Finite Group Databasebeta

← #13168441

Subgroups — #13168441

Order 1728.

1202 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723683C211yesmaximal, characteristic, complemented
2#11723528C211yesmaximal, characteristic, complemented
3#11723429C211yesmaximal, characteristic, complemented
4#11723395C211yesmaximal, characteristic, complemented
5C3×#63886C211yesmaximal, characteristic, complemented
6C3×#63885C211yesmaximal, characteristic, complemented
7C3×#63878C211yesmaximal, characteristic, complemented
8#11723004C211yesmaximal, characteristic, complemented
9#11723002C211yesmaximal, characteristic, complemented
10#11722965C211yesmaximal, characteristic, complemented
11#11722956C211yesmaximal, characteristic, complemented
12#11722927C211yesmaximal, characteristic, complemented
13Dic3×#625C211yesmaximal, characteristic, complemented
14#11722914C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595247—31nomaximal
17#10594486—31nomaximal
18#10594104—31nomaximal
19C2×#6308C2211yescharacteristic
20C2×C32×D12C2211yescharacteristic
21C2×#6294C2211yescharacteristic
22C2×#6293C2211yescharacteristic
23C2×#6290C2211yescharacteristic
24C2×C3×#626C2211yescharacteristic
25C2×C3×#626C2211yescharacteristic
26C2×C3×#625C2211yescharacteristic
27C2×C3×#625C2211yescharacteristic
28C2×C3×D3×Dic3C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×C4×C3⋊Dic3C2211yescharacteristic
34C32×(C2×D3)⋊C4C2211yescharacteristic
35C32×Dic3⋊C4C2211yescharacteristic
36#88815C2211yescharacteristic
37#88814C2211yescharacteristic
38#88813C2211yescharacteristic
39#88807C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48Dic3×C3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64145—31no—
55#64097—31no—
56#64094—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#895—31no—
60C3×#892—31no—
61C3×#884—31no—
62C3×#877—31no—
63#63978—31no—
64Dic3×#67—31no—
65Dic3×#67—31no—
66Dic3×#67—31no—
67#63970—31no—
68#63970—31no—
69#63959—31no—
70#63959—31no—
71#63959—31no—
72#63958—31no—
73#63955—31no—
74#63955—31no—
75#63913—31no—
76#63913—31no—
77#63913—31no—
78#63913—61no—
79#63908—31no—
80#63904—31no—
81C4×#625—31no—
82#63898—31no—
83#63886D311yescharacteristic, complemented
84#63885—31no—
85#63885D311yescharacteristic, complemented
86#63878—31no—
87#63878—31no—
88#63878D311yescharacteristic, complemented
89#63877—31no—
90#63877—31no—
91#63860—31no—
92#63860—31no—
93#63860—31no—
94#63860—61no—
95#63855—31no—
96#63852—31no—
97#63841—31no—
98#63840—31no—
99#63840—31no—
100#63840—61no—
101#63836—31no—
102C22×C3×C3⋊D3C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109#6308—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C32×D12—41no—
119#6294—22no—
120#6293—41no—
121#6290—41no—
122C3×#626—22no—
123C3×#626—41no—
124C3×#625—22no—
125C3×#625—41no—
126C3×D3×Dic3—22no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—22no—
129#5616—91no—
130#5616—91no—
131#5532—91no—
132C2×C32×D4—31no—
133C2×#638—31no—
134C2×#634—31no—
135C2×#634—31no—
136C2×#634—31no—
137C2×#634—31no—
138C2×#634—61no—
139C2×#634—61no—
140C2×#634—61no—
141C2×#634—121no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C2×C3×D12—21no—
152C2×C3×D12—31no—
153C2×C3×D12—31no—
154C2×C3×D12C2×D311yescharacteristic
