Finite Group Databasebeta

← #13172085

Subgroups — #13172085

Order 1728.

1264 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723718C211yesmaximal, characteristic, complemented
2#11723626C211yesmaximal, characteristic, complemented
3#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4#11723603C211yesmaximal, characteristic, complemented
5C3×#63979C211yesmaximal, characteristic
6C3×#63969C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11723006C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722990C211yesmaximal, characteristic, complemented
12#11722944C211yesmaximal, characteristic, complemented
13#11722940C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15#11722924C211yesmaximal, characteristic, complemented
16#10595200—31nomaximal
17#10595199—31nomaximal
18#10594219—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×Dic3×C3⋊D3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×C3×#627C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88813C2211yescharacteristic
37#88807C2211yescharacteristic
38#88807C2211yescharacteristic
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
45Dic3×C3⋊Dic3C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64144—31no—
55D4×C3⋊Dic3—31no—
56#64090—31no—
57C3×#940—31no—
58C3×#940—31no—
59C3×#936—31no—
60C3×#935—31no—
61C3×#885—31no—
62C3×#883—31no—
63#63979D311yescharacteristic
64#67⋊Dic3—31no—
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—61no—
70#67⋊Dic3—61no—
71Dic3×#67—31no—
72Dic3×#67—31no—
73#63969—31no—
74#63969D311yescharacteristic, complemented
75#63962—31no—
76#63962—31no—
77#63962—31no—
78#63962—61no—
79#63959—31no—
80#63959—31no—
81#63959—31no—
82#63959—31no—
83#63959—31no—
84#63959D311yescharacteristic, complemented
85#63953—31no—
86C4×#627—31no—
87#63915—31no—
88#63907—31no—
89C4×#626—31no—
90Dic3×D12—31no—
91#63890—31no—
92#63884—31no—
93#63884—31no—
94#63879—31no—
95#63863—31no—
96#63853—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63837—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)—41no—
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638—22no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C32×#67—22no—
116C32×#67—41no—
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121#6296—22no—
122Dic3×C3⋊D3—41no—
123D3×C3⋊Dic3—41no—
124C3×#627—22no—
125C3×#626—22no—
126C3×#626—41no—
127C3×#625—22no—
128C3×D3×Dic3—41no—
129#5713—91no—
130#5681—91no—
131#5664—91no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C2×#638C2×D311yescharacteristic
135C22×C3⋊Dic3—31no—
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—61no—
140C22×C3⋊Dic3—61no—
141C22×C3⋊Dic3—61no—
142C22×C3⋊Dic3—121no—
143C2×C4×C3⋊D3—31no—
144C2×C3×#67—21no—
145C2×C3×#67—21no—
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—61no—
153C2×C3×#67C2×D311yescharacteristic
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C2×D311yescharacteristic
156C2×C3×#67C2×D311yescharacteristic
157C22×C3×Dic3—31no—
158C2×C3×D12—31no—
159C2×C3×D12—31no—
160C2×C3×C4×D3—31no—
161C2×C3×Dic6—31no—
162C2×C3×Dic6—31no—
163C2×#627—31no—
164C2×#627—31no—
165C2×#627—31no—
166C2×#627C2×D311yescharacteristic
167C2×#626C2×D311yescharacteristic
168C2×#626C2×D311yescharacteristic
169C2×#625C2×D311yescharacteristic
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—61no—
175C2×D3×Dic3—61no—
176C2×D3×Dic3C2×D311yescharacteristic
177C32×C22⋊C4—31no—
178#3757—31no—
179#3757—31no—
180#3757—31no—
181#3757C2×D311yescharacteristic
182#3757C2×D311yescharacteristic
183#3752—31no—
184C4⋊(C3⋊Dic3)—31no—
185#3750—31no—
186#3750—31no—
187#3750—31no—
188C4×C3⋊Dic3—31no—
189C4×C3⋊Dic3—31no—
