Finite Group Databasebeta

← #13178210

Subgroups — #13178210

Order 1728.

1094 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64094C211yesmaximal, characteristic
2C3×#64088C211yesmaximal, characteristic, complemented
3C3×#64086C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic
5#11723721C211yesmaximal, characteristic, complemented
6#11723718C211yesmaximal, characteristic
7#11723716C211yesmaximal, characteristic, complemented
8C4×#6296C211yesmaximal, characteristic, complemented
9#11723692C211yesmaximal, characteristic, complemented
10#11723683C211yesmaximal, characteristic, complemented
11#11723676C211yesmaximal, characteristic, complemented
12#11723676C211yesmaximal, characteristic, complemented
13#11723668C211yesmaximal, characteristic, complemented
14#11723666C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10594145—31nomaximal
17#10594110—31nomaximal
18#10594105—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C22×C3×C3⋊Dic3C2211yescharacteristic
21C2×C3×#634C2211yescharacteristic
22C2×#6296C2211yescharacteristic
23C2×#6296C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C33×C22⋊C4C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3752C2211yescharacteristic
31C3×#3752C2211yescharacteristic
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×C4×C3⋊Dic3C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
39C3×C4×C3⋊Dic3C2211yescharacteristic
40C3×C4×C3⋊Dic3C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64094D311yescharacteristic
55#64088D311yescharacteristic, complemented
56#64086D311yescharacteristic, complemented
57C3×#885—31no—
58C3×#885—31no—
59C3×#885—61no—
60C3×#879—31no—
61C3×#879—31no—
62C3×#879—61no—
63C3×#877—31no—
64C3×#877—31no—
65C3×#877—61no—
66#63982—31no—
67#67⋊Dic3—31no—
68Dic3×#67—31no—
69#63964—31no—
70#63964—31no—
71#63959—31no—
72#63959—31no—
73#63956—31no—
74#63956—31no—
75#63956—31no—
76#63953—31no—
77#63952—31no—
78C4×#627—31no—
79C4×#627—31no—
80C4×#627—31no—
81#63899—31no—
82#63895—31no—
83#63893—31no—
84#63878—31no—
85#63877—31no—
86#63868—31no—
87#63868—31no—
88#63862—31no—
89#63862—31no—
90#63859—31no—
91#63859—31no—
92#63844—31no—
93#63843—31no—
94Dic3×Dic6—31no—
95#63840—31no—
96#63839—31no—
97#63839—31no—
98#63838—31no—
99#63837—31no—
100#63837—31no—
101#63836—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C33×C4C2311yescharacteristic
106C3×#638—22no—
107C2×C3×C3⋊Dic3—22no—
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
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
119C3×#634—22no—
120#6296—22no—
121#6296—22no—
122#6294—22no—
123#5702—91no—
124#5671—91no—
125#5533—91no—
126C2×#638C2×D311yescharacteristic
127C22×C3⋊Dic3C2×D311yescharacteristic
128C2×#634C2×D311yescharacteristic
129C2×C3×#67—31no—
130C2×C3×#67—31no—
131C2×C3×#67—61no—
132C22×C3×Dic3—31no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—61no—
135C2×C3×Dic6—31no—
136C2×C3×Dic6—31no—
137C2×C3×Dic6—61no—
138C2×#627—31no—
139C2×#627—31no—
140C2×#627—31no—
141C2×#627—31no—
142C2×#627—31no—
143C2×#627—31no—
144C2×#624—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C32×C22⋊C4—21no—
