Finite Group Databasebeta

← #13178682

Subgroups — #13178682

Order 1728.

1200 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64148C211yesmaximal, characteristic, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4#11723725C211yesmaximal, characteristic, complemented
5#11723724C211yesmaximal, characteristic, complemented
6#11723721C211yesmaximal, characteristic, complemented
7#11723721C211yesmaximal, characteristic, complemented
8#11723720C211yesmaximal, characteristic, complemented
9#11723718C211yesmaximal, characteristic, complemented
10#11723718C211yesmaximal, characteristic, complemented
11#11723717C211yesmaximal, characteristic, complemented
12#11723694C211yesmaximal, characteristic, complemented
13#11723692C211yesmaximal, characteristic, complemented
14#11723671C211yesmaximal, characteristic, complemented
15#11723669C211yesmaximal, characteristic, complemented
16#10595265—31nomaximal
17#10595263—31nomaximal
18#10595260—31nomaximal
19C2×C33×D4C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic
24C22×C3×C3⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊Dic3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic
27C2×#6296C2211yescharacteristic
28C2×#6296C2211yescharacteristic
29C2×#6295C2211yescharacteristic
30C2×#6294C2211yescharacteristic
31C3×#3757C2211yescharacteristic
32C3×#3757C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C3×#3757C2211yescharacteristic
36C3×#3757C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
39C3×#3750C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88814C2211yescharacteristic
49#88814C2211yescharacteristic
50#88814C2211yescharacteristic
51#88814C2211yescharacteristic
52#88814C2211yescharacteristic
53#88813C2211yescharacteristic
54#64148D311yescharacteristic, complemented
55#64147D311yescharacteristic, complemented
56#64144D311yescharacteristic, complemented
57C3×#939—31no—
58C3×#939—31no—
59C3×#939—61no—
60C3×#938—31no—
61C3×#938—31no—
62C3×#938—61no—
63C3×#935—31no—
64C3×#935—31no—
65C3×#935—61no—
66#63982—31no—
67#63982—31no—
68#63980—31no—
69#63978—31no—
70#63978—31no—
71#63975—31no—
72#63971—31no—
73#63970—31no—
74#63969—31no—
75#63969—31no—
76#63966—31no—
77#63964—31no—
78#63964—31no—
79#63964—31no—
80#63964—31no—
81#63962—31no—
82#63961—31no—
83#63959—31no—
84#63959—31no—
85#63959—31no—
86#63959—31no—
87#63958—31no—
88#63953—31no—
89#63953—31no—
90#63905—31no—
91#63899—31no—
92#63895—31no—
93#63893—31no—
94#63865—31no—
95#63853—31no—
96#63851—31no—
97#63851—31no—
98#63850—31no—
99#63847—31no—
100#63846—31no—
101#63845—31no—
102C23×C33C2311yescharacteristic
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C33×D4—41no—
107C2×C33×C4C2311yescharacteristic
108C3×#638—41no—
109C3×#638—41no—
110C3×#638—41no—
111C3×#638—41no—
112C2×C3×C3⋊Dic3—41no—
113C2×C3×C3⋊Dic3—41no—
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
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C3×C4×C3⋊D3—41no—
125#6296—41no—
126#6296—41no—
127#6295—41no—
128#6294—41no—
129#5667—91no—
130#5621—91no—
131#5621—91no—
132C2×C32×D4—21no—
133C2×C32×D4—21no—
134C2×C32×D4—21no—
135C2×C32×D4—41no—
136C2×C32×D4C2×D311yescharacteristic
137C2×C32×D4C2×D311yescharacteristic
138C2×C32×D4C2×D311yescharacteristic
139C2×#638C2×D311yescharacteristic
140C2×#638C2×D311yescharacteristic
