Finite Group Databasebeta

← C2×#72220152 #72244625

Subgroups — C2×#72220152 #72244625

Order 5184.

4236 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊(#1094⋊C4)C211yesmaximal, characteristic, complemented
2C22×C3⋊(((C22⋊C9)⋊C2)⋊C3)C211yesmaximal, characteristic, complemented
3C23×C3×#1094C211yesmaximal, characteristic, complemented
4#72220152C214yesmaximal, direct product factor
5C2×C3×#64162—31nomaximal
6C2×#11722396C311yesmaximal, characteristic, complemented
7C2×#63694⋊C3—33nomaximal
8C22×C3×#1094—22no—
9C22×C3×#1094C2211yescharacteristic
10C22×C3×#1094C2212yescomplemented
11C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)—22no—
12C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)C2212yescomplemented
13C2×#10619980—41nomaximal
14C3⋊(#1094⋊C4)C2212yescomplemented
15C25×C33D311yescharacteristic
16C22×C3×#638—31no—
17C22×C3×#638—31no—
18C22×C3×#638—31no—
19C23×#1094—23no—
20C23×#1094D313yescomplemented
21C23×C3×C22⋊C9—21no—
22C23×C3×C22⋊C9C2×C311yescharacteristic, complemented
23C22×C3⋊((C22⋊C9)⋊C2)C2×C311yescharacteristic, complemented
24C22×((C22⋊C9)⋊C2)⋊C3—33no—
25C3×#64162—34no—
26C3×#64162—34no—
27C2×C3×#3757—31no—
28C2×C3×#3757—31no—
29C2×C3×#3757—31no—
30#11722396C2×C314yescomplemented
31C2×C3⋊((C22⋊C9)⋊C4)C2×C311yescharacteristic, complemented
32#63694⋊C3—312no—
33C2×#1094⋊C4—33no—
34C23×C3×3−1+2—41no—
35C22×C3⋊AGL(1,ℤ/9)—41no—
36C2×C3×#1094—22no—
37C2×C3×#1094D412yescomplemented
38C2×C3×#1094C2311yescharacteristic
39C3⋊(((C22⋊C9)⋊C2)⋊C3)—22no—
40#10619980—44no—
41C2×C3⋊(3−1+2⋊C4)—41no—
42C2×#64162—31no—
43C2×C3×#953—93no—
44C2×C3×#953—91no—
45C2×#63694—33no—
46C24×C33—22no—
47C24×C33—31no—
48C24×C33—31no—
49C24×C33—32no—
50C24×C33—62no—
51C24×C33C2×D312yes—
52C24×C33C2×D311yescharacteristic
53C23×C3×C3⋊D3—31no—
54C2×C3×#638—34no—
55C2×C3×#638—32no—
56C2×C3×#638—34no—
57C2×C3×#638—32no—
58C2×C3×#638—62no—
59C2×C3×#638—64no—
60C2×C3×#638—62no—
61C2×C3×#638—61no—
62C2×C3×#638—62no—
63C2×C3×#638—61no—
64C22×C3×C3⋊Dic3—31no—
65C22×C3×C3⋊Dic3—31no—
66C22×C3×C3⋊Dic3—31no—
67C22×#1094—212no—
68C22×#1094—23no—
69C22×#1094—26no—
70C22×#1094—26no—
71C22×#1094C2×D313yes—
72C22×#1094C2×D316yescomplemented
73C22×C3×C22⋊C9—24no—
74C22×C3×C22⋊C9—22no—
75C22×C3×C22⋊C9—21no—
76C22×C3×C22⋊C9—22no—
77C22×C3×C22⋊C9C22×C311yescharacteristic
78C22×C3×C22⋊C9C22×C312yescomplemented
79C2×C3⋊((C22⋊C9)⋊C2)—22no—
80C2×C3⋊((C22⋊C9)⋊C2)C22×C312yescomplemented
81C2×((C22⋊C9)⋊C2)⋊C3—36no—
82C2×((C22⋊C9)⋊C2)⋊C3—66no—
83C3×#3757—34no—
84C3×#3757—32no—
85C3×#3757—34no—
86C3×#3757—32no—
87C2×#6233—41no—
88C2×#611⋊C3—123no—
89C3⋊((C22⋊C9)⋊C4)C22×C312yescomplemented
90#1094⋊C4—36no—
91C22×C3×3−1+2—41no—
92C22×C3×3−1+2—42no—
93C22×C3×3−1+2—82no—
