Finite Group Databasebeta

← #13171903

Subgroups — #13171903

Order 1728.

1224 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723718C211yesmaximal, characteristic, complemented
2#11723631C211yesmaximal, characteristic, complemented
3#11723600C211yesmaximal, characteristic, complemented
4#11723594C211yesmaximal, characteristic, complemented
5C3×#63978C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×#63970C211yesmaximal, characteristic, complemented
8#11723036C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11723006C211yesmaximal, characteristic, complemented
11#11722956C211yesmaximal, characteristic, complemented
12Dic3×#626C211yesmaximal, characteristic, complemented
13#11722921C211yesmaximal, characteristic, complemented
14#11722914C211yesmaximal, characteristic, complemented
15#11722914C211yesmaximal, characteristic, complemented
16#10595249—31nomaximal
17#10595247—31nomaximal
18#10595026—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic
29C2×C3×D3×Dic3C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31#88864C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88813C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64145—31no—
56#64135—31no—
57C3×#939—31no—
58C3×#939—31no—
59C3×#938—31no—
60C3×D4×Dic3—31no—
61C3×#930—31no—
62C3×C4×#67—31no—
63#63978—31no—
64#63978D311yescharacteristic, complemented
65Dic3×#67—31no—
66Dic3×#67D311yescharacteristic, complemented
67#63970—31no—
68#63970—31no—
69#63970—31no—
70#63970—61no—
71#63970D311yescharacteristic, complemented
72#63959—31no—
73#63959—31no—
74#63959—31no—
75#63959—31no—
76#63959—31no—
77#63959—31no—
78#63959—61no—
79#63955—31no—
80#63955—31no—
81#63955—31no—
82#63955—31no—
83#63955—61no—
84#63953—31no—
85#63953—31no—
86#63918—31no—
87#63918—31no—
88#63915—31no—
89#63915—31no—
90#63913—31no—
91#63908—31no—
92C4×#626—31no—
93Dic3×D12—31no—
94#63878—31no—
95#63878—31no—
96#63878—31no—
97#63878—31no—
98#63849—31no—
99#63841—31no—
100#63841—31no—
101#63840—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C32×#67—22no—
115C32×#67—41no—
116C2×C32×Dic3—22no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6296—41no—
122#6293—41no—
123#6290—41no—
124Dic3×C3⋊D3—22no—
125C3×#626—22no—
126C3×#625—41no—
127C3×D3×Dic3—22no—
128C3×D3×Dic3—22no—
129#5616—91no—
130#5616—91no—
131#5563—91no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C22×C32×C4—31no—
135C2×#638—31no—
136C2×#638C2×D311yescharacteristic
137C2×C4×C3⋊D3—31no—
138C2×#634—31no—
139C2×C3×#67—21no—
140C2×C3×#67—21no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—31no—
146C2×C3×#67—61no—
147C2×C3×#67C2×D311yescharacteristic
148C2×C3×#67C2×D311yescharacteristic
149C2×C3×#67C2×D311yescharacteristic
150C2×C3×#67C2×D311yescharacteristic
151C22×C3×Dic3—21no—
152C22×C3×Dic3—31no—
153C22×C3×Dic3—31no—
154C22×C3×Dic3C2×D311yescharacteristic
155C22×C3×Dic3C2×D311yescharacteristic
156C2×C3×D12—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—31no—
159C2×#627—31no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—31no—
163C2×#627—31no—
164C2×#627—61no—
165C2×#626C2×D311yescharacteristic
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—61no—
169C2×#625C2×D311yescharacteristic
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—61no—
173C2×D3×Dic3C2×D311yescharacteristic
174C2×D3×Dic3C2×D311yescharacteristic
175#3757—31no—
176#3757—31no—
177#3757—31no—
178#3757—31no—
179#3757—31no—
180#3757—31no—
181#3757—61no—
182#3757—61no—
183#3757—61no—
184#3757—121no—
185#3757C2×D311yescharacteristic
186#3757C2×D311yescharacteristic
187C4⋊(C3⋊Dic3)—31no—
188C4⋊(C3⋊Dic3)—31no—
189C4⋊(C3⋊Dic3)—31no—
