Finite Group Databasebeta

← #13168301

Subgroups — #13168301

Order 1728.

1122 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723680C211yesmaximal, characteristic, complemented
2#11723479C211yesmaximal, characteristic, complemented
3#11723446C211yesmaximal, characteristic, complemented
4#11723422C211yesmaximal, characteristic, complemented
5C3×#63902C211yesmaximal, characteristic, complemented
6C3×#63893C211yesmaximal, characteristic, complemented
7C3×#63861C211yesmaximal, characteristic, complemented
8#11723011C211yesmaximal, characteristic, complemented
9#11722989C211yesmaximal, characteristic, complemented
10#11722987C211yesmaximal, characteristic, complemented
11#11722977C211yesmaximal, characteristic, complemented
12#11722969C211yesmaximal, characteristic, complemented
13#11722958C211yesmaximal, characteristic
14#11722932C211yesmaximal, characteristic, complemented
15D3×#3724C211yesmaximal, characteristic, complemented
16#10594439—31nomaximal
17#10594241—31nomaximal
18#10594090—31nomaximal
19C2×#6291C2211yescharacteristic
20C2×#6291C2211yescharacteristic
21C2×#6289C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×C3×#627C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C2×C3×D3×Dic3C2211yescharacteristic
26C2×C3×D3×Dic3C2211yescharacteristic
27C2×C3×D3×Dic3C2211yescharacteristic
28#88859C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×C4×C3⋊Dic3C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×Dic3⋊C4C2211yescharacteristic
35#88815C2211yescharacteristic
36#88815C2211yescharacteristic
37#88815C2211yescharacteristic
38#88815C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41Dic3⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88804C2211yescharacteristic
44#88804C2211yescharacteristic
45#88804C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×#3724C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54#64107—31no—
55#64095—31no—
56#64092—31no—
57C3×#898—31no—
58C3×#897—31no—
59C3×#67⋊C4—31no—
60C3×#67⋊C4—31no—
61C3×#879—31no—
62C3×#878—31no—
63#63978—31no—
64#63971—31no—
65#63969—31no—
66C2×#3724—31no—
67#63966—31no—
68#63964—31no—
69#63962—31no—
70#63952—31no—
71#63906—31no—
72C4×#626—31no—
73#63902D311yescharacteristic, complemented
74#63893D311yescharacteristic, complemented
75#63891—31no—
76#63890—31no—
77#63890—31no—
78#63890—31no—
79#63890—61no—
80#63888—31no—
81#63888—31no—
82#63887—31no—
83#63880—31no—
84D3×Dic3⋊C4—31no—
85D3×Dic3⋊C4—31no—
86#63872—31no—
87#63869—31no—
88#63869—31no—
89#63869—31no—
90#63868—31no—
91#63868—31no—
92#63868—61no—
93#63867—31no—
94#63865—31no—
95#63861D311yescharacteristic, complemented
96#63856—31no—
97#63854—31no—
98#63854—31no—
99#63854—61no—
100#63850—31no—
101#63845—31no—
102C22×C3⋊(C3⋊D3)C2311yescharacteristic
103C22×C32×D3C2311yescharacteristic
104C22×C32×D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117#6291—22no—
