Finite Group Databasebeta

← #13172053

Subgroups — #13172053

Order 1728.

1244 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723631C211yesmaximal, characteristic, complemented
3#11723621C211yesmaximal, characteristic, complemented
4#11723602C211yesmaximal, characteristic, complemented
5C3×#63979C211yesmaximal, characteristic, complemented
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8#11723011C211yesmaximal, characteristic, complemented
9#11722986C211yesmaximal, characteristic, complemented
10#11722985C211yesmaximal, characteristic, complemented
11#11722967C211yesmaximal, characteristic, complemented
12#11722962C211yesmaximal, characteristic, complemented
13#11722956C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722919C211yesmaximal, characteristic, complemented
16#10595218—31nomaximal
17#10595188—31nomaximal
18#10594100—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34#88864C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88815C2211yescharacteristic
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64147—31no—
55#64144—31no—
56#64092—31no—
57C3×#940—31no—
58C3×#940—31no—
59C3×#939—31no—
60C3×D4×Dic3—31no—
61C3×#884—31no—
62C3×#67⋊C4—31no—
63#63980—31no—
64#63979D311yescharacteristic, complemented
65#63978—31no—
66#63978—31no—
67#63978—31no—
68#67⋊Dic3D311yescharacteristic, complemented
69Dic3×#67—31no—
70#63971—31no—
71#63971D311yescharacteristic, complemented
72#63970—31no—
73#63970—31no—
74#63970—31no—
75#63970—31no—
76#63970—61no—
77#63969—31no—
78#63969—31no—
79#63969—31no—
80#63969—61no—
81#63961—31no—
82#63961—31no—
83#63961—31no—
84#63961—31no—
85#63961—61no—
86#63916—31no—
87#63912—31no—
88#63908—31no—
89#63905—31no—
90C4×#626—31no—
91Dic3×D12—31no—
92#63886—31no—
93#63885—31no—
94#63884—31no—
95#63877—31no—
96#63877—31no—
97#63874—31no—
98#63869—31no—
99#63867—31no—
100#63850—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638—41no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3—41no—
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—22no—
117C32×#67—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6295—41no—
123#6290—41no—
124Dic3×C3⋊D3—22no—
125Dic3×C3⋊D3—41no—
126C3×#626—22no—
127C3×#626—41no—
128C3×#626—41no—
129C3×#625—41no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5719—91no—
133#5615—91no—
134#5562—91no—
135C2×C32×D4—31no—
136C2×C32×D4—31no—
137C2×#638—31no—
138C2×#638C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C22×C3⋊Dic3C2×D311yescharacteristic
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C3×#67—21no—
144C2×C3×#67—21no—
145C2×C3×#67—31no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C2×C3×#67—61no—
156C2×C3×#67C2×D311yescharacteristic
157C2×C3×#67C2×D311yescharacteristic
158C2×C3×#67C2×D311yescharacteristic
159C2×C3×#67C2×D311yescharacteristic
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—61no—
165C2×C3×D12—31no—
166C2×C3×D12—31no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×#626—31no—
171C2×#626—31no—
172C2×#626C2×D311yescharacteristic
173C2×#626C2×D311yescharacteristic
174C2×#626C2×D311yescharacteristic
175C2×#625—31no—
176C2×#625—31no—
177C2×#625—31no—
178C2×#625—61no—
179C2×#625C2×D311yescharacteristic
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—61no—
185C2×D3×Dic3—61no—
186C2×D3×Dic3C2×D311yescharacteristic
187C2×D3×Dic3C2×D311yescharacteristic
188C32×C22⋊C4—31no—
189#3757—31no—
190#3757—31no—
191#3757—31no—
192#3757—31no—
193#3757—31no—
194#3757—31no—
195#3757—61no—
196#3757—61no—
197#3757—61no—
198#3757—121no—
199#3752—31no—
200C4⋊(C3⋊Dic3)—31no—
201C4⋊(C3⋊Dic3)—31no—
202#3750—31no—
203#3750—31no—
