Finite Group Databasebeta

← #13172247

Subgroups — #13172247

Order 1728.

1226 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#11723728C211yesmaximal, characteristic
2#11723621C211yesmaximal, characteristic, complemented
3Dic3×#638C211yesmaximal, characteristic, complemented
4#11723591C211yesmaximal, characteristic, complemented
5C3×#63966C211yesmaximal, characteristic, complemented
6C3×#63953C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723010C211yesmaximal, characteristic, complemented
9#11723007C211yesmaximal, characteristic, complemented
10#11722997C211yesmaximal, characteristic, complemented
11#11722995C211yesmaximal, characteristic, complemented
12#11722943C211yesmaximal, characteristic, complemented
13#11722940C211yesmaximal, characteristic, complemented
14#11722938C211yesmaximal, characteristic, complemented
15#11722934C211yesmaximal, characteristic, complemented
16#10594957—31nomaximal
17#10594200—31nomaximal
18#10594143—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C32×Dic3C2211yescharacteristic
23C2×#6295C2211yescharacteristic
24C2×#6295C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6293C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic
29C2×C3×#627C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31#88864C2211yescharacteristic
32C32×#217C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88813C2211yescharacteristic
35#88807C2211yescharacteristic
36#88806C2211yescharacteristic
37Dic3⋊(C3⋊Dic3)C2211yescharacteristic
38#88803C2211yescharacteristic
39#88803C2211yescharacteristic
40#88803C2211yescharacteristic
41#88803C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×#3722C2211yescharacteristic
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C4×#638—31no—
55#64094—31no—
56#64092—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#886—31no—
60C3×#885—31no—
61C3×#885—31no—
62C3×#67⋊C4—31no—
63#63979—31no—
64#63979—31no—
65#63979—31no—
66Dic3×#67—31no—
67Dic3×#67—31no—
68Dic3×#67—61no—
69#63969—31no—
70#63969—31no—
71#63969—61no—
72#63966D311yescharacteristic, complemented
73#63959—31no—
74#63959—31no—
75#63959—61no—
76#63953D311yescharacteristic, complemented
77#63952D311yescharacteristic, complemented
78#63915—31no—
79#63913—31no—
80#63907—31no—
81#63907—31no—
82#63905—31no—
83C4×#626—31no—
84#63902—31no—
85#63891—31no—
86#63890—31no—
87#63881—31no—
88#63881—31no—
89#63880—31no—
90#63879—31no—
91#63854—31no—
92#63853—31no—
93#63852—31no—
94#63852—31no—
95#63850—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C3×#638—22no—
109C3×#638—22no—
110C3×#638—41no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C32×Dic3—41no—
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6295—22no—
122#6295—22no—
123#6295—41no—
124#6293—22no—
125Dic3×C3⋊D3—41no—
126Dic3×C3⋊D3—41no—
127C3×#627—22no—
128C3×#624—41no—
129#5681—91no—
130#5664—91no—
131#5559—91no—
132C22×C32×C4—31no—
133C2×#638C2×D311yescharacteristic
134C2×#638C2×D311yescharacteristic
135C2×#638C2×D311yescharacteristic
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—31no—
138C2×#634—31no—
139C2×C3×#67—31no—
140C2×C3×#67—31no—
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67—61no—
147C2×C3×#67—61no—
148C22×C3×Dic3—21no—
149C22×C3×Dic3C2×D311yescharacteristic
150C22×C3×Dic3C2×D311yescharacteristic
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×#627—31no—
156C2×#627—31no—
157C2×#627—61no—
158C2×#627C2×D311yescharacteristic
159C2×#626—31no—
160C2×#626—31no—
161C2×#626—31no—
162C2×#626—31no—
163C2×#626—31no—
164C2×#626—31no—
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#624C2×D311yescharacteristic
169C2×D3×Dic3—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—61no—
174C2×D3×Dic3—61no—
175C32×C22⋊C4—31no—