148C32×C22⋊C4—21no—
149C32×C22⋊C4—21no—
150C32×C22⋊C4—41no—
151C32×C22⋊C4C2×D311yescharacteristic
152C32×C22⋊C4C2×D311yescharacteristic
153C32×C22⋊C4C2×D311yescharacteristic
154#3757C2×D311yescharacteristic
155#3757C2×D311yescharacteristic
156#3757C2×D311yescharacteristic
157#3757C2×D311yescharacteristic
158#3752C2×D311yescharacteristic
159#3752C2×D311yescharacteristic
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic
161#3750C2×D311yescharacteristic
162#3750C2×D311yescharacteristic
163#3750C2×D311yescharacteristic
164#3750C2×D311yescharacteristic
165C4×C3⋊Dic3C2×D311yescharacteristic
166C4×C3⋊Dic3C2×D311yescharacteristic
167C4×C3⋊Dic3C2×D311yescharacteristic
168C4×C3⋊Dic3C2×D311yescharacteristic
169C3×#217—31no—
170C3×#217—31no—
171C3×#217—31no—
172C3×#217—31no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—31no—
177C3×#217—61no—
178C3×#217—61no—
179C3×#217—61no—
180C3×#217—61no—
181C3×(C2×D3)⋊C4—31no—
182C3×(C2×D3)⋊C4—31no—
183C3×(C2×D3)⋊C4—31no—
184C3×(C2×D3)⋊C4—31no—
185C3×(C2×D3)⋊C4—61no—
186C3×(C2×D3)⋊C4—61no—
187C3×C4⋊Dic3—31no—
188C3×C4⋊Dic3—31no—
189C3×C4⋊Dic3—61no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—31no—
194C3×Dic3⋊C4—31no—
195C3×Dic3⋊C4—31no—
196C3×Dic3⋊C4—31no—
197C3×Dic3⋊C4—31no—
198C3×Dic3⋊C4—61no—
199C3×Dic3⋊C4—61no—
200C3×Dic3⋊C4—61no—
201C3×Dic3⋊C4—61no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—31no—
204C3×C4×Dic3—31no—
205C3×C4×Dic3—31no—
206C3×C4×Dic3—31no—
207C3×C4×Dic3—31no—
208C3×C4×Dic3—31no—
209C3×C4×Dic3—31no—
210C3×C4×Dic3—61no—
211C3×C4×Dic3—61no—
212C3×C4×Dic3—61no—
213C3×C4×Dic3—61no—
214#3724—31no—
215#3724—31no—
216#3724—31no—
217#3724—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—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—
235#3722—31no—
236#3722—31no—
237#3722—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—
253C22×C33—21no—
254C22×C33—21no—
255C22×C33—21no—
256C22×C33C2411yescharacteristic
257C2×C3×C3⋊D3—21no—
258C2×C3×C3⋊D3—21no—
259C2×C3×C3⋊D3—21no—
260C33×C4—21no—
261C33×C4—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3—21no—
268C3×C3⋊Dic3—21no—
269C3×C3⋊Dic3—21no—
270C3×C3⋊Dic3—21no—
271C3×C3⋊Dic3#4112yes—
272C3×C3⋊Dic3#4112yes—
273C3×#126—91no—
274C3×#124—91no—
275C3×#117—91no—
276Q8×Dic3—91no—
277#944—91no—
278#936—91no—
279D4×Dic3—91no—
280C4×#67—91no—
281#924—91no—
282#898—91no—
283#898—91no—
284#897—91no—
285#896—91no—
286#892—91no—
287#888—91no—
288#888—91no—
289#887—91no—
290#887—91no—
291#887—91no—
292#885—31no—
293#885—31no—
294#885—61no—
295#885—91no—
296#885—91no—
297#67⋊C4—91no—
298#879—31no—
299#879—31no—
300#879—61no—
301#879—91no—
302#879—91no—
303#879—91no—
304#879—91no—
305#879—91no—
306#878—91no—
307#878—91no—
308#878—91no—
309#877—31no—
310#877—31no—
311#877—61no—
312#877—91no—
313#876—91no—
314#876—91no—
315#872—91no—
316C4×Dic6—91no—
317C4×Dic6—91no—
318C4×Dic6—91no—
319C4×Dic6—91no—
320C4×Dic6—91no—
321C23×C32—21no—
322C23×C32—21no—
323C23×C32—21no—
324C23×C32—41no—
325C23×C32C22×D311yescharacteristic
326C23×C32C22×D311yescharacteristic
327C23×C32C22×D311yescharacteristic
328C22×C3⋊D3C22×D311yescharacteristic
