Finite Group Databasebeta

← #13178253

Subgroups — #13178253

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
1C3×#64092C211yesmaximal, characteristic, complemented
2C3×#64092C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723725C211yesmaximal, characteristic
6#11723720C211yesmaximal, characteristic, complemented
7#11723716C211yesmaximal, characteristic, complemented
8#11723694C211yesmaximal, characteristic, complemented
9#11723689C211yesmaximal, characteristic, complemented
10#11723688C211yesmaximal, characteristic, complemented
11#11723684C211yesmaximal, characteristic, complemented
12#11723675C211yesmaximal, characteristic, complemented
13#11723674C211yesmaximal, characteristic, complemented
14#11723669C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10594129—31nomaximal
17#10594121—31nomaximal
18#10594041—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64092D311yescharacteristic, complemented
55#64092D311yescharacteristic, complemented
56#64087D311yescharacteristic, complemented
57C3×#883—31no—
58C3×#883—31no—
59C3×#883—31no—
60C3×#883—31no—
61C3×#883—61no—
62C3×#883—61no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#67⋊Dic3—31no—
67Dic3×#67—31no—
68#63971—31no—
69#63970—31no—
70#63966—31no—
71#63962—31no—
72#63961—31no—
73#63958—31no—
74#63956—31no—
75#63956—31no—
76#63956—31no—
77#63952—31no—
78#63905—31no—
79#63904—31no—
80#63900—31no—
81#63896—31no—
82D3×C4⋊Dic3—31no—
83D3×C4⋊Dic3—31no—
84#63888—31no—
85#63887—31no—
86#63881—31no—
87#63879—31no—
88#63871—31no—
89#63861—31no—
90#63858—31no—
91#63857—31no—
92#63856—31no—
93#63853—31no—
94#63850—31no—
95#63848—31no—
96#63847—31no—
97#63847—31no—
98#63846—31no—
99#63846—31no—
100#63845—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C3×#638—22no—
108C3×#638—41no—
109C2×C3×C3⋊Dic3—41no—
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C3×C4×C3⋊D3—22no—
121C3×C4×C3⋊D3—41no—
122C3×#634—41no—
123#6295—22no—
124#6294—41no—
125#6294—41no—
126#5665—91no—
127#5660—91no—
128#5638—91no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3C2×D311yescharacteristic
132C2×C4×C3⋊D3C2×D311yescharacteristic
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×#634C2×D311yescharacteristic
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—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—61no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—61no—
149C2×C3×C4×D3—61no—
150C2×C3×Dic6—31no—
151C2×C3×Dic6—31no—
152C2×C3×Dic6—61no—
153C2×#626—31no—
154C2×#626—31no—
155C2×#625—31no—
156C2×#624—31no—
157C2×#624—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C2×D3×Dic3—31no—
162C32×C22⋊C4—21no—
163C32×C22⋊C4—21no—
164C32×C22⋊C4—21no—
165C32×C22⋊C4—41no—
166C32×C22⋊C4C2×D311yescharacteristic
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic
169#3757C2×D311yescharacteristic
170#3757C2×D311yescharacteristic
171#3757C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173#3752C2×D311yescharacteristic
174C4⋊(C3⋊Dic3)C2×D311yescharacteristic
175C4⋊(C3⋊Dic3)C2×D311yescharacteristic
176C4⋊(C3⋊Dic3)C2×D311yescharacteristic
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179#3750C2×D311yescharacteristic
180#3750C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—61no—
188C3×#217—61no—
189C3×#217—61no—
190C3×(C2×D3)⋊C4—31no—
191C3×(C2×D3)⋊C4—31no—
192C3×(C2×D3)⋊C4—31no—
193C3×(C2×D3)⋊C4—31no—
194C3×(C2×D3)⋊C4—61no—
195C3×(C2×D3)⋊C4—61no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—31no—
201C3×C4⋊Dic3—31no—
202C3×C4⋊Dic3—61no—
203C3×C4⋊Dic3—61no—
204C3×C4⋊Dic3—61no—
205C3×Dic3⋊C4—31no—