176C32×C22⋊C4—31no—
177#3757—31no—
178#3757—31no—
179#3757—31no—
180#3757—61no—
181#3757—61no—
182#3757—61no—
183#3757—121no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—31no—
188C4⋊(C3⋊Dic3)—31no—
189#3750—31no—
190#3750—31no—
191C4×C3⋊Dic3—31no—
192C4×C3⋊Dic3—31no—
193C3×#217—21no—
194C3×#217—21no—
195C3×#217C2×D311yescharacteristic
196C3×#217C2×D311yescharacteristic
197C3×#217C2×D311yescharacteristic
198C3×#217C2×D311yescharacteristic
199C3×(C2×D3)⋊C4—31no—
200C3×(C2×D3)⋊C4—31no—
201C3×(C2×D3)⋊C4—31no—
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×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×C4⋊Dic3—31no—
210C3×C4⋊Dic3—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219#3724—31no—
220#3724—31no—
221#3724—61no—
222#3724C2×D311yescharacteristic
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—61no—
228Dic3⋊Dic3—61no—
229Dic3⋊Dic3C2×D311yescharacteristic
230Dic3⋊Dic3C2×D311yescharacteristic
231#3722C2×D311yescharacteristic
232#3722C2×D311yescharacteristic
233#3722C2×D311yescharacteristic
234#3722C2×D311yescharacteristic
235#3722C2×D311yescharacteristic
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—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32—61no—
257Dic32C2×D311yescharacteristic
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×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—
272C3⋊(C3⋊Dic3)—21no—
273C3⋊(C3⋊Dic3)—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3#4112yes—
276C3×C3⋊Dic3#4112yes—
277C32×Dic3—21no—
278C32×Dic3—21no—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3—21no—
283C3×#124—91no—
284C3×#123—91no—
285C3×C4×D4—91no—
286#947—91no—
287Q8×Dic3—91no—
288#940—91no—
289#940—91no—
290#940—91no—
291#936—91no—
292#935—91no—
293D4×Dic3—91no—
294#929—31no—
295#929—91no—
296C4×#67—31no—
297C4×#67—91no—
298C4×#67—91no—
299C4×#67—91no—
300C4×#67—181no—
301#894—91no—
302#894—91no—
303#893—91no—
304#887—91no—
305#887—91no—
306#887—91no—
307#886—31no—
308#886—91no—
309#885—31no—
310#885—31no—
311#885—91no—
312#885—91no—
313#885—91no—
314#885—91no—
315#885—91no—
316#885—91no—
317#885—181no—
318#883—91no—
319#883—91no—
320#883—91no—
321#883—91no—
322#883—181no—
323#67⋊C4—31no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326#67⋊C4—91no—
327#875—91no—
328C4×D12—91no—
329C4×Dic6—91no—
330C4×Dic6—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—41no—
335C23×C32C22×D311yescharacteristic
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C22×C3⋊D3C22×D311yescharacteristic
339C22×C3⋊D3C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—31no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—61no—
348C22×C3×D3—61no—
349C22×C3×D3—61no—
350C2×C32×C4—31no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—121no—
357#638—22no—
358#638—22no—
359#638—41no—
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—121no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C4×C3⋊D3—121no—
378C4×C3⋊D3—121no—
379#634—62no—
380C3×#67—62no—
381C3×#67—62no—
382C3×#67—62no—
383C3×#67—62no—
384C3×#67—64no—
385C3×#67—122no—
386C3×#67—121no—
387C3×#67—121no—
388C3×#67—122no—
389C2×C3×Dic3—21no—
390C2×C3×Dic3—21no—
391C2×C3×Dic3—21no—
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—41no—
402C2×C3×Dic3—41no—
403C2×C3×Dic3—42no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C2×C3×Dic3C22×D311yescharacteristic
411C2×C3×Dic3C22×D311yescharacteristic
412C2×C3×Dic3C22×D311yescharacteristic
413C2×C3×Dic3C22×D311yescharacteristic
414C2×C3×Dic3C22×D311yescharacteristic
415C2×C3×Dic3C22×D311yescharacteristic
416C2×C3×Dic3C22×D311yescharacteristic
417C2×C3×Dic3C22×D311yescharacteristic
418C2×C3×Dic3C22×D311yescharacteristic
419C3×C4×D3—121no—
420C3×C4×D3—121no—
421C3×Dic6—62no—