155C2×C3×D12C2×D311yescharacteristic
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×#627—31no—
160C2×#627—31no—
161C2×#627—61no—
162C2×#626C2×D311yescharacteristic
163C2×#626C2×D311yescharacteristic
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—61no—
167C2×#625C2×D311yescharacteristic
168C2×#625C2×D311yescharacteristic
169C2×#624—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3C2×D311yescharacteristic
173C2×D3×Dic3C2×D311yescharacteristic
174C2×D3×Dic3C2×D311yescharacteristic
175C32×C4⋊C4—31no—
176C32×C22⋊C4—31no—
177#3757—31no—
178#3757—31no—
179#3757—31no—
180#3757—31no—
181#3757—31no—
182#3752—31no—
183#3752C2×D311yescharacteristic
184C4⋊(C3⋊Dic3)—31no—
185#3750—31no—
186#3750C2×D311yescharacteristic
187C4×C3⋊Dic3—31no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3C2×D311yescharacteristic
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×(C2×D3)⋊C4—21no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×(C2×D3)⋊C4—31no—
197C3×(C2×D3)⋊C4—31no—
198C3×(C2×D3)⋊C4—31no—
199C3×(C2×D3)⋊C4—61no—
200C3×(C2×D3)⋊C4C2×D311yescharacteristic
201C3×(C2×D3)⋊C4C2×D311yescharacteristic
202C3×C4⋊Dic3—31no—
203C3×Dic3⋊C4—21no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—61no—
208C3×Dic3⋊C4C2×D311yescharacteristic
209C3×Dic3⋊C4C2×D311yescharacteristic
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—61no—
215#3724—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⋊Dic3C2×D311yescharacteristic
225#3722—31no—
226(C2×D3)⋊Dic3—31no—
227(C2×D3)⋊Dic3—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)⋊Dic3—61no—
245(C2×D3)⋊Dic3—61no—
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
248(C2×D3)⋊Dic3C2×D311yescharacteristic
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic
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—
266C2×C32×D3—21no—
267C2×C32×D3—21no—
268C2×C32×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—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3#4112yes—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×#121—91no—
285C3×#117—91no—
286#939—31no—
287#939—31no—
288#939—91no—
289#939—91no—
290#938—91no—
291#938—91no—
292#936—91no—
293#936—91no—
294#936—91no—
295#936—91no—
296#936—181no—
297D4×Dic3—91no—
298D4×Dic3—91no—
299#930—91no—
300C4×#67—91no—
301C4×#67—91no—
302C4×#67—91no—
303#926—91no—
304#926—91no—
305#895—31no—
306#893—91no—
307#892—31no—
308#892—91no—
309#892—91no—
310#888—91no—
311#888—91no—
312#888—91no—
313#888—181no—
314#885—91no—
315#885—91no—
316#885—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#885—181no—
321#884—31no—
322#884—91no—
323#877—31no—
324#877—91no—
325#877—91no—
326#877—91no—
327#875—91no—
328#875—91no—
329#872—91no—
330#872—91no—
331C23×C32—31no—
332C23×C32—31no—
333C23×C32—31no—
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3—21no—
338C22×C3×D3—31no—
339C22×C3×D3—31no—
340C22×C3×D3—61no—
341C22×C3×D3C22×D311yescharacteristic
342C22×C3×D3C22×D311yescharacteristic
343C22×C3×D3C22×D311yescharacteristic
344C22×C3×D3C22×D311yescharacteristic
345C22×C3×D3C22×D311yescharacteristic
346C22×C3×D3C22×D311yescharacteristic
347C32×D4—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—41no—
355C2×C32×C4C22×D311yescharacteristic
