Finite Group Databasebeta

← #13178205

Subgroups — #13178205

Order 1728.

1202 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64092C211yesmaximal, characteristic, complemented
2C3×#64090C211yesmaximal, characteristic, complemented
3C3×#64088C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723725C211yesmaximal, characteristic
6#11723718C211yesmaximal, characteristic, complemented
7#11723715C211yesmaximal, characteristic, complemented
8#11723694C211yesmaximal, characteristic, complemented
9#11723692C211yesmaximal, characteristic, complemented
10#11723684C211yesmaximal, characteristic, complemented
11C4×#6294C211yesmaximal, characteristic, complemented
12#11723676C211yesmaximal, characteristic, complemented
13#11723669C211yesmaximal, characteristic, complemented
14#11723667C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10594130—31nomaximal
17#10594107—31nomaximal
18#10594098—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic
24C2×#6296C2211yescharacteristic
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×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41C3×C4×C3⋊Dic3C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88813C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64092D311yescharacteristic, complemented
55#64090D311yescharacteristic, complemented
56#64088D311yescharacteristic, complemented
57C3×#883—31no—
58C3×#883—31no—
59C3×#883—61no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4—31no—
62C3×#67⋊C4—61no—
63C3×#879—31no—
64C3×#879—31no—
65C3×#879—61no—
66#67⋊Dic3—31no—
67Dic3×#67—31no—
68#63971—31no—
69#63970—31no—
70#63959—31no—
71#63959—31no—
72#63958—31no—
73#63957—31no—
74#63955—31no—
75#63955—31no—
76#63953—31no—
77#63952—31no—
78#63905—31no—
79#63904—31no—
80#63899—31no—
81#63895—31no—
82#63893—31no—
83C4×#624—31no—
84#63881—31no—
85#63879—31no—
86C4×D3×Dic3—31no—
87C4×D3×Dic3—31no—
88#63868—31no—
89#63862—31no—
90#63859—31no—
91#63853—31no—
92#63850—31no—
93#63849—31no—
94#63847—31no—
95#63846—31no—
96#63845—31no—
97#63841—31no—
98#63841—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C2×C33×C4C2311yescharacteristic
107C3×#638—22no—
108C3×#638—22no—
109C2×C3×C3⋊Dic3—22no—
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—22no—
122#6296—22no—
123#6295—22no—
124#6294—22no—
125#6294—22no—
126#5706—91no—
127#5649—91no—
128#5557—91no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3C2×D311yescharacteristic
132C2×C4×C3⋊D3C2×D311yescharacteristic
133C2×C4×C3⋊D3C2×D311yescharacteristic
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—61no—
139C2×C3×#67—61no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—61no—
143C2×C3×C4×D3—31no—
144C2×C3×C4×D3—31no—
145C2×C3×C4×D3—31no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—61no—
148C2×C3×C4×D3—61no—
149C2×#627—31no—
150C2×#627—31no—
151C2×#627—31no—
152C2×#626—31no—
153C2×#626—31no—
154C2×#625—31no—
155C2×#624—31no—
156C2×#624—31no—
157C2×D3×Dic3—31no—
158C2×D3×Dic3—31no—
159C2×D3×Dic3—31no—
160C2×D3×Dic3—31no—
161C32×C22⋊C4—21no—
162C32×C22⋊C4—21no—
163C32×C22⋊C4—21no—
164C32×C22⋊C4—41no—
165C32×C22⋊C4C2×D311yescharacteristic
166C32×C22⋊C4C2×D311yescharacteristic
167C32×C22⋊C4C2×D311yescharacteristic
168#3757C2×D311yescharacteristic
169#3757C2×D311yescharacteristic