204#3750—31no—
205C3×#217—21no—
206C3×#217—31no—
207C3×#217C2×D311yescharacteristic
208C3×#217C2×D311yescharacteristic
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×C4⋊Dic3—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—61no—
228#3724—61no—
229#3724—61no—
230#3724C2×D311yescharacteristic
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic
240#3722—31no—
241#3722—31no—
242#3722C2×D311yescharacteristic
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—61no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260Dic32C2×D311yescharacteristic
261Dic32C2×D311yescharacteristic
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C3⋊(C3⋊Dic3)—21no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3#4112yes—
288C3×#127—91no—
289C3×#121—91no—
290C3×C4×D4—91no—
291#940—31no—
292#940—31no—
293#939—31no—
294#939—91no—
295#939—91no—
296#939—91no—
297#939—91no—
298#939—91no—
299#939—91no—
300#938—91no—
301#938—91no—
302#938—91no—
303#938—91no—
304#938—181no—
305#935—91no—
306#935—91no—
307#935—91no—
308#935—91no—
309#935—91no—
310#935—181no—
311D4×Dic3—31no—
312D4×Dic3—91no—
313#930—91no—
314#930—91no—
315#929—91no—
316#929—91no—
317#929—91no—
318C4×#67—91no—
319#895—91no—
320#894—91no—
321#890—91no—
322#889—91no—
323#884—31no—
324#884—91no—
325#884—91no—
326#883—91no—
327#883—91no—
328#883—91no—
329#883—181no—
330#67⋊C4—31no—
331#877—91no—
332C4×D12—91no—
333#872—91no—
334#872—91no—
335#870—91no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—31no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—31no—
352C22×C3×D3—31no—
353C22×C3×D3—61no—
354C22×C3×D3—61no—
355C22×C3×D3C22×D311yescharacteristic
356C22×C3×D3C22×D311yescharacteristic
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C32×D4—62no—
360C32×D4—121no—
361C2×C32×C4—31no—
362C2×C32×C4—31no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365#638—41no—
366#638—41no—
367#638—121no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—31no—
370C2×C3⋊Dic3—31no—
371C2×C3⋊Dic3—31no—
372C2×C3⋊Dic3—31no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—41no—
375C2×C3⋊Dic3—61no—
376C2×C3⋊Dic3—61no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3—121no—
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4×C3⋊D3—62no—
388C4×C3⋊D3—121no—
389C3×#67—22no—
390C3×#67—22no—
391C3×#67—42no—
392C3×#67—41no—
393C3×#67—41no—
394C3×#67—42no—
395C3×#67—62no—
396C3×#67—121no—
397C3×#67—121no—
398C3×#67—121no—
399C3×#67—121no—
400C3×#67—121no—
401C3×#67—121no—
402C3×#67—121no—
403C3×#67—121no—
404C3×#67—122no—
405C3×#67—122no—
406C2×C3×Dic3—21no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—121no—
423C2×C3×Dic3—121no—
424C2×C3×Dic3—121no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3—122no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C3×D12—62no—
436C3×D12—121no—
437C3×D12—121no—
438C3×C4×D3—121no—
439C3×C4×D3—121no—
440#626—22no—
441#626—41no—
442#626—41no—
443#626—121no—
444#626—121no—
445#625—41no—
446#625—121no—
447#625—121no—
448#625—121no—
449#625—122no—
450D3×Dic3—41no—
451D3×Dic3—41no—
452D3×Dic3—62no—
453D3×Dic3—62no—
454D3×Dic3—122no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—122no—
458#540—271noSylow
459C2×C33—41no—
460C2×C33C2×#4111yescharacteristic
461C2×C33H(5,𝔽2)11yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C3×C3⋊D3—41no—
464C3×C3⋊D3—41no—
465C32×D3—41no—
466C32×D3—41no—
467C2×C3×D4—31no—
468C2×C3×D4—31no—
469C2×C3×D4—31no—
470C2×C3×D4—31no—
471C2×C3×D4—61no—
472C2×C3×D4—61no—
473C2×C3×D4—91no—
474C2×C3×D4—91no—
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C22×C3×C4—91no—
480C22×C3×C4—91no—
