Finite Group Databasebeta

← #13178215

Subgroups — #13178215

Order 1728.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64095C211yesmaximal, characteristic, complemented
2C3×#64090C211yesmaximal, characteristic, complemented
3C3×#64087C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723720C211yesmaximal, characteristic, complemented
6#11723717C211yesmaximal, characteristic
7C2×#88813C211yesmaximal, characteristic, complemented
8#11723684C211yesmaximal, characteristic, complemented
9#11723683C211yesmaximal, characteristic, complemented
10#11723675C211yesmaximal, characteristic, complemented
11#11723675C211yesmaximal, characteristic, complemented
12#11723670C211yesmaximal, characteristic, complemented
13#11723669C211yesmaximal, characteristic, complemented
14#11723668C211yesmaximal, characteristic, complemented
15#11723667C211yesmaximal, characteristic, complemented
16#10594216—31nomaximal
17#10594144—31nomaximal
18#10594131—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×#634C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C33×C22⋊C4C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×#3752C2211yescharacteristic
33C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
34C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40#88815C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88814C2211yescharacteristic
45#88814C2211yescharacteristic
46#88814C2211yescharacteristic
47#88814C2211yescharacteristic
48#88814C2211yescharacteristic
49#88813C2211yescharacteristic
50#88813C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64095D311yescharacteristic, complemented
55#64090D311yescharacteristic, complemented
56#64087D311yescharacteristic, complemented
57C3×#886—31no—
58C3×#886—31no—
59C3×#886—61no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4—31no—
62C3×#67⋊C4—61no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#63980—31no—
67#63978—31no—
68#63978—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71#63966—31no—
72#63962—31no—
73#63961—31no—
74C2×Dic32—31no—
75C2×Dic32—31no—
76C2×Dic32—31no—
77#63952—31no—
78#63913—31no—
79#63907—31no—
80#63907—31no—
81#63904—31no—
82#63881—31no—
83#63879—31no—
84#63878—31no—
85#63877—31no—
86#63861—31no—
87#63861—31no—
88#63858—31no—
89#63858—31no—
90#63849—31no—
91#63848—31no—
92#63848—31no—
93#63847—31no—
94#63846—31no—
95#63845—31no—
96#63844—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63841—31no—
100#63841—31no—
101#63836—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⋊Dic3—22no—
111C2×C3×C3⋊Dic3—22no—
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
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C3×C4×C3⋊D3—22no—
123C3×#634—22no—
124#6295—22no—
125#6294—22no—
126#5649—91no—
127#5624—91no—
128#5538—91no—
129C2×#638C2×D311yescharacteristic
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3C2×D311yescharacteristic
132C22×C3⋊Dic3C2×D311yescharacteristic
133C22×C3⋊Dic3C2×D311yescharacteristic
134C2×C4×C3⋊D3C2×D311yescharacteristic
135C2×#634C2×D311yescharacteristic
136C2×C3×#67—31no—
137C2×C3×#67—31no—
138C2×C3×#67—31no—
139C2×C3×#67—31no—
140C2×C3×#67—61no—
141C2×C3×#67—61no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—31no—
145C22×C3×Dic3—31no—
146C22×C3×Dic3—31no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—61no—
149C22×C3×Dic3—61no—
150C22×C3×Dic3—61no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—61no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—61no—
157C2×#626—31no—