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358#638—121no—
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—61no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—121no—
372C2×C3⋊Dic3—121no—
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378#634—121no—
379#634—121no—
380#634—121no—
381#634—121no—
382#634—122no—
383#634—122no—
384#634—122no—
385#634—124no—
386C3×#67—62no—
387C3×#67—62no—
388C3×#67—62no—
389C3×#67—121no—
390C3×#67—121no—
391C3×#67—121no—
392C2×C3×Dic3—21no—
393C2×C3×Dic3—21no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—31no—
398C2×C3×Dic3—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—61no—
408C2×C3×Dic3—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—62no—
411C2×C3×Dic3—62no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C3×D12—41no—
420C3×D12—41no—
421C3×D12—42no—
422C3×D12—62no—
423C3×D12—121no—
424C3×C4×D3—62no—
425C3×C4×D3—62no—
426C3×C4×D3—62no—
427#627—121no—
428#627—121no—
429#627—122no—
430#626—22no—
431#626—41no—
432#625—22no—
433#625—41no—
434#625—121no—
435#625—121no—
436#625—122no—
437#624—62no—
438D3×Dic3—22no—
439D3×Dic3—22no—
440D3×Dic3—22no—
441D3×Dic3—62no—
442D3×Dic3—62no—
443#555—271noSylow
444C2×C33C2×#4111yescharacteristic
445C2×C33C2×#4111yescharacteristic
446C2×C33H(5,𝔽2)11yescharacteristic
447C3×C3⋊D3—41no—
448C32×D3—41no—
449C32×D3—41no—
450C32×D3—41no—
451C2×C3×D4—31no—
452C2×C3×D4—31no—
453C2×C3×D4—61no—
454C2×C3×D4—91no—
455C2×C3×D4—91no—
456C2×C3×D4—91no—
457C2×C3×D4—91no—
458C22×C3×C4—91no—
459C22×C3×C4—91no—
460C22×C3×C4—91no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—91no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—181no—
471C22×Dic3—31no—
472C22×Dic3—31no—
473C22×Dic3—31no—
474C22×Dic3—91no—
475C2×D12—31no—
476C2×D12—31no—
477C2×D12D3211yescharacteristic
478C2×C4×D3—31no—
479C2×C4×D3—31no—
480C2×C4×D3—31no—
481C2×C4×D3—91no—
482C2×C4×D3—91no—
483C2×Dic6—91no—
484C2×Dic6—91no—
485C2×Dic6—91no—
486C2×Dic6—91no—
487C2×Dic6—91no—
488C2×Dic6—91no—
489C2×Dic6—181no—
490C2×Dic6—181no—
491C2×Dic6—181no—
492C2×Dic6—181no—
493C2×Dic6—361no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—31no—
496C3×C4⋊C4—61no—
497C3×C4⋊C4—91no—
498C3×C4⋊C4—91no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—61no—
502C3×C22⋊C4—91no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C42—91no—
507C3×C42—91no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—91no—
518#217—91no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—181no—
524#217—181no—
525#217—181no—
526#217—181no—
527#217—181no—
528(C2×D3)⋊C4—31no—
529(C2×D3)⋊C4—31no—
530(C2×D3)⋊C4—31no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—61no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—91no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4D3211yescharacteristic
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—181no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—61no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—181no—
561Dic3⋊C4D3211yescharacteristic
562C4×Dic3—31no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—61no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—181no—
577C4×Dic3—181no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—41no—
582C22×C32—61no—