141C2×#638C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145C2×C4×C3⋊D3C2×D311yescharacteristic
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C2×C3×#67—61no—
156C2×C3×#67—61no—
157C2×C3×#67—61no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C22×C3×Dic3—61no—
163C22×C3×Dic3—61no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—61no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—31no—
171C2×#627—31no—
172C2×#627—31no—
173C2×#626—31no—
174C2×#626—31no—
175C2×#625—31no—
176C2×#624—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179#3757C2×D311yescharacteristic
180#3757C2×D311yescharacteristic
181#3757C2×D311yescharacteristic
182#3757C2×D311yescharacteristic
183#3757C2×D311yescharacteristic
184#3757C2×D311yescharacteristic
185#3752C2×D311yescharacteristic
186C4⋊(C3⋊Dic3)C2×D311yescharacteristic
187#3750C2×D311yescharacteristic
188#3750C2×D311yescharacteristic
189#3750C2×D311yescharacteristic
190C3×#217—31no—
191C3×#217—31no—
192C3×#217—31no—
193C3×#217—31no—
194C3×#217—31no—
195C3×#217—31no—
196C3×#217—31no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217—61no—
204C3×#217—61no—
205C3×#217—61no—
206C3×#217—61no—
207C3×#217—61no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—61no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—61no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—61no—
221C3×Dic3⋊C4—61no—
222C3×Dic3⋊C4—61no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—31no—
228#3724—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—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—31no—
240Dic3⋊Dic3—31no—
241#3722—31no—
242#3722—31no—
243#3722—31no—
244#3722—31no—
245#3722—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259C22×C33—21no—
260C22×C33—21no—
261C22×C33—21no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C33×C4—21no—
273C3×C3⋊Dic3—21no—
274C3×C3⋊Dic3—21no—
275C3×C3⋊Dic3—21no—
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×#123—91no—
284C3×#121—91no—
285C3×#121—91no—
286#939—31no—
287#939—31no—
288#939—61no—
289#939—91no—
290#939—91no—
291#939—91no—
292#938—31no—
293#938—31no—
294#938—61no—
295#938—91no—
296#936—91no—
297#936—91no—
298#935—31no—
299#935—31no—
300#935—61no—
301#935—91no—
302#935—91no—
303#930—91no—
304#929—91no—
305#929—91no—
306#924—91no—
307#924—91no—
308#924—91no—
309#897—91no—
310#896—91no—
311#896—91no—
312#896—91no—
313#894—91no—
314#890—91no—
315#889—91no—
316#889—91no—
317#886—91no—
318#885—91no—
319#885—91no—
320#885—91no—
321#885—91no—
322#884—91no—
323#883—91no—
324#883—91no—
325#883—91no—
326#878—91no—
327#878—91no—
328#878—91no—
329#878—91no—
330#878—91no—
331C23×C32—21no—
332C23×C32—21no—
333C23×C32—21no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—41no—
338C23×C32—41no—
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—31no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—61no—
352C22×C3×D3—61no—
353C32×D4—41no—
354C32×D4—41no—
355C32×D4—41no—
356C32×D4—42no—
357C32×D4—42no—
358C32×D4—42no—
359C32×D4—44no—
360C2×C32×C4—21no—
361C2×C32×C4—21no—
362C2×C32×C4—21no—
363C2×C32×C4—41no—
364C2×C32×C4C22×D311yescharacteristic
365C2×C32×C4C22×D311yescharacteristic
366C2×C32×C4C22×D311yescharacteristic
367#638—41no—
368#638—41no—
369#638—41no—
370#638—41no—