190C3×#217—21no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—61no—
199C3×#217—61no—
200C3×#217C2×D311yescharacteristic
201C3×#217C2×D311yescharacteristic
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×C4⋊Dic3—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213#3724C2×D311yescharacteristic
214Dic3⋊Dic3—31no—
215Dic3⋊Dic3—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⋊Dic3—61no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3C2×D311yescharacteristic
227#3722—31no—
228#3722—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—31no—
241(C2×D3)⋊Dic3—61no—
242(C2×D3)⋊Dic3—61no—
243(C2×D3)⋊Dic3—61no—
244(C2×D3)⋊Dic3—61no—
245(C2×D3)⋊Dic3C2×D311yescharacteristic
246(C2×D3)⋊Dic3C2×D311yescharacteristic
247(C2×D3)⋊Dic3C2×D311yescharacteristic
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×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#4112yes—
279C32×Dic3—21no—
280C32×Dic3—21no—
281C32×Dic3—21no—
282C32×Dic3#4112yes—
283C3×#127—91no—
284C3×#124—91no—
285C3×#123—91no—
286#947—91no—
287Q8×Dic3—91no—
288#940—31no—
289#940—31no—
290#936—31no—
291#936—91no—
292#936—91no—
293#936—91no—
294#935—31no—
295#935—91no—
296#935—91no—
297#935—91no—
298#935—91no—
299#935—181no—
300D4×Dic3—91no—
301D4×Dic3—91no—
302D4×Dic3—91no—
303D4×Dic3—91no—
304D4×Dic3—91no—
305D4×Dic3—181no—
306C4×#67—91no—
307C4×#67—91no—
308#894—91no—
309#894—91no—
310#887—91no—
311#887—91no—
312#886—91no—
313#886—91no—
314#885—31no—
315#885—91no—
316#885—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#883—31no—
321#883—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326#67⋊C4—181no—
327C4×D12—91no—
328C4×Dic6—91no—
329C4×Dic6—91no—
330C4×Dic6—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—
356#638—22no—
357C2×C3⋊Dic3—31no—
358C2×C3⋊Dic3—31no—
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—61no—
364C2×C3⋊Dic3—61no—
365C2×C3⋊Dic3—61no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—121no—
370C2×C3⋊Dic3—121no—
371C2×C3⋊Dic3—121no—
372C2×C3⋊Dic3—121no—
373C2×C3⋊Dic3—121no—
374C2×C3⋊Dic3—121no—
375C2×C3⋊Dic3—122no—
376C2×C3⋊Dic3—122no—
377C2×C3⋊Dic3—122no—
378C2×C3⋊Dic3—124no—
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C4×C3⋊D3—121no—
385C3×#67—24no—
386C3×#67—22no—
387C3×#67—22no—
388C3×#67—41no—
389C3×#67—41no—
390C3×#67—42no—
391C3×#67—62no—
392C3×#67—62no—
393C3×#67—62no—
394C3×#67—62no—
395C3×#67—64no—
396C3×#67—62no—
397C3×#67—121no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
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—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3C22×D311yescharacteristic
419C2×C3×Dic3C22×D311yescharacteristic
420C2×C3×Dic3C22×D311yescharacteristic
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C3×D12—62no—
427C3×D12—121no—
428C3×C4×D3—121no—
429C3×Dic6—62no—
430C3×Dic6—62no—
431#627—22no—
432#627—62no—
433#627—62no—
434#627—62no—
435#626—22no—
436#626—41no—
437#625—22no—
438D3×Dic3—41no—
439D3×Dic3—121no—
440D3×Dic3—121no—
441D3×Dic3—122no—
442D3×Dic3—121no—
443D3×Dic3—121no—
444D3×Dic3—122no—
445#559—271noSylow
446C2×C33—41no—
447C2×C33C2×#4111yescharacteristic
448C2×C33C2×#4111yescharacteristic
449C2×C33H(5,𝔽2)11yescharacteristic
450C3×C3⋊D3—41no—
451C32×D3—41no—
452C32×D3—41no—
453C2×C3×Q8—91no—
454C2×C3×D4—31no—
455C2×C3×D4—31no—
456C2×C3×D4—31no—
457C2×C3×D4—31no—
458C2×C3×D4—61no—
459C2×C3×D4—61no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C2×C3×D4—91no—
464C22×C3×C4—91no—
465C2×#67—31no—
466C2×#67—31no—
467C2×#67—31no—
468C2×#67—31no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—61no—
472C2×#67D3211yescharacteristic
473C2×#67D3211yescharacteristic
