Finite Group Databasebeta

← #13172179

Subgroups — #13172179

Order 1728.

1136 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723725C211yesmaximal, characteristic
2#11723640C211yesmaximal, characteristic, complemented
3#11723621C211yesmaximal, characteristic, complemented
4#11723621C211yesmaximal, characteristic, complemented
5C3×#63966C211yesmaximal, characteristic, complemented
6C3×#63956C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723012C211yesmaximal, characteristic, complemented
10#11723011C211yesmaximal, characteristic, complemented
11#11722997C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722983C211yesmaximal, characteristic, complemented
14#11722934C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10594935—31nomaximal
17#10594163—31nomaximal
18#10594090—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×C3×#624C2211yescharacteristic
28#88864C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C32×#217C2211yescharacteristic
31C32×#217C2211yescharacteristic
32#88815C2211yescharacteristic
33#88814C2211yescharacteristic
34#88807C2211yescharacteristic
35#88806C2211yescharacteristic
36#88806C2211yescharacteristic
37#88806C2211yescharacteristic
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43C3×#3724C2211yescharacteristic
44C3×#3724C2211yescharacteristic
45C3×Dic3⋊Dic3C2211yescharacteristic
46C3×Dic3⋊Dic3C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64133—31no—
55#64092—31no—
56#64092—31no—
57C3×#929—31no—
58C3×C4×#67—31no—
59C3×#886—31no—
60C3×#67⋊C4—31no—
61C3×#879—31no—
62C3×#879—31no—
63#63971—31no—
64#63970—31no—
65#63969—31no—
66#63969—31no—
67#63969—31no—
68#63969—31no—
69#63969—61no—
70#63969—61no—
71#63966D311yescharacteristic, complemented
72#63964—31no—
73#63964—31no—
74#63964—61no—
75#63958—31no—
76#63956D311yescharacteristic, complemented
77#63952D311yescharacteristic, complemented
78C4×#626—31no—
79#63900—31no—
80#63899—31no—
81#63896—31no—
82#63896—31no—
83#63895—31no—
84#63893—31no—
85#63891—31no—
86#63890—31no—
87#63880—31no—
88#63879—31no—
89D3×Dic3⋊C4—31no—
90D3×Dic3⋊C4—31no—
91#63869—31no—
92#63869—31no—
93#63868—31no—
94#63867—31no—
95#63867—31no—
96#63865—31no—
97#63861—31no—
98#63859—31no—
99#63853—31no—
100#63846—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C3×#638—22no—
108C3×#638—41no—
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3—41no—
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C2×C32×Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120#6295—22no—
121#6294—41no—
122#6293—41no—
123Dic3×C3⋊D3—22no—
124Dic3×C3⋊D3—41no—
125C3×#624—41no—
126#5707—91no—
127#5660—91no—
128#5564—91no—
129C22×C32×C4—31no—
130C2×#638C2×D311yescharacteristic
131C2×#638C2×D311yescharacteristic
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×#634—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—61no—
140C2×C3×#67—61no—
141C22×C3×Dic3—21no—
142C22×C3×Dic3C2×D311yescharacteristic
143C22×C3×Dic3C2×D311yescharacteristic
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×#627—31no—
147C2×#627—31no—
148C2×#627—61no—
149C2×#626—31no—
150C2×#626—31no—
151C2×#625—31no—
152C2×#624—31no—
153C2×#624C2×D311yescharacteristic
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—61no—
161C2×D3×Dic3—61no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164#3757—31no—
165#3757—31no—
166#3757—31no—
167#3757—61no—
168#3757—61no—
169#3757—61no—
170#3757—121no—
171#3757C2×D311yescharacteristic
172#3752—31no—
173#3752—31no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)—31no—
177#3750—31no—
178#3750—31no—
179#3750—31no—
180#3750—31no—
181C3×#217—21no—
