Finite Group Databasebeta

← #13178697

Subgroups — #13178697

Order 1728.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic
2C3×#64145C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4#11723726C211yesmaximal, characteristic, complemented
5#11723724C211yesmaximal, characteristic, complemented
6#11723721C211yesmaximal, characteristic, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723718C211yesmaximal, characteristic, complemented
9#11723718C211yesmaximal, characteristic, complemented
10#11723716C211yesmaximal, characteristic, complemented
11#11723715C211yesmaximal, characteristic, complemented
12#11723688C211yesmaximal, characteristic, complemented
13#11723676C211yesmaximal, characteristic, complemented
14#11723666C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10595211—31nomaximal
17#10595203—31nomaximal
18#10595201—31nomaximal
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic
24C2×C3×#634C2211yescharacteristic
25C2×#6296C2211yescharacteristic
26C2×#6296C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C3×#3757C2211yescharacteristic
29C3×#3757C2211yescharacteristic
30C3×#3757C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic
38C3×#3750C2211yescharacteristic
39C3×#3750C2211yescharacteristic
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#64148D311yescharacteristic
55#64145D311yescharacteristic, complemented
56#64144D311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—61no—
60C3×#936—31no—
61C3×#936—31no—
62C3×#936—61no—
63C3×#935—31no—
64C3×#935—31no—
65C3×#935—61no—
66#63982—31no—
67#63982—31no—
68#63975—31no—
69#67⋊Dic3—31no—
70Dic3×#67—31no—
71#63969—31no—
72#63969—31no—
73#63964—31no—
74#63964—31no—
75#63964—31no—
76#63964—31no—
77#63959—31no—
78#63959—31no—
79#63959—31no—
80#63959—31no—
81#63957—31no—
82#63956—31no—
83#63956—31no—
84#63956—31no—
85#63955—31no—
86#63955—31no—
87#63953—31no—
88#63953—31no—
89#63952—31no—
90#63896—31no—
91#63888—31no—
92#63887—31no—
93#63868—31no—
94#63862—31no—
95#63859—31no—
96#63840—31no—
97#63839—31no—
98#63839—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C33×D4—41no—
106C2×C33×C4C2311yescharacteristic
107C3×#638—22no—
108C3×#638—41no—
109C2×C3×C3⋊Dic3—22no—
110C2×C3×C3⋊Dic3—41no—
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
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C3×#634—41no—
123#6296—22no—
124#6296—41no—
125#6294—41no—
126#5669—91no—
127#5662—91no—
128#5603—91no—
129C2×C32×D4—21no—
130C2×C32×D4—21no—
131C2×C32×D4—21no—
132C2×C32×D4—41no—
133C2×C32×D4C2×D311yescharacteristic
134C2×C32×D4C2×D311yescharacteristic
135C2×C32×D4C2×D311yescharacteristic
136C2×#638C2×D311yescharacteristic
137C2×#638C2×D311yescharacteristic
138C22×C3⋊Dic3C2×D311yescharacteristic
139C22×C3⋊Dic3C2×D311yescharacteristic
140C2×#634C2×D311yescharacteristic
141C2×C3×#67—31no—
142C2×C3×#67—31no—
143C2×C3×#67—31no—
144C2×C3×#67—31no—
145C2×C3×#67—61no—
146C2×C3×#67—61no—
147C22×C3×Dic3—31no—
148C22×C3×Dic3—31no—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—61no—
152C22×C3×Dic3—61no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—31no—
155C2×C3×Dic6—61no—
156C2×#627—31no—
157C2×#627—31no—
158C2×#627—31no—