474C22×Dic3—31no—
475C22×Dic3—91no—
476C22×Dic3—91no—
477C22×Dic3—91no—
478C22×Dic3—91no—
479C22×Dic3—91no—
480C22×Dic3—91no—
481C22×Dic3—181no—
482C22×Dic3—181no—
483C22×Dic3—181no—
484C22×Dic3—181no—
485C22×Dic3—361no—
486C2×D12—31no—
487C2×D12—31no—
488C2×C4×D3—31no—
489C2×C4×D3—91no—
490C2×C4×D3—91no—
491C2×C4×D3—91no—
492C2×C4×D3—181no—
493C2×Dic6—31no—
494C2×Dic6—31no—
495C2×Dic6—91no—
496C2×Dic6—91no—
497C2×Dic6—91no—
498C3×C4⋊C4—91no—
499C3×C4⋊C4—91no—
500C3×C22⋊C4—31no—
501C3×C22⋊C4—31no—
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—31no—
511#217—31no—
512#217—31no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—61no—
518#217—61no—
519#217—91no—
520#217—91no—
521#217—91no—
522#217—91no—
523#217—91no—
524#217—91no—
525#217—91no—
526#217—91no—
527#217—91no—
528#217—181no—
529#217—181no—
530#217—181no—
531#217D3211yescharacteristic
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—31no—
534(C2×D3)⋊C4—31no—
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—91no—
544(C2×D3)⋊C4—181no—
545C4⋊Dic3—31no—
546C4⋊Dic3—91no—
547C4⋊Dic3—91no—
548C4⋊Dic3—91no—
549C4⋊Dic3—91no—
550C4⋊Dic3—91no—
551C4⋊Dic3—181no—
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—91no—
562Dic3⋊C4—181no—
563Dic3⋊C4—181no—
564Dic3⋊C4—181no—
565C4×Dic3—31no—
566C4×Dic3—31no—
567C4×Dic3—31no—
568C4×Dic3—31no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—181no—
579C4×Dic3—181no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—22no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—42no—
603C22×C32—42no—
604C22×C32—42no—
605C22×C32—61no—
606C22×C32—61no—
607C22×C32—61no—
608C22×C32—61no—
609C22×C32—61no—
610C22×C32—61no—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3×D3—22no—
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—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—41no—
633C2×C3×D3—41no—
634C2×C3×D3—41no—
635C2×C3×D3—62no—
636C2×C3×D3—61no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—121no—
643C2×C3×D3—121no—
644C32×C4—32no—
645C32×C4—61no—
646C32×C4—61no—
647C32×C4—61no—
648C3⋊Dic3—21no—
649C3⋊Dic3—21no—
650C3⋊Dic3—21no—
651C3⋊Dic3—21no—
652C3⋊Dic3—61no—
653C3⋊Dic3—61no—
654C3⋊Dic3—62no—
655C3⋊Dic3—62no—
656C3⋊Dic3—61no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—61no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—121no—
663C3⋊Dic3—121no—
664C3⋊Dic3—122no—
665C3⋊Dic3—122no—
666C3⋊Dic3#23712yes—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—21no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—22no—
674C3×Dic3—32no—
675C3×Dic3—32no—
676C3×Dic3—41no—
677C3×Dic3—41no—
678C3×Dic3—41no—
679C3×Dic3—62no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—121no—
689C3×Dic3—121no—
690C3×Dic3—121no—
691C3×Dic3—121no—
692C3×Dic3#23712yes—
693C3×Dic3#23712yes—
694#127—91no—
695#124—91no—
696#124—271no—
697#124—271no—
698#124—271no—
699#123—91no—
700#123—271no—
701#123—271no—
702#123—271no—
703C4×Q8—271no—
704C4×Q8—271no—
705C4×D4—271no—
706C4×D4—271no—
707C4×D4—271no—
708C4×D4—271no—
709C33#55911yescharacteristic, complemented, Sylow
710C23×C3—21no—
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—31no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—31no—
717C23×C3—41no—
718C23×C3—61no—
719C23×C3—61no—
720C23×C3—91no—
721C23×C3C2×D3211yescharacteristic
722C23×C3C2×D3211yescharacteristic
723C23×C3C2×D3211yescharacteristic
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—61no—
727C22×D3C2×D3211yescharacteristic
728C22×D3C2×D3211yescharacteristic
729C3×Q8—182no—
730C3×D4—62no—
731C3×D4—62no—
732C3×D4—64no—
733C3×D4—121no—
734C3×D4—121no—
735C3×D4—122no—