158C2×#626—31no—
159C2×#625—31no—
160C2×#624—31no—
161C2×D3×Dic3—31no—
162C2×D3×Dic3—31no—
163C32×C22⋊C4—21no—
164C32×C22⋊C4—21no—
165C32×C22⋊C4—21no—
166C32×C22⋊C4—41no—
167C32×C22⋊C4C2×D311yescharacteristic
168C32×C22⋊C4C2×D311yescharacteristic
169C32×C22⋊C4C2×D311yescharacteristic
170#3757C2×D311yescharacteristic
171#3752C2×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
180C4×C3⋊Dic3C2×D311yescharacteristic
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—61no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—31no—
186C3×(C2×D3)⋊C4—31no—
187C3×(C2×D3)⋊C4—31no—
188C3×(C2×D3)⋊C4—31no—
189C3×(C2×D3)⋊C4—31no—
190C3×(C2×D3)⋊C4—61no—
191C3×(C2×D3)⋊C4—61no—
192C3×(C2×D3)⋊C4—61no—
193C3×C4⋊Dic3—31no—
194C3×C4⋊Dic3—31no—
195C3×C4⋊Dic3—31no—
196C3×C4⋊Dic3—31no—
197C3×C4⋊Dic3—31no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—61no—
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—61no—
209C3×Dic3⋊C4—61no—
210C3×Dic3⋊C4—61no—
211C3×C4×Dic3—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—61no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226#3722—31no—
227#3722—31no—
228#3722—31no—
229#3722—31no—
230#3722—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—
241Dic32—31no—
242Dic32—31no—
243Dic32—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#4112yes—
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—21no—
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×#123—91no—
279C3×C22⋊Q8—91no—
280C3×C4×D4—91no—
281#947—91no—
282Q8×Dic3—91no—
283#939—91no—
284#939—91no—
285#935—91no—
286D4×Dic3—91no—
287#930—91no—
288#929—91no—
289C4×#67—91no—
290C4×#67—91no—
291#926—91no—
292C2×C4×Dic3—91no—
293C2×C4×Dic3—91no—
294C2×C4×Dic3—91no—
295#898—91no—
296#898—91no—
297#898—91no—
298#898—91no—
299#893—91no—
300#892—91no—
301#892—91no—
302#892—91no—
303#890—91no—
304#889—91no—
305#889—91no—
306#887—91no—
307#886—31no—
308#886—31no—
309#886—61no—
310#886—91no—
311#885—91no—
312#885—91no—
313#67⋊C4—31no—
314#67⋊C4—31no—
315#67⋊C4—61no—
316#67⋊C4—91no—
317#67⋊C4—91no—
318#879—91no—
319#879—91no—
320#878—31no—
321#878—31no—
322#878—61no—
323#877—91no—
324#872—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⋊Dic3—22no—
359C2×C3⋊Dic3—22no—
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
368C2×C3⋊Dic3C22×D311yescharacteristic
369C2×C3⋊Dic3C22×D311yescharacteristic
370C4×C3⋊D3—22no—
371#634—22no—
372C3×#67—64no—
373C3×#67—62no—
374C3×#67—62no—
375C3×#67—62no—
376C3×#67—62no—
377C3×#67—122no—
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—31no—
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—61no—
408C2×C3×Dic3—62no—
409C2×C3×Dic3—62no—
410C2×C3×Dic3—62no—
411C2×C3×Dic3—62no—
412C2×C3×Dic3—62no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—122no—
415C2×C3×Dic3—122no—
416C2×C3×Dic3—122no—
417C3×C4×D3—62no—
418C3×C4×D3—62no—
419C3×C4×D3—122no—
420C3×Dic6—62no—
421C3×Dic6—62no—
422C3×Dic6—122no—
423#626—62no—
424#626—62no—
425#625—62no—
426#624—62no—
427D3×Dic3—62no—
428D3×Dic3—62no—
429#529—271noSylow
430C2×C33—22no—
431C2×C33C2×#4111yescharacteristic
432C2×C33C2×#4111yescharacteristic
433C2×C33C2×#4111yescharacteristic
434C3×C3⋊D3—41no—
435C3×C3⋊D3—41no—
436C2×C3×Q8—91no—
437C2×C3×D4—91no—
438C2×C3×D4—91no—
439C22×C3×C4—91no—
440C22×C3×C4—91no—
441C22×C3×C4—91no—
442C22×C3×C4—91no—
443C2×#67—31no—
444C2×#67—31no—
445C2×#67—31no—
446C2×#67—31no—
447C2×#67—61no—
448C2×#67—61no—
449C2×#67—91no—