159C2×#627—31no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#624—31no—
163C2×D3×Dic3—31no—
164C2×D3×Dic3—31no—
165#3757C2×D311yescharacteristic
166#3757C2×D311yescharacteristic
167#3757C2×D311yescharacteristic
168#3757C2×D311yescharacteristic
169#3757C2×D311yescharacteristic
170#3757C2×D311yescharacteristic
171#3757C2×D311yescharacteristic
172#3757C2×D311yescharacteristic
173#3752C2×D311yescharacteristic
174#3750C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176#3750C2×D311yescharacteristic
177C4×C3⋊Dic3C2×D311yescharacteristic
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—31no—
181C3×#217—31no—
182C3×#217—31no—
183C3×#217—31no—
184C3×#217—31no—
185C3×#217—31no—
186C3×#217—31no—
187C3×#217—31no—
188C3×#217—31no—
189C3×#217—31no—
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—61no—
195C3×#217—61no—
196C3×#217—61no—
197C3×#217—61no—
198C3×#217—61no—
199C3×#217—61no—
200C3×#217—61no—
201C3×#217—61no—
202C3×(C2×D3)⋊C4—31no—
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—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—61no—
212C3×Dic3⋊C4—61no—
213C3×Dic3⋊C4—61no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—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(C2×D3)⋊Dic3—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—
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×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33C2411yescharacteristic
263C2×C3×C3⋊D3—21no—
264C2×C3×C3⋊D3—21no—
265C2×C3×C3⋊D3—21no—
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—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3#4112yes—
278C3×#124—91no—
279C3×#123—91no—
280C3×#121—91no—
281#946—91no—
282#944—91no—
283#939—31no—
284#939—31no—
285#939—61no—
286#936—31no—
287#936—31no—
288#936—61no—
289#936—91no—
290#936—91no—
291#935—31no—
292#935—31no—
293#935—61no—
294#935—91no—
295D4×Dic3—91no—
296C4×#67—91no—
297#926—91no—
298#924—91no—
299#924—91no—
300#898—91no—
301#896—91no—
302#888—91no—
303#888—91no—
304#887—91no—
305#887—91no—
306#885—91no—
307#885—91no—
308#885—91no—
309#885—91no—
310#883—91no—
311#883—91no—
312#67⋊C4—91no—
313#879—91no—
314#879—91no—
315#879—91no—
316#879—91no—
317#878—91no—
318#878—91no—
319#878—91no—
320#878—91no—
321#878—91no—
322#877—91no—
323#877—91no—
324#876—91no—
325C4×Dic6—91no—
326C23×C32—21no—
327C23×C32—21no—
328C23×C32—21no—
329C23×C32—21no—
330C23×C32—21no—
331C23×C32—21no—
332C23×C32—41no—
333C23×C32—41no—
334C23×C32C22×D311yescharacteristic
335C23×C32C22×D311yescharacteristic
336C23×C32C22×D311yescharacteristic
337C23×C32C22×D311yescharacteristic
338C23×C32C22×D311yescharacteristic
339C23×C32C22×D311yescharacteristic
340C22×C3⋊D3C22×D311yescharacteristic
341C22×C3×D3—31no—
342C22×C3×D3—31no—
343C22×C3×D3—61no—
344C32×D4—41no—
345C32×D4—41no—
346C32×D4—41no—
347C32×D4—42no—
348C32×D4—42no—
349C32×D4—42no—
350C32×D4—44no—
351C2×C32×C4—21no—
352C2×C32×C4—21no—
353C2×C32×C4—21no—
354C2×C32×C4—41no—
355C2×C32×C4C22×D311yescharacteristic
356C2×C32×C4C22×D311yescharacteristic
357C2×C32×C4C22×D311yescharacteristic
358#638—22no—
359#638—41no—
360C2×C3⋊Dic3—22no—
361C2×C3⋊Dic3—41no—
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