170#3757C2×D311yescharacteristic
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic
173C4⋊(C3⋊Dic3)C2×D311yescharacteristic
174C4⋊(C3⋊Dic3)C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177#3750C2×D311yescharacteristic
178#3750C2×D311yescharacteristic
179C4×C3⋊Dic3C2×D311yescharacteristic
180C4×C3⋊Dic3C2×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—61no—
201C3×C4⋊Dic3—61no—
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×Dic3⋊C4—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—61no—
211C3×Dic3⋊C4—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—61no—
219C3×C4×Dic3—61no—
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—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—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—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—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#4112yes—
277C3×C3⋊Dic3#4112yes—
278C3×#126—91no—
279C3×#123—91no—
280C3×C4×D4—91no—
281#939—91no—
282#938—91no—
283#936—91no—
284D4×Dic3—91no—
285#929—91no—
286C4×#67—91no—
287C4×#67—91no—
288#926—91no—
289#926—91no—
290C2×C4×Dic3—91no—
291#898—91no—
292#897—91no—
293#896—91no—
294#894—91no—
295#893—91no—
296#892—91no—
297#892—91no—
298#890—91no—
299#889—91no—
300#889—91no—
301#887—91no—
302#887—91no—
303#885—91no—
304#885—91no—
305#884—91no—
306#883—31no—
307#883—31no—
308#883—61no—
309#883—91no—
310#67⋊C4—31no—
311#67⋊C4—31no—
312#67⋊C4—61no—
313#67⋊C4—91no—
314#67⋊C4—91no—
315#879—31no—
316#879—31no—
317#879—61no—
318#879—91no—
319#878—91no—
320#877—91no—
321#877—91no—
322#876—91no—
323C42×D3—91no—
324C42×D3—91no—
325C4×Dic6—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—22no—
357C2×C3⋊Dic3—22no—
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—22no—
370C3×#67—62no—
371C3×#67—62no—
372C3×#67—62no—
373C3×#67—62no—
374C3×#67—64no—
375C3×#67—122no—
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—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—61no—
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—62no—
407C2×C3×Dic3—62no—
408C2×C3×Dic3—122no—
409C3×C4×D3—62no—
410C3×C4×D3—62no—
411C3×C4×D3—62no—
412C3×C4×D3—62no—
413C3×C4×D3—122no—
414C3×C4×D3—122no—
415#627—62no—
416#627—62no—
417#627—62no—
418#626—62no—
419#626—62no—
420#625—62no—
421#624—62no—
422#624—62no—
423D3×Dic3—62no—
424D3×Dic3—62no—
425D3×Dic3—62no—
426D3×Dic3—62no—
427#529—271noSylow
428C2×C33—41no—
429C2×C33C2×#4111yescharacteristic
430C2×C33C2×#4111yescharacteristic
431C2×C33C2×#4111yescharacteristic
432C3×C3⋊D3—22no—
433C3×C3⋊D3—41no—
434C2×C3×D4—91no—
435C2×C3×D4—91no—
436C22×C3×C4—91no—
437C22×C3×C4—91no—
438C22×C3×C4—91no—
439C2×#67—31no—
440C2×#67—31no—
441C2×#67—31no—
442C2×#67—31no—
443C2×#67—61no—
444C2×#67—61no—
445C2×#67—91no—
446C2×#67—91no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—61no—
450C22×Dic3—91no—
451C22×Dic3—91no—
452C2×D12—91no—
453C2×C4×D3—31no—
454C2×C4×D3—31no—
455C2×C4×D3—31no—
456C2×C4×D3—31no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—91no—
460C2×C4×D3—91no—
461C2×C4×D3—91no—
462C2×C4×D3—91no—
463C2×Dic6—91no—
464C2×Dic6—91no—
465C2×Dic6—91no—
466C3×C4⋊C4—91no—
467C3×C4⋊C4—91no—
468C3×C4⋊C4—91no—
469C3×C4⋊C4—91no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C22⋊C4—21no—
473C3×C22⋊C4—21no—