450C2×#67—91no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—61no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—91no—
461C2×D12—91no—
462C2×C4×D3—31no—
463C2×C4×D3—31no—
464C2×C4×D3—61no—
465C2×C4×D3—91no—
466C2×C4×D3—91no—
467C2×Dic6—31no—
468C2×Dic6—31no—
469C2×Dic6—61no—
470C3×C4⋊C4—91no—
471C3×C4⋊C4—91no—
472C3×C4⋊C4—91no—
473C3×C4⋊C4—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C22⋊C4—21no—
477C3×C22⋊C4—21no—
478C3×C22⋊C4—21no—
479C3×C22⋊C4—41no—
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
487C3×C42—91no—
488#217—31no—
489#217—31no—
490#217—61no—
491#217—91no—
492#217—91no—
493#217—91no—
494#217—91no—
495#217—91no—
496(C2×D3)⋊C4—31no—
497(C2×D3)⋊C4—31no—
498(C2×D3)⋊C4—31no—
499(C2×D3)⋊C4—31no—
500(C2×D3)⋊C4—31no—
501(C2×D3)⋊C4—31no—
502(C2×D3)⋊C4—61no—
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—
513(C2×D3)⋊C4—91no—
514(C2×D3)⋊C4—91no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—31no—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—31no—
521C4⋊Dic3—61no—
522C4⋊Dic3—61no—
523C4⋊Dic3—61no—
524C4⋊Dic3—91no—
525C4⋊Dic3—91no—
526C4⋊Dic3—91no—
527C4⋊Dic3—91no—
528Dic3⋊C4—31no—
529Dic3⋊C4—31no—
530Dic3⋊C4—31no—
531Dic3⋊C4—31no—
532Dic3⋊C4—31no—
533Dic3⋊C4—31no—
534Dic3⋊C4—61no—
535Dic3⋊C4—61no—
536Dic3⋊C4—61no—
537Dic3⋊C4—91no—
538Dic3⋊C4—91no—
539Dic3⋊C4—91no—
540Dic3⋊C4—91no—
541Dic3⋊C4—91no—
542Dic3⋊C4—91no—
543Dic3⋊C4—91no—
544Dic3⋊C4—91no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—61no—
548C4×Dic3—91no—
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—
561C4×Dic3—91no—
562C4×Dic3—91no—
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—22no—
573C22×C32—22no—
574C22×C32—22no—
575C22×C32—41no—
576C22×C32—42no—
577C22×C32—41no—
578C22×C32—41no—
579C22×C32—41no—
580C22×C32—41no—
581C22×C32—41no—
582C22×C32—41no—
583C22×C32—81no—
584C22×C32—81no—
585C22×C32#23512yes—
586C22×C32#23712yes—
587C22×C32#23912yes—
588C22×C32C23×D311yescharacteristic
589C22×C32C23×D311yescharacteristic
590C22×C32C23×D311yescharacteristic
591C2×C3⋊D3—21no—
592C2×C3⋊D3—21no—
593C2×C3⋊D3—21no—
594C2×C3⋊D3—21no—
595C2×C3⋊D3—21no—
596C2×C3⋊D3—21no—
597C2×C3×D3—62no—
598C2×C3×D3—61no—
599C2×C3×D3—61no—
600C2×C3×D3—61no—
601C2×C3×D3—61no—
602C2×C3×D3—61no—
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—61no—
610C2×C3×D3—121no—
611C2×C3×D3—121no—
612C2×C3×D3—121no—
613C2×C3×D3—121no—
614C2×C3×D3—121no—
615C32×C4—21no—
616C32×C4—21no—
617C32×C4—21no—
618C32×C4—21no—
619C32×C4—21no—
620C32×C4—21no—
621C32×C4—41no—
622C32×C4—41no—
623C32×C4—41no—
624C32×C4—41no—
625C32×C4—41no—
626C32×C4—41no—
627C32×C4—81no—
628C32×C4—81no—
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#23712yes—
638C3⋊Dic3#23712yes—
639C3×Dic3—32no—
640C3×Dic3—32no—
641C3×Dic3—32no—
642C3×Dic3—32no—
643C3×Dic3—62no—
644C3×Dic3—62no—
645C3×Dic3—62no—
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—61no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—121no—
663C3×Dic3—121no—
664C3×Dic3—121no—
665C3×Dic3—121no—
666C3×Dic3—121no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669#126—271no—
670#126—271no—
671#125—271no—
672#124—271no—
673#123—91no—
674#123—271no—
675C22⋊Q8—91no—
676#121—271no—
677C4×Q8—271no—
678C4×D4—91no—
679C4×D4—271no—
680C4×D4—271no—
681#117—271no—
682#117—271no—
683C2×C42—271no—
684C33#52911yescharacteristic, complemented, Sylow
685C23×C3—21no—
686C23×C3—21no—
687C23×C3—21no—
688C23×C3—41no—
689C23×C3—91no—
690C23×C3—91no—
691C23×C3C2×D3211yescharacteristic
692C23×C3C2×D3211yescharacteristic
693C23×C3C2×D3211yescharacteristic