206C3×Dic3⋊C4—31no—
207C3×Dic3⋊C4—31no—
208C3×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—61no—
214C3×Dic3⋊C4—61no—
215C3×Dic3⋊C4—61no—
216C3×Dic3⋊C4—61no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—31no—
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—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
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—
266C33×C4—21no—
267C33×C4—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—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×#123—91no—
279C3×#123—91no—
280C3×C22⋊Q8—91no—
281#946—91no—
282#946—91no—
283#939—91no—
284#938—91no—
285#935—91no—
286D4×Dic3—91no—
287#929—91no—
288#929—91no—
289C4×#67—91no—
290C4×#67—91no—
291C2×C4⋊Dic3—91no—
292#924—91no—
293#898—91no—
294#898—91no—
295#897—91no—
296#896—91no—
297#894—91no—
298#893—91no—
299D3×C4⋊C4—91no—
300D3×C4⋊C4—91no—
301#890—91no—
302#890—91no—
303#889—91no—
304#889—91no—
305#889—91no—
306#889—91no—
307#886—91no—
308#884—91no—
309#883—31no—
310#883—31no—
311#883—31no—
312#883—31no—
313#883—61no—
314#883—61no—
315#883—91no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#879—91no—
319#879—91no—
320#879—91no—
321#879—91no—
322#878—31no—
323#878—31no—
324#878—61no—
325#878—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—21no—
342C2×C32×C4—21no—
343C2×C32×C4—21no—
344C2×C32×C4—21no—
345C2×C32×C4—21no—
346C2×C32×C4—21no—
347C2×C32×C4—41no—
348C2×C32×C4—41no—
349C2×C32×C4C22×D311yescharacteristic
350C2×C32×C4C22×D311yescharacteristic
351C2×C32×C4C22×D311yescharacteristic
352C2×C32×C4C22×D311yescharacteristic
353C2×C32×C4C22×D311yescharacteristic
354C2×C32×C4C22×D311yescharacteristic
355#638—22no—
356#638—41no—
357C2×C3⋊Dic3—41no—
358C2×C3⋊Dic3C22×D311yescharacteristic
359C2×C3⋊Dic3C22×D311yescharacteristic
360C2×C3⋊Dic3C22×D311yescharacteristic
361C2×C3⋊Dic3C22×D311yescharacteristic
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—22no—
369C4×C3⋊D3—41no—
370#634—41no—
371C3×#67—62no—
372C3×#67—62no—
373C3×#67—122no—
374C3×#67—121no—
375C3×#67—121no—
376C3×#67—122no—
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—31no—
388C2×C3×Dic3—31no—
389C2×C3×Dic3—31no—
390C2×C3×Dic3—31no—
391C2×C3×Dic3—31no—
392C2×C3×Dic3—31no—
393C2×C3×Dic3—31no—
394C2×C3×Dic3—31no—
395C2×C3×Dic3—31no—
396C2×C3×Dic3—31no—
397C2×C3×Dic3—61no—
398C2×C3×Dic3—61no—
399C2×C3×Dic3—61no—
400C2×C3×Dic3—61no—
401C2×C3×Dic3—61no—
402C2×C3×Dic3—61no—
403C2×C3×Dic3—61no—
404C2×C3×Dic3—61no—
405C2×C3×Dic3—61no—
406C2×C3×Dic3—61no—
407C2×C3×Dic3—121no—
408C2×C3×Dic3—121no—
409C2×C3×Dic3—122no—
410C3×C4×D3—62no—
411C3×C4×D3—62no—
412C3×C4×D3—122no—
413C3×C4×D3—121no—
414C3×C4×D3—121no—
415C3×C4×D3—122no—
416C3×Dic6—121no—
417C3×Dic6—121no—
418C3×Dic6—122no—
419#626—62no—
420#626—62no—
421#625—62no—
422#624—121no—
423#624—121no—
424D3×Dic3—121no—
425D3×Dic3—121no—
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×Q8—91no—
436C2×C3×D4—91no—
437C2×C3×D4—91no—
438C22×C3×C4—91no—
439C22×C3×C4—91no—
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—31no—
450C22×Dic3—31no—
451C22×Dic3—61no—
452C22×Dic3—91no—
453C22×Dic3—91no—
454C2×D12—91no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—31no—
458C2×C4×D3—31no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—61no—
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×C4⋊C4—91no—
475C3×C22⋊C4—21no—
476C3×C22⋊C4—21no—
477C3×C22⋊C4—21no—
478C3×C22⋊C4—41no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4D3211yescharacteristic
485C3×C22⋊C4D3211yescharacteristic
486C3×C22⋊C4D3211yescharacteristic
487#217—31no—
488#217—31no—