583C22×C32—61no—
584C22×C32—61no—
585C22×C32—61no—
586C22×C32—61no—
587C22×C32—61no—
588C22×C32—61no—
589C22×C32—61no—
590C22×C32—61no—
591C22×C32C23×D311yescharacteristic
592C22×C32C23×D311yescharacteristic
593C22×C32C23×D311yescharacteristic
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—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—21no—
605C2×C3×D3—21no—
606C2×C3×D3—21no—
607C2×C3×D3—21no—
608C2×C3×D3—21no—
609C2×C3×D3—21no—
610C2×C3×D3—21no—
611C2×C3×D3—21no—
612C2×C3×D3—21no—
613C2×C3×D3—21no—
614C2×C3×D3—21no—
615C2×C3×D3—41no—
616C2×C3×D3—41no—
617C2×C3×D3—41no—
618C2×C3×D3—41no—
619C2×C3×D3—41no—
620C2×C3×D3—41no—
621C2×C3×D3—41no—
622C2×C3×D3—41no—
623C2×C3×D3—41no—
624C2×C3×D3—61no—
625C2×C3×D3—61no—
626C2×C3×D3—61no—
627C2×C3×D3—61no—
628C2×C3×D3—61no—
629C2×C3×D3—61no—
630C2×C3×D3—121no—
631C2×C3×D3—121no—
632C2×C3×D3—121no—
633C32×C4—21no—
634C32×C4—22no—
635C32×C4—21no—
636C32×C4—21no—
637C32×C4—32no—
638C32×C4—41no—
639C32×C4—41no—
640C32×C4—42no—
641C32×C4—61no—
642C32×C4—61no—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—21no—
646C3⋊Dic3—21no—
647C3⋊Dic3—61no—
648C3⋊Dic3—61no—
649C3⋊Dic3—62no—
650C3⋊Dic3—62no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—121no—
656C3⋊Dic3—121no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—122no—
660C3⋊Dic3—122no—
661C3⋊Dic3#23712yes—
662C3×Dic3—21no—
663C3×Dic3—21no—
664C3×Dic3—21no—
665C3×Dic3—21no—
666C3×Dic3—22no—
667C3×Dic3—32no—
668C3×Dic3—32no—
669C3×Dic3—41no—
670C3×Dic3—41no—
671C3×Dic3—62no—
672C3×Dic3—61no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—121no—
681C3×Dic3—121no—
682C3×Dic3—121no—
683C3×Dic3—121no—
684C3×Dic3#23512yes—
685C3×Dic3#23712yes—
686C4⋊Q8—271no—
687#124—271no—
688#124—271no—
689#124—271no—
690#124—271no—
691#121—91no—
692#121—91no—
693#121—271no—
694#121—271no—
695C4×D4—271no—
696C4×D4—271no—
697#117—91no—
698#117—271no—
699#117—271no—
700#117—271no—
701C33#55511yescharacteristic, complemented, Sylow
702C23×C3—31no—
703C23×C3—31no—
704C23×C3—31no—
705C23×C3—31no—
706C23×C3—31no—
707C23×C3—31no—
708C23×C3—61no—
709C23×C3—61no—
710C23×C3—61no—
711C23×C3—91no—
712C22×D3—31no—
713C22×D3—31no—
714C22×D3—61no—
715C22×D3C2×D3211yescharacteristic
716C22×D3C2×D3211yescharacteristic
717C22×D3C2×D3211yescharacteristic
718C3×D4—121no—
719C3×D4—121no—
720C3×D4—122no—
721C3×D4—182no—
722C3×D4—182no—
723C3×D4—361no—
724C3×D4—361no—
725C2×C3×C4—21no—
726C2×C3×C4—21no—
727C2×C3×C4—21no—
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—41no—
735C2×C3×C4—61no—
736C2×C3×C4—61no—
737C2×C3×C4—61no—
738C2×C3×C4—91no—
739C2×C3×C4—91no—
740C2×C3×C4—91no—
741C2×C3×C4—91no—
742C2×C3×C4—91no—
743C2×C3×C4—182no—
744C2×C3×C4—182no—
745C2×C3×C4—182no—
746C2×C3×C4C2×D3211yescharacteristic
747C2×C3×C4C2×D3211yescharacteristic
748C2×C3×C4C2×D3211yescharacteristic
749#67—62no—
750#67—62no—
751#67—62no—
752#67—121no—
753#67—121no—
754#67—121no—
755#67—361no—
756#67—361no—
757#67—361no—
758#67—362no—
759C2×Dic3—31no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—62no—
775C2×Dic3—62no—
776C2×Dic3—62no—
777C2×Dic3—91no—
778C2×Dic3—91no—
779C2×Dic3—91no—
780C2×Dic3—91no—
781C2×Dic3—91no—
782C2×Dic3—91no—
783C2×Dic3—181no—
784C2×Dic3—181no—
785C2×Dic3—181no—