736C3×D4—182no—
737C3×D4—182no—
738C3×D4—182no—
739C3×D4—361no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—31no—
745C2×C3×C4—31no—
746C2×C3×C4—31no—
747C2×C3×C4—31no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—61no—
751C2×C3×C4—61no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—361no—
758#67—22no—
759#67—41no—
760#67—62no—
761#67—62no—
762#67—62no—
763#67—62no—
764#67—64no—
765#67—62no—
766#67—121no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—91no—
783C2×Dic3—91no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—91no—
787C2×Dic3—91no—
788C2×Dic3—121no—
789C2×Dic3—181no—
790C2×Dic3—181no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—181no—
794C2×Dic3—181no—
795C2×Dic3—361no—
796C2×Dic3—361no—
797C2×Dic3—361no—
798C2×Dic3—361no—
799C2×Dic3—361no—
800C2×Dic3—362no—
801C2×Dic3—361no—
802C2×Dic3—361no—
803C2×Dic3—361no—
804C2×Dic3—362no—
805C2×Dic3—362no—
806C2×Dic3—362no—
807C2×Dic3—364no—
808C2×Dic3C2×D3211yescharacteristic
809C2×Dic3C2×D3211yescharacteristic
810C2×Dic3C2×D3211yescharacteristic
811C2×Dic3C2×D3211yescharacteristic
812D12—62no—
813D12—121no—
814C4×D3—121no—
815C4×D3—361no—
816C4×D3—361no—
817C4×D3—362no—
818C4×D3—361no—
819Dic6—62no—
820Dic6—62no—
821Dic6—182no—
822Dic6—182no—
823Dic6—182no—
824C2×C32—21no—
825C2×C32—21no—
826C2×C32—21no—
827C2×C32—21no—
828C2×C32—21no—
829C2×C32—21no—
830C2×C32—21no—
831C2×C32—21no—
832C2×C32—21no—
833C2×C32—41no—
834C2×C32—41no—
835C2×C32—41no—
836C2×C32—42no—
837C2×C32—42no—
838C2×C32—42no—
839C2×C32—44no—
840C2×C32—41no—
841C2×C32—41no—
842C2×C32—41no—
843C2×C32—121no—
844C2×C32—121no—
845C2×C32C2×#23711yescharacteristic
846C2×C32C2×#23711yescharacteristic
847C2×C32C2×#23711yescharacteristic
848C2×C32#100411yescharacteristic
849C2×C32#100411yescharacteristic
850C2×C32D3×#4111yescharacteristic
851C2×C32D3×#4111yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32#100911yescharacteristic
854C3⋊D3—41no—
855C3×D3—42no—
856C3×D3—41no—
857C3×D3—41no—
858C3×D3—41no—
859C3×D3—41no—
860C3×D3—81no—
861C3×D3—122no—
862C3×D3—121no—
863C3×D3—121no—
864C2×Q8—91no—
865C2×Q8—271no—
866C2×D4—31no—
867C2×D4—31no—
868C2×D4—91no—
869C2×D4—91no—
870C2×D4—91no—
871C2×D4—91no—
872C22×C4—91no—
873C22×C4—271no—
874C22×C4—271no—
875C22×C4—271no—
876C4⋊C4—91no—
877C4⋊C4—91no—
878C4⋊C4—271no—
879C4⋊C4—271no—
880C4⋊C4—271no—
881C4⋊C4—271no—
882C22⋊C4—31no—
883C22⋊C4—91no—
884C22⋊C4—91no—
885C22⋊C4—91no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C22⋊C4—271no—
891C22⋊C4—271no—
892C22⋊C4—271no—
893C22⋊C4—271no—
894C42—91no—
895C42—91no—
896C42—271no—
897C42—271no—
898C42—271no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—21no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—41no—
915C22×C3—41no—
916C22×C3—41no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—42no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—41no—
924C22×C3—62no—
925C22×C3—61no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—61no—
931C22×C3—61no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—61no—
937C22×C3—121no—
938C22×C3—121no—
939C22×C3—121no—
940C22×C3—121no—
941C22×C3—121no—
942C22×C3—181no—
943C22×C3—181no—
944C22×C3—181no—
945C22×C3C22×D3211yescharacteristic
946C22×C3C22×D3211yescharacteristic
947C22×C3C22×D3211yescharacteristic
948C2×D3—21no—
949C2×D3—21no—
950C2×D3—21no—
951C2×D3—21no—
952C2×D3—21no—
953C2×D3—21no—
954C2×D3—62no—
955C2×D3—61no—
956C2×D3—61no—
957C2×D3—61no—
958C2×D3—61no—
959C2×D3—61no—
960C2×D3—61no—
961C2×D3—121no—
962C2×D3—121no—
963C3×C4—32no—
964C3×C4—32no—
965C3×C4—62no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—92no—