118#6291—41no—
119#6289—41no—
120D3×C3⋊Dic3—22no—
121C3×#627—41no—
122C3×#625—22no—
123C3×D3×Dic3—41no—
124C3×D3×Dic3—41no—
125C3×D3×Dic3—41no—
126#5707—91no—
127#5645—91no—
128#5564—91no—
129C2×#638—31no—
130C2×#638—31no—
131C22×C3⋊Dic3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3—31no—
140C2×C3×C4×D3—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—31no—
143C2×#627C2×D311yescharacteristic
144C2×#626—31no—
145C2×#626—31no—
146C2×#626—31no—
147C2×#626—31no—
148C2×#626—61no—
149C2×#626—61no—
150C2×#625C2×D311yescharacteristic
151C2×#624—31no—
152C2×#624—31no—
153C2×#624—61no—
154C2×D3×Dic3—31no—
155C2×D3×Dic3—31no—
156C2×D3×Dic3—61no—
157C2×D3×Dic3C2×D311yescharacteristic
158C2×D3×Dic3C2×D311yescharacteristic
159C2×D3×Dic3C2×D311yescharacteristic
160C32×C4⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163#3757—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—61no—
171#3752—61no—
172#3752—61no—
173#3752—121no—
174C4⋊(C3⋊Dic3)—31no—
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic
177C4⋊(C3⋊Dic3)C2×D311yescharacteristic
178#3750—31no—
179#3750—31no—
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×(C2×D3)⋊C4—21no—
185C3×(C2×D3)⋊C4—21no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4C2×D311yescharacteristic
190C3×(C2×D3)⋊C4C2×D311yescharacteristic
191C3×(C2×D3)⋊C4C2×D311yescharacteristic
192C3×(C2×D3)⋊C4C2×D311yescharacteristic
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—61no—
199C3×C4⋊Dic3—61no—
200C3×Dic3⋊C4—21no—
201C3×Dic3⋊C4—31no—
202C3×Dic3⋊C4—31no—
203C3×Dic3⋊C4—31no—
204C3×Dic3⋊C4—31no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4C2×D311yescharacteristic
207C3×Dic3⋊C4C2×D311yescharacteristic
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—31no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—61no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—61no—
222#3724—61no—
223#3724C2×D311yescharacteristic
224#3724C2×D311yescharacteristic
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—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3C2×D311yescharacteristic
240#3722—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—31no—
246#3722—61no—
247#3722—61no—
248#3722—61no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255Dic32C2×D311yescharacteristic
256C22×C33C2411yescharacteristic
257C2×C3⋊(C3⋊D3)—21no—
258C2×C3⋊(C3⋊D3)—21no—
259C2×C3⋊(C3⋊D3)—21no—
260C2×C32×D3—21no—
261C2×C32×D3—21no—
262C2×C32×D3—21no—
263C2×C32×D3—21no—
264C2×C32×D3—21no—
265C2×C32×D3#4112yes—
266C33×C4—21no—
267C3⋊(C3⋊Dic3)—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3—21no—
272C3×C3⋊Dic3—21no—
273C3×C3⋊Dic3—21no—
274C32×Dic3—21no—
275C32×Dic3—21no—
276C32×Dic3—21no—
277C32×Dic3—21no—
278C3×#126—91no—
279C3×C22⋊Q8—91no—
280C3×C4×D4—91no—
281#946—91no—
282#946—91no—
283#939—91no—
284#935—91no—
285#930—91no—
286#929—91no—