329C22×C3×D3—31no—
330C22×C3×D3—31no—
331C22×C3×D3—61no—
332C2×C32×C4—21no—
333C2×C32×C4—21no—
334C2×C32×C4—21no—
335C2×C32×C4—21no—
336C2×C32×C4—21no—
337C2×C32×C4—21no—
338C2×C32×C4—41no—
339C2×C32×C4—41no—
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C22×D311yescharacteristic
342C2×C32×C4C22×D311yescharacteristic
343C2×C32×C4C22×D311yescharacteristic
344C2×C32×C4C22×D311yescharacteristic
345C2×C32×C4C22×D311yescharacteristic
346#638—22no—
347C2×C3⋊Dic3—22no—
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350C2×C3⋊Dic3C22×D311yescharacteristic
351C2×C3⋊Dic3C22×D311yescharacteristic
352C2×C3⋊Dic3C22×D311yescharacteristic
353C2×C3⋊Dic3C22×D311yescharacteristic
354C2×C3⋊Dic3C22×D311yescharacteristic
355C2×C3⋊Dic3C22×D311yescharacteristic
356C2×C3⋊Dic3C22×D311yescharacteristic
357C2×C3⋊Dic3C22×D311yescharacteristic
358C2×C3⋊Dic3C22×D311yescharacteristic
359#634—22no—
360C3×#67—62no—
361C3×#67—62no—
362C3×#67—122no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
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—61no—
386C2×C3×Dic3—61no—
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—61no—
394C2×C3×Dic3—61no—
395C2×C3×Dic3—61no—
396C2×C3×Dic3—62no—
397C2×C3×Dic3—62no—
398C2×C3×Dic3—64no—
399C3×Dic6—62no—
400C3×Dic6—62no—
401C3×Dic6—122no—
402#627—62no—
403#627—62no—
404#627—62no—
405#627—62no—
406#627—62no—
407#627—62no—
408#624—62no—
409D3×Dic3—62no—
410D3×Dic3—62no—
411#556—271noSylow
412C2×C33—41no—
413C2×C33C2×#4111yescharacteristic
414C2×C33C2×#4111yescharacteristic
415C2×C332−1+411yescharacteristic
416C3×C3⋊D3—41no—
417C2×C3×Q8—91no—
418C2×C3×D4—91no—
419C22×C3×C4—91no—
420C2×#67—31no—
421C2×#67—31no—
422C2×#67—61no—
423C22×Dic3—31no—
424C22×Dic3—31no—
425C22×Dic3—61no—
426C22×Dic3—91no—
427C2×C4×D3—91no—
428C2×C4×D3—91no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—61no—
432C2×Dic6—91no—
433C2×Dic6—91no—
434C2×Dic6—91no—
435C2×Dic6—91no—
436C2×Dic6—91no—
437C2×Dic6—91no—
438C3×C4⋊C4—91no—
439C3×C4⋊C4—91no—
440C3×C4⋊C4—91no—
441C3×C4⋊C4—91no—
442C3×C4⋊C4—91no—
443C3×C22⋊C4—21no—
444C3×C22⋊C4—21no—
445C3×C22⋊C4—21no—
446C3×C22⋊C4—41no—
447C3×C22⋊C4—91no—
448C3×C22⋊C4—91no—
449C3×C22⋊C4—91no—
450C3×C22⋊C4—91no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4D3211yescharacteristic
454C3×C22⋊C4D3211yescharacteristic
455C3×C22⋊C4D3211yescharacteristic
456C3×C42—91no—
457C3×C42—91no—
458C3×C42—91no—
459C3×C42—91no—
460#217—31no—
461#217—31no—
462#217—31no—
463#217—31no—
464#217—31no—
465#217—31no—
466#217—31no—
467#217—31no—
468#217—61no—
469#217—61no—
470#217—61no—
471#217—61no—
472#217—91no—
473#217—91no—
474#217—91no—
475(C2×D3)⋊C4—31no—
476(C2×D3)⋊C4—31no—
477(C2×D3)⋊C4—31no—
478(C2×D3)⋊C4—31no—
479(C2×D3)⋊C4—61no—
480(C2×D3)⋊C4—61no—
481(C2×D3)⋊C4—91no—
482(C2×D3)⋊C4—91no—
483(C2×D3)⋊C4—91no—
484(C2×D3)⋊C4—91no—
485(C2×D3)⋊C4—91no—
486(C2×D3)⋊C4—91no—
487C4⋊Dic3—31no—
488C4⋊Dic3—31no—
489C4⋊Dic3—61no—
490C4⋊Dic3—91no—
491C4⋊Dic3—91no—
492C4⋊Dic3—91no—
493C4⋊Dic3—91no—
494C4⋊Dic3—91no—
495C4⋊Dic3—91no—
496C4⋊Dic3—91no—
497Dic3⋊C4—31no—
498Dic3⋊C4—31no—
499Dic3⋊C4—31no—