694C22×D3—31no—
695C22×D3—31no—
696C22×D3—31no—
697C22×D3—31no—
698C22×D3—61no—
699C22×D3—61no—
700C3×Q8—182no—
701C3×D4—182no—
702C3×D4—182no—
703C2×C3×C4—21no—
704C2×C3×C4—21no—
705C2×C3×C4—21no—
706C2×C3×C4—21no—
707C2×C3×C4—21no—
708C2×C3×C4—21no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
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—91no—
721C2×C3×C4—182no—
722C2×C3×C4—182no—
723C2×C3×C4—182no—
724C2×C3×C4—182no—
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C2×D3211yescharacteristic
727C2×C3×C4C2×D3211yescharacteristic
728C2×C3×C4C2×D3211yescharacteristic
729C2×C3×C4C2×D3211yescharacteristic
730C2×C3×C4C2×D3211yescharacteristic
731#67—64no—
732#67—62no—
733#67—62no—
734#67—62no—
735#67—62no—
736#67—122no—
737#67—182no—
738#67—182no—
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—31no—
758C2×Dic3—31no—
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—61no—
768C2×Dic3—61no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—62no—
772C2×Dic3—62no—
773C2×Dic3—62no—
774C2×Dic3—62no—
775C2×Dic3—122no—
776C2×Dic3—122no—
777C2×Dic3—122no—
778C2×Dic3—182no—
779D12—182no—
780C4×D3—62no—
781C4×D3—62no—
782C4×D3—122no—
783C4×D3—182no—
784C4×D3—182no—
785Dic6—62no—
786Dic6—62no—
787Dic6—122no—
788C2×C32—22no—
789C2×C32—22no—
790C2×C32—22no—
791C2×C32—21no—
792C2×C32—21no—
793C2×C32—21no—
794C2×C32—21no—
795C2×C32—21no—
796C2×C32—21no—
797C2×C32—21no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—41no—
801C2×C32—41no—
802C2×C32—41no—
803C2×C32—42no—
804C2×C32—42no—
805C2×C32—42no—
806C2×C32—82no—
807C2×C32C2×#23511yescharacteristic
808C2×C32C2×#23711yescharacteristic
809C2×C32C2×#23711yescharacteristic
810C2×C32C2×#23711yescharacteristic
811C2×C32C2×#23911yescharacteristic
812C2×C32D3×#4111yescharacteristic
813C2×C32D3×#4111yescharacteristic
814C2×C32D3×#4111yescharacteristic
815C2×C32D3×#4111yescharacteristic
816C3⋊D3—41no—
817C3⋊D3—41no—
818C3×D3—122no—
819C3×D3—121no—
820C3×D3—121no—
821C3×D3—121no—
822C3×D3—121no—
823C3×D3—241no—
824C2×Q8—91no—
825C2×D4—91no—
826C2×D4—91no—
827C2×D4—271no—
828C22×C4—91no—
829C22×C4—91no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—271no—
833C4⋊C4—91no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4—91no—
837C4⋊C4—91no—
838C4⋊C4—91no—
839C4⋊C4—271no—
840C4⋊C4—271no—
841C4⋊C4—271no—
842C4⋊C4—271no—
843C22⋊C4—91no—
844C22⋊C4—91no—
845C22⋊C4—91no—
846C22⋊C4—91no—
847C22⋊C4—271no—
848C22⋊C4—271no—
849C22⋊C4—271no—
850C22⋊C4—271no—
851C22⋊C4—271no—
852C22⋊C4#111311yescharacteristic
853C42—91no—
854C42—271no—
855C42—271no—
856C42—271no—
857C42—271no—
858C42—271no—
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—22no—
869C22×C3—22no—
870C22×C3—22no—
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—81no—
880C22×C3—81no—
881C22×C3—181no—
882C22×C3—181no—
883C22×C3—181no—
884C22×C3—181no—
885C22×C3—181no—
886C22×C3—181no—
887C22×C3#379512yes—
888C22×C3#379612yes—
889C22×C3#379912yes—
890C22×C3C22×D3211yescharacteristic
891C22×C3C22×D3211yescharacteristic
892C22×C3C22×D3211yescharacteristic
893C2×D3—62no—
894C2×D3—61no—
895C2×D3—61no—
896C2×D3—61no—
897C2×D3—61no—
898C2×D3—61no—
899C2×D3—61no—
900C2×D3—61no—
901C2×D3—61no—
902C2×D3—61no—
903C2×D3—61no—
904C2×D3—61no—
905C2×D3—61no—
906C2×D3—121no—
907C2×D3—121no—
908C2×D3—121no—
909C2×D3—121no—
910C2×D3—121no—
911C3×C4—21no—
912C3×C4—21no—
913C3×C4—21no—
914C3×C4—21no—
915C3×C4—21no—
916C3×C4—21no—
917C3×C4—41no—
918C3×C4—41no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—41no—