287C4×#67—91no—
288#924—91no—
289C2×Dic3⋊C4—91no—
290C2×Dic3⋊C4—91no—
291#898—31no—
292#898—91no—
293#898—91no—
294#898—181no—
295#897—31no—
296#896—91no—
297#896—91no—
298#894—91no—
299#894—91no—
300#894—91no—
301D3×C4⋊C4—91no—
302#890—91no—
303#890—91no—
304#890—91no—
305#889—91no—
306#886—91no—
307#886—91no—
308#886—91no—
309#886—91no—
310#886—181no—
311#884—91no—
312#883—91no—
313#883—91no—
314#883—91no—
315#883—181no—
316#67⋊C4—31no—
317#67⋊C4—31no—
318#67⋊C4—91no—
319#879—31no—
320#878—31no—
321#878—91no—
322#876—91no—
323C4×D12—91no—
324#870—91no—
325#870—91no—
326C23×C32—31no—
327C23×C32—31no—
328C22×C3⋊D3—31no—
329C22×C3⋊D3—31no—
330C22×C3⋊D3—31no—
331C22×C3⋊D3—61no—
332C22×C3⋊D3—61no—
333C22×C3⋊D3—61no—
334C22×C3⋊D3—121no—
335C22×C3×D3—21no—
336C22×C3×D3—21no—
337C22×C3×D3C22×D311yescharacteristic
338C22×C3×D3C22×D311yescharacteristic
339C22×C3×D3C22×D311yescharacteristic
340C22×C3×D3C22×D311yescharacteristic
341C2×C32×C4—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—31no—
345C2×C32×C4—31no—
346C2×C32×C4—31no—
347C2×C32×C4—31no—
348C2×C32×C4—41no—
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352#638—62no—
353#638—121no—
354C2×C3⋊Dic3—31no—
355C2×C3⋊Dic3—31no—
356C2×C3⋊Dic3—31no—
357C2×C3⋊Dic3—61no—
358C2×C3⋊Dic3—61no—
359C2×C3⋊Dic3—61no—
360C2×C3⋊Dic3—62no—
361C2×C3⋊Dic3—121no—
362C2×C3⋊Dic3C22×D311yescharacteristic
363C2×C3⋊Dic3C22×D311yescharacteristic
364C2×C3⋊Dic3C22×D311yescharacteristic
365C2×C3⋊Dic3C22×D311yescharacteristic
366C2×C3⋊Dic3C22×D311yescharacteristic
367C2×C3⋊Dic3C22×D311yescharacteristic
368C4×C3⋊D3—121no—
369C3×#67—62no—
370C3×#67—62no—
371C2×C3×Dic3—21no—
372C2×C3×Dic3—21no—
373C2×C3×Dic3—21no—
374C2×C3×Dic3—21no—
375C2×C3×Dic3—31no—
376C2×C3×Dic3—31no—
377C2×C3×Dic3—31no—
378C2×C3×Dic3—31no—
379C2×C3×Dic3—31no—
380C2×C3×Dic3—31no—
381C2×C3×Dic3—31no—
382C2×C3×Dic3—31no—
383C2×C3×Dic3—31no—
384C2×C3×Dic3—31no—
385C2×C3×Dic3—31no—
386C2×C3×Dic3—31no—
387C2×C3×Dic3—61no—
388C2×C3×Dic3—61no—
389C2×C3×Dic3—61no—
390C2×C3×Dic3—61no—
391C2×C3×Dic3—61no—
392C2×C3×Dic3—61no—
393C2×C3×Dic3—121no—
394C2×C3×Dic3—121no—
395C2×C3×Dic3—121no—
396C2×C3×Dic3C22×D311yescharacteristic
397C2×C3×Dic3C22×D311yescharacteristic
398C2×C3×Dic3C22×D311yescharacteristic
399C2×C3×Dic3C22×D311yescharacteristic
400C2×C3×Dic3C22×D311yescharacteristic
401C2×C3×Dic3C22×D311yescharacteristic
402C2×C3×Dic3C22×D311yescharacteristic
403C2×C3×Dic3C22×D311yescharacteristic
404C3×C4×D3—121no—
405C3×C4×D3—121no—
406C3×C4×D3—121no—
407C3×Dic6—121no—
408C3×Dic6—121no—
409#627—41no—
410#626—62no—
411#626—62no—
412#626—122no—
413#626—121no—
414#626—121no—
415#626—122no—
416#625—22no—
417#624—121no—
418#624—121no—
419#624—122no—
420D3×Dic3—41no—
421D3×Dic3—41no—
422D3×Dic3—41no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—122no—
426#539—271noSylow
427C2×C33C2×#4111yescharacteristic