786C2×Dic3—181no—
787C2×Dic3—181no—
788C2×Dic3—181no—
789C2×Dic3—182no—
790C2×Dic3—361no—
791C2×Dic3—361no—
792C2×Dic3C2×D3211yescharacteristic
793C2×Dic3C2×D3211yescharacteristic
794C2×Dic3C2×D3211yescharacteristic
795D12—41no—
796D12—62no—
797D12—121no—
798C4×D3—62no—
799C4×D3—62no—
800C4×D3—62no—
801C4×D3—182no—
802C4×D3—182no—
803Dic6—361no—
804Dic6—361no—
805Dic6—361no—
806Dic6—362no—
807Dic6—361no—
808Dic6—361no—
809Dic6—361no—
810Dic6—362no—
811Dic6—362no—
812Dic6—362no—
813Dic6—364no—
814C2×C32—21no—
815C2×C32—21no—
816C2×C32—21no—
817C2×C32—21no—
818C2×C32—21no—
819C2×C32—21no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—41no—
824C2×C32—41no—
825C2×C32—41no—
826C2×C32—121no—
827C2×C32—121no—
828C2×C32—121no—
829C2×C32C2×#23511yescharacteristic
830C2×C32C2×#23711yescharacteristic
831C2×C32C2×#23711yescharacteristic
832C2×C32#100411yescharacteristic
833C2×C32#100411yescharacteristic
834C2×C32D3×#4111yescharacteristic
835C2×C32D3×#4111yescharacteristic
836C2×C32D3×#4111yescharacteristic
837C2×C32#100911yescharacteristic
838C3⋊D3—41no—
839C3×D3—41no—
840C3×D3—41no—
841C3×D3—41no—
842C3×D3—41no—
843C3×D3—41no—
844C3×D3—41no—
845C3×D3—81no—
846C3×D3—81no—
847C3×D3—81no—
848C3×D3—121no—
849C3×D3—121no—
850C3×D3—241no—
851C2×Q8—271no—
852C2×Q8—271no—
853C2×D4—31no—
854C2×D4—91no—
855C2×D4—91no—
856C2×D4—91no—
857C2×D4—91no—
858C2×D4—271no—
859C22×C4—91no—
860C22×C4—91no—
861C22×C4—91no—
862C22×C4—271no—
863C4⋊C4—31no—
864C4⋊C4—91no—
865C4⋊C4—91no—
866C4⋊C4—271no—
867C4⋊C4—271no—
868C4⋊C4—271no—
869C22⋊C4—31no—
870C22⋊C4—91no—
871C22⋊C4—91no—
872C22⋊C4—91no—
873C22⋊C4—91no—
874C22⋊C4—271no—
875C22⋊C4—271no—
876C22⋊C4—271no—
877C22⋊C4—271no—
878C22⋊C4—271no—
879C22⋊C4—271no—
880C22⋊C4—271no—
881C42—91no—
882C42—91no—
883C42—271no—
884C42—271no—
885C42—271no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—41no—
890C22×C3—61no—
891C22×C3—61no—
892C22×C3—61no—
893C22×C3—61no—
894C22×C3—61no—
895C22×C3—61no—
896C22×C3—61no—
897C22×C3—61no—
898C22×C3—61no—
899C22×C3—61no—
900C22×C3—61no—
901C22×C3—61no—
902C22×C3—61no—
903C22×C3—61no—
904C22×C3—61no—
905C22×C3—61no—
906C22×C3—61no—
907C22×C3—61no—
908C22×C3—121no—
909C22×C3—121no—
910C22×C3—121no—
911C22×C3—121no—
912C22×C3—121no—
913C22×C3—121no—
914C22×C3—121no—
915C22×C3—121no—
916C22×C3—121no—
917C22×C3—181no—
918C22×C3—181no—
919C22×C3—181no—
920C22×C3C22×D3211yescharacteristic
921C22×C3C22×D3211yescharacteristic
922C22×C3C22×D3211yescharacteristic
923C2×D3—21no—
924C2×D3—21no—
925C2×D3—21no—
926C2×D3—21no—
927C2×D3—21no—
928C2×D3—21no—
929C2×D3—21no—
930C2×D3—21no—
931C2×D3—21no—
932C2×D3—61no—
933C2×D3—61no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C3×C4—22no—
942C3×C4—21no—
943C3×C4—21no—
944C3×C4—21no—
945C3×C4—32no—
946C3×C4—32no—
947C3×C4—41no—
948C3×C4—41no—
949C3×C4—42no—
950C3×C4—62no—
951C3×C4—61no—
952C3×C4—61no—
953C3×C4—61no—
954C3×C4—61no—
955C3×C4—92no—
956C3×C4—121no—
957C3×C4—121no—
958C3×C4—181no—
959C3×C4—181no—
960C3×C4—181no—
961C3×C4—181no—
962Dic3—21no—
963Dic3—21no—
964Dic3—32no—
965Dic3—32no—
966Dic3—62no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—61no—
973Dic3—61no—
974Dic3—61no—
975Dic3—121no—
976Dic3—121no—
977Dic3—121no—
978Dic3—121no—