489#217—31no—
490#217—31no—
491#217—31no—
492#217—31no—
493#217—61no—
494#217—61no—
495#217—61no—
496#217—91no—
497#217—91no—
498#217—91no—
499#217—91no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—31no—
504(C2×D3)⋊C4—61no—
505(C2×D3)⋊C4—61no—
506(C2×D3)⋊C4—91no—
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—91no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—61no—
521C4⋊Dic3—61no—
522C4⋊Dic3—61no—
523C4⋊Dic3—91no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528C4⋊Dic3—91no—
529C4⋊Dic3—91no—
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—61no—
539Dic3⋊C4—61no—
540Dic3⋊C4—61no—
541Dic3⋊C4—61no—
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—91no—
555Dic3⋊C4—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
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#23712yes—
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—21no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—21no—
618C32×C4—21no—
619C32×C4—21no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—41no—
624C32×C4—41no—
625C32×C4—41no—
626C32×C4—81no—
627C32×C4—81no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3—21no—
636C3⋊Dic3—21no—
637C3⋊Dic3—21no—
638C3×Dic3—62no—
639C3×Dic3—61no—
640C3×Dic3—61no—
641C3×Dic3—61no—
642C3×Dic3—61no—
643C3×Dic3—61no—
644C3×Dic3—61no—
645C3×Dic3—61no—
646C3×Dic3—61no—
647C3×Dic3—61no—
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—121no—
660C3×Dic3—121no—
661C3×Dic3—121no—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668#126—271no—
669#126—271no—
670#125—271no—
671#125—271no—
672#123—91no—
673#123—91no—
674#123—271no—
675#123—271no—
676C22⋊Q8—91no—
677C22⋊Q8—271no—
678C22⋊Q8—271no—
679#121—271no—
680C4×D4—271no—
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×Q8—361no—
700C3×D4—182no—
701C3×D4—361no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—91no—
711C2×C3×C4—91no—
712C2×C3×C4—91no—
713C2×C3×C4—91no—
714C2×C3×C4—91no—
715C2×C3×C4—91no—
716C2×C3×C4—91no—
717C2×C3×C4—91no—
718C2×C3×C4—91no—
719C2×C3×C4—91no—
720C2×C3×C4—182no—
721C2×C3×C4—361no—
722C2×C3×C4—361no—
723C2×C3×C4C2×D3211yescharacteristic
724C2×C3×C4C2×D3211yescharacteristic
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C2×D3211yescharacteristic
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729#67—62no—
730#67—62no—
731#67—122no—
732#67—121no—
733#67—121no—
734#67—122no—
735#67—182no—
736#67—182no—
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—31no—
748C2×Dic3—31no—
749C2×Dic3—31no—
750C2×Dic3—31no—
751C2×Dic3—31no—
752C2×Dic3—31no—
753C2×Dic3—31no—
754C2×Dic3—31no—
755C2×Dic3—31no—
756C2×Dic3—31no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—61no—
763C2×Dic3—61no—
764C2×Dic3—61no—
765C2×Dic3—61no—
766C2×Dic3—61no—
767C2×Dic3—121no—
768C2×Dic3—121no—
769C2×Dic3—122no—
770C2×Dic3—361no—
771C2×Dic3—361no—
772D12—182no—
773C4×D3—62no—
774C4×D3—62no—
775C4×D3—122no—
776C4×D3—121no—
777C4×D3—121no—
778C4×D3—122no—
779C4×D3—361no—
780C4×D3—361no—
781C4×D3—361no—
782C4×D3—361no—
783Dic6—121no—
784Dic6—121no—
785Dic6—122no—
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×#23711yescharacteristic
806C2×C32#100411yescharacteristic
807C2×C32#100411yescharacteristic
808C2×C32#100711yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32D3×#4111yescharacteristic
811C2×C32#100911yescharacteristic
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—91no—
823C2×D4—91no—
824C2×D4—91no—
825C2×D4—271no—
826C22×C4—91no—
827C22×C4—91no—
828C22×C4—91no—
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—91no—