474C3×C22⋊C4—21no—
475C3×C22⋊C4—41no—
476C3×C22⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4D3211yescharacteristic
482C3×C22⋊C4D3211yescharacteristic
483C3×C22⋊C4D3211yescharacteristic
484C3×C42—91no—
485C3×C42—91no—
486#217—31no—
487#217—31no—
488#217—31no—
489#217—31no—
490#217—31no—
491#217—31no—
492#217—61no—
493#217—61no—
494#217—61no—
495#217—91no—
496#217—91no—
497#217—91no—
498#217—91no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—31no—
503(C2×D3)⋊C4—61no—
504(C2×D3)⋊C4—61no—
505(C2×D3)⋊C4—91no—
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—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—61no—
518C4⋊Dic3—61no—
519C4⋊Dic3—91no—
520C4⋊Dic3—91no—
521C4⋊Dic3—91no—
522C4⋊Dic3—91no—
523Dic3⋊C4—31no—
524Dic3⋊C4—31no—
525Dic3⋊C4—31no—
526Dic3⋊C4—31no—
527Dic3⋊C4—31no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—61no—
532Dic3⋊C4—61no—
533Dic3⋊C4—61no—
534Dic3⋊C4—61no—
535Dic3⋊C4—91no—
536Dic3⋊C4—91no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—61no—
548C4×Dic3—61no—
549C4×Dic3—91no—
550C4×Dic3—91no—
551C4×Dic3—91no—
552C4×Dic3—91no—
553C4×Dic3—91no—
554C4×Dic3—91no—
555C4×Dic3—91no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C22×C32—21no—
562C22×C32—22no—
563C22×C32—21no—
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—41no—
575C22×C32—41no—
576C22×C32—41no—
577C22×C32—42no—
578C22×C32—41no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—41no—
584C22×C32—81no—
585C22×C32—81no—
586C22×C32C23×D311yescharacteristic
587C22×C32C23×D311yescharacteristic
588C22×C32C23×D311yescharacteristic
589C2×C3⋊D3—21no—
590C2×C3⋊D3—21no—
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3#23712yes—
595C2×C3×D3—32no—
596C2×C3×D3—32no—
597C2×C3×D3—62no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—62no—
603C2×C3×D3—61no—
604C2×C3×D3—61no—
605C2×C3×D3—61no—
606C2×C3×D3—61no—
607C2×C3×D3—61no—
608C2×C3×D3—61no—
609C2×C3×D3—121no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C32×C4—21no—
614C32×C4—21no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—21no—
618C32×C4—21no—
619C32×C4—41no—
620C32×C4—41no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—41no—
624C32×C4—41no—
625C32×C4—81no—
626C32×C4—81no—
627C3⋊Dic3—21no—
628C3⋊Dic3—21no—
629C3⋊Dic3—21no—
630C3⋊Dic3—21no—
631C3⋊Dic3—21no—
632C3⋊Dic3—21no—
633C3⋊Dic3—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3#23512yes—
636C3⋊Dic3#23712yes—
637C3×Dic3—32no—
638C3×Dic3—32no—
639C3×Dic3—32no—
640C3×Dic3—32no—
641C3×Dic3—62no—
642C3×Dic3—62no—
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—
667#126—91no—
668#126—271no—
669#125—271no—
670#124—271no—
671#123—91no—
672#123—271no—
673C22⋊Q8—271no—
674#121—271no—
675C4×Q8—271no—
676C4×D4—91no—
677C4×D4—271no—
678C4×D4—271no—
679#117—271no—
680#117—271no—
681C2×C42—271no—
682C33#52911yescharacteristic, complemented, Sylow
683C23×C3—21no—
684C23×C3—21no—
685C23×C3—21no—
686C23×C3—41no—
687C23×C3—91no—
688C23×C3—91no—
689C23×C3C2×D3211yescharacteristic
690C23×C3C2×D3211yescharacteristic
691C23×C3C2×D3211yescharacteristic
692C22×D3—31no—
693C22×D3—31no—
694C22×D3—31no—
695C22×D3—31no—
696C22×D3—61no—
697C22×D3—61no—
698C3×D4—182no—
699C3×D4—182no—
700C2×C3×C4—21no—
701C2×C3×C4—21no—
702C2×C3×C4—21no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—91no—