422C3×Dic6—62no—
423#627—22no—
424#627—62no—
425#627—62no—
426#627—122no—
427#626—62no—
428#626—62no—
429#626—62no—
430#626—62no—
431#626—121no—
432#626—121no—
433#625—62no—
434#625—62no—
435#625—121no—
436#624—41no—
437D3×Dic3—121no—
438D3×Dic3—121no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—122no—
442D3×Dic3—122no—
443#559—271noSylow
444C2×C33—41no—
445C2×C33C2×#4111yescharacteristic
446C2×C33C2×#4111yescharacteristic
447C2×C33H(5,𝔽2)11yescharacteristic
448C3×C3⋊D3—41no—
449C3×C3⋊D3—41no—
450C3×C3⋊D3—41no—
451C2×C3×Q8—91no—
452C2×C3×D4—91no—
453C2×C3×D4—91no—
454C2×C3×D4—91no—
455C22×C3×C4—31no—
456C22×C3×C4—31no—
457C22×C3×C4—61no—
458C22×C3×C4—91no—
459C2×#67—31no—
460C2×#67—31no—
461C2×#67—31no—
462C2×#67—31no—
463C2×#67—31no—
464C2×#67—31no—
465C2×#67—61no—
466C2×#67—61no—
467C2×#67—61no—
468C2×#67—91no—
469C2×#67—91no—
470C2×#67—91no—
471C2×#67—91no—
472C2×#67—91no—
473C2×#67—91no—
474C22×Dic3—91no—
475C22×Dic3—91no—
476C22×Dic3D3211yescharacteristic
477C2×D12—91no—
478C2×D12—91no—
479C2×D12—91no—
480C2×C4×D3—31no—
481C2×C4×D3—31no—
482C2×C4×D3—91no—
483C2×C4×D3—91no—
484C2×C4×D3—91no—
485C2×C4×D3—91no—
486C2×C4×D3—181no—
487C2×C4×D3—181no—
488C2×Dic6—31no—
489C2×Dic6—31no—
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—31no—
498C3×C22⋊C4—31no—
499C3×C22⋊C4—31no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—61no—
502C3×C22⋊C4—61no—
503C3×C22⋊C4—91no—
504C3×C22⋊C4—91no—
505C3×C22⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C42—91no—
509C3×C42—91no—
510#217—91no—
511#217—91no—
512#217—91no—
513#217—91no—
514#217—91no—
515#217—91no—
516#217—91no—
517#217—181no—
518#217—181no—
519#217—181no—
520#217—361no—
521#217D3211yescharacteristic
522#217D3211yescharacteristic
523(C2×D3)⋊C4—31no—
524(C2×D3)⋊C4—31no—
525(C2×D3)⋊C4—31no—
526(C2×D3)⋊C4—31no—
527(C2×D3)⋊C4—31no—
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—91no—
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—181no—
542(C2×D3)⋊C4—181no—
543(C2×D3)⋊C4—181no—
544(C2×D3)⋊C4—181no—
545C4⋊Dic3—31no—
546C4⋊Dic3—31no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—181no—
551Dic3⋊C4—31no—
552Dic3⋊C4—31no—
553Dic3⋊C4—31no—
554Dic3⋊C4—31no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—91no—
559Dic3⋊C4—91no—
560Dic3⋊C4—91no—
561Dic3⋊C4—181no—
562Dic3⋊C4—181no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—31no—
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—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—81no—
602C22×C32—81no—
603C22×C32C23×D311yescharacteristic
604C22×C32C23×D311yescharacteristic
605C22×C32C23×D311yescharacteristic
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—62no—
616C2×C3×D3—62no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—61no—
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—61no—
631C2×C3×D3—61no—
632C2×C3×D3—61no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—121no—
636C2×C3×D3—121no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3—121no—
640C2×C3×D3—121no—
641C2×C3×D3—121no—
642C32×C4—61no—
643C32×C4—61no—
644C32×C4—61no—
645C32×C4—61no—
646C32×C4—61no—
647C32×C4—61no—
648C3⋊Dic3—21no—
649C3⋊Dic3—61no—
650C3⋊Dic3—61no—
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—121no—
660C3⋊Dic3—121no—
661C3⋊Dic3—241no—
662C3⋊Dic3—241no—
663C3⋊Dic3#23512yes—
664C3⋊Dic3#23712yes—
665C3×Dic3—22no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—21no—
677C3×Dic3—21no—
678C3×Dic3—32no—
679C3×Dic3—32no—
680C3×Dic3—32no—
681C3×Dic3—32no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—41no—
685C3×Dic3—41no—
686C3×Dic3—41no—
687C3×Dic3—62no—
688C3×Dic3—62no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—121no—
692#127—271no—
693#124—91no—
694#124—271no—