94C2×C3⋊AGL(1,ℤ/9)—42no—
95C2×C3⋊AGL(1,ℤ/9)—82no—
96C3×#1094C2×D411yescharacteristic, complemented
97C3⋊(3−1+2⋊C4)—42no—
98C25×C32—21no—
99C25×C32—33no—
100C25×C32C3×D311yescharacteristic
101C25×C32C3⋊D311yescharacteristic
102C22×#638—31no—
103C22×#638—31no—
104C22×#638—31no—
105C22×C3×#67—91no—
106C22×C3×#67—93no—
107C22×C3×#67—93no—
108C22×C3×#67—93no—
109C22×C3×#67—91no—
110C22×C3×#67—91no—
111C23×C22⋊C9—23no—
112C23×C22⋊C9C3×D313yescomplemented
113C22×(C22⋊C9)⋊C2—33no—
114#64162—34no—
115#64162—34no—
116C2×#3757—31no—
117C2×#3757—31no—
118C2×#3757—31no—
119C3×#953—94no—
120C3×#953—912no—
121C3×#953—912no—
122C3×#953—94no—
123C2×C3×#217—91no—
124C2×C3×#217—93no—
125C2×C3×#217—93no—
126C2×C3×#217—93no—
127C2×C3×#217—91no—
128C2×C3×#217—91no—
129#63694—312no—
130C2×(C22⋊C9)⋊C4—33no—
131C23×C33—22no—
132C23×C33—31no—
133C23×C33—31no—
134C23×C33—32no—
135C23×C33—32no—
136C23×C33—34no—
137C23×C33—32no—
138C23×C33—32no—
139C23×C33—31no—
140C23×C33—62no—
141C23×C33—62no—
142C23×C33—61no—
143C23×C33—62no—
144C23×C33—64no—
145C23×C33—62no—
146C23×C33—64no—
147C23×C33#6712yes—
148C23×C33S411yescharacteristic
149C23×C33C22×D311yescharacteristic
150C22×C3×C3⋊D3—32no—
151C22×C3×C3⋊D3—62no—
152C22×C3×C3⋊D3—62no—
153C22×C3×C3⋊D3—61no—
154C22×C3×C3⋊D3—61no—
155C3×#638—64no—
156C3×#638—62no—
157C3×#638—68no—
158C3×#638—64no—
159C3×#638—62no—
160C3×#638—64no—
161C2×C3×C3⋊Dic3—32no—
162C2×C3×C3⋊Dic3—32no—
163C2×C3×C3⋊Dic3—32no—
164C2×C3×C3⋊Dic3—62no—
165C2×C3×C3⋊Dic3—62no—
166C2×C3×C3⋊Dic3—61no—
167C2×C3×C3⋊Dic3—61no—
168C23×3−1+2—43no—
169C23×3−1+2—83no—
170C23×C3×C9—41no—
171C23×C3×C9—81no—
172C22×C3⋊D9—41no—
173C22×AGL(1,ℤ/9)—123no—
174C2×#1094—212no—
175C2×#1094—26no—
176C2×#1094—23no—
177C2×#1094—26no—
178C2×#1094#6716yescomplemented
179C2×#1094C22×D313yes—
180C2×C3×C22⋊C9—24no—
181C2×C3×C22⋊C9—22no—
182C2×C3×C22⋊C9—21no—
183C2×C3×C22⋊C9—22no—
184C2×C3×C22⋊C9C3×D412yescomplemented
185C2×C3×C22⋊C9C23×C311yescharacteristic
186C3⋊((C22⋊C9)⋊C2)—22no—
187((C22⋊C9)⋊C2)⋊C3—66no—
188#6233—44no—
189C2×C3⋊Dic9—41no—
190#611⋊C3—1212no—
191C2×3−1+2⋊C4—123no—
192C2×C3×#120—271no—
193C2×#953—93no—
194C2×#953—91no—
195C2×C3×3−1+2—42no—
196C2×C3×3−1+2—41no—
197C2×C3×3−1+2—82no—
198C3⋊AGL(1,ℤ/9)—82no—
199C24×C32—24no—
200C24×C32—22no—
201C24×C32—21no—
202C24×C32—22no—
203C24×C32—22no—
204C24×C32—31no—
205C24×C32—31no—
206C24×C32—33no—
207C24×C32—33no—
208C24×C32—33no—
209C24×C32—31no—
210C24×C32—31no—
211C24×C32—32no—
212C24×C32—32no—
213C24×C32—36no—
214C24×C32—36no—
215C24×C32—61no—
216C24×C32—62no—
217C24×C32—62no—
218C24×C32—66no—
219C24×C32—63no—
220C24×C32—66no—
221C24×C32—63no—
222C24×C32—612no—
223C24×C32—66no—
224C24×C32—61no—
225C24×C32—62no—