500Dic3⋊C4—31no—
501Dic3⋊C4—31no—
502Dic3⋊C4—31no—
503Dic3⋊C4—31no—
504Dic3⋊C4—31no—
505Dic3⋊C4—61no—
506Dic3⋊C4—61no—
507Dic3⋊C4—61no—
508Dic3⋊C4—61no—
509Dic3⋊C4—91no—
510Dic3⋊C4—91no—
511Dic3⋊C4—91no—
512Dic3⋊C4—91no—
513Dic3⋊C4—91no—
514Dic3⋊C4—91no—
515Dic3⋊C4—91no—
516Dic3⋊C4—91no—
517Dic3⋊C4—91no—
518Dic3⋊C4—91no—
519Dic3⋊C4—91no—
520Dic3⋊C4—91no—
521Dic3⋊C4—91no—
522Dic3⋊C4—91no—
523C4×Dic3—31no—
524C4×Dic3—31no—
525C4×Dic3—31no—
526C4×Dic3—31no—
527C4×Dic3—31no—
528C4×Dic3—31no—
529C4×Dic3—31no—
530C4×Dic3—31no—
531C4×Dic3—61no—
532C4×Dic3—61no—
533C4×Dic3—61no—
534C4×Dic3—61no—
535C4×Dic3—91no—
536C4×Dic3—91no—
537C4×Dic3—91no—
538C4×Dic3—91no—
539C4×Dic3—91no—
540C4×Dic3—91no—
541C4×Dic3—91no—
542C4×Dic3—91no—
543C4×Dic3—91no—
544C22×C32—21no—
545C22×C32—22no—
546C22×C32—21no—
547C22×C32—21no—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32—21no—
552C22×C32—21no—
553C22×C32—21no—
554C22×C32—21no—
555C22×C32—21no—
556C22×C32—21no—
557C22×C32—41no—
558C22×C32—41no—
559C22×C32—41no—
560C22×C32—42no—
561C22×C32—41no—
562C22×C32—41no—
563C22×C32—41no—
564C22×C32—41no—
565C22×C32—41no—
566C22×C32—41no—
567C22×C32—81no—
568C22×C32—81no—
569C22×C32C23×D311yescharacteristic
570C22×C32C23×D311yescharacteristic
571C22×C32C23×D311yescharacteristic
572C2×C3⋊D3—21no—
573C2×C3⋊D3—21no—
574C2×C3⋊D3—21no—
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—121no—
582C2×C3×D3—121no—
583C2×C3×D3—121no—
584C32×C4—21no—
585C32×C4—21no—
586C32×C4—21no—
587C32×C4—21no—
588C32×C4—21no—
589C32×C4—21no—
590C32×C4—41no—
591C32×C4—41no—
592C32×C4—41no—
593C32×C4—41no—
594C32×C4—41no—
595C32×C4—41no—
596C32×C4—81no—
597C32×C4—81no—
598C3⋊Dic3—21no—
599C3⋊Dic3—21no—
600C3⋊Dic3—21no—
601C3⋊Dic3—21no—
602C3⋊Dic3—21no—
603C3⋊Dic3—21no—
604C3⋊Dic3—21no—
605C3⋊Dic3—21no—
606C3⋊Dic3—21no—
607C3⋊Dic3#23512yes—
608C3⋊Dic3#23712yes—
609C3×Dic3—32no—
610C3×Dic3—32no—
611C3×Dic3—32no—
612C3×Dic3—32no—
613C3×Dic3—62no—
614C3×Dic3—62no—
615C3×Dic3—62no—
616C3×Dic3—61no—
617C3×Dic3—61no—
618C3×Dic3—61no—
619C3×Dic3—61no—
620C3×Dic3—61no—
621C3×Dic3—61no—
622C3×Dic3—61no—
623C3×Dic3—61no—
624C3×Dic3—61no—
625C3×Dic3—61no—
626C3×Dic3—61no—
627C3×Dic3—61no—
628C3×Dic3—61no—
629C3×Dic3—61no—
630C3×Dic3—61no—
631C3×Dic3—61no—
632C3×Dic3—61no—
633C3×Dic3—61no—
634C3×Dic3—121no—
635C3×Dic3—121no—
636C3×Dic3—121no—
637C3×Dic3—121no—
638C3×Dic3—121no—
639C3×Dic3—121no—
640C3×Dic3—121no—
641C3×Dic3—121no—
642C4⋊Q8—271no—
643#126—91no—
644#126—271no—
645#126—271no—
646#126—271no—
647#124—91no—
648#124—271no—
649C22⋊Q8—271no—
650C22⋊Q8—271no—
651C4×Q8—271no—
652C4×Q8—271no—
653C4×Q8—271no—
654C4×D4—271no—
655#117—91no—
656#117—271no—
657C33#55611yescharacteristic, complemented, Sylow
658C23×C3—21no—
659C23×C3—21no—
660C23×C3—21no—
661C23×C3—41no—
662C23×C3—91no—
663C23×C3C2×D3211yescharacteristic
664C23×C3C2×D3211yescharacteristic
665C23×C3C2×D3211yescharacteristic
666C22×D3—31no—
667C22×D3—31no—
668C22×D3—61no—
669C3×Q8—182no—
670C3×D4—182no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—91no—
680C2×C3×C4—91no—
681C2×C3×C4—91no—
682C2×C3×C4—91no—
683C2×C3×C4—91no—