695#124—271no—
696#124—271no—
697#123—91no—
698#123—271no—
699#123—271no—
700#123—271no—
701C4×Q8—271no—
702C4×Q8—271no—
703C4×D4—91no—
704C4×D4—271no—
705C4×D4—271no—
706C4×D4—271no—
707C33#55911yescharacteristic, complemented, Sylow
708C23×C3—21no—
709C23×C3—21no—
710C23×C3—21no—
711C23×C3—41no—
712C23×C3—91no—
713C23×C3—91no—
714C23×C3—91no—
715C23×C3C2×D3211yescharacteristic
716C23×C3C2×D3211yescharacteristic
717C23×C3C2×D3211yescharacteristic
718C22×D3—31no—
719C22×D3—31no—
720C22×D3—31no—
721C22×D3—31no—
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3—61no—
726C22×D3—61no—
727C3×Q8—182no—
728C3×D4—182no—
729C3×D4—182no—
730C3×D4—361no—
731C2×C3×C4—31no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
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—61no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—91no—
750C2×C3×C4—91no—
751C2×C3×C4—91no—
752C2×C3×C4—121no—
753C2×C3×C4—121no—
754C2×C3×C4—122no—
755C2×C3×C4—361no—
756#67—62no—
757#67—62no—
758#67—62no—
759#67—62no—
760#67—64no—
761#67—122no—
762#67—121no—
763#67—121no—
764#67—122no—
765#67—182no—
766#67—182no—
767#67—182no—
768#67—182no—
769#67—361no—
770#67—361no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—41no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—91no—
782C2×Dic3—91no—
783C2×Dic3—91no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—91no—
787C2×Dic3—181no—
788C2×Dic3—181no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—361no—
794C2×Dic3—361no—
795C2×Dic3—361no—
796C2×Dic3—361no—
797C2×Dic3C2×D3211yescharacteristic
798C2×Dic3C2×D3211yescharacteristic
799C2×Dic3C2×D3211yescharacteristic
800C2×Dic3C2×D3211yescharacteristic
801C2×Dic3C2×D3211yescharacteristic
802C2×Dic3C2×D3211yescharacteristic
803D12—182no—
804D12—182no—
805D12—361no—
806C4×D3—121no—
807C4×D3—121no—
808C4×D3—361no—
809C4×D3—361no—
810C4×D3—361no—
811C4×D3—361no—
812C4×D3—362no—
813C4×D3—362no—
814Dic6—62no—
815Dic6—62no—
816Dic6—182no—
817Dic6—182no—
818Dic6—182no—
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×C32C2×#23511yescharacteristic
840C2×C32C2×#23711yescharacteristic
841C2×C32#100411yescharacteristic
842C2×C32#100411yescharacteristic
843C2×C32D3×#4111yescharacteristic
844C2×C32D3×#4111yescharacteristic
845C2×C32D3×#4111yescharacteristic
846C2×C32D3×#4111yescharacteristic
847C2×C32#100911yescharacteristic
848C3⋊D3—41no—
849C3⋊D3—41no—
850C3⋊D3—41no—
851C3×D3—122no—
852C3×D3—122no—
853C3×D3—121no—
854C3×D3—121no—
855C3×D3—121no—
856C3×D3—121no—
857C3×D3—121no—
858C3×D3—121no—
859C3×D3—241no—
860C2×Q8—91no—
861C2×Q8—271no—
862C2×D4—91no—
863C2×D4—91no—
864C2×D4—91no—
865C2×D4—271no—
866C2×D4—271no—
867C2×D4—271no—
868C22×C4—31no—
869C22×C4—91no—
870C22×C4—271no—
871C22×C4—271no—
872C4⋊C4—91no—
873C4⋊C4—91no—
874C4⋊C4—91no—
875C4⋊C4—271no—
876C4⋊C4—271no—
877C4⋊C4—271no—
878C22⋊C4—31no—
879C22⋊C4—31no—
880C22⋊C4—91no—
881C22⋊C4—91no—
882C22⋊C4—91no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—271no—
886C22⋊C4—271no—
887C22⋊C4—271no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C42—91no—
891C42—91no—
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—81no—
919C22×C3—81no—
920C22×C3—181no—
921C22×C3—181no—
922C22×C3—181no—
923C22×C3—181no—
924C22×C3—181no—
925C22×C3—181no—
926C22×C3—181no—
927C22×C3—181no—
928C22×C3—181no—
929C22×C3C22×D3211yescharacteristic
930C22×C3C22×D3211yescharacteristic
931C22×C3C22×D3211yescharacteristic
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—61no—
935C2×D3—61no—
936C2×D3—61no—
937C2×D3—61no—
938C2×D3—61no—
939C2×D3—61no—
940C2×D3—61no—
941C2×D3—61no—
942C2×D3—61no—
943C2×D3—61no—
944C2×D3—61no—
945C2×D3—61no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—61no—