190C4×C3⋊Dic3—31no—
191C4×C3⋊Dic3—31no—
192C4×C3⋊Dic3—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—61no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×C4⋊Dic3—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215Dic3⋊Dic3—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—61no—
222Dic3⋊Dic3—61no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic
225Dic3⋊Dic3C2×D311yescharacteristic
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722—31no—
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—61no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3C2×D311yescharacteristic
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—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32—61no—
257Dic32—61no—
258Dic32C2×D311yescharacteristic
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊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—
272C3⋊(C3⋊Dic3)—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—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3#4112yes—
282C32×Dic3#4112yes—
283C3×#121—91no—
284C3×#121—91no—
285C3×C4×D4—91no—
286#939—31no—
287#939—31no—
288#939—91no—
289#939—91no—
290#938—31no—
291#938—91no—
292#938—91no—
293#938—91no—
294#938—181no—
295#936—91no—
296#936—91no—
297#936—91no—
298#936—91no—
299#936—181no—
300D4×Dic3—31no—
301D4×Dic3—91no—
302#930—31no—
303#930—91no—
304C4×#67—31no—
305C4×#67—91no—
306#926—91no—
307#926—91no—
308#926—91no—
309#926—91no—
310#926—181no—
311#892—91no—
312#892—91no—
313#892—91no—
314#892—91no—
315#888—91no—
316#888—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#885—91no—
321#885—91no—
322#885—91no—
323#885—91no—
324#885—91no—
325#877—91no—
326#877—91no—
327#877—91no—
328#877—91no—
329C4×D12—91no—
330#869—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—31no—
335C23×C32—31no—
336C23×C32—41no—
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—21no—
342C22×C3×D3—21no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—61no—
346C22×C3×D3C22×D311yescharacteristic
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—62no—
351C32×D4—121no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—62no—
357#638—41no—
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
378C4×C3⋊D3—62no—
379#634—121no—
380C3×#67—22no—
381C3×#67—22no—
382C3×#67—42no—
383C3×#67—41no—
384C3×#67—41no—
385C3×#67—42no—
386C3×#67—62no—
387C3×#67—121no—
388C3×#67—121no—
389C3×#67—121no—
390C3×#67—121no—
391C3×#67—122no—
392C2×C3×Dic3—24no—
393C2×C3×Dic3—22no—
394C2×C3×Dic3—22no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
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—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—62no—
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C3×D12—62no—
425C3×C4×D3—62no—
426C3×C4×D3—62no—
427#627—121no—
428#627—121no—
429#627—122no—
430#627—121no—
431#627—121no—
432#627—121no—
433#626—22no—
434#625—41no—
435#625—121no—
436#625—121no—
437#625—122no—
438D3×Dic3—22no—
439D3×Dic3—22no—
440D3×Dic3—62no—
441D3×Dic3—62no—
442D3×Dic3—122no—
443#555—271noSylow
444C2×C33—41no—
445C2×C33C2×#4111yescharacteristic
446C2×C33C2×#4111yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C3×C3⋊D3—41no—
449C32×D3—41no—
450C32×D3—41no—
451C2×C3×D4—31no—
452C2×C3×D4—31no—
453C2×C3×D4—31no—
454C2×C3×D4—31no—
455C2×C3×D4—61no—
456C2×C3×D4—61no—
457C2×C3×D4—91no—
458C2×C3×D4—91no—
459C2×C3×D4—91no—
460C22×C3×C4—31no—
461C22×C3×C4—31no—
462C22×C3×C4—61no—
463C22×C3×C4—91no—
464C22×C3×C4—91no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—61no—
471C2×#67—91no—
472C2×#67—91no—
473C2×#67—91no—
474C2×#67—181no—
475C2×#67D3211yescharacteristic