973C3×C4—121no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—181no—
977C3×C4—181no—
978C3×C4—181no—
979C3×C4—181no—
980Dic3—21no—
981Dic3—21no—
982Dic3—21no—
983Dic3—32no—
984Dic3—32no—
985Dic3—62no—
986Dic3—61no—
987Dic3—61no—
988Dic3—61no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—121no—
995Dic3—121no—
996Dic3—121no—
997Dic3—121no—
998Dic3—182no—
999Dic3—182no—
1000Dic3—181no—
1001Dic3—181no—
1002Dic3—181no—
1003Dic3—181no—
1004Dic3—181no—
1005Dic3—181no—
1006Dic3—361no—
1007Dic3—361no—
1008Dic3—361no—
1009Dic3—361no—
1010Dic3—362no—
1011Dic3—362no—
1012Dic3#380512yes—
1013C32—21no—
1014C32—21no—
1015C32—21no—
1016C32—41no—
1017C32#566411yescharacteristic, complemented
1018C32#568111yescharacteristic, complemented
1019C32#571311yescharacteristic, complemented
1020C23—31no—
1021C23—31no—
1022C23—91no—
1023C23D3311yescharacteristic
1024Q8—182no—
1025Q8—542no—
1026D4—62no—
1027D4—121no—
1028D4—182no—
1029D4—182no—
1030D4—182no—
1031D4—361no—
1032C2×C4—31no—
1033C2×C4—31no—
1034C2×C4—31no—
1035C2×C4—31no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—91no—
1041C2×C4—271no—
1042C2×C4—271no—
1043C2×C4—361no—
1044C2×C4—1081no—
1045C2×C4—1081no—
1046C2×C4—1081no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—42no—
1059C2×C3—44no—
1060C2×C3—41no—
1061C2×C3—41no—
1062C2×C3—41no—
1063C2×C3—41no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—122no—
1067C2×C3—121no—
1068C2×C3—121no—
1069C2×C3—121no—
1070C2×C3—121no—
1071C2×C3—241no—
1072C2×C3—361no—
1073C2×C3#6430611yescharacteristic
1074C2×C3D3×#23711yescharacteristic
1075C2×C3D3×#23711yescharacteristic
1076C2×C3D3×#23711yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3#6431411yescharacteristic
1079C2×C3#6431411yescharacteristic
1080C2×C3C2×#380511yescharacteristic
1081C2×C3#6433011yescharacteristic
1082D3—41no—
1083D3—41no—
1084D3—122no—
1085D3—121no—
1086D3—121no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—61no—
1091C22—61no—
1092C22—61no—
1093C22—61no—
1094C22—61no—
1095C22—61no—
1096C22—181no—
1097C22—181no—
1098C22—181no—
1099C22C2×D3311yescharacteristic
1100C4—32no—
1101C4—61no—
1102C4—61no—
1103C4—61no—
1104C4—92no—
1105C4—181no—
1106C4—181no—
1107C4—181no—
1108C4—181no—
1109C4—541no—
1110C4—541no—
1111C3—21no—
1112C3—21no—
1113C3—21no—
1114C3—41no—
1115C3#1059421911yescharacteristic, complemented
1116C3#1059519911yescharacteristic, complemented
1117C3#1059520011yescharacteristic, complemented
1118C2—41no—
1119C2—121no—
1120C2—121no—
1121C2—361no—
1122C2D3×#380511yescharacteristic
1123C2#1172440711yescharacteristic
1124C2#1172441911yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radicalC3×#63979C2
hypercenterC23D33
hypocenterC33#559
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723718C2semidirect
2. #11723626C2semidirect
3. #67⋊(C3⋊Dic3)C2semidirect
4. #11723603C2semidirect
6. C3×#63969C2semidirect
7. C3×#63959C2semidirect
8. #11723006C2semidirect
9. #11723001C2semidirect
10. #11722991C2semidirect
11. #11722990C2semidirect
12. #11722944C2semidirect
13. #11722940C2semidirect
14. Dic3×#626C2semidirect
15. #11722924C2semidirect
74. #63969D3semidirect
84. #63959D3semidirect
709. C33#559semidirect
1017. C32#5664semidirect
1018. C32#5681semidirect
1019. C32#5713semidirect
1115. C3#10594219semidirect
1116. C3#10595199semidirect
1117. C3#10595200semidirect

Maximal subgroups

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

subgroupindex
#117237182
#117236262
#67⋊(C3⋊Dic3)2
#117236032
C3×#639792
C3×#639692
C3×#639592
#117230062
#117230012
#117229912
#117229902
#117229442
#117229402
Dic3×#6262
#117229242
#105952003
#105951993
#105942193