428C2×C33H(5,𝔽2)11yescharacteristic
429C2×C332−1+411yescharacteristic
430C3⋊(C3⋊D3)—41no—
431C32×D3—22no—
432C32×D3—41no—
433C2×C3×Q8—91no—
434C2×C3×D4—91no—
435C22×C3×C4—91no—
436C22×C3×C4—91no—
437C22×C3×C4—91no—
438C2×#67—31no—
439C2×#67—31no—
440C2×#67—91no—
441C2×#67—91no—
442C2×#67—91no—
443C2×#67—91no—
444C2×#67—181no—
445C2×#67—181no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—91no—
450C22×Dic3—91no—
451C22×Dic3—181no—
452C2×D12—91no—
453C2×D12—91no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—91no—
458C2×C4×D3—91no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—181no—
462C2×Dic6—31no—
463C2×Dic6—31no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—61no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C22⋊C4—31no—
473C3×C22⋊C4—31no—
474C3×C22⋊C4—31no—
475C3×C22⋊C4—31no—
476C3×C22⋊C4—61no—
477C3×C22⋊C4—61no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C42—91no—
482C3×C42—91no—
483#217—31no—
484#217—31no—
485#217—31no—
486#217—91no—
487#217—91no—
488#217—181no—
489(C2×D3)⋊C4—31no—
490(C2×D3)⋊C4—31no—
491(C2×D3)⋊C4—31no—
492(C2×D3)⋊C4—91no—
493(C2×D3)⋊C4—91no—
494(C2×D3)⋊C4—91no—
495(C2×D3)⋊C4—91no—
496(C2×D3)⋊C4—91no—
497(C2×D3)⋊C4—91no—
498(C2×D3)⋊C4—91no—
499(C2×D3)⋊C4—91no—
500(C2×D3)⋊C4—91no—
501(C2×D3)⋊C4—91no—
502(C2×D3)⋊C4—91no—
503(C2×D3)⋊C4—91no—
504(C2×D3)⋊C4—91no—
505(C2×D3)⋊C4—181no—
506(C2×D3)⋊C4—181no—
507(C2×D3)⋊C4—181no—
508(C2×D3)⋊C4—181no—
509(C2×D3)⋊C4—181no—
510(C2×D3)⋊C4—181no—
511(C2×D3)⋊C4—361no—
512(C2×D3)⋊C4D3211yescharacteristic
513(C2×D3)⋊C4D3211yescharacteristic
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—61no—
520C4⋊Dic3—61no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528C4⋊Dic3—91no—
529C4⋊Dic3—181no—
530C4⋊Dic3—181no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—31no—
535Dic3⋊C4—31no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
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—181no—
553Dic3⋊C4—181no—
554Dic3⋊C4D3211yescharacteristic
555C4×Dic3—31no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—61no—
560C22×C32—21no—
561C22×C32—21no—
562C22×C32—21no—
563C22×C32—32no—
564C22×C32—41no—
565C22×C32—61no—
566C22×C32—61no—
567C22×C32—61no—
568C22×C32—61no—
569C22×C32—61no—
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C22×C32C23×D311yescharacteristic
573C2×C3⋊D3—61no—
574C2×C3⋊D3—62no—
575C2×C3⋊D3—61no—
576C2×C3⋊D3—61no—
577C2×C3⋊D3—61no—
578C2×C3⋊D3—61no—
579C2×C3⋊D3—61no—
580C2×C3⋊D3—61no—
581C2×C3⋊D3—61no—
582C2×C3⋊D3—61no—
583C2×C3⋊D3—121no—
584C2×C3⋊D3—121no—
585C2×C3⋊D3—122no—
586C2×C3⋊D3—121no—
587C2×C3⋊D3—121no—
588C2×C3⋊D3—121no—
589C2×C3⋊D3—121no—
590C2×C3⋊D3—121no—
591C2×C3⋊D3—121no—
592C2×C3⋊D3—241no—
593C2×C3⋊D3—241no—
594C2×C3×D3—21no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—21no—
598C2×C3×D3—21no—
599C2×C3×D3—21no—
600C2×C3×D3—21no—
601C2×C3×D3—21no—
602C2×C3×D3—21no—