476C2×#67D3211yescharacteristic
477C22×Dic3—31no—
478C22×Dic3—31no—
479C22×Dic3—91no—
480C22×Dic3D3211yescharacteristic
481C2×D12—31no—
482C2×C4×D3—31no—
483C2×C4×D3—31no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—181no—
487C2×Dic6—91no—
488C2×Dic6—91no—
489C2×Dic6—91no—
490C2×Dic6—91no—
491C2×Dic6—91no—
492C2×Dic6—91no—
493C2×Dic6—181no—
494C3×C4⋊C4—91no—
495C3×C4⋊C4—91no—
496C3×C4⋊C4—91no—
497C3×C22⋊C4—91no—
498C3×C22⋊C4—91no—
499C3×C22⋊C4—91no—
500C3×C22⋊C4—91no—
501C3×C22⋊C4—91no—
502C3×C22⋊C4—91no—
503C3×C42—91no—
504#217—31no—
505#217—31no—
506#217—31no—
507#217—31no—
508#217—31no—
509#217—31no—
510#217—31no—
511#217—61no—
512#217—61no—
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—91no—
524#217—181no—
525#217—181no—
526#217—181no—
527#217—181no—
528#217—181no—
529#217—181no—
530#217—361no—
531(C2×D3)⋊C4—31no—
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
535(C2×D3)⋊C4—31no—
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—
543C4⋊Dic3—31no—
544C4⋊Dic3—31no—
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—91no—
552C4⋊Dic3—181no—
553C4⋊Dic3—181no—
554C4⋊Dic3—181no—
555Dic3⋊C4—31no—
556Dic3⋊C4—31no—
557Dic3⋊C4—31no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561C4×Dic3—31no—
562C4×Dic3—31no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—91no—
566C4×Dic3—91no—
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—181no—
576C4×Dic3—181no—
577C4×Dic3—181no—
578C22×C32—21no—
579C22×C32—22no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—41no—
592C22×C32—41no—
593C22×C32—41no—
594C22×C32—42no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—61no—
602C22×C32—61no—
603C22×C32—61no—
604C22×C32—61no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—81no—
608C22×C32—81no—
609C22×C32C23×D311yescharacteristic
610C22×C32C23×D311yescharacteristic
611C22×C32C23×D311yescharacteristic
612C2×C3⋊D3—21no—
613C2×C3⋊D3—21no—
614C2×C3⋊D3—21no—
615C2×C3×D3—21no—
616C2×C3×D3—21no—
617C2×C3×D3—21no—
618C2×C3×D3—21no—
619C2×C3×D3—21no—
620C2×C3×D3—21no—
621C2×C3×D3—21no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—41no—
628C2×C3×D3—41no—
629C2×C3×D3—41no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—62no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C32×C4—32no—
643C32×C4—32no—
644C32×C4—61no—
645C32×C4—61no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—21no—
651C3⋊Dic3—61no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—61no—
655C3⋊Dic3—61no—
656C3⋊Dic3—61no—
657C3⋊Dic3—121no—
658C3⋊Dic3—121no—
659C3⋊Dic3—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—241no—
664C3⋊Dic3—241no—
665C3×Dic3—22no—
666C3×Dic3—22no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—22no—
672C3×Dic3—22no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—121no—
684C3×Dic3—121no—
685C3×Dic3—121no—
686C3×Dic3—121no—
687C3×Dic3—121no—
688C3×Dic3#23512yes—
689C3×Dic3#23712yes—
690C3×Dic3#23712yes—
691C3×Dic3#23712yes—
692C4⋊Q8—271no—
693#124—271no—
694#124—271no—
695#124—271no—
696#124—271no—
697#121—91no—
698#121—91no—
699#121—271no—
700#121—271no—
701C4×D4—91no—
702C4×D4—271no—
703#117—271no—
704#117—271no—
705#117—271no—
706#117—271no—
707C33#55511yescharacteristic, complemented, Sylow
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—31no—
712C23×C3—31no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—41no—
716C23×C3—61no—
717C23×C3—61no—
718C23×C3—91no—
719C23×C3C2×D3211yescharacteristic
720C23×C3C2×D3211yescharacteristic
721C23×C3C2×D3211yescharacteristic
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3C2×D3211yescharacteristic
726C22×D3C2×D3211yescharacteristic