951C2×D3—61no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—121no—
955C2×D3—121no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3—121no—
959C3×C4—62no—
960C3×C4—61no—
961C3×C4—61no—
962C3×C4—61no—
963C3×C4—61no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—92no—
973C3×C4—92no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—121no—
977C3×C4—121no—
978C3×C4—121no—
979C3×C4—181no—
980Dic3—21no—
981Dic3—21no—
982Dic3—21no—
983Dic3—21no—
984Dic3—21no—
985Dic3—21no—
986Dic3—32no—
987Dic3—32no—
988Dic3—32no—
989Dic3—32no—
990Dic3—62no—
991Dic3—62no—
992Dic3—61no—
993Dic3—61no—
994Dic3—121no—
995Dic3—181no—
996Dic3—181no—
997Dic3—181no—
998Dic3—181no—
999Dic3—181no—
1000Dic3—181no—
1001Dic3—361no—
1002Dic3—361no—
1003Dic3—361no—
1004Dic3—361no—
1005Dic3—361no—
1006Dic3—361no—
1007Dic3—721no—
1008Dic3—721no—
1009C32—21no—
1010C32—21no—
1011C32—21no—
1012C32—41no—
1013C32#555911yescharacteristic, complemented
1014C32#566411yescharacteristic, complemented
1015C32#568111yescharacteristic, complemented
1016C23—91no—
1017C23—91no—
1018C23—91no—
1019C23D3311yescharacteristic
1020Q8—182no—
1021Q8—542no—
1022D4—182no—
1023D4—182no—
1024D4—361no—
1025D4—542no—
1026D4—542no—
1027D4—1081no—
1028C2×C4—31no—
1029C2×C4—31no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—31no—
1033C2×C4—31no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—121no—
1038C2×C4—271no—
1039C2×C4—271no—
1040C2×C4—361no—
1041C2×C4—1081no—
1042C2×C4—1081no—
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—361no—
1063C2×C3—361no—
1064C2×C3—361no—
1065C2×C3D3×#23511yescharacteristic
1066C2×C3D3×#23511yescharacteristic
1067C2×C3#6430611yescharacteristic
1068C2×C3#6430711yescharacteristic
1069C2×C3D3×#23711yescharacteristic
1070C2×C3D3×#23711yescharacteristic
1071C2×C3#6431211yescharacteristic
1072C2×C3#6431411yescharacteristic
1073C2×C3#6433011yescharacteristic
1074D3—122no—
1075D3—122no—
1076D3—121no—
1077D3—121no—
1078D3—121no—
1079D3—121no—
1080D3—121no—
1081D3—121no—
1082D3—241no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—181no—
1087C22—181no—
1088C22—181no—
1089C22—181no—
1090C22—181no—
1091C22—181no—
1092C22—181no—
1093C22—181no—
1094C22—181no—
1095C22C2×D3311yescharacteristic
1096C4—61no—
1097C4—61no—
1098C4—61no—
1099C4—61no—
1100C4—61no—
1101C4—61no—
1102C4—92no—
1103C4—92no—
1104C4—181no—
1105C4—541no—
1106C4—541no—
1107C3—21no—
1108C3—21no—
1109C3—21no—
1110C3—41no—
1111C3#1059414311yescharacteristic, complemented
1112C3#1059420011yescharacteristic, complemented
1113C3#1059495711yescharacteristic, complemented
1114C2—41no—
1115C2—361no—
1116C2—361no—
1117C2—361no—
1118C2#1172440711yescharacteristic
1119C2#1172441011yescharacteristic
1120C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723728C2
hypercenterC23D33
hypocenterC33#559
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723621C2semidirect
3. Dic3×#638C2semidirect
4. #11723591C2semidirect
5. C3×#63966C2semidirect
6. C3×#63953C2semidirect
7. C3×#63952C2semidirect
8. #11723010C2semidirect
9. #11723007C2semidirect
10. #11722997C2semidirect
11. #11722995C2semidirect
12. #11722943C2semidirect
13. #11722940C2semidirect
14. #11722938C2semidirect
15. #11722934C2semidirect
72. #63966D3semidirect
76. #63953D3semidirect
77. #63952D3semidirect
707. C33#559semidirect
1013. C32#5559semidirect
1014. C32#5664semidirect
1015. C32#5681semidirect
1111. C3#10594143semidirect
1112. C3#10594200semidirect
1113. C3#10594957semidirect

Maximal subgroups

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

subgroupindex
#117237282
#117236212
Dic3×#6382
#117235912
C3×#639662
C3×#639532
C3×#639522
#117230102
#117230072
#117229972
#117229952
#117229432
#117229402
#117229382
#117229342
#105949573
#105942003
#105941433