481C22×C3×C4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—61no—
492C2×#67—61no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—181no—
499C2×#67D3211yescharacteristic
500C2×#67D3211yescharacteristic
501C22×Dic3—31no—
502C22×Dic3—31no—
503C22×Dic3—31no—
504C22×Dic3—31no—
505C22×Dic3—61no—
506C22×Dic3—91no—
507C22×Dic3—91no—
508C2×D12—31no—
509C2×D12—31no—
510C2×D12—31no—
511C2×D12—91no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—181no—
519C2×C4×D3—181no—
520C3×C4⋊C4—91no—
521C3×C4⋊C4—91no—
522C3×C22⋊C4—31no—
523C3×C22⋊C4—31no—
524C3×C22⋊C4—61no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C42—91no—
528C3×C42—91no—
529#217—31no—
530#217—91no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—181no—
543#217—181no—
544#217—181no—
545#217—181no—
546#217—181no—
547#217—181no—
548#217—361no—
549#217D3211yescharacteristic
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—181no—
563C4⋊Dic3—31no—
564C4⋊Dic3—91no—
565C4⋊Dic3—91no—
566C4⋊Dic3—91no—
567C4⋊Dic3—91no—
568C4⋊Dic3—91no—
569C4⋊Dic3—181no—
570C4⋊Dic3—181no—
571Dic3⋊C4—31no—
572Dic3⋊C4—31no—
573Dic3⋊C4—31no—
574Dic3⋊C4—91no—
575Dic3⋊C4—91no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—181no—
588Dic3⋊C4—181no—
589Dic3⋊C4—181no—
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C22×C32—21no—
595C22×C32—22no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—61no—
618C22×C32—61no—
619C22×C32—61no—
620C22×C32—61no—
621C22×C32—61no—
622C22×C32—61no—
623C22×C32—81no—
624C22×C32—81no—
625C22×C32C23×D311yescharacteristic
626C22×C32C23×D311yescharacteristic
627C22×C32C23×D311yescharacteristic
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3×D3—21no—
635C2×C3×D3—21no—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
645C2×C3×D3—21no—
646C2×C3×D3—41no—
647C2×C3×D3—41no—
648C2×C3×D3—41no—
649C2×C3×D3—41no—
650C2×C3×D3—41no—
651C2×C3×D3—41no—
652C2×C3×D3—62no—
653C2×C3×D3—62no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—121no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C32×C4—32no—
671C32×C4—61no—
672C32×C4—61no—
673C32×C4—61no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—21no—
677C3⋊Dic3—21no—
678C3⋊Dic3—61no—
679C3⋊Dic3—61no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—61no—
683C3⋊Dic3—61no—
684C3⋊Dic3—121no—
685C3⋊Dic3—121no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—121no—
689C3⋊Dic3—121no—
690C3⋊Dic3—241no—
691C3⋊Dic3—241no—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—22no—
699C3×Dic3—41no—
700C3×Dic3—41no—
701C3×Dic3—41no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—61no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—121no—
711C3×Dic3—121no—
712C3×Dic3—121no—
713C3×Dic3—121no—
714C3×Dic3#23512yes—
715C3×Dic3#23712yes—
716#127—91no—
717#125—271no—
718#123—271no—
719#123—271no—
720#123—271no—
721#123—271no—
722#121—91no—
723#121—271no—
724#121—271no—
725#121—271no—
726#121—271no—
727#121—271no—
728C4×D4—91no—
729C4×D4—271no—
730#117—271no—
731C33#54011yescharacteristic, complemented, Sylow
732C23×C3—21no—
733C23×C3—21no—
734C23×C3—21no—
735C23×C3—31no—
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—41no—
740C23×C3—61no—
741C23×C3—61no—
742C23×C3—91no—
743C23×C3—91no—
744C23×C3C2×D3211yescharacteristic
745C23×C3C2×D3211yescharacteristic
746C23×C3C2×D3211yescharacteristic
747C22×D3—31no—
748C22×D3—31no—
749C22×D3—31no—
750C22×D3—31no—
751C22×D3—61no—
752C22×D3—61no—
753C22×D3C2×D3211yescharacteristic
754C22×D3C2×D3211yescharacteristic
755C3×D4—62no—
756C3×D4—62no—
757C3×D4—122no—
758C3×D4—121no—
759C3×D4—121no—
760C3×D4—122no—
761C3×D4—182no—
762C3×D4—361no—
763C3×D4—361no—
764C3×D4—361no—
765C3×D4—361no—