371C2×C3⋊Dic3—41no—
372C2×C3⋊Dic3—41no—
373C2×C3⋊Dic3C22×D311yescharacteristic
374C2×C3⋊Dic3C22×D311yescharacteristic
375C2×C3⋊Dic3C22×D311yescharacteristic
376C2×C3⋊Dic3C22×D311yescharacteristic
377C2×C3⋊Dic3C22×D311yescharacteristic
378C2×C3⋊Dic3C22×D311yescharacteristic
379C2×C3⋊Dic3C22×D311yescharacteristic
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C4×C3⋊D3—41no—
384C3×#67—121no—
385C3×#67—121no—
386C3×#67—121no—
387C3×#67—121no—
388C3×#67—121no—
389C3×#67—121no—
390C3×#67—121no—
391C3×#67—121no—
392C3×#67—122no—
393C3×#67—122no—
394C3×#67—122no—
395C3×#67—122no—
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—31no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3—121no—
428C2×C3×Dic3—121no—
429C2×C3×Dic3—121no—
430C2×C3×Dic3—122no—
431C2×C3×Dic3—122no—
432C3×C4×D3—121no—
433C3×C4×D3—121no—
434C3×C4×D3—122no—
435#627—121no—
436#627—121no—
437#627—121no—
438#627—121no—
439#627—121no—
440#627—121no—
441#626—121no—
442#626—121no—
443#625—121no—
444#624—121no—
445D3×Dic3—121no—
446D3×Dic3—121no—
447#562—271noSylow
448C2×C33—41no—
449C2×C33—41no—
450C2×C33H(5,𝔽2)11yescharacteristic
451C2×C33H(5,𝔽2)11yescharacteristic
452C2×C332−1+411yescharacteristic
453C3×C3⋊D3—41no—
454C3×C3⋊D3—41no—
455C2×C3×D4—21no—
456C2×C3×D4—21no—
457C2×C3×D4—21no—
458C2×C3×D4—41no—
459C2×C3×D4—91no—
460C2×C3×D4—91no—
461C2×C3×D4—91no—
462C2×C3×D4—91no—
463C2×C3×D4D3211yescharacteristic
464C2×C3×D4D3211yescharacteristic
465C2×C3×D4D3211yescharacteristic
466C22×C3×C4—91no—
467C22×C3×C4—91no—
468C22×C3×C4—91no—
469C2×#67—31no—
470C2×#67—31no—
471C2×#67—31no—
472C2×#67—31no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—31no—
477C2×#67—61no—
478C2×#67—61no—
479C2×#67—61no—
480C2×#67—61no—
481C2×#67—91no—
482C2×#67—91no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—31no—
486C22×Dic3—31no—
487C22×Dic3—61no—
488C22×Dic3—61no—
489C22×Dic3—91no—
490C2×D12—91no—
491C2×C4×D3—31no—
492C2×C4×D3—31no—
493C2×C4×D3—61no—
494C2×C4×D3—91no—
495C2×C4×D3—91no—
496C2×Dic6—91no—
497C2×Dic6—91no—
498C2×Dic6—91no—
499C2×Dic6—91no—
500C2×Dic6—91no—
501C2×Dic6—91no—
502C3×C4⋊C4—91no—
503C3×C4⋊C4—91no—
504C3×C4⋊C4—91no—
505C3×C4⋊C4—91no—
506C3×C22⋊C4—91no—
507C3×C22⋊C4—91no—
508C3×C22⋊C4—91no—
509C3×C22⋊C4—91no—
510C3×C22⋊C4—91no—
511C3×C22⋊C4—91no—
512C3×C22⋊C4—91no—
513#217—31no—
514#217—31no—
515#217—31no—
516#217—31no—
517#217—31no—
518#217—31no—
519#217—31no—
520#217—31no—
521#217—31no—
522#217—31no—
523#217—31no—
524#217—31no—
525#217—61no—
526#217—61no—
527#217—61no—
528#217—61no—
529#217—61no—
530#217—61no—
531#217—91no—
532#217—91no—
533#217—91no—
534#217—91no—
535#217—91no—
536(C2×D3)⋊C4—31no—
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—61no—
539(C2×D3)⋊C4—91no—
540(C2×D3)⋊C4—91no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543(C2×D3)⋊C4—91no—
544(C2×D3)⋊C4—91no—
545(C2×D3)⋊C4—91no—
546(C2×D3)⋊C4—91no—
547(C2×D3)⋊C4—91no—
548(C2×D3)⋊C4—91no—
549C4⋊Dic3—31no—
550C4⋊Dic3—31no—
551C4⋊Dic3—61no—
552C4⋊Dic3—91no—
553C4⋊Dic3—91no—
554C4⋊Dic3—91no—
555C4⋊Dic3—91no—
556C4⋊Dic3—91no—
557C4⋊Dic3—91no—
558Dic3⋊C4—31no—
559Dic3⋊C4—31no—
560Dic3⋊C4—31no—
561Dic3⋊C4—31no—
562Dic3⋊C4—31no—
563Dic3⋊C4—31no—
564Dic3⋊C4—61no—
565Dic3⋊C4—61no—
566Dic3⋊C4—61no—
567Dic3⋊C4—91no—
568Dic3⋊C4—91no—
569Dic3⋊C4—91no—