182C3×#217—21no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—61no—
186C3×#217C2×D311yescharacteristic
187C3×#217C2×D311yescharacteristic
188C3×#217C2×D311yescharacteristic
189C3×#217C2×D311yescharacteristic
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—31no—
195C3×(C2×D3)⋊C4—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×Dic3⋊C4—31no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—61no—
220#3724—61no—
221#3724—61no—
222#3724C2×D311yescharacteristic
223#3724C2×D311yescharacteristic
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236Dic3⋊Dic3—61no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3C2×D311yescharacteristic
239Dic3⋊Dic3C2×D311yescharacteristic
240Dic3⋊Dic3C2×D311yescharacteristic
241Dic3⋊Dic3C2×D311yescharacteristic
242#3722—31no—
243#3722C2×D311yescharacteristic
244#3722C2×D311yescharacteristic
245#3722C2×D311yescharacteristic
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—61no—
253(C2×D3)⋊Dic3—61no—
254Dic32C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33—21no—
257C22×C33—21no—
258C22×C33—21no—
259C22×C33C2411yescharacteristic
260C2×C3×C3⋊D3—21no—
261C2×C3×C3⋊D3—21no—
262C2×C3×C3⋊D3—21no—
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3#4112yes—
266C3⋊(C3⋊Dic3)—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C32×Dic3—21no—
273C32×Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×#123—91no—
280C3×C4×D4—91no—
281#939—91no—
282#938—91no—
283#935—91no—
284#935—91no—
285#929—31no—
286C4×#67—31no—
287C4×#67—91no—
288#924—91no—
289#924—91no—
290#924—181no—
291C2×Dic3⋊C4—91no—
292#898—91no—
293#897—91no—
294#896—91no—
295#896—91no—
296#896—91no—
297#894—91no—
298D3×C4⋊C4—91no—
299D3×C4⋊C4—91no—
300#890—91no—
301#890—91no—
302#889—91no—
303#889—91no—
304#886—31no—
305#886—91no—
306#884—91no—
307#883—91no—
308#883—91no—
309#883—91no—
310#883—91no—
311#883—91no—
312#883—181no—
313#883—181no—
314#67⋊C4—31no—
315#67⋊C4—91no—
316#879—31no—
317#879—31no—
318#879—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#876—91no—
323C4×D12—91no—
324#870—91no—
325#870—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—41no—
330C23×C32C22×D311yescharacteristic
331C23×C32C22×D311yescharacteristic
332C23×C32C22×D311yescharacteristic
333C22×C3⋊D3C22×D311yescharacteristic
334C22×C3⋊D3C22×D311yescharacteristic
335C22×C3×D3—31no—
336C22×C3×D3—31no—
337C22×C3×D3—31no—
338C22×C3×D3—31no—
339C22×C3×D3—61no—
340C22×C3×D3—61no—
341C2×C32×C4—31no—
342C2×C32×C4—31no—
343C2×C32×C4—31no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—121no—
348#638—22no—
349#638—41no—
350C2×C3⋊Dic3—31no—
351C2×C3⋊Dic3—31no—
352C2×C3⋊Dic3—31no—
353C2×C3⋊Dic3—31no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—61no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—61no—
361C2×C3⋊Dic3—61no—
362C2×C3⋊Dic3—121no—
363C2×C3⋊Dic3—121no—
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4×C3⋊D3—62no—
369C4×C3⋊D3—121no—
370#634—121no—
371C3×#67—62no—
372C3×#67—62no—
373C3×#67—122no—
374C3×#67—121no—
375C3×#67—121no—
376C3×#67—122no—
377C2×C3×Dic3—21no—
378C2×C3×Dic3—21no—
379C2×C3×Dic3—21no—
380C2×C3×Dic3—21no—
381C2×C3×Dic3—21no—
382C2×C3×Dic3—21no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—41no—
392C2×C3×Dic3—41no—
393C2×C3×Dic3—42no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—61no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C2×C3×Dic3C22×D311yescharacteristic
405C2×C3×Dic3C22×D311yescharacteristic
406C2×C3×Dic3C22×D311yescharacteristic
407C2×C3×Dic3C22×D311yescharacteristic
408C2×C3×Dic3C22×D311yescharacteristic
409C2×C3×Dic3C22×D311yescharacteristic
410C3×C4×D3—121no—