684C2×C3×C4—91no—
685C2×C3×C4—91no—
686C2×C3×C4—91no—
687C2×C3×C4—91no—
688C2×C3×C4—91no—
689C2×C3×C4—91no—
690C2×C3×C4—182no—
691C2×C3×C4C2×D3211yescharacteristic
692C2×C3×C4C2×D3211yescharacteristic
693C2×C3×C4C2×D3211yescharacteristic
694C2×C3×C4C2×D3211yescharacteristic
695C2×C3×C4C2×D3211yescharacteristic
696C2×C3×C4C2×D3211yescharacteristic
697#67—62no—
698#67—62no—
699#67—122no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—31no—
704C2×Dic3—31no—
705C2×Dic3—31no—
706C2×Dic3—31no—
707C2×Dic3—31no—
708C2×Dic3—31no—
709C2×Dic3—31no—
710C2×Dic3—31no—
711C2×Dic3—31no—
712C2×Dic3—31no—
713C2×Dic3—31no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—31no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—31no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—62no—
734C2×Dic3—62no—
735C2×Dic3—64no—
736C2×Dic3—182no—
737C4×D3—182no—
738C4×D3—182no—
739Dic6—62no—
740Dic6—62no—
741Dic6—122no—
742Dic6—182no—
743Dic6—182no—
744Dic6—182no—
745Dic6—182no—
746Dic6—182no—
747Dic6—182no—
748C2×C32—21no—
749C2×C32—21no—
750C2×C32—21no—
751C2×C32—21no—
752C2×C32—21no—
753C2×C32—21no—
754C2×C32—21no—
755C2×C32—21no—
756C2×C32—21no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—41no—
760C2×C32—41no—
761C2×C32—42no—
762C2×C32—41no—
763C2×C32—41no—
764C2×C32—81no—
765C2×C32—81no—
766C2×C32—82no—
767C2×C32C2×#23511yescharacteristic
768C2×C32C2×#23711yescharacteristic
769C2×C32D3×#4111yescharacteristic
770C2×C32D3×#4111yescharacteristic
771C2×C32D3×#4111yescharacteristic
772C2×C32D3×#4111yescharacteristic
773C2×C32#101011yescharacteristic
774C2×C32#101011yescharacteristic
775C2×C32#101011yescharacteristic
776C3⋊D3—41no—
777C3×D3—121no—
778C3×D3—121no—
779C3×D3—241no—
780C2×Q8—91no—
781C2×Q8—271no—
782C2×Q8—271no—
783C2×D4—91no—
784C22×C4—91no—
785C22×C4—271no—
786C4⋊C4—91no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—271no—
792C4⋊C4—271no—
793C4⋊C4—271no—
794C4⋊C4—271no—
795C4⋊C4—271no—
796C4⋊C4—271no—
797C4⋊C4—271no—
798C22⋊C4—91no—
799C22⋊C4—91no—
800C22⋊C4—91no—
801C22⋊C4—91no—
802C22⋊C4—91no—
803C22⋊C4—91no—
804C22⋊C4—271no—
805C22⋊C4—271no—
806C22⋊C4—271no—
807C22⋊C4#111311yescharacteristic
808C42—91no—
809C42—91no—
810C42—91no—
811C42—91no—
812C42—271no—
813C42—271no—
814C42—271no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—21no—
818C22×C3—21no—
819C22×C3—21no—
820C22×C3—21no—
821C22×C3—21no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—42no—
837C22×C3—41no—
838C22×C3—81no—
839C22×C3—81no—
840C22×C3—181no—
841C22×C3—181no—
842C22×C3—181no—
843C22×C3C22×D3211yescharacteristic
844C22×C3C22×D3211yescharacteristic
845C22×C3C22×D3211yescharacteristic
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—61no—
850C2×D3—61no—
851C2×D3—61no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C3×C4—21no—
856C3×C4—21no—
857C3×C4—21no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—41no—
862C3×C4—41no—
863C3×C4—41no—
864C3×C4—41no—
865C3×C4—41no—
866C3×C4—41no—
867C3×C4—81no—
868C3×C4—81no—
869C3×C4—92no—
870C3×C4—92no—
871C3×C4—181no—
872C3×C4—181no—
873C3×C4—181no—
874C3×C4—181no—
875C3×C4—181no—
876C3×C4—181no—