570Dic3⋊C4—91no—
571Dic3⋊C4—91no—
572Dic3⋊C4—91no—
573Dic3⋊C4—91no—
574Dic3⋊C4—91no—
575Dic3⋊C4—91no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C22×C32—21no—
583C22×C32—21no—
584C22×C32—22no—
585C22×C32—22no—
586C22×C32—21no—
587C22×C32—21no—
588C22×C32—21no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—21no—
592C22×C32—21no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—41no—
606C22×C32—41no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
611C22×C32—42no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—81no—
625C22×C32—81no—
626C22×C32—81no—
627C22×C32—81no—
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3×D3—62no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—61no—
645C2×C3×D3—61no—
646C2×C3×D3—61no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—121no—
651C2×C3×D3—121no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3—121no—
655C32×C4—21no—
656C32×C4—22no—
657C32×C4—21no—
658C32×C4—21no—
659C32×C4—41no—
660C32×C4—41no—
661C32×C4—42no—
662C3⋊Dic3—21no—
663C3⋊Dic3—21no—
664C3⋊Dic3—21no—
665C3⋊Dic3—21no—
666C3⋊Dic3—21no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—21no—
672C3×Dic3—62no—
673C3×Dic3—61no—
674C3×Dic3—61no—
675C3×Dic3—61no—
676C3×Dic3—61no—
677C3×Dic3—61no—
678C3×Dic3—61no—
679C3×Dic3—61no—
680C3×Dic3—61no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3—121no—
696C3×Dic3—121no—
697C3×Dic3—121no—
698C3×Dic3—121no—
699C3×Dic3—121no—
700C3×Dic3—121no—
701C3×Dic3—121no—
702#125—271no—
703#124—271no—
704#124—271no—
705#123—91no—
706#123—271no—
707#123—271no—
708#123—271no—
709C22⋊Q8—271no—
710C22⋊Q8—271no—
711C22⋊Q8—271no—
712C22⋊Q8—271no—
713#121—91no—
714#121—91no—
715#121—271no—
716#121—271no—
717C33#56211yescharacteristic, complemented, Sylow
718C23×C3—21no—
719C23×C3—21no—
720C23×C3—21no—
721C23×C3—21no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—41no—
725C23×C3—41no—
726C23×C3—91no—
727C23×C3—91no—
728C23×C3C2×D3211yescharacteristic
729C23×C3C2×D3211yescharacteristic
730C23×C3C2×D3211yescharacteristic
731C23×C3C2×D3211yescharacteristic
732C23×C3C2×D3211yescharacteristic
733C23×C3C2×D3211yescharacteristic
734C22×D3—31no—
735C22×D3—31no—
736C22×D3—31no—
737C22×D3—31no—
738C22×D3—61no—
739C22×D3—61no—
740C3×D4—41no—
741C3×D4—41no—
742C3×D4—41no—
743C3×D4—42no—
744C3×D4—42no—
745C3×D4—42no—
746C3×D4—44no—
747C3×D4—361no—
748C3×D4—361no—
749C3×D4—361no—
750C3×D4—361no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—41no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—91no—
758C2×C3×C4—91no—
759C2×C3×C4—91no—
760C2×C3×C4—91no—
761C2×C3×C4—91no—
762C2×C3×C4—91no—
763C2×C3×C4—91no—
764C2×C3×C4—91no—
765C2×C3×C4—361no—
766C2×C3×C4—361no—
767C2×C3×C4—361no—
768C2×C3×C4C2×D3211yescharacteristic
769C2×C3×C4C2×D3211yescharacteristic
770C2×C3×C4C2×D3211yescharacteristic
771#67—121no—
772#67—121no—
773#67—121no—
774#67—121no—
775#67—121no—
776#67—121no—
777#67—121no—
778#67—121no—
779#67—122no—
780#67—122no—
781#67—122no—
782#67—122no—
783#67—361no—
784#67—361no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—31no—
800C2×Dic3—31no—
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—31no—
804C2×Dic3—31no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—61no—
808C2×Dic3—61no—
809C2×Dic3—61no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—121no—
