3⋊D3—41no—
832C3⋊D3—41no—
833C3×D3—42no—
834C3×D3—41no—
835C3×D3—41no—
836C3×D3—122no—
837C3×D3—121no—
838C3×D3—121no—
839C3×D3—121no—
840C3×D3—121no—
841C3×D3—121no—
842C3×D3—121no—
843C3×D3—241no—
844C3×D3—241no—
845C2×Q8—31no—
846C2×Q8—91no—
847C2×D4—91no—
848C2×D4—91no—
849C2×D4—91no—
850C2×D4—91no—
851C2×D4—271no—
852C2×D4—271no—
853C22×C4—91no—
854C22×C4—271no—
855C22×C4—271no—
856C22×C4—271no—
857C4⋊C4—31no—
858C4⋊C4—91no—
859C4⋊C4—91no—
860C4⋊C4—91no—
861C4⋊C4—271no—
862C4⋊C4—271no—
863C22⋊C4—31no—
864C22⋊C4—91no—
865C22⋊C4—91no—
866C22⋊C4—91no—
867C22⋊C4—91no—
868C22⋊C4—271no—
869C22⋊C4—271no—
870C22⋊C4—271no—
871C22⋊C4—271no—
872C22⋊C4—271no—
873C22⋊C4—271no—
874C22⋊C4—271no—
875C42—91no—
876C42—91no—
877C42—271no—
878C42—271no—
879C42—271no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—41no—
884C22×C3—62no—
885C22×C3—61no—
886C22×C3—61no—
887C22×C3—61no—
888C22×C3—61no—
889C22×C3—61no—
890C22×C3—61no—
891C22×C3—121no—
892C22×C3—121no—
893C22×C3—181no—
894C22×C3—181no—
895C22×C3—181no—
896C22×C3—181no—
897C22×C3—181no—
898C22×C3—181no—
899C22×C3—181no—
900C22×C3—181no—
901C22×C3—181no—
902C22×C3C22×D3211yescharacteristic
903C22×C3C22×D3211yescharacteristic
904C22×C3C22×D3211yescharacteristic
905C2×D3—21no—
906C2×D3—21no—
907C2×D3—21no—
908C2×D3—62no—
909C2×D3—61no—
910C2×D3—61no—
911C2×D3—61no—
912C2×D3—61no—
913C2×D3—61no—
914C2×D3—61no—
915C2×D3—61no—
916C2×D3—61no—
917C2×D3—61no—
918C2×D3—61no—
919C2×D3—61no—
920C2×D3—61no—
921C2×D3—61no—
922C2×D3—61no—
923C2×D3—61no—
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C2×D3—121no—
934C2×D3—121no—
935C3×C4—22no—
936C3×C4—21no—
937C3×C4—21no—
938C3×C4—21no—
939C3×C4—32no—
940C3×C4—32no—
941C3×C4—41no—
942C3×C4—41no—
943C3×C4—42no—
944C3×C4—62no—
945C3×C4—61no—
946C3×C4—61no—
947C3×C4—61no—
948C3×C4—61no—
949C3×C4—61no—
950C3×C4—61no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—92no—
954C3×C4—121no—
955C3×C4—121no—
956C3×C4—121no—
957C3×C4—121no—
958C3×C4—181no—
959C3×C4—181no—
960Dic3—21no—
961Dic3—21no—
962Dic3—21no—
963Dic3—21no—
964Dic3—32no—
965Dic3—32no—
966Dic3—62no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—121no—
972Dic3—121no—
973Dic3—182no—
974Dic3—182no—
975Dic3—181no—
976Dic3—181no—
977Dic3—181no—
978Dic3—181no—
979Dic3—181no—
980Dic3—181no—
981Dic3—361no—
982Dic3—361no—
983Dic3—361no—
984Dic3—361no—
985Dic3—362no—
986Dic3—362no—
987Dic3#379612yes—
988C32—21no—
989C32—21no—
990C32—21no—
991C32—41no—
992C32#561611yescharacteristic, complemented
993C32#567011yescharacteristic, complemented
994C32#573411yescharacteristic, complemented
995C23—31no—
996C23—91no—
997C23—91no—
998C23—91no—
999Q8—121no—
1000Q8—361no—
1001D4—182no—
1002D4—361no—
1003D4—361no—
1004D4—361no—
1005D4—542no—