411C3×C4×D3—121no—
412#627—121no—
413#627—121no—
414#627—122no—
415#626—62no—
416#626—62no—
417#625—62no—
418#624—41no—
419#624—121no—
420D3×Dic3—62no—
421D3×Dic3—62no—
422D3×Dic3—122no—
423D3×Dic3—121no—
424D3×Dic3—121no—
425D3×Dic3—122no—
426D3×Dic3—121no—
427D3×Dic3—121no—
428#539—271noSylow
429C2×C33—41no—
430C2×C33C2×#4111yescharacteristic
431C2×C33H(5,𝔽2)11yescharacteristic
432C2×C332−1+411yescharacteristic
433C3×C3⋊D3—22no—
434C3×C3⋊D3—41no—
435C2×C3×D4—91no—
436C2×C3×D4—91no—
437C22×C3×C4—31no—
438C22×C3×C4—31no—
439C22×C3×C4—61no—
440C22×C3×C4—91no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—31no—
444C2×#67—31no—
445C2×#67—61no—
446C2×#67—61no—
447C2×#67—91no—
448C2×#67—91no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—91no—
452C22×Dic3D3211yescharacteristic
453C2×D12—91no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—91no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—181no—
463C2×C4×D3—181no—
464C2×Dic6—91no—
465C2×Dic6—91no—
466C2×Dic6—91no—
467C2×Dic6—181no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—31no—
477C3×C22⋊C4—31no—
478C3×C22⋊C4—61no—
479C3×C22⋊C4—61no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C42—91no—
485C3×C42—91no—
486#217—31no—
487#217—31no—
488#217—61no—
489#217—91no—
490#217—91no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—181no—
496#217—181no—
497#217—181no—
498#217—361no—
499#217D3211yescharacteristic
500#217D3211yescharacteristic
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—31no—
505(C2×D3)⋊C4—31no—
506(C2×D3)⋊C4—31no—
507(C2×D3)⋊C4—91no—
508(C2×D3)⋊C4—91no—
509(C2×D3)⋊C4—91no—
510(C2×D3)⋊C4—91no—
511(C2×D3)⋊C4—91no—
512(C2×D3)⋊C4—91no—
513(C2×D3)⋊C4—181no—
514(C2×D3)⋊C4—181no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—181no—
528C4⋊Dic3—181no—
529C4⋊Dic3—181no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—31no—
537Dic3⋊C4—31no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545Dic3⋊C4—91no—
546Dic3⋊C4—91no—
547Dic3⋊C4—91no—
548Dic3⋊C4—91no—
549Dic3⋊C4—91no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—181no—
555Dic3⋊C4—181no—
556Dic3⋊C4—181no—
557Dic3⋊C4—181no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C22×C32—21no—
563C22×C32—22no—
564C22×C32—21no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—21no—
568C22×C32—21no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—41no—
576C22×C32—41no—
577C22×C32—41no—
578C22×C32—42no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—41no—
585C22×C32—81no—
586C22×C32—81no—
587C22×C32C23×D311yescharacteristic
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3#23512yes—
596C2×C3×D3—32no—
597C2×C3×D3—32no—
598C2×C3×D3—62no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
603C2×C3×D3—62no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—61no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C32×C4—61no—
615C32×C4—61no—
616C32×C4—61no—
617C32×C4—61no—
618C32×C4—61no—
619C32×C4—61no—
620C3⋊Dic3—21no—
621C3⋊Dic3—21no—
622C3⋊Dic3—21no—
623C3⋊Dic3—21no—
624C3⋊Dic3—61no—
625C3⋊Dic3—61no—
626C3⋊Dic3—61no—
627C3⋊Dic3—61no—
628C3⋊Dic3—61no—
629C3⋊Dic3—61no—
630C3⋊Dic3—121no—
631C3⋊Dic3—121no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—121no—
636C3⋊Dic3—241no—
637C3⋊Dic3—241no—
638C3×Dic3—22no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—21no—
645C3×Dic3—21no—
646C3×Dic3—21no—
647C3×Dic3—21no—
648C3×Dic3—21no—
649C3×Dic3—21no—
650C3×Dic3—21no—
651C3×Dic3—41no—
652C3×Dic3—41no—
653C3×Dic3—41no—
654C3×Dic3—41no—
655C3×Dic3—41no—
656C3×Dic3—61no—
657C3×Dic3—61no—
658C3×Dic3—61no—
659C3×Dic3—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668#126—91no—