979Dic3—182no—
980Dic3—182no—
981Dic3—181no—
982Dic3—181no—
983Dic3—181no—
984Dic3—181no—
985Dic3—181no—
986Dic3—181no—
987Dic3—361no—
988Dic3—361no—
989Dic3—361no—
990Dic3—361no—
991Dic3—362no—
992Dic3—362no—
993Dic3#379512yes—
994C32—21no—
995C32—21no—
996C32—21no—
997C32—41no—
998C32#553211yescharacteristic, complemented
999C32#561611yescharacteristic, complemented
1000C32#561611yescharacteristic, complemented
1001C23—31no—
1002C23—31no—
1003C23—31no—
1004C23—91no—
1005Q8—1081no—
1006Q8—1081no—
1007D4—121no—
1008D4—182no—
1009D4—182no—
1010D4—361no—
1011D4—361no—
1012D4—1081no—
1013C2×C4—31no—
1014C2×C4—31no—
1015C2×C4—31no—
1016C2×C4—91no—
1017C2×C4—91no—
1018C2×C4—91no—
1019C2×C4—91no—
1020C2×C4—91no—
1021C2×C4—182no—
1022C2×C4—182no—
1023C2×C4—182no—
1024C2×C4—271no—
1025C2×C4—271no—
1026C2×C4—542no—
1027C2×C4D3311yescharacteristic
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—21no—
1037C2×C3—41no—
1038C2×C3—41no—
1039C2×C3—41no—
1040C2×C3—121no—
1041C2×C3—121no—
1042C2×C3—121no—
1043C2×C3—121no—
1044C2×C3—121no—
1045C2×C3—121no—
1046C2×C3—241no—
1047C2×C3—241no—
1048C2×C3—241no—
1049C2×C3—361no—
1050C2×C3C2×#379511yescharacteristic
1051C2×C3D3×#23511yescharacteristic
1052C2×C3D3×#23711yescharacteristic
1053C2×C3D3×#23711yescharacteristic
1054C2×C3D3×#23711yescharacteristic
1055C2×C3#6431411yescharacteristic
1056C2×C3#6431411yescharacteristic
1057C2×C3#6431911yescharacteristic
1058C2×C3#6433011yescharacteristic
1059D3—41no—
1060D3—41no—
1061D3—41no—
1062D3—121no—
1063D3—121no—
1064D3—241no—
1065C22—61no—
1066C22—61no—
1067C22—61no—
1068C22—61no—
1069C22—61no—
1070C22—61no—
1071C22—61no—
1072C22—61no—
1073C22—61no—
1074C22—181no—
1075C22—181no—
1076C22—181no—
1077C22C2×D3311yescharacteristic
1078C4—21no—
1079C4—32no—
1080C4—61no—
1081C4—61no—
1082C4—92no—
1083C4—181no—
1084C4—181no—
1085C4—181no—
1086C4—181no—
1087C4—541no—
1088C4—541no—
1089C3—21no—
1090C3—21no—
1091C3—21no—
1092C3—41no—
1093C3#1059410411yescharacteristic, complemented
1094C3#1059448611yescharacteristic, complemented
1095C3#1059524711yescharacteristic, complemented
1096C2—121no—
1097C2—121no—
1098C2—121no—
1099C2—361no—
1100C2D3×#379511yescharacteristic
1101C2#1172437411yescharacteristic
1102C2#1172441911yescharacteristic
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. #11723683C2semidirect
2. #11723528C2semidirect
3. #11723429C2semidirect
4. #11723395C2semidirect
5. C3×#63886C2semidirect
6. C3×#63885C2semidirect
7. C3×#63878C2semidirect
8. #11723004C2semidirect
9. #11723002C2semidirect
10. #11722965C2semidirect
11. #11722956C2semidirect
12. #11722927C2semidirect
13. Dic3×#625C2semidirect
14. #11722914C2semidirect
15. #11722913C2semidirect
83. #63886D3semidirect
85. #63885D3semidirect
88. #63878D3semidirect
701. C33#555semidirect
998. C32#5532semidirect
999. C32#5616semidirect
1000. C32#5616semidirect
1093. C3#10594104semidirect
1094. C3#10594486semidirect
1095. C3#10595247semidirect

Maximal subgroups

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

subgroupindex
#117236832
#117235282
#117234292
#117233952
C3×#638862
C3×#638852
C3×#638782
#117230042
#117230022
#117229652
#117229562
#117229272
Dic3×#6252
#117229142
#117229132
#105952473
#105944863
#105941043