838C4⋊C4—271no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C4⋊C4—271no—
844C4⋊C4—271no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—91no—
848C22⋊C4—91no—
849C22⋊C4—91no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4—271no—
853C22⋊C4—271no—
854C22⋊C4#111311yescharacteristic
855C42—271no—
856C42—271no—
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—21no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—21no—
913C3×C4—21no—
914C3×C4—21no—
915C3×C4—41no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—81no—
922C3×C4—81no—
923C3×C4—181no—
924C3×C4—181no—
925C3×C4—181no—
926C3×C4—181no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931C3×C4—181no—
932C3×C4—181no—
933Dic3—62no—
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—61no—
947Dic3—61no—
948Dic3—61no—
949Dic3—61no—
950Dic3—61no—
951Dic3—61no—
952Dic3—61no—
953Dic3—61no—
954Dic3—121no—
955Dic3—121no—
956Dic3—121no—
957Dic3—121no—
958Dic3—121no—
959Dic3—121no—
960Dic3—121no—
961Dic3—121no—
962Dic3—121no—
963C32—21no—
964C32—21no—
965C32—21no—
966C32—41no—
967C32#563811yescharacteristic, complemented
968C32#566011yescharacteristic, complemented
969C32#566511yescharacteristic, complemented
970C23—91no—
971C23—91no—
972C23C2×#111311yescharacteristic
973Q8—361no—
974D4—182no—
975D4—361no—
976D4—542no—
977C2×C4—91no—
978C2×C4—91no—
979C2×C4—91no—
980C2×C4—91no—
981C2×C4—91no—
982C2×C4—91no—
983C2×C4—91no—
984C2×C4—91no—
985C2×C4—91no—
986C2×C4—91no—
987C2×C4—182no—
988C2×C4—361no—
989C2×C4—361no—
990C2×C4—1081no—
991C2×C4—1081no—
992C2×C4C2×#111311yescharacteristic
993C2×C4C2×#111311yescharacteristic
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#6429711yescharacteristic
1016C2×C3#6429711yescharacteristic
1017C2×C3#6429811yescharacteristic
1018C2×C3D3×#23711yescharacteristic
1019C2×C3D3×#23711yescharacteristic
1020C2×C3#6431211yescharacteristic
1021C2×C3#6431311yescharacteristic
1022C2×C3#6431411yescharacteristic
1023C2×C3#6431411yescharacteristic
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—
1039C22C22×#111311yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—181no—
1043C4—181no—
1044C4—181no—
1045C4—181no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—181no—
1052C3—21no—
1053C3—21no—
1054C3—21no—
1055C3—41no—
1056C3#1059404111yescharacteristic, complemented
1057C3#1059412111yescharacteristic, complemented
1058C3#1059412911yescharacteristic, complemented
1059C2—41no—
1060C2—182no—
1061C2—361no—
1062C2#1172461411yescharacteristic
1063C2#1172462211yescharacteristic
1064C2#1172462311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723725C2
hypercenterC22⋊C4#1113
hypocenterC33#539
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#64092C2semidirect
2. C3×#64092C2semidirect
3. C3×#64087C2semidirect
4. #11723726C2semidirect
6. #11723720C2semidirect
7. #11723716C2semidirect
8. #11723694C2semidirect
9. #11723689C2semidirect
10. #11723688C2semidirect
11. #11723684C2semidirect
12. #11723675C2semidirect
13. #11723674C2semidirect
14. #11723669C2semidirect
15. #11723669C2semidirect
54. #64092D3semidirect
55. #64092D3semidirect
56. #64087D3semidirect
683. C33#539semidirect
967. C32#5638semidirect
968. C32#5660semidirect
969. C32#5665semidirect
1056. C3#10594041semidirect
1057. C3#10594121semidirect
1058. C3#10594129semidirect

Maximal subgroups

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

subgroupindex
C3×#640922
C3×#640872
#117237262
#117237252
#117237202
#117237162
#117236942
#117236892
#117236882
#117236842
#117236752
#117236742
#117236692
#105941293
#105941213
#105940413