727C3×D4—62no—
728C3×D4—62no—
729C3×D4—122no—
730C3×D4—121no—
731C3×D4—121no—
732C3×D4—122no—
733C3×D4—182no—
734C3×D4—361no—
735C3×D4—361no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—62no—
749C2×C3×C4—62no—
750C2×C3×C4—64no—
751C2×C3×C4—91no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—182no—
757C2×C3×C4—182no—
758#67—22no—
759#67—41no—
760#67—62no—
761#67—121no—
762#67—121no—
763#67—121no—
764#67—121no—
765#67—122no—
766#67—361no—
767#67—361no—
768#67—361no—
769#67—362no—
770C2×Dic3—22no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—31no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—61no—
786C2×Dic3—62no—
787C2×Dic3—62no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—91no—
791C2×Dic3—91no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—181no—
795C2×Dic3—181no—
796C2×Dic3—181no—
797C2×Dic3—181no—
798C2×Dic3—181no—
799C2×Dic3—181no—
800C2×Dic3—182no—
801C2×Dic3—361no—
802C2×Dic3—361no—
803C2×Dic3C2×D3211yescharacteristic
804C2×Dic3C2×D3211yescharacteristic
805C2×Dic3C2×D3211yescharacteristic
806C2×Dic3C2×D3211yescharacteristic
807D12—62no—
808C4×D3—62no—
809C4×D3—62no—
810C4×D3—182no—
811C4×D3—182no—
812C4×D3—362no—
813Dic6—361no—
814Dic6—361no—
815Dic6—361no—
816Dic6—361no—
817Dic6—361no—
818Dic6—361no—
819Dic6—362no—
820C2×C32—21no—
821C2×C32—21no—
822C2×C32—21no—
823C2×C32—21no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—41no—
830C2×C32—41no—
831C2×C32—41no—
832C2×C32—41no—
833C2×C32—42no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—81no—
837C2×C32—81no—
838C2×C32—82no—
839C2×C32—121no—
840C2×C32—121no—
841C2×C32C2×#23511yescharacteristic
842C2×C32C2×#23711yescharacteristic
843C2×C32C2×#23711yescharacteristic
844C2×C32C2×#23711yescharacteristic
845C2×C32#100411yescharacteristic
846C2×C32#100411yescharacteristic
847C2×C32D3×#4111yescharacteristic
848C2×C32D3×#4111yescharacteristic
849C2×C32#100911yescharacteristic
850C3⋊D3—41no—
851C3×D3—41no—
852C3×D3—41no—
853C3×D3—41no—
854C3×D3—41no—
855C3×D3—81no—
856C3×D3—81no—
857C3×D3—122no—
858C3×D3—121no—
859C3×D3—121no—
860C2×Q8—271no—
861C2×Q8—271no—
862C2×D4—31no—
863C2×D4—31no—
864C2×D4—91no—
865C2×D4—91no—
866C2×D4—91no—
867C2×D4—271no—
868C22×C4—31no—
869C22×C4—91no—
870C22×C4—91no—
871C22×C4—271no—
872C4⋊C4—91no—
873C4⋊C4—91no—
874C4⋊C4—91no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C22⋊C4—91no—
879C22⋊C4—91no—
880C22⋊C4—91no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—271no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C42—91no—
891C42—271no—
892C42—271no—
893C42—271no—
894C42—271no—
895C22×C3—22no—
896C22×C3—21no—
897C22×C3—21no—
898C22×C3—21no—
899C22×C3—21no—
900C22×C3—21no—
901C22×C3—21no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—41no—
911C22×C3—41no—
912C22×C3—41no—
913C22×C3—41no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—42no—
917C22×C3—41no—
918C22×C3—61no—
919C22×C3—61no—
920C22×C3—61no—
921C22×C3—61no—
922C22×C3—61no—
923C22×C3—61no—
924C22×C3—61no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—81no—
931C22×C3—81no—
932C22×C3—121no—
933C22×C3—121no—
934C22×C3—121no—
935C22×C3—121no—
936C22×C3—121no—
937C22×C3—121no—
938C22×C3—181no—
939C22×C3—181no—
940C22×C3—181no—
941C22×C3C22×D3211yescharacteristic
942C22×C3C22×D3211yescharacteristic
943C22×C3C22×D3211yescharacteristic
944C2×D3—21no—
945C2×D3—21no—
946C2×D3—21no—
947C2×D3—21no—
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—62no—
951C2×D3—61no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—121no—
958C2×D3—121no—
959C3×C4—32no—
960C3×C4—32no—
961C3×C4—32no—
962C3×C4—32no—