370C2×C3⋊Dic3C22×D311yescharacteristic
371C2×C3⋊Dic3C22×D311yescharacteristic
372C2×C3⋊Dic3C22×D311yescharacteristic
373#634—41no—
374C3×#67—62no—
375C3×#67—62no—
376C3×#67—122no—
377C3×#67—121no—
378C3×#67—121no—
379C3×#67—122no—
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—31no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
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—61no—
409C2×C3×Dic3—61no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—62no—
414C2×C3×Dic3—62no—
415C2×C3×Dic3—122no—
416C2×C3×Dic3—121no—
417C2×C3×Dic3—121no—
418C2×C3×Dic3—122no—
419C3×Dic6—121no—
420C3×Dic6—121no—
421C3×Dic6—122no—
422#627—62no—
423#627—62no—
424#627—62no—
425#627—121no—
426#627—121no—
427#627—121no—
428#624—121no—
429D3×Dic3—121no—
430D3×Dic3—121no—
431#542—271noSylow
432C2×C33—41no—
433C2×C33—41no—
434C2×C33C2×#4111yescharacteristic
435C2×C33H(5,𝔽2)11yescharacteristic
436C2×C332−1+411yescharacteristic
437C3×C3⋊D3—41no—
438C2×C3×Q8—91no—
439C2×C3×D4—21no—
440C2×C3×D4—21no—
441C2×C3×D4—21no—
442C2×C3×D4—41no—
443C2×C3×D4—91no—
444C2×C3×D4—91no—
445C2×C3×D4D3211yescharacteristic
446C2×C3×D4D3211yescharacteristic
447C2×C3×D4D3211yescharacteristic
448C22×C3×C4—91no—
449C22×C3×C4—91no—
450C2×#67—31no—
451C2×#67—31no—
452C2×#67—31no—
453C2×#67—31no—
454C2×#67—61no—
455C2×#67—61no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—31no—
460C22×Dic3—61no—
461C22×Dic3—61no—
462C22×Dic3—91no—
463C2×C4×D3—91no—
464C2×C4×D3—91no—
465C2×Dic6—31no—
466C2×Dic6—31no—
467C2×Dic6—61no—
468C2×Dic6—91no—
469C2×Dic6—91no—
470C2×Dic6—91no—
471C2×Dic6—91no—
472C2×Dic6—91no—
473C2×Dic6—91no—
474C3×C4⋊C4—91no—
475C3×C4⋊C4—91no—
476C3×C4⋊C4—91no—
477C3×C22⋊C4—91no—
478C3×C22⋊C4—91no—
479C3×C22⋊C4—91no—
480C3×C22⋊C4—91no—
481C3×C22⋊C4—91no—
482C3×C22⋊C4—91no—
483C3×C22⋊C4—91no—
484C3×C22⋊C4—91no—
485C3×C22⋊C4—91no—
486C3×C42—91no—
487#217—31no—
488#217—31no—
489#217—31no—
490#217—31no—
491#217—31no—
492#217—31no—
493#217—31no—
494#217—31no—
495#217—31no—
496#217—31no—
497#217—31no—
498#217—31no—
499#217—31no—
500#217—31no—
501#217—31no—
502#217—31no—
503#217—61no—
504#217—61no—
505#217—61no—
506#217—61no—
507#217—61no—
508#217—61no—
509#217—61no—
510#217—61no—
511#217—91no—
512#217—91no—
513#217—91no—
514(C2×D3)⋊C4—31no—
515(C2×D3)⋊C4—31no—
516(C2×D3)⋊C4—61no—
517(C2×D3)⋊C4—91no—
518(C2×D3)⋊C4—91no—
519(C2×D3)⋊C4—91no—
520(C2×D3)⋊C4—91no—
521(C2×D3)⋊C4—91no—
522(C2×D3)⋊C4—91no—
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—61no—
537Dic3⋊C4—61no—
538Dic3⋊C4—61no—
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—91no—
553C4×Dic3—31no—
554C4×Dic3—31no—
555C4×Dic3—61no—
556C4×Dic3—91no—
557C4×Dic3—91no—
558C4×Dic3—91no—
559C4×Dic3—91no—
560C4×Dic3—91no—
561C4×Dic3—91no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C22×C32—21no—
566C22×C32—21no—
567C22×C32—22no—
568C22×C32—22no—
569C22×C32—21no—
570C22×C32—21no—
571C22×C32—21no—
572C22×C32—21no—
573C22×C32—21no—
574C22×C32—21no—
575C22×C32—21no—
576C22×C32—21no—
577C22×C32—21no—
578C22×C32—21no—
579C22×C32—21no—
580C22×C32—21no—
581C22×C32—21no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—21no—