669#126—271no—
670#125—271no—
671#125—271no—
672#123—91no—
673#123—271no—
674#123—271no—
675#123—271no—
676C22⋊Q8—271no—
677C22⋊Q8—271no—
678C22⋊Q8—271no—
679#121—271no—
680C4×D4—91no—
681C4×D4—271no—
682C2×C4⋊C4—271no—
683C33#53911yescharacteristic, complemented, Sylow
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—41no—
688C23×C3—91no—
689C23×C3—91no—
690C23×C3C2×D3211yescharacteristic
691C23×C3C2×D3211yescharacteristic
692C23×C3C2×D3211yescharacteristic
693C22×D3—31no—
694C22×D3—31no—
695C22×D3—31no—
696C22×D3—31no—
697C22×D3—61no—
698C22×D3—61no—
699C3×D4—182no—
700C3×D4—361no—
701C2×C3×C4—31no—
702C2×C3×C4—31no—
703C2×C3×C4—31no—
704C2×C3×C4—31no—
705C2×C3×C4—31no—
706C2×C3×C4—31no—
707C2×C3×C4—31no—
708C2×C3×C4—31no—
709C2×C3×C4—31no—
710C2×C3×C4—31no—
711C2×C3×C4—31no—
712C2×C3×C4—31no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—91no—
722C2×C3×C4—91no—
723C2×C3×C4—121no—
724C2×C3×C4—121no—
725C2×C3×C4—122no—
726C2×C3×C4—361no—
727#67—62no—
728#67—62no—
729#67—122no—
730#67—121no—
731#67—121no—
732#67—122no—
733#67—182no—
734#67—182no—
735C2×Dic3—31no—
736C2×Dic3—31no—
737C2×Dic3—31no—
738C2×Dic3—31no—
739C2×Dic3—31no—
740C2×Dic3—31no—
741C2×Dic3—31no—
742C2×Dic3—31no—
743C2×Dic3—41no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—91no—
749C2×Dic3—91no—
750C2×Dic3—91no—
751C2×Dic3—91no—
752C2×Dic3—91no—
753C2×Dic3—91no—
754C2×Dic3—181no—
755C2×Dic3—181no—
756C2×Dic3—181no—
757C2×Dic3—181no—
758C2×Dic3—181no—
759C2×Dic3—181no—
760C2×Dic3—182no—
761C2×Dic3—361no—
762C2×Dic3—361no—
763C2×Dic3—361no—
764C2×Dic3—361no—
765C2×Dic3C2×D3211yescharacteristic
766C2×Dic3C2×D3211yescharacteristic
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770C2×Dic3C2×D3211yescharacteristic
771D12—182no—
772C4×D3—121no—
773C4×D3—121no—
774C4×D3—182no—
775C4×D3—182no—
776C4×D3—362no—
777C4×D3—361no—
778C4×D3—361no—
779C4×D3—361no—
780C4×D3—361no—
781C4×D3—362no—
782Dic6—361no—
783Dic6—361no—
784Dic6—361no—
785Dic6—362no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—41no—
796C2×C32—41no—
797C2×C32—41no—
798C2×C32—41no—
799C2×C32—42no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—81no—
803C2×C32—81no—
804C2×C32—82no—
805C2×C32C2×#23511yescharacteristic
806C2×C32#100411yescharacteristic
807C2×C32#100411yescharacteristic
808C2×C32D3×#4111yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32#100911yescharacteristic
811C2×C32#101011yescharacteristic
812C2×C32#101011yescharacteristic
813C2×C32#101011yescharacteristic
814C3⋊D3—22no—
815C3⋊D3—41no—
816C3×D3—62no—
817C3×D3—62no—
818C3×D3—122no—
819C3×D3—122no—
820C3×D3—121no—
821C3×D3—121no—
822C2×Q8—271no—
823C2×D4—91no—
824C2×D4—91no—
825C2×D4—271no—
826C22×C4—31no—
827C22×C4—91no—
828C22×C4—271no—
829C22×C4—271no—
830C22×C4—271no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—31no—
846C22⋊C4—31no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—91no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4—271no—
855C42—91no—
856C42—91no—
857C22×C3—22no—
858C22×C3—21no—
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—41no—
877C22×C3—41no—
878C22×C3—42no—
879C22×C3—41no—
880C22×C3—81no—
881C22×C3—81no—
882C22×C3—92no—
883C22×C3—181no—
884C22×C3—181no—
885C22×C3—181no—
886C22×C3—181no—
887C22×C3—181no—
888C22×C3C22×D3211yescharacteristic
889C22×C3C22×D3211yescharacteristic
890C22×C3C22×D3211yescharacteristic
891C2×D3—32no—
892C2×D3—32no—
893C2×D3—62no—
894C2×D3—61no—
895C2×D3—61no—
896C2×D3—61no—
897C2×D3—61no—
898C2×D3—62no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—61no—
904C2×D3—61no—
905C2×D3—121no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—121no—