709C2×C3×C4—91no—
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—182no—
719C2×C3×C4—182no—
720C2×C3×C4—182no—
721C2×C3×C4C2×D3211yescharacteristic
722C2×C3×C4C2×D3211yescharacteristic
723C2×C3×C4C2×D3211yescharacteristic
724C2×C3×C4C2×D3211yescharacteristic
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C2×D3211yescharacteristic
727#67—62no—
728#67—62no—
729#67—62no—
730#67—62no—
731#67—64no—
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—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—61no—
756C2×Dic3—61no—
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—62no—
766C2×Dic3—62no—
767C2×Dic3—122no—
768C2×Dic3—182no—
769C2×Dic3—182no—
770D12—182no—
771C4×D3—62no—
772C4×D3—62no—
773C4×D3—62no—
774C4×D3—62no—
775C4×D3—122no—
776C4×D3—122no—
777C4×D3—182no—
778C4×D3—182no—
779C4×D3—182no—
780C4×D3—182no—
781Dic6—182no—
782Dic6—182no—
783Dic6—182no—
784C2×C32—21no—
785C2×C32—21no—
786C2×C32—21no—
787C2×C32—21no—
788C2×C32—21no—
789C2×C32—21no—
790C2×C32—21no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—41no—
794C2×C32—41no—
795C2×C32—41no—
796C2×C32—41no—
797C2×C32—42no—
798C2×C32—41no—
799C2×C32—41no—
800C2×C32—81no—
801C2×C32—81no—
802C2×C32—82no—
803C2×C32C2×#23511yescharacteristic
804C2×C32C2×#23711yescharacteristic
805C2×C32C2×#23711yescharacteristic
806C2×C32D3×#4111yescharacteristic
807C2×C32D3×#4111yescharacteristic
808C2×C32D3×#4111yescharacteristic
809C2×C32D3×#4111yescharacteristic
810C2×C32D3×#4111yescharacteristic
811C2×C32D3×#4111yescharacteristic
812C3⋊D3—22no—
813C3⋊D3—41no—
814C3×D3—62no—
815C3×D3—62no—
816C3×D3—122no—
817C3×D3—122no—
818C3×D3—121no—
819C3×D3—121no—
820C2×Q8—271no—
821C2×D4—91no—
822C2×D4—91no—
823C2×D4—271no—
824C22×C4—91no—
825C22×C4—91no—
826C22×C4—91no—
827C22×C4—271no—
828C22×C4—271no—
829C4⋊C4—91no—
830C4⋊C4—91no—
831C4⋊C4—91no—
832C4⋊C4—91no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—271no—
836C4⋊C4—271no—
837C4⋊C4—271no—
838C4⋊C4—271no—
839C22⋊C4—91no—
840C22⋊C4—91no—
841C22⋊C4—91no—
842C22⋊C4—91no—
843C22⋊C4—91no—
844C22⋊C4—271no—
845C22⋊C4—271no—
846C22⋊C4—271no—
847C22⋊C4—271no—
848C22⋊C4#111311yescharacteristic
849C42—91no—
850C42—91no—
851C42—271no—
852C42—271no—
853C42—271no—
854C42—271no—
855C22×C3—22no—
856C22×C3—21no—
857C22×C3—21no—
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—41no—
869C22×C3—41no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—41no—
873C22×C3—41no—
874C22×C3—41no—
875C22×C3—41no—
876C22×C3—42no—
877C22×C3—41no—
878C22×C3—81no—
879C22×C3—81no—
880C22×C3—92no—
881C22×C3—181no—
882C22×C3—181no—
883C22×C3—181no—
884C22×C3—181no—
885C22×C3—181no—
886C22×C3C22×D3211yescharacteristic
887C22×C3C22×D3211yescharacteristic
888C22×C3C22×D3211yescharacteristic
889C2×D3—32no—
890C2×D3—32no—
891C2×D3—62no—
892C2×D3—61no—
893C2×D3—61no—
894C2×D3—61no—
895C2×D3—61no—
896C2×D3—62no—
897C2×D3—61no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—121no—
904C2×D3—121no—
905C2×D3—121no—
906C2×D3—121no—
907C3×C4—21no—
908C3×C4—21no—
909C3×C4—21no—
910C3×C4—21no—
911C3×C4—21no—
912C3×C4—21no—
913C3×C4—41no—
914C3×C4—41no—
915C3×C4—41no—
916C3×C4—41no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—81no—
920C3×C4—81no—
921C3×C4—92no—
922C3×C4—92no—
923C3×C4—181no—
924C3×C4—181no—