585C22×C32—21no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—41no—
589C22×C32—41no—
590C22×C32—41no—
591C22×C32—41no—
592C22×C32—41no—
593C22×C32—42no—
594C22×C32—42no—
595C22×C32—41no—
596C22×C32—41no—
597C22×C32—41no—
598C22×C32—41no—
599C22×C32—41no—
600C22×C32—41no—
601C22×C32—41no—
602C22×C32—41no—
603C22×C32—41no—
604C22×C32—41no—
605C22×C32—41no—
606C22×C32—41no—
607C22×C32—81no—
608C22×C32—81no—
609C22×C32—81no—
610C22×C32—81no—
611C22×C32C23×D311yescharacteristic
612C22×C32C23×D311yescharacteristic
613C22×C32C23×D311yescharacteristic
614C2×C3⋊D3—21no—
615C2×C3⋊D3—21no—
616C2×C3⋊D3—21no—
617C2×C3×D3—61no—
618C2×C3×D3—61no—
619C2×C3×D3—61no—
620C2×C3×D3—61no—
621C2×C3×D3—61no—
622C2×C3×D3—61no—
623C2×C3×D3—121no—
624C2×C3×D3—121no—
625C2×C3×D3—121no—
626C32×C4—21no—
627C32×C4—22no—
628C32×C4—21no—
629C32×C4—21no—
630C32×C4—41no—
631C32×C4—41no—
632C32×C4—42no—
633C3⋊Dic3—21no—
634C3⋊Dic3—21no—
635C3⋊Dic3—21no—
636C3⋊Dic3—21no—
637C3⋊Dic3—21no—
638C3⋊Dic3—21no—
639C3⋊Dic3—21no—
640C3⋊Dic3—21no—
641C3⋊Dic3—21no—
642C3⋊Dic3—21no—
643C3⋊Dic3#23712yes—
644C3×Dic3—32no—
645C3×Dic3—32no—
646C3×Dic3—62no—
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—61no—
663C3×Dic3—61no—
664C3×Dic3—61no—
665C3×Dic3—61no—
666C3×Dic3—61no—
667C3×Dic3—121no—
668C3×Dic3—121no—
669C3×Dic3—121no—
670C3×Dic3—121no—
671C3×Dic3—121no—
672C3×Dic3—121no—
673C3×Dic3—121no—
674C3×Dic3—121no—
675C3×Dic3—121no—
676C3×Dic3—121no—
677C4⋊Q8—271no—
678#126—271no—
679#126—271no—
680#124—91no—
681#124—271no—
682#124—271no—
683#123—91no—
684#123—271no—
685C22⋊Q8—271no—
686C22⋊Q8—271no—
687C22⋊Q8—271no—
688#121—91no—
689C4×Q8—271no—
690C4×D4—271no—
691#117—271no—
692C33#54211yescharacteristic, complemented, Sylow
693C23×C3—21no—
694C23×C3—21no—
695C23×C3—21no—
696C23×C3—21no—
697C23×C3—21no—
698C23×C3—21no—
699C23×C3—41no—
700C23×C3—41no—
701C23×C3—91no—
702C23×C3C2×D3211yescharacteristic
703C23×C3C2×D3211yescharacteristic
704C23×C3C2×D3211yescharacteristic
705C23×C3C2×D3211yescharacteristic
706C23×C3C2×D3211yescharacteristic
707C23×C3C2×D3211yescharacteristic
708C22×D3—31no—
709C22×D3—31no—
710C22×D3—61no—
711C3×Q8—361no—
712C3×D4—41no—
713C3×D4—41no—
714C3×D4—41no—
715C3×D4—42no—
716C3×D4—42no—
717C3×D4—42no—
718C3×D4—44no—
719C3×D4—182no—
720C3×D4—361no—
721C2×C3×C4—21no—
722C2×C3×C4—21no—
723C2×C3×C4—21no—
724C2×C3×C4—41no—
725C2×C3×C4—91no—
726C2×C3×C4—91no—
727C2×C3×C4—91no—
728C2×C3×C4—91no—
729C2×C3×C4—91no—
730C2×C3×C4—91no—
731C2×C3×C4—91no—
732C2×C3×C4—91no—
733C2×C3×C4—91no—
734C2×C3×C4—91no—
735C2×C3×C4—91no—
736C2×C3×C4—182no—
737C2×C3×C4—361no—
738C2×C3×C4C2×D3211yescharacteristic
739C2×C3×C4C2×D3211yescharacteristic
740C2×C3×C4C2×D3211yescharacteristic
741#67—62no—
742#67—62no—
743#67—122no—
744#67—121no—
745#67—121no—
746#67—122no—
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—31no—
760C2×Dic3—31no—
761C2×Dic3—31no—
762C2×Dic3—31no—
763C2×Dic3—31no—
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—31no—
769C2×Dic3—61no—
770C2×Dic3—61no—
771C2×Dic3—61no—
772C2×Dic3—61no—
773C2×Dic3—61no—
774C2×Dic3—61no—
775C2×Dic3—61no—
776C2×Dic3—61no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—62no—
781C2×Dic3—62no—