816C2×Dic3—121no—
817C2×Dic3—121no—
818C2×Dic3—121no—
819C2×Dic3—122no—
820C2×Dic3—122no—
821C2×Dic3—361no—
822D12—361no—
823C4×D3—121no—
824C4×D3—121no—
825C4×D3—122no—
826C4×D3—361no—
827C4×D3—361no—
828Dic6—361no—
829Dic6—361no—
830Dic6—361no—
831Dic6—361no—
832Dic6—361no—
833Dic6—361no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—41no—
844C2×C32—41no—
845C2×C32—41no—
846C2×C32—41no—
847C2×C32—41no—
848C2×C32—42no—
849C2×C32—42no—
850C2×C32—41no—
851C2×C32—41no—
852C2×C32—41no—
853C2×C32—41no—
854C2×C32—81no—
855C2×C32—81no—
856C2×C32—81no—
857C2×C32—81no—
858C2×C32—82no—
859C2×C32—82no—
860C2×C32#100411yescharacteristic
861C2×C32#100411yescharacteristic
862C2×C32#100411yescharacteristic
863C2×C32#100411yescharacteristic
864C2×C32#100411yescharacteristic
865C2×C32#100911yescharacteristic
866C2×C32#101011yescharacteristic
867C2×C32#101011yescharacteristic
868C2×C32#101011yescharacteristic
869C3⋊D3—41no—
870C3⋊D3—41no—
871C3×D3—122no—
872C3×D3—121no—
873C3×D3—121no—
874C3×D3—121no—
875C3×D3—121no—
876C3×D3—241no—
877C2×Q8—271no—
878C2×Q8—271no—
879C2×D4—91no—
880C2×D4—91no—
881C2×D4—91no—
882C2×D4—91no—
883C2×D4—271no—
884C2×D4#111311yescharacteristic
885C22×C4—91no—
886C22×C4—91no—
887C22×C4—91no—
888C22×C4—271no—
889C4⋊C4—91no—
890C4⋊C4—91no—
891C4⋊C4—91no—
892C4⋊C4—91no—
893C4⋊C4—271no—
894C4⋊C4—271no—
895C4⋊C4—271no—
896C4⋊C4—271no—
897C4⋊C4—271no—
898C4⋊C4—271no—
899C22⋊C4—91no—
900C22⋊C4—91no—
901C22⋊C4—91no—
902C22⋊C4—91no—
903C22⋊C4—91no—
904C22⋊C4—91no—
905C22⋊C4—91no—
906C22⋊C4—271no—
907C22⋊C4—271no—
908C22⋊C4—271no—
909C22⋊C4—271no—
910C22⋊C4—271no—
911C42—271no—
912C22×C3—22no—
913C22×C3—22no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—21no—
919C22×C3—21no—
920C22×C3—21no—
921C22×C3—21no—
922C22×C3—21no—
923C22×C3—21no—
924C22×C3—21no—
925C22×C3—21no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—21no—
930C22×C3—21no—
931C22×C3—21no—
932C22×C3—21no—
933C22×C3—21no—
934C22×C3—21no—
935C22×C3—41no—
936C22×C3—41no—
937C22×C3—41no—
938C22×C3—41no—
939C22×C3—41no—
940C22×C3—41no—
941C22×C3—41no—
942C22×C3—41no—
943C22×C3—41no—
944C22×C3—41no—
945C22×C3—41no—
946C22×C3—41no—
947C22×C3—41no—
948C22×C3—41no—
949C22×C3—41no—
950C22×C3—41no—
951C22×C3—42no—
952C22×C3—42no—
953C22×C3—41no—
954C22×C3—81no—
955C22×C3—81no—
956C22×C3—81no—
957C22×C3—81no—
958C22×C3—181no—
959C22×C3—181no—
960C22×C3—181no—
961C22×C3—181no—
962C22×C3—181no—
963C22×C3—181no—
964C22×C3C22×D3211yescharacteristic
965C22×C3C22×D3211yescharacteristic
966C22×C3C22×D3211yescharacteristic
967C2×D3—62no—
968C2×D3—61no—
969C2×D3—61no—
970C2×D3—61no—
971C2×D3—61no—
972C2×D3—61no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—61no—
978C2×D3—61no—
979C2×D3—61no—
980C2×D3—121no—
981C2×D3—121no—
982C2×D3—121no—
983C2×D3—121no—
984C2×D3—121no—
985C3×C4—22no—
986C3×C4—21no—
987C3×C4—21no—
988C3×C4—21no—
989C3×C4—41no—
990C3×C4—41no—
991C3×C4—42no—
992C3×C4—181no—
993C3×C4—181no—
994C3×C4—181no—
995C3×C4—181no—
996C3×C4—181no—
997C3×C4—181no—
998C3×C4—181no—
999C3×C4—181no—
1000C3×C4—181no—
1001C3×C4—181no—
1002Dic3—62no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—61no—
1011Dic3—61no—
1012Dic3—61no—
1013Dic3—61no—
1014Dic3—61no—
1015Dic3—61no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—121no—