603C2×C3×D3—21no—
604C2×C3×D3—22no—
605C2×C3×D3—41no—
606C2×C3×D3—41no—
607C2×C3×D3—41no—
608C2×C3×D3—41no—
609C2×C3×D3—41no—
610C2×C3×D3#23512yes—
611C2×C3×D3#23912yes—
612C32×C4—21no—
613C32×C4—21no—
614C32×C4—21no—
615C32×C4—41no—
616C32×C4—41no—
617C32×C4—41no—
618C32×C4—61no—
619C32×C4—61no—
620C32×C4—61no—
621C32×C4—61no—
622C32×C4—81no—
623C3⋊Dic3—21no—
624C3⋊Dic3—21no—
625C3⋊Dic3—21no—
626C3⋊Dic3—21no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—61no—
630C3⋊Dic3—61no—
631C3⋊Dic3—61no—
632C3⋊Dic3—121no—
633C3⋊Dic3—121no—
634C3⋊Dic3—121no—
635C3⋊Dic3—241no—
636C3×Dic3—21no—
637C3×Dic3—21no—
638C3×Dic3—21no—
639C3×Dic3—21no—
640C3×Dic3—21no—
641C3×Dic3—21no—
642C3×Dic3—21no—
643C3×Dic3—21no—
644C3×Dic3—41no—
645C3×Dic3—41no—
646C3×Dic3—41no—
647C3×Dic3—41no—
648C3×Dic3—61no—
649C3×Dic3—61no—
650C3×Dic3—61no—
651C3×Dic3—61no—
652C3×Dic3—61no—
653C3×Dic3—61no—
654C3×Dic3—61no—
655C3×Dic3—61no—
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—121no—
665C3×Dic3—121no—
666#126—91no—
667#126—271no—
668#125—271no—
669#125—271no—
670#123—271no—
671#123—271no—
672#123—271no—
673#123—271no—
674C22⋊Q8—91no—
675C22⋊Q8—271no—
676C22⋊Q8—271no—
677#121—271no—
678C4×D4—91no—
679C4×D4—271no—
680C2×C4⋊C4—271no—
681C33#53911yescharacteristic, complemented, Sylow
682C23×C3—31no—
683C23×C3—31no—
684C23×C3—31no—
685C23×C3—31no—
686C23×C3—61no—
687C23×C3—61no—
688C22×D3—91no—
689C22×D3—91no—
690C22×D3—91no—
691C22×D3—181no—
692C22×D3—181no—
693C22×D3—181no—
694C22×D3—361no—
695C22×D3C2×D3211yescharacteristic
696C22×D3C2×D3211yescharacteristic
697C3×Q8—361no—
698C3×D4—182no—
699C2×C3×C4—21no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
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—41no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—61no—
714C2×C3×C4—61no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—91no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—91no—
721C2×C3×C4—361no—
722C2×C3×C4—361no—
723C2×C3×C4—361no—
724C2×C3×C4C2×D3211yescharacteristic
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C2×D3211yescharacteristic
727#67—62no—
728#67—62no—
729#67—182no—
730#67—182no—
731#67—362no—
732#67—361no—
733#67—361no—
734#67—362no—
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—31no—
744C2×Dic3—31no—
745C2×Dic3—31no—
746C2×Dic3—31no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—91no—
754C2×Dic3—91no—
755C2×Dic3—91no—
756C2×Dic3—121no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—181no—
760C2×Dic3—181no—
761C2×Dic3—181no—
762C2×Dic3—182no—
763C2×Dic3—182no—
764C2×Dic3—361no—
765C2×Dic3—362no—
766C2×Dic3C2×D3211yescharacteristic
767C2×Dic3C2×D3211yescharacteristic
768C2×Dic3C2×D3211yescharacteristic
769C2×Dic3C2×D3211yescharacteristic
770D12—182no—
771D12—361no—
772C4×D3—121no—
773C4×D3—121no—
774C4×D3—121no—
775C4×D3—182no—
776C4×D3—361no—
777C4×D3—361no—