226C24×C32—64no—
227C24×C32C2×C3×D312yes—
228C24×C32C2×C3×D311yescharacteristic
229C24×C32C2×C3⋊D312yes—
230C24×C32C2×C3⋊D311yescharacteristic
231C23×C3⋊D3—31no—
232C23×C3×D3—93no—
233C23×C3×D3—91no—
234C2×#638—34no—
235C2×#638—32no—
236C2×#638—34no—
237C2×#638—32no—
238C2×#638—62no—
239C2×#638—64no—
240C2×#638—62no—
241C2×#638—61no—
242C2×#638—62no—
243C2×#638—61no—
244C22×C3⋊Dic3—31no—
245C22×C3⋊Dic3—31no—
246C22×C3⋊Dic3—31no—
247C2×C3×#67—92no—
248C2×C3×#67—94no—
249C2×C3×#67—96no—
250C2×C3×#67—912no—
251C2×C3×#67—912no—
252C2×C3×#67—96no—
253C2×C3×#67—94no—
254C2×C3×#67—92no—
255C2×C3×#67—182no—
256C2×C3×#67—186no—
257C2×C3×#67—1812no—
258C2×C3×#67—186no—
259C2×C3×#67—184no—
260C2×C3×#67—183no—
261C2×C3×#67—186no—
262C2×C3×#67—183no—
263C2×C3×#67—182no—
264C2×C3×#67—181no—
265C2×C3×#67—182no—
266C2×C3×#67—181no—
267C22×C3×Dic3—93no—
268C22×C3×Dic3—93no—
269C22×C3×Dic3—93no—
270C22×C3×Dic3—91no—
271C22×C3×Dic3—91no—
272C22×C3×Dic3—91no—
273C22×C22⋊C9—212no—
274C22×C22⋊C9—23no—
275C22×C22⋊C9—26no—
276C22×C22⋊C9—26no—
277C22×C22⋊C9C2×C3×D313yes—
278C22×C22⋊C9C2×C3×D316yescomplemented
279C2×(C22⋊C9)⋊C2—36no—
280C2×(C22⋊C9)⋊C2—66no—
281#3757—34no—
282#3757—32no—
283#3757—34no—
284#3757—32no—
285C3×#217—94no—
286C3×#217—92no—
287C3×#217—96no—
288C3×#217—912no—
289C3×#217—912no—
290C3×#217—94no—
291C3×#217—96no—
292C3×#217—92no—
293C2×#611—123no—
294(C22⋊C9)⋊C4—36no—
295C22×C33—22no—
296C22×C33—32no—
297C22×C33—32no—
298C22×C33—31no—
299C22×C33—31no—
300C22×C33—32no—
301C22×C33—31no—
302C22×C33—34no—
303C22×C33—32no—
304C22×C33—62no—
305C22×C33—62no—
306C22×C33—64no—
307C22×C33—61no—
308C22×C33—64no—
309C22×C33—62no—
310C22×C33—62no—
311C22×C33C2×#6711yescharacteristic
312C22×C33C2×S412yes—
313C22×C33C2×S411yescharacteristic
314C2×C3×C3⋊D3—62no—
315C2×C3×C3⋊D3—62no—
316C2×C3×C3⋊D3—62no—
317C2×C3×C3⋊D3—122no—
318C2×C3×C3⋊D3—122no—
319C3×C3⋊Dic3—62no—
320C3×C3⋊Dic3—62no—
321C3×C3⋊Dic3—62no—
322C22×3−1+2—43no—
323C22×3−1+2—46no—
324C22×3−1+2—86no—
325C22×3−1+2—83no—
326C22×3−1+2—86no—
327C22×3−1+2—812no—
328C22×C3×C9—41no—
329C22×C3×C9—42no—
330C22×C3×C9—82no—
331C22×C3×C9—84no—
332C22×C3×C9—82no—
333C22×C3×C9—81no—
334C2×C3⋊D9—42no—
335C2×C3⋊D9—82no—
336C2×AGL(1,ℤ/9)—126no—
337C2×AGL(1,ℤ/9)—246no—
338#1094—23no—
339#1094C2×#6713yescomplemented
340C3×C22⋊C9—21no—
341C3×C22⋊C9C2×C3×D411yescharacteristic, complemented
342C3⋊Dic9—42no—
3433−1+2⋊C4—126no—
344C25×C3—31no—
345C25×C3—61no—
346C25×C3AGL(1,ℤ/9)13yescomplemented
347C25×C3C3×C3⋊D311yescharacteristic
348C22×C3×D4—271no—
349C22×C3×D4—271no—
350C22×C3×D4—271no—
351C22×#67—93no—
352C22×#67—91no—
353C22×#67—93no—
354C22×#67—91no—
355C22×#67—93no—
356C22×#67—91no—
357C3×#120—274no—
358C3×#120—274no—