925C3×C4—181no—
926C3×C4—181no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931Dic3—32no—
932Dic3—32no—
933Dic3—32no—
934Dic3—32no—
935Dic3—62no—
936Dic3—62no—
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—121no—
954Dic3—121no—
955Dic3—121no—
956Dic3—121no—
957Dic3—121no—
958Dic3—121no—
959Dic3—121no—
960Dic3—121no—
961C32—21no—
962C32—21no—
963C32—21no—
964C32—41no—
965C32#555711yescharacteristic, complemented
966C32#564911yescharacteristic, complemented
967C32#570611yescharacteristic, complemented
968C23—91no—
969C23—91no—
970C23C2×#111311yescharacteristic
971Q8—542no—
972D4—182no—
973D4—182no—
974D4—542no—
975C2×C4—91no—
976C2×C4—91no—
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—182no—
986C2×C4—182no—
987C2×C4—182no—
988C2×C4—542no—
989C2×C4—542no—
990C2×C4C2×#111311yescharacteristic
991C2×C4C2×#111311yescharacteristic
992C2×C3—21no—
993C2×C3—21no—
994C2×C3—21no—
995C2×C3—21no—
996C2×C3—21no—
997C2×C3—21no—
998C2×C3—21no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—42no—
1002C2×C3—41no—
1003C2×C3—41no—
1004C2×C3—41no—
1005C2×C3—41no—
1006C2×C3—41no—
1007C2×C3—41no—
1008C2×C3—81no—
1009C2×C3—81no—
1010C2×C3—82no—
1011C2×C3—182no—
1012C2×C3—361no—
1013C2×C3D3×#23511yescharacteristic
1014C2×C3D3×#23511yescharacteristic
1015C2×C3#6430611yescharacteristic
1016C2×C3D3×#23711yescharacteristic
1017C2×C3D3×#23711yescharacteristic
1018C2×C3D3×#23711yescharacteristic
1019C2×C3D3×#23711yescharacteristic
1020C2×C3#6431211yescharacteristic
1021C2×C3#6431211yescharacteristic
1022D3—62no—
1023D3—62no—
1024D3—122no—
1025D3—122no—
1026D3—121no—
1027D3—121no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—92no—
1032C22—181no—
1033C22—181no—
1034C22—181no—
1035C22—181no—
1036C22—181no—
1037C22C22×#111311yescharacteristic
1038C4—21no—
1039C4—21no—
1040C4—92no—
1041C4—92no—
1042C4—181no—
1043C4—181no—
1044C4—181no—
1045C4—181no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C3—21no—
1051C3—21no—
1052C3—21no—
1053C3—41no—
1054C3#1059409811yescharacteristic, complemented
1055C3#1059410711yescharacteristic, complemented
1056C3#1059413011yescharacteristic, complemented
1057C2—41no—
1058C2—182no—
1059C2—361no—
1060C2#1172461811yescharacteristic
1061C2#1172462211yescharacteristic
1062C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723725C2
hypercenterC22⋊C4#1113
hypocenterC33#529
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×#64090C2semidirect
3. C3×#64088C2semidirect
4. #11723726C2semidirect
6. #11723718C2semidirect
7. #11723715C2semidirect
8. #11723694C2semidirect
9. #11723692C2semidirect
10. #11723684C2semidirect
11. C4×#6294C2semidirect
12. #11723676C2semidirect
13. #11723669C2semidirect
14. #11723667C2semidirect
15. #11723665C2semidirect
54. #64092D3semidirect
55. #64090D3semidirect
56. #64088D3semidirect
682. C33#529semidirect
965. C32#5557semidirect
966. C32#5649semidirect
967. C32#5706semidirect
1054. C3#10594098semidirect
1055. C3#10594107semidirect
1056. C3#10594130semidirect

Maximal subgroups

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

subgroupindex
C3×#640922
C3×#640902
C3×#640882
#117237262
#117237252
#117237182
#117237152
#117236942
#117236922
#117236842
C4×#62942
#117236762
#117236692
#117236672
#117236652
#105941303
#105941073
#105940983