782C2×Dic3—122no—
783C2×Dic3—121no—
784C2×Dic3—121no—
785C2×Dic3—122no—
786C2×Dic3—361no—
787C4×D3—361no—
788C4×D3—361no—
789Dic6—121no—
790Dic6—121no—
791Dic6—122no—
792Dic6—182no—
793Dic6—182no—
794Dic6—182no—
795Dic6—361no—
796Dic6—361no—
797Dic6—361no—
798C2×C32—21no—
799C2×C32—21no—
800C2×C32—21no—
801C2×C32—21no—
802C2×C32—21no—
803C2×C32—21no—
804C2×C32—21no—
805C2×C32—21no—
806C2×C32—21no—
807C2×C32—41no—
808C2×C32—41no—
809C2×C32—41no—
810C2×C32—41no—
811C2×C32—41no—
812C2×C32—42no—
813C2×C32—42no—
814C2×C32—41no—
815C2×C32—41no—
816C2×C32—41no—
817C2×C32—41no—
818C2×C32—81no—
819C2×C32—81no—
820C2×C32—81no—
821C2×C32—81no—
822C2×C32—82no—
823C2×C32—82no—
824C2×C32C2×#23711yescharacteristic
825C2×C32#100411yescharacteristic
826C2×C32#100411yescharacteristic
827C2×C32#100411yescharacteristic
828C2×C32D3×#4111yescharacteristic
829C2×C32D3×#4111yescharacteristic
830C2×C32#101011yescharacteristic
831C2×C32#101011yescharacteristic
832C2×C32#101011yescharacteristic
833C3⋊D3—41no—
834C3×D3—121no—
835C3×D3—121no—
836C3×D3—241no—
837C2×Q8—91no—
838C2×Q8—271no—
839C2×Q8—271no—
840C2×D4—91no—
841C2×D4—91no—
842C2×D4#111311yescharacteristic
843C22×C4—91no—
844C22×C4—91no—
845C22×C4—271no—
846C4⋊C4—91no—
847C4⋊C4—91no—
848C4⋊C4—91no—
849C4⋊C4—271no—
850C4⋊C4—271no—
851C4⋊C4—271no—
852C4⋊C4—271no—
853C4⋊C4—271no—
854C4⋊C4—271no—
855C4⋊C4—271no—
856C22⋊C4—91no—
857C22⋊C4—91no—
858C22⋊C4—91no—
859C22⋊C4—91no—
860C22⋊C4—91no—
861C22⋊C4—91no—
862C22⋊C4—91no—
863C22⋊C4—91no—
864C22⋊C4—91no—
865C22⋊C4—271no—
866C22⋊C4—271no—
867C22⋊C4—271no—
868C42—91no—
869C42—271no—
870C42—271no—
871C42—271no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—21no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—21no—
885C22×C3—21no—
886C22×C3—21no—
887C22×C3—21no—
888C22×C3—21no—
889C22×C3—21no—
890C22×C3—21no—
891C22×C3—21no—
892C22×C3—21no—
893C22×C3—21no—
894C22×C3—21no—
895C22×C3—41no—
896C22×C3—41no—
897C22×C3—41no—
898C22×C3—41no—
899C22×C3—41no—
900C22×C3—41no—
901C22×C3—41no—
902C22×C3—41no—
903C22×C3—41no—
904C22×C3—41no—
905C22×C3—41no—
906C22×C3—41no—
907C22×C3—41no—
908C22×C3—41no—
909C22×C3—41no—
910C22×C3—41no—
911C22×C3—42no—
912C22×C3—42no—
913C22×C3—41no—
914C22×C3—81no—
915C22×C3—81no—
916C22×C3—81no—
917C22×C3—81no—
918C22×C3—181no—
919C22×C3—181no—
920C22×C3—181no—
921C22×C3C22×D3211yescharacteristic
922C22×C3C22×D3211yescharacteristic
923C22×C3C22×D3211yescharacteristic
924C2×D3—61no—
925C2×D3—61no—
926C2×D3—61no—
927C2×D3—61no—
928C2×D3—61no—
929C2×D3—61no—
930C2×D3—121no—
931C2×D3—121no—
932C2×D3—121no—
933C3×C4—22no—
934C3×C4—21no—
935C3×C4—21no—
936C3×C4—21no—
937C3×C4—41no—
938C3×C4—41no—
939C3×C4—42no—
940C3×C4—92no—
941C3×C4—181no—
942C3×C4—181no—
943C3×C4—181no—
944C3×C4—181no—
945C3×C4—181no—
946C3×C4—181no—
947C3×C4—181no—
948C3×C4—181no—
949C3×C4—181no—
950C3×C4—181no—
951Dic3—32no—
952Dic3—32no—
953Dic3—62no—
954Dic3—61no—
955Dic3—61no—
956Dic3—61no—
957Dic3—61no—
958Dic3—61no—
959Dic3—61no—
960Dic3—61no—
961Dic3—61no—
962Dic3—61no—
963Dic3—61no—
964Dic3—61no—
965Dic3—61no—
966Dic3—61no—
967Dic3—61no—
968Dic3—61no—
969Dic3—61no—
970Dic3—61no—
971Dic3—61no—
972Dic3—61no—