877C3×C4—181no—
878C3×C4—181no—
879C3×C4—181no—
880Dic3—32no—
881Dic3—32no—
882Dic3—32no—
883Dic3—32no—
884Dic3—62no—
885Dic3—62no—
886Dic3—62no—
887Dic3—61no—
888Dic3—61no—
889Dic3—61no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—61no—
895Dic3—61no—
896Dic3—61no—
897Dic3—61no—
898Dic3—61no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—121no—
906Dic3—121no—
907Dic3—121no—
908Dic3—121no—
909Dic3—121no—
910Dic3—121no—
911Dic3—121no—
912Dic3—121no—
913C32—21no—
914C32—21no—
915C32—21no—
916C32—41no—
917C32#553311yescharacteristic, complemented
918C32#567111yescharacteristic, complemented
919C32#570211yescharacteristic, complemented
920C23—91no—
921C23C2×#111311yescharacteristic
922Q8—182no—
923Q8—542no—
924Q8—542no—
925D4—182no—
926C2×C4—91no—
927C2×C4—91no—
928C2×C4—91no—
929C2×C4—91no—
930C2×C4—91no—
931C2×C4—91no—
932C2×C4—91no—
933C2×C4—91no—
934C2×C4—91no—
935C2×C4—91no—
936C2×C4—91no—
937C2×C4—182no—
938C2×C4—542no—
939C2×C4C2×#111311yescharacteristic
940C2×C4C2×#111311yescharacteristic
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—41no—
953C2×C3—41no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—81no—
958C2×C3—81no—
959C2×C3—82no—
960C2×C3—361no—
961C2×C3D3×#23511yescharacteristic
962C2×C3D3×#23511yescharacteristic
963C2×C3#6430611yescharacteristic
964C2×C3#6430911yescharacteristic
965C2×C3#6430911yescharacteristic
966C2×C3#6430911yescharacteristic
967C2×C3D3×#23711yescharacteristic
968C2×C3D3×#23711yescharacteristic
969C2×C3#6431211yescharacteristic
970D3—121no—
971D3—121no—
972D3—241no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—181no—
977C22—181no—
978C22—181no—
979C22C22×#111311yescharacteristic
980C4—21no—
981C4—21no—
982C4—92no—
983C4—92no—
984C4—181no—
985C4—181no—
986C4—181no—
987C4—181no—
988C4—181no—
989C4—181no—
990C4—181no—
991C4—181no—
992C4—181no—
993C3—21no—
994C3—21no—
995C3—21no—
996C3—41no—
997C3#1059410511yescharacteristic, complemented
998C3#1059411011yescharacteristic, complemented
999C3#1059414511yescharacteristic, complemented
1000C2—41no—
1001C2—361no—
1002C2#1172461811yescharacteristic
1003C2#1172462011yescharacteristic
1004C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×C3×#638C22
hypercenterC22⋊C4#1113
hypocenterC33#556
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#64088C2semidirect
3. C3×#64086C2semidirect
5. #11723721C2semidirect
7. #11723716C2semidirect
8. C4×#6296C2semidirect
9. #11723692C2semidirect
10. #11723683C2semidirect
11. #11723676C2semidirect
12. #11723676C2semidirect
13. #11723668C2semidirect
14. #11723666C2semidirect
15. #11723665C2semidirect
55. #64088D3semidirect
56. #64086D3semidirect
657. C33#556semidirect
917. C32#5533semidirect
918. C32#5671semidirect
919. C32#5702semidirect
997. C3#10594105semidirect
998. C3#10594110semidirect
999. C3#10594145semidirect

Maximal subgroups

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

subgroupindex
C3×#640942
C3×#640882
C3×#640862
#117237262
#117237212
#117237182
#117237162
C4×#62962
#117236922
#117236832
#117236762
#117236682
#117236662
#117236652
#105941453
#105941103
#105941053