766C3×D4—361no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—91no—
783C2×C3×C4—361no—
784C2×C3×C4—361no—
785C2×C3×C4—361no—
786#67—22no—
787#67—41no—
788#67—62no—
789#67—121no—
790#67—121no—
791#67—121no—
792#67—121no—
793#67—121no—
794#67—121no—
795#67—121no—
796#67—121no—
797#67—122no—
798#67—122no—
799#67—361no—
800#67—361no—
801#67—361no—
802#67—361no—
803#67—361no—
804#67—362no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—91no—
818C2×Dic3—91no—
819C2×Dic3—91no—
820C2×Dic3—91no—
821C2×Dic3—91no—
822C2×Dic3—91no—
823C2×Dic3—121no—
824C2×Dic3—121no—
825C2×Dic3—121no—
826C2×Dic3—121no—
827C2×Dic3—122no—
828C2×Dic3—181no—
829C2×Dic3—181no—
830C2×Dic3—181no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—182no—
835C2×Dic3—361no—
836C2×Dic3—361no—
837C2×Dic3—361no—
838C2×Dic3C2×D3211yescharacteristic
839C2×Dic3C2×D3211yescharacteristic
840C2×Dic3C2×D3211yescharacteristic
841C2×Dic3C2×D3211yescharacteristic
842D12—62no—
843D12—121no—
844D12—121no—
845D12—361no—
846C4×D3—121no—
847C4×D3—121no—
848C4×D3—182no—
849C4×D3—182no—
850C4×D3—362no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—362no—
854C2×C32—21no—
855C2×C32—21no—
856C2×C32—21no—
857C2×C32—21no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—41no—
864C2×C32—41no—
865C2×C32—41no—
866C2×C32—41no—
867C2×C32—42no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—81no—
871C2×C32—81no—
872C2×C32—82no—
873C2×C32—121no—
874C2×C32—121no—
875C2×C32C2×#23511yescharacteristic
876C2×C32C2×#23711yescharacteristic
877C2×C32#100411yescharacteristic
878C2×C32#100411yescharacteristic
879C2×C32#100411yescharacteristic
880C2×C32#100411yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32D3×#4111yescharacteristic
883C2×C32#100911yescharacteristic
884C3⋊D3—41no—
885C3⋊D3—41no—
886C3×D3—41no—
887C3×D3—41no—
888C3×D3—41no—
889C3×D3—41no—
890C3×D3—81no—
891C3×D3—81no—
892C3×D3—122no—
893C3×D3—122no—
894C3×D3—121no—
895C3×D3—121no—
896C3×D3—121no—
897C3×D3—121no—
898C2×D4—31no—
899C2×D4—31no—
900C2×D4—91no—
901C2×D4—91no—
902C2×D4—91no—
903C2×D4—91no—
904C2×D4—91no—
905C2×D4—91no—
906C2×D4—271no—
907C2×D4—271no—
908C22×C4—91no—
909C22×C4—91no—
910C22×C4—91no—
911C22×C4—271no—
912C22×C4—271no—
913C4⋊C4—91no—
914C4⋊C4—91no—
915C4⋊C4—271no—
916C4⋊C4—271no—
917C4⋊C4—271no—
918C4⋊C4—271no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C22⋊C4—31no—
922C22⋊C4—91no—
923C22⋊C4—91no—
924C22⋊C4—271no—
925C22⋊C4—271no—
926C22⋊C4—271no—
927C22⋊C4—271no—
928C22⋊C4—271no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C42—91no—
932C42—91no—
933C22×C3—22no—
934C22×C3—21no—
935C22×C3—21no—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—41no—
947C22×C3—41no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—42no—
955C22×C3—41no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—81no—
969C22×C3—81no—
970C22×C3—121no—
971C22×C3—121no—
972C22×C3—121no—
973C22×C3—121no—
974C22×C3—121no—
975C22×C3—121no—
976C22×C3—181no—
977C22×C3—181no—
978C22×C3—181no—
979C22×C3—181no—
980C22×C3—181no—
981C22×C3—181no—
982C22×C3C22×D3211yescharacteristic
983C22×C3C22×D3211yescharacteristic
984C22×C3C22×D3211yescharacteristic
985C2×D3—21no—
986C2×D3—21no—
987C2×D3—21no—
988C2×D3—21no—
989C2×D3—21no—
990C2×D3—21no—
991C2×D3—62no—
992C2×D3—62no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—61no—
1005C2×D3—121no—
1006C2×D3—121no—
1007C2×D3—121no—
1008C2×D3—121no—
1009C3×C4—32no—
1010C3×C4—32no—
1011C3×C4—62no—
1012C3×C4—61no—
1013C3×C4—61no—
1014C3×C4—61no—
1015C3×C4—61no—
1016C3×C4—61no—
1017C3×C4—61no—
1018C3×C4—121no—
1019C3×C4—121no—
1020C3×C4—121no—
1021C3×C4—181no—
1022C3×C4—181no—