1024Dic3—121no—
1025Dic3—121no—
1026Dic3—121no—
1027Dic3—121no—
1028Dic3—121no—
1029Dic3—121no—
1030Dic3—121no—
1031Dic3—121no—
1032C32—21no—
1033C32—21no—
1034C32—21no—
1035C32—41no—
1036C32#562111yescharacteristic, complemented
1037C32#562111yescharacteristic, complemented
1038C32#566711yescharacteristic, complemented
1039C23—91no—
1040C23—91no—
1041C23C2×#111311yescharacteristic
1042C23C2×#111311yescharacteristic
1043Q8—1081no—
1044Q8—1081no—
1045D4—41no—
1046D4—361no—
1047D4—361no—
1048D4—361no—
1049D4—361no—
1050D4—1081no—
1051C2×C4—91no—
1052C2×C4—91no—
1053C2×C4—91no—
1054C2×C4—91no—
1055C2×C4—91no—
1056C2×C4—91no—
1057C2×C4—91no—
1058C2×C4—91no—
1059C2×C4—91no—
1060C2×C4—91no—
1061C2×C4—361no—
1062C2×C4—361no—
1063C2×C4—361no—
1064C2×C4—1081no—
1065C2×C4C2×#111311yescharacteristic
1066C2×C3—21no—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—42no—
1076C2×C3—42no—
1077C2×C3—41no—
1078C2×C3—41no—
1079C2×C3—41no—
1080C2×C3—41no—
1081C2×C3—41no—
1082C2×C3—41no—
1083C2×C3—41no—
1084C2×C3—41no—
1085C2×C3—41no—
1086C2×C3—81no—
1087C2×C3—81no—
1088C2×C3—81no—
1089C2×C3—81no—
1090C2×C3—82no—
1091C2×C3—82no—
1092C2×C3—361no—
1093C2×C3—361no—
1094C2×C3#6430911yescharacteristic
1095C2×C3#6430911yescharacteristic
1096C2×C3#6430911yescharacteristic
1097C2×C3#6431311yescharacteristic
1098C2×C3#6431411yescharacteristic
1099C2×C3#6431411yescharacteristic
1100C2×C3#6433011yescharacteristic
1101C2×C3#6433011yescharacteristic
1102C2×C3#6433011yescharacteristic
1103D3—122no—
1104D3—121no—
1105D3—121no—
1106D3—121no—
1107D3—121no—
1108D3—241no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—181no—
1116C22—181no—
1117C22—181no—
1118C22—181no—
1119C22—181no—
1120C22—181no—
1121C22C22×#111311yescharacteristic
1122C4—21no—
1123C4—181no—
1124C4—181no—
1125C4—181no—
1126C4—181no—
1127C4—181no—
1128C4—181no—
1129C4—181no—
1130C4—181no—
1131C4—181no—
1132C4—181no—
1133C3—21no—
1134C3—21no—
1135C3—21no—
1136C3—41no—
1137C3#1059526011yescharacteristic, complemented
1138C3#1059526311yescharacteristic, complemented
1139C3#1059526511yescharacteristic, complemented
1140C2—41no—
1141C2—41no—
1142C2—361no—
1143C2—361no—
1144C2#1172462011yescharacteristic
1145C2#1172462311yescharacteristic
1146C2#1172463311yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#562
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C3×#64148C2semidirect
2. C3×#64147C2semidirect
3. C3×#64144C2semidirect
4. #11723725C2semidirect
5. #11723724C2semidirect
6. #11723721C2semidirect
7. #11723721C2semidirect
8. #11723720C2semidirect
9. #11723718C2semidirect
10. #11723718C2semidirect
11. #11723717C2semidirect
12. #11723694C2semidirect
13. #11723692C2semidirect
14. #11723671C2semidirect
15. #11723669C2semidirect
54. #64148D3semidirect
55. #64147D3semidirect
56. #64144D3semidirect
717. C33#562semidirect
1036. C32#5621semidirect
1037. C32#5621semidirect
1038. C32#5667semidirect
1137. C3#10595260semidirect
1138. C3#10595263semidirect
1139. C3#10595265semidirect

Maximal subgroups

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

subgroupindex
C3×#641482
C3×#641472
C3×#641442
#117237252
#117237242
#117237212
#117237202
#117237182
#117237172
#117236942
#117236922
#117236712
#117236692
#105952653
#105952633
#105952603