922C3×C4—41no—
923C3×C4—81no—
924C3×C4—81no—
925C3×C4—92no—
926C3×C4—92no—
927C3×C4—181no—
928C3×C4—181no—
929C3×C4—181no—
930C3×C4—181no—
931C3×C4—181no—
932C3×C4—181no—
933C3×C4—181no—
934C3×C4—181no—
935Dic3—32no—
936Dic3—32no—
937Dic3—32no—
938Dic3—32no—
939Dic3—62no—
940Dic3—62no—
941Dic3—62no—
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—61no—
955Dic3—61no—
956Dic3—61no—
957Dic3—61no—
958Dic3—121no—
959Dic3—121no—
960Dic3—121no—
961Dic3—121no—
962Dic3—121no—
963Dic3—121no—
964Dic3—121no—
965C32—21no—
966C32—21no—
967C32—21no—
968C32—41no—
969C32#553811yescharacteristic, complemented
970C32#562411yescharacteristic, complemented
971C32#564911yescharacteristic, complemented
972C23—91no—
973C23—91no—
974C23C2×#111311yescharacteristic
975Q8—182no—
976D4—182no—
977D4—182no—
978D4—542no—
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—91no—
988C2×C4—91no—
989C2×C4—182no—
990C2×C4—182no—
991C2×C4—182no—
992C2×C4—182no—
993C2×C4—542no—
994C2×C4C2×#111311yescharacteristic
995C2×C4C2×#111311yescharacteristic
996C2×C3—22no—
997C2×C3—22no—
998C2×C3—22no—
999C2×C3—21no—
1000C2×C3—21no—
1001C2×C3—21no—
1002C2×C3—21no—
1003C2×C3—21no—
1004C2×C3—21no—
1005C2×C3—21no—
1006C2×C3—21no—
1007C2×C3—21no—
1008C2×C3—42no—
1009C2×C3—42no—
1010C2×C3—42no—
1011C2×C3—41no—
1012C2×C3—41no—
1013C2×C3—41no—
1014C2×C3—82no—
1015C2×C3—361no—
1016C2×C3—361no—
1017C2×C3C2×#379511yescharacteristic
1018C2×C3C2×#379611yescharacteristic
1019C2×C3C2×#379911yescharacteristic
1020C2×C3D3×#23711yescharacteristic
1021C2×C3D3×#23711yescharacteristic
1022C2×C3D3×#23711yescharacteristic
1023C2×C3D3×#23711yescharacteristic
1024C2×C3#6431211yescharacteristic
1025C2×C3#6431211yescharacteristic
1026D3—122no—
1027D3—121no—
1028D3—121no—
1029D3—121no—
1030D3—121no—
1031D3—241no—
1032C22—21no—
1033C22—21no—
1034C22—181no—
1035C22—181no—
1036C22—181no—
1037C22—181no—
1038C22—181no—
1039C22—181no—
1040C22#8904112yes—
1041C22C22×#111311yescharacteristic
1042C4—21no—
1043C4—21no—
1044C4—92no—
1045C4—92no—
1046C4—181no—
1047C4—181no—
1048C4—181no—
1049C4—181no—
1050C4—181no—
1051C4—181no—
1052C4—181no—
1053C4—181no—
1054C3—21no—
1055C3—21no—
1056C3—21no—
1057C3—41no—
1058C3#1059413111yescharacteristic, complemented
1059C3#1059414411yescharacteristic, complemented
1060C3#1059421611yescharacteristic, complemented
1061C2—22no—
1062C2—361no—
1063C2—361no—
1064C2C2×#8904111yescharacteristic
1065C2#1172462211yescharacteristic
1066C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radical#11723717C2
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×#64095C2semidirect
2. C3×#64090C2semidirect
3. C3×#64087C2semidirect
4. #11723726C2semidirect
5. #11723720C2semidirect
7. C2×#88813C2semidirect
8. #11723684C2semidirect
9. #11723683C2semidirect
10. #11723675C2semidirect
11. #11723675C2semidirect
12. #11723670C2semidirect
13. #11723669C2semidirect
14. #11723668C2semidirect
15. #11723667C2semidirect
54. #64095D3semidirect
55. #64090D3semidirect
56. #64087D3semidirect
684. C33#529semidirect
969. C32#5538semidirect
970. C32#5624semidirect
971. C32#5649semidirect
1058. C3#10594131semidirect
1059. C3#10594144semidirect
1060. C3#10594216semidirect

Maximal subgroups

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

subgroupindex
C3×#640952
C3×#640902
C3×#640872
#117237262
#117237202
#117237172
C2×#888132
#117236842
#117236832
#117236752
#117236702
#117236692
#117236682
#117236672
#105942163
#105941443
#105941313