963C3×C4—62no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—62no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—181no—
972C3×C4—181no—
973C3×C4—181no—
974C3×C4—181no—
975C3×C4—181no—
976Dic3—21no—
977Dic3—21no—
978Dic3—61no—
979Dic3—61no—
980Dic3—61no—
981Dic3—61no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—121no—
989Dic3—121no—
990Dic3—121no—
991Dic3—121no—
992Dic3—121no—
993Dic3—181no—
994Dic3—181no—
995Dic3—181no—
996Dic3—181no—
997Dic3—181no—
998Dic3—181no—
999Dic3—361no—
1000Dic3—361no—
1001Dic3—361no—
1002Dic3—361no—
1003Dic3—361no—
1004Dic3—361no—
1005Dic3—721no—
1006Dic3—721no—
1007Dic3#380412yes—
1008Dic3#380512yes—
1009C32—21no—
1010C32—21no—
1011C32—21no—
1012C32—41no—
1013C32#556311yescharacteristic, complemented
1014C32#561611yescharacteristic, complemented
1015C32#561611yescharacteristic, complemented
1016C23—31no—
1017C23—31no—
1018C23—91no—
1019C23D3311yescharacteristic
1020Q8—1081no—
1021Q8—1081no—
1022D4—62no—
1023D4—121no—
1024D4—182no—
1025D4—361no—
1026D4—361no—
1027D4—1081no—
1028C2×C4—31no—
1029C2×C4—31no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—62no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4—271no—
1041C2×C4—271no—
1042C2×C4—542no—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—42no—
1053C2×C3—41no—
1054C2×C3—41no—
1055C2×C3—41no—
1056C2×C3—41no—
1057C2×C3—41no—
1058C2×C3—41no—
1059C2×C3—81no—
1060C2×C3—81no—
1061C2×C3—82no—
1062C2×C3—121no—
1063C2×C3—121no—
1064C2×C3—121no—
1065C2×C3—121no—
1066C2×C3—241no—
1067C2×C3—241no—
1068C2×C3—361no—
1069C2×C3D3×#23511yescharacteristic
1070C2×C3#6430711yescharacteristic
1071C2×C3D3×#23711yescharacteristic
1072C2×C3D3×#23711yescharacteristic
1073C2×C3D3×#23711yescharacteristic
1074C2×C3#6431411yescharacteristic
1075C2×C3C2×#380411yescharacteristic
1076C2×C3C2×#380511yescharacteristic
1077C2×C3#6433011yescharacteristic
1078D3—41no—
1079D3—41no—
1080D3—122no—
1081D3—121no—
1082D3—121no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—61no—
1087C22—61no—
1088C22—61no—
1089C22—61no—
1090C22—61no—
1091C22—61no—
1092C22—181no—
1093C22—181no—
1094C22—181no—
1095C22C2×D3311yescharacteristic
1096C4—32no—
1097C4—32no—
1098C4—61no—
1099C4—61no—
1100C4—181no—
1101C4—181no—
1102C4—181no—
1103C4—181no—
1104C4—181no—
1105C4—541no—
1106C4—541no—
1107C3—21no—
1108C3—21no—
1109C3—21no—
1110C3—41no—
1111C3#1059502611yescharacteristic, complemented
1112C3#1059524711yescharacteristic, complemented
1113C3#1059524911yescharacteristic, complemented
1114C2—41no—
1115C2—121no—
1116C2—121no—
1117C2—361no—
1118C2D3×#380411yescharacteristic
1119C2D3×#380511yescharacteristic
1120C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#555
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723718C2semidirect
2. #11723631C2semidirect
3. #11723600C2semidirect
4. #11723594C2semidirect
5. C3×#63978C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63970C2semidirect
8. #11723036C2semidirect
9. #11723009C2semidirect
10. #11723006C2semidirect
11. #11722956C2semidirect
12. Dic3×#626C2semidirect
13. #11722921C2semidirect
14. #11722914C2semidirect
15. #11722914C2semidirect
64. #63978D3semidirect
66. Dic3×#67D3semidirect
71. #63970D3semidirect
707. C33#555semidirect
1013. C32#5563semidirect
1014. C32#5616semidirect
1015. C32#5616semidirect
1111. C3#10595026semidirect
1112. C3#10595247semidirect
1113. C3#10595249semidirect

Maximal subgroups

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

subgroupindex
#117237182
#117236312
#117236002
#117235942
C3×#639782
C3×Dic3×#672
C3×#639702
#117230362
#117230092
#117230062
#117229562
Dic3×#6262
#117229212
#117229142
#105952493
#105952473
#105950263