778C4×D3—361no—
779C4×D3—362no—
780Dic6—121no—
781Dic6—121no—
782C2×C32—21no—
783C2×C32—21no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—41no—
792C2×C32—41no—
793C2×C32—41no—
794C2×C32—62no—
795C2×C32—121no—
796C2×C32C2×#23511yescharacteristic
797C2×C32#100411yescharacteristic
798C2×C32#100411yescharacteristic
799C2×C32C2×#23911yescharacteristic
800C2×C32D3×#4111yescharacteristic
801C2×C32#100911yescharacteristic
802C2×C32#101011yescharacteristic
803C2×C32#101011yescharacteristic
804C2×C32#101011yescharacteristic
805C3⋊D3—121no—
806C3⋊D3—122no—
807C3⋊D3—121no—
808C3⋊D3—121no—
809C3⋊D3—241no—
810C3⋊D3—241no—
811C3⋊D3—242no—
812C3×D3—22no—
813C3×D3—22no—
814C3×D3—42no—
815C3×D3—41no—
816C3×D3—41no—
817C3×D3—81no—
818C2×Q8—91no—
819C2×D4—91no—
820C2×D4—271no—
821C2×D4—271no—
822C22×C4—91no—
823C22×C4—91no—
824C22×C4—91no—
825C22×C4—271no—
826C22×C4—271no—
827C4⋊C4—31no—
828C4⋊C4—91no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—271no—
834C4⋊C4—271no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C22⋊C4—31no—
842C22⋊C4—31no—
843C22⋊C4—91no—
844C22⋊C4—91no—
845C22⋊C4—91no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C22⋊C4—271no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C42—91no—
852C42—91no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—21no—
856C22×C3—32no—
857C22×C3—32no—
858C22×C3—41no—
859C22×C3—62no—
860C22×C3—61no—
861C22×C3—61no—
862C22×C3—61no—
863C22×C3—61no—
864C22×C3—61no—
865C22×C3—61no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3C22×D3211yescharacteristic
876C22×C3C22×D3211yescharacteristic
877C22×C3C22×D3211yescharacteristic
878C2×D3—21no—
879C2×D3—21no—
880C2×D3—21no—
881C2×D3—21no—
882C2×D3—21no—
883C2×D3—182no—
884C2×D3—181no—
885C2×D3—181no—
886C2×D3—181no—
887C2×D3—181no—
888C2×D3—181no—
889C2×D3—181no—
890C2×D3—181no—
891C2×D3—181no—
892C2×D3—181no—
893C2×D3—361no—
894C2×D3—361no—
895C2×D3—361no—
896C2×D3—361no—
897C2×D3—361no—
898C2×D3—361no—
899C2×D3—361no—
900C2×D3—361no—
901C2×D3—362no—
902C2×D3—721no—
903C2×D3—721no—
904C2×D3#379912yes—
905C3×C4—21no—
906C3×C4—21no—
907C3×C4—21no—
908C3×C4—41no—
909C3×C4—41no—
910C3×C4—41no—
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—81no—
920C3×C4—121no—
921C3×C4—121no—
922C3×C4—121no—
923C3×C4—121no—
924C3×C4—181no—
925C3×C4—181no—
926C3×C4—181no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930Dic3—21no—
931Dic3—21no—
932Dic3—21no—
933Dic3—21no—
934Dic3—61no—
935Dic3—61no—
936Dic3—61no—
937Dic3—61no—
938Dic3—61no—
939Dic3—61no—
940Dic3—61no—
941Dic3—61no—
942Dic3—61no—
943Dic3—61no—
944Dic3—61no—
945Dic3—61no—
946Dic3—121no—
947Dic3—121no—
948Dic3—121no—
949Dic3—121no—
950Dic3—121no—
951Dic3—121no—
952Dic3—181no—
953Dic3—181no—
954Dic3—181no—
955Dic3—361no—
956Dic3—361no—
957Dic3—361no—
958Dic3—721no—
959C32—21no—
960C32—21no—
961C32—21no—
962C32—41no—