973Dic3—61no—
974Dic3—121no—
975Dic3—121no—
976Dic3—121no—
977Dic3—121no—
978Dic3—121no—
979Dic3—121no—
980Dic3—121no—
981Dic3—121no—
982Dic3—121no—
983Dic3—121no—
984C32—21no—
985C32—21no—
986C32—21no—
987C32—41no—
988C32#560311yescharacteristic, complemented
989C32#566211yescharacteristic, complemented
990C32#566911yescharacteristic, complemented
991C23—91no—
992C23C2×#111311yescharacteristic
993C23C2×#111311yescharacteristic
994Q8—361no—
995Q8—542no—
996Q8—1081no—
997D4—41no—
998D4—182no—
999D4—361no—
1000C2×C4—91no—
1001C2×C4—91no—
1002C2×C4—91no—
1003C2×C4—91no—
1004C2×C4—91no—
1005C2×C4—91no—
1006C2×C4—91no—
1007C2×C4—91no—
1008C2×C4—91no—
1009C2×C4—91no—
1010C2×C4—91no—
1011C2×C4—182no—
1012C2×C4—361no—
1013C2×C4—1081no—
1014C2×C4C2×#111311yescharacteristic
1015C2×C3—21no—
1016C2×C3—21no—
1017C2×C3—21no—
1018C2×C3—21no—
1019C2×C3—21no—
1020C2×C3—21no—
1021C2×C3—21no—
1022C2×C3—21no—
1023C2×C3—21no—
1024C2×C3—42no—
1025C2×C3—42no—
1026C2×C3—41no—
1027C2×C3—41no—
1028C2×C3—41no—
1029C2×C3—41no—
1030C2×C3—41no—
1031C2×C3—41no—
1032C2×C3—41no—
1033C2×C3—41no—
1034C2×C3—41no—
1035C2×C3—81no—
1036C2×C3—81no—
1037C2×C3—81no—
1038C2×C3—81no—
1039C2×C3—82no—
1040C2×C3—82no—
1041C2×C3—361no—
1042C2×C3#6430911yescharacteristic
1043C2×C3#6430911yescharacteristic
1044C2×C3#6430911yescharacteristic
1045C2×C3D3×#23711yescharacteristic
1046C2×C3D3×#23711yescharacteristic
1047C2×C3#6431211yescharacteristic
1048C2×C3#6433011yescharacteristic
1049C2×C3#6433011yescharacteristic
1050C2×C3#6433011yescharacteristic
1051D3—121no—
1052D3—121no—
1053D3—241no—
1054C22—21no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22—21no—
1059C22—21no—
1060C22—181no—
1061C22—181no—
1062C22—181no—
1063C22C22×#111311yescharacteristic
1064C4—21no—
1065C4—92no—
1066C4—181no—
1067C4—181no—
1068C4—181no—
1069C4—181no—
1070C4—181no—
1071C4—181no—
1072C4—181no—
1073C4—181no—
1074C4—181no—
1075C4—181no—
1076C3—21no—
1077C3—21no—
1078C3—21no—
1079C3—41no—
1080C3#1059520111yescharacteristic, complemented
1081C3#1059520311yescharacteristic, complemented
1082C3#1059521111yescharacteristic, complemented
1083C2—41no—
1084C2—41no—
1085C2—361no—
1086C2#1172462011yescharacteristic
1087C2#1172462211yescharacteristic
1088C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC3×#64148C2
hypercenterC2×D4#1113
hypocenterC33#542
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64145C2semidirect
3. C3×#64144C2semidirect
4. #11723726C2semidirect
5. #11723724C2semidirect
6. #11723721C2semidirect
7. #11723721C2semidirect
8. #11723718C2semidirect
9. #11723718C2semidirect
10. #11723716C2semidirect
11. #11723715C2semidirect
12. #11723688C2semidirect
13. #11723676C2semidirect
14. #11723666C2semidirect
15. #11723665C2semidirect
55. #64145D3semidirect
56. #64144D3semidirect
692. C33#542semidirect
988. C32#5603semidirect
989. C32#5662semidirect
990. C32#5669semidirect
1080. C3#10595201semidirect
1081. C3#10595203semidirect
1082. C3#10595211semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C3×#641452
C3×#641442
#117237262
#117237242
#117237212
#117237182
#117237162
#117237152
#117236882
#117236762
#117236662
#117236652
#105952113
#105952033
#105952013