1006D4—1081no—
1007C2×C4—31no—
1008C2×C4—31no—
1009C2×C4—31no—
1010C2×C4—31no—
1011C2×C4—31no—
1012C2×C4—91no—
1013C2×C4—91no—
1014C2×C4—91no—
1015C2×C4—182no—
1016C2×C4—271no—
1017C2×C4—271no—
1018C2×C4—542no—
1019C2×C4—542no—
1020C2×C4—542no—
1021C2×C4D3311yescharacteristic
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—21no—
1025C2×C3—21no—
1026C2×C3—21no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—41no—
1032C2×C3—41no—
1033C2×C3—41no—
1034C2×C3—122no—
1035C2×C3—121no—
1036C2×C3—121no—
1037C2×C3—361no—
1038C2×C3—361no—
1039C2×C3—361no—
1040C2×C3C2×#379611yescharacteristic
1041C2×C3#6430611yescharacteristic
1042C2×C3D3×#23711yescharacteristic
1043C2×C3#6431311yescharacteristic
1044C2×C3#6431311yescharacteristic
1045C2×C3D3×#23911yescharacteristic
1046C2×C3D3×#23911yescharacteristic
1047C2×C3D3×#23911yescharacteristic
1048C2×C3#6433011yescharacteristic
1049D3—41no—
1050D3—122no—
1051D3—121no—
1052D3—121no—
1053D3—121no—
1054D3—121no—
1055D3—121no—
1056D3—121no—
1057D3—241no—
1058D3—241no—
1059C22—61no—
1060C22—61no—
1061C22—61no—
1062C22—181no—
1063C22—181no—
1064C22—181no—
1065C22—181no—
1066C22—181no—
1067C22—181no—
1068C22—181no—
1069C22—181no—
1070C22—181no—
1071C22C2×D3311yescharacteristic
1072C4—21no—
1073C4—32no—
1074C4—61no—
1075C4—61no—
1076C4—61no—
1077C4—61no—
1078C4—92no—
1079C4—181no—
1080C4—181no—
1081C4—541no—
1082C4—541no—
1083C3—21no—
1084C3—21no—
1085C3—21no—
1086C3—41no—
1087C3#1059413611yescharacteristic, complemented
1088C3#1059446311yescharacteristic, complemented
1089C3#1059538511yescharacteristic, complemented
1090C2—121no—
1091C2—361no—
1092C2—361no—
1093C2—361no—
1094C2D3×#379611yescharacteristic
1095C2#1172439111yescharacteristic
1096C2#1172441511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#555
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723687C2semidirect
2. #11723466C2semidirect
3. #11723460C2semidirect
4. #11723436C2semidirect
5. C3×#63910C2semidirect
6. C3×#63907C2semidirect
7. C3×#63839C2semidirect
8. #11723007C2semidirect
9. #11723001C2semidirect
10. #11722962C2semidirect
11. #11722955C2semidirect
12. #11722934C2semidirect
13. #11722928C2semidirect
14. #11722922C2semidirect
15. #11722915C2semidirect
70. #63910D3semidirect
74. #63907D3semidirect
99. #63839D3semidirect
698. C33#555semidirect
992. C32#5616semidirect
993. C32#5670semidirect
994. C32#5734semidirect
1087. C3#10594136semidirect
1088. C3#10594463semidirect
1089. C3#10595385semidirect

Maximal subgroups

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

subgroupindex
#117236872
#117234662
#117234602
#117234362
C3×#639102
C3×#639072
C3×#638392
#117230072
#117230012
#117229622
#117229552
#117229342
#117229282
#117229222
#117229152
#105953853
#105944633
#105941363