963C32#556411yescharacteristic, complemented
964C32#564511yescharacteristic, complemented
965C32#570711yescharacteristic, complemented
966C23—31no—
967C23—31no—
968C23—271no—
969Q8—361no—
970D4—182no—
971D4—542no—
972D4—1081no—
973C2×C4—31no—
974C2×C4—31no—
975C2×C4—31no—
976C2×C4—31no—
977C2×C4—91no—
978C2×C4—91no—
979C2×C4—91no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—91no—
983C2×C4—271no—
984C2×C4—361no—
985C2×C4—361no—
986C2×C4—361no—
987C2×C4—542no—
988C2×C4—1081no—
989C2×C4D3311yescharacteristic
990C2×C3—21no—
991C2×C3—21no—
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—41no—
1000C2×C3—41no—
1001C2×C3—41no—
1002C2×C3—62no—
1003C2×C3—62no—
1004C2×C3—122no—
1005C2×C3—121no—
1006C2×C3—121no—
1007C2×C3—241no—
1008C2×C3C2×#379911yescharacteristic
1009C2×C3D3×#23511yescharacteristic
1010C2×C3#6430711yescharacteristic
1011C2×C3#6430911yescharacteristic
1012C2×C3#6430911yescharacteristic
1013C2×C3#6430911yescharacteristic
1014C2×C3#6431311yescharacteristic
1015C2×C3#6431411yescharacteristic
1016C2×C3D3×#23911yescharacteristic
1017D3—22no—
1018D3—41no—
1019D3—362no—
1020D3—361no—
1021D3—361no—
1022D3—361no—
1023D3—721no—
1024D3—721no—
1025D3—722no—
1026C22—32no—
1027C22—61no—
1028C22—61no—
1029C22—61no—
1030C22—61no—
1031C22—61no—
1032C22—541no—
1033C22—541no—
1034C22—541no—
1035C22C2×D3311yescharacteristic
1036C4—21no—
1037C4—61no—
1038C4—61no—
1039C4—61no—
1040C4—61no—
1041C4—181no—
1042C4—181no—
1043C4—181no—
1044C4—181no—
1045C4—181no—
1046C4—181no—
1047C4—541no—
1048C3—21no—
1049C3—21no—
1050C3—21no—
1051C3—41no—
1052C3#1059409011yescharacteristic, complemented
1053C3#1059424111yescharacteristic, complemented
1054C3#1059443911yescharacteristic, complemented
1055C2—62no—
1056C2—121no—
1057C2—1081no—
1058C2#1172438111yescharacteristic
1059C2D3×#379911yescharacteristic
1060C2#1172442811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radical#11722958C2
hypercenterC2×C4D33
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. #11723680C2semidirect
2. #11723479C2semidirect
3. #11723446C2semidirect
4. #11723422C2semidirect
5. C3×#63902C2semidirect
6. C3×#63893C2semidirect
7. C3×#63861C2semidirect
8. #11723011C2semidirect
9. #11722989C2semidirect
10. #11722987C2semidirect
11. #11722977C2semidirect
12. #11722969C2semidirect
14. #11722932C2semidirect
15. D3×#3724C2semidirect
73. #63902D3semidirect
74. #63893D3semidirect
95. #63861D3semidirect
681. C33#539semidirect
963. C32#5564semidirect
964. C32#5645semidirect
965. C32#5707semidirect
1052. C3#10594090semidirect
1053. C3#10594241semidirect
1054. C3#10594439semidirect

Maximal subgroups

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

subgroupindex
#117236802
#117234792
#117234462
#117234222
C3×#639022
C3×#638932
C3×#638612
#117230112
#117229892
#117229872
#117229772
#117229692
#117229582
#117229322
D3×#37242
#105944393
#105942413
#105940903