1023C3×C4—181no—
1024C3×C4—181no—
1025Dic3—21no—
1026Dic3—21no—
1027Dic3—21no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—121no—
1037Dic3—121no—
1038Dic3—121no—
1039Dic3—121no—
1040Dic3—181no—
1041Dic3—181no—
1042Dic3—181no—
1043Dic3—181no—
1044Dic3—181no—
1045Dic3—181no—
1046Dic3—361no—
1047Dic3—361no—
1048Dic3—361no—
1049Dic3—361no—
1050Dic3—361no—
1051Dic3—361no—
1052Dic3—721no—
1053Dic3—721no—
1054Dic3#380412yes—
1055C32—21no—
1056C32—21no—
1057C32—21no—
1058C32—41no—
1059C32#556211yescharacteristic, complemented
1060C32#561511yescharacteristic, complemented
1061C32#571911yescharacteristic, complemented
1062C23—31no—
1063C23—31no—
1064C23—91no—
1065C23—91no—
1066C23D3311yescharacteristic
1067D4—62no—
1068D4—121no—
1069D4—182no—
1070D4—361no—
1071D4—361no—
1072D4—361no—
1073D4—361no—
1074D4—361no—
1075D4—1081no—
1076D4—1081no—
1077C2×C4—31no—
1078C2×C4—31no—
1079C2×C4—31no—
1080C2×C4—31no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—91no—
1084C2×C4—91no—
1085C2×C4—271no—
1086C2×C4—271no—
1087C2×C4—361no—
1088C2×C4—361no—
1089C2×C4—361no—
1090C2×C4—542no—
1091C2×C4—1081no—
1092C2×C3—21no—
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—42no—
1102C2×C3—41no—
1103C2×C3—41no—
1104C2×C3—41no—
1105C2×C3—41no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—81no—
1109C2×C3—81no—
1110C2×C3—82no—
1111C2×C3—121no—
1112C2×C3—121no—
1113C2×C3—121no—
1114C2×C3—121no—
1115C2×C3—241no—
1116C2×C3—241no—
1117C2×C3—361no—
1118C2×C3—361no—
1119C2×C3D3×#23511yescharacteristic
1120C2×C3D3×#23711yescharacteristic
1121C2×C3#6431311yescharacteristic
1122C2×C3#6431311yescharacteristic
1123C2×C3#6431311yescharacteristic
1124C2×C3#6431411yescharacteristic
1125C2×C3#6431411yescharacteristic
1126C2×C3C2×#380411yescharacteristic
1127C2×C3#6433011yescharacteristic
1128D3—41no—
1129D3—41no—
1130D3—122no—
1131D3—122no—
1132D3—121no—
1133D3—121no—
1134D3—121no—
1135D3—121no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—61no—
1140C22—61no—
1141C22—61no—
1142C22—61no—
1143C22—61no—
1144C22—61no—
1145C22—181no—
1146C22—181no—
1147C22—181no—
1148C22—181no—
1149C22—181no—
1150C22—181no—
1151C22C2×D3311yescharacteristic
1152C4—32no—
1153C4—61no—
1154C4—61no—
1155C4—61no—
1156C4—181no—
1157C4—181no—
1158C4—181no—
1159C4—181no—
1160C4—541no—
1161C4—541no—
1162C3—21no—
1163C3—21no—
1164C3—21no—
1165C3—41no—
1166C3#1059410011yescharacteristic, complemented
1167C3#1059518811yescharacteristic, complemented
1168C3#1059521811yescharacteristic, complemented
1169C2—41no—
1170C2—121no—
1171C2—121no—
1172C2—361no—
1173C2—361no—
1174C2D3×#380411yescharacteristic
1175C2#1172441511yescharacteristic
1176C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#540
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723717C2semidirect
2. #11723631C2semidirect
3. #11723621C2semidirect
4. #11723602C2semidirect
5. C3×#63979C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63971C2semidirect
8. #11723011C2semidirect
9. #11722986C2semidirect
10. #11722985C2semidirect
11. #11722967C2semidirect
12. #11722962C2semidirect
13. #11722956C2semidirect
14. Dic3×#626C2semidirect
15. #11722919C2semidirect
64. #63979D3semidirect
68. #67⋊Dic3D3semidirect
71. #63971D3semidirect
731. C33#540semidirect
1059. C32#5562semidirect
1060. C32#5615semidirect
1061. C32#5719semidirect
1166. C3#10594100semidirect
1167. C3#10595188semidirect
1168. C3#10595218semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236312
#117236212
#117236022
C3×#639792
C3×#67⋊Dic32
C3×#639712
#117230112
#117229862
#117229852
#117229672
#117229622
#117229562
Dic3×#6262
#117229192
#105952183
#105951883
#105941003