909C3×C4—62no—
910C3×C4—61no—
911C3×C4—61no—
912C3×C4—61no—
913C3×C4—61no—
914C3×C4—61no—
915C3×C4—61no—
916C3×C4—61no—
917C3×C4—61no—
918C3×C4—61no—
919C3×C4—61no—
920C3×C4—61no—
921C3×C4—61no—
922C3×C4—121no—
923C3×C4—121no—
924C3×C4—121no—
925C3×C4—121no—
926C3×C4—121no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931Dic3—21no—
932Dic3—21no—
933Dic3—21no—
934Dic3—21no—
935Dic3—21no—
936Dic3—21no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—121no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949Dic3—181no—
950Dic3—181no—
951Dic3—181no—
952Dic3—181no—
953Dic3—181no—
954Dic3—181no—
955Dic3—361no—
956Dic3—361no—
957Dic3—361no—
958Dic3—361no—
959Dic3—361no—
960Dic3—361no—
961Dic3—721no—
962Dic3—721no—
963C32—21no—
964C32—21no—
965C32—21no—
966C32—41no—
967C32#556411yescharacteristic, complemented
968C32#566011yescharacteristic, complemented
969C32#570711yescharacteristic, complemented
970C23—91no—
971C23—91no—
972C23D3311yescharacteristic
973Q8—1081no—
974D4—182no—
975D4—361no—
976D4—542no—
977C2×C4—31no—
978C2×C4—31no—
979C2×C4—31no—
980C2×C4—31no—
981C2×C4—31no—
982C2×C4—31no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—121no—
988C2×C4—271no—
989C2×C4—271no—
990C2×C4—361no—
991C2×C4—542no—
992C2×C4—1081no—
993C2×C4—1081no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—42no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—41no—
1007C2×C3—41no—
1008C2×C3—41no—
1009C2×C3—41no—
1010C2×C3—81no—
1011C2×C3—81no—
1012C2×C3—82no—
1013C2×C3—182no—
1014C2×C3—361no—
1015C2×C3#6429811yescharacteristic
1016C2×C3D3×#23511yescharacteristic
1017C2×C3D3×#23511yescharacteristic
1018C2×C3#6430711yescharacteristic
1019C2×C3#6430911yescharacteristic
1020C2×C3#6430911yescharacteristic
1021C2×C3#6431211yescharacteristic
1022C2×C3#6431411yescharacteristic
1023C2×C3#6433011yescharacteristic
1024D3—62no—
1025D3—62no—
1026D3—122no—
1027D3—122no—
1028D3—121no—
1029D3—121no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—92no—
1034C22—181no—
1035C22—181no—
1036C22—181no—
1037C22—181no—
1038C22—181no—
1039C22C2×D3311yescharacteristic
1040C4—61no—
1041C4—61no—
1042C4—61no—
1043C4—61no—
1044C4—61no—
1045C4—61no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—541no—
1051C4—541no—
1052C3—21no—
1053C3—21no—
1054C3—21no—
1055C3—41no—
1056C3#1059409011yescharacteristic, complemented
1057C3#1059416311yescharacteristic, complemented
1058C3#1059493511yescharacteristic, complemented
1059C2—41no—
1060C2—182no—
1061C2—361no—
1062C2#1172441011yescharacteristic
1063C2#1172441811yescharacteristic
1064C2#1172442711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
prime radical#11723725C2
hypercenterC23D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723640C2semidirect
3. #11723621C2semidirect
4. #11723621C2semidirect
5. C3×#63966C2semidirect
6. C3×#63956C2semidirect
7. C3×#63952C2semidirect
8. #11723023C2semidirect
9. #11723012C2semidirect
10. #11723011C2semidirect
11. #11722997C2semidirect
12. #11722984C2semidirect
13. #11722983C2semidirect
14. #11722934C2semidirect
15. #11722911C2semidirect
71. #63966D3semidirect
76. #63956D3semidirect
77. #63952D3semidirect
683. C33#539semidirect
967. C32#5564semidirect
968. C32#5660semidirect
969. C32#5707semidirect
1056. C3#10594090semidirect
1057. C3#10594163semidirect
1058. C3#10594935semidirect

Maximal subgroups

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

subgroupindex
#117237252
#117236402
#117236212
C3×#639662
C3×#639562
C3×#639522
#117230232
#117230122
#117230112
#117229972
#117229842
#117229832
#117229342
#117229112
#105949353
#105941633
#105940903