359C2×C3×C22⋊C4—271no—
360C2×C3×C22⋊C4—271no—
361C2×C3×C22⋊C4—271no—
362#953—912no—
363#953—94no—
364#953—912no—
365#953—94no—
366C2×#217—93no—
367C2×#217—91no—
368C2×#217—93no—
369C2×#217—91no—
370C2×#217—93no—
371C2×#217—91no—
372C3×3−1+2—41noSylow
373C23×C32—22no—
374C23×C32—24no—
375C23×C32—22no—
376C23×C32—22no—
377C23×C32—21no—
378C23×C32—21no—
379C23×C32—31no—
380C23×C32—31no—
381C23×C32—32no—
382C23×C32—32no—
383C23×C32—34no—
384C23×C32—32no—
385C23×C32—31no—
386C23×C32—32no—
387C23×C32—33no—
388C23×C32—31no—
389C23×C32—31no—
390C23×C32—32no—
391C23×C32—32no—
392C23×C32—33no—
393C23×C32—36no—
394C23×C32—36no—
395C23×C32—36no—
396C23×C32—312no—
397C23×C32—34no—
398C23×C32—33no—
399C23×C32—36no—
400C23×C32—32no—
401C23×C32—32no—
402C23×C32—31no—
403C23×C32—36no—
404C23×C32—33no—
405C23×C32—33no—
406C23×C32—66no—
407C23×C32—61no—
408C23×C32—62no—
409C23×C32—61no—
410C23×C32—62no—
411C23×C32—63no—
412C23×C32—63no—
413C23×C32—66no—
414C23×C32—66no—
415C23×C32—63no—
416C23×C32—66no—
417C23×C32—66no—
418C23×C32—61no—
419C23×C32—62no—
420C23×C32—62no—
421C23×C32—64no—
422C23×C32—612no—
423C23×C32—62no—
424C23×C32—62no—
425C23×C32—62no—
426C23×C32—62no—
427C23×C32—64no—
428C23×C32—64no—
429C23×C32—62no—
430C23×C32—62no—
431C23×C32—61no—
432C23×C32—61no—
433C23×C32—64no—
434C23×C32—62no—
435C23×C32—64no—
436C23×C32—62no—
437C23×C32—66no—
438C23×C32—66no—
439C23×C32—612no—
440C23×C32—66no—
441C23×C32—63no—
442C23×C32—66no—
443C23×C32—66no—
444C23×C32—612no—
445C23×C32—64no—
446C23×C32—64no—
447C23×C32—612no—
448C23×C32—64no—
449C23×C32—64no—
450C23×C32—68no—
451C23×C32—612no—
452C23×C32—612no—
453C23×C32—62no—
454C23×C32—624no—
455C23×C32—612no—
456C23×C32—68no—
457C23×C32—624no—
458C23×C32C3×#6712yes—
459C23×C32#63812yes—
460C23×C32C3×S411yescharacteristic
461C23×C32C3⋊S411yescharacteristic
462C23×C32C22×C3×D311yescharacteristic
463C23×C32C22×C3⋊D311yescharacteristic
464C22×C3⋊D3—32no—
465C22×C3⋊D3—62no—
466C22×C3⋊D3—62no—
467C22×C3⋊D3—61no—
468C22×C3⋊D3—61no—
469C22×C3×D3—96no—
470C22×C3×D3—92no—
471C22×C3×D3—186no—
472C22×C3×D3—186no—
473C22×C3×D3—183no—
474C22×C3×D3—182no—
475C22×C3×D3—182no—
476C22×C3×D3—181no—
477C22×C3×D3—183no—
478C22×C3×D3—181no—
479#638—64no—
480#638—62no—
481#638—68no—
482#638—64no—
483#638—64no—
484#638—62no—
485C2×C3⋊Dic3—32no—
486C2×C3⋊Dic3—32no—
487C2×C3⋊Dic3—32no—
488C2×C3⋊Dic3—62no—
489C2×C3⋊Dic3—62no—
490C2×C3⋊Dic3—61no—
491C2×C3⋊Dic3—61no—
492C3×#67—184no—
493C3×#67—182no—
494C3×#67—1812no—
495C3×#67—186no—
496C3×#67—1824no—
497C3×#67—188no—
498C3×#67—1812no—
499C3×#67—184no—
500C3×#67—1812no—
501C3×#67—186no—
502C3×#67—184no—
503C3×#67—182no—
504C2×C3×Dic3—96no—
505C2×C3×Dic3—96no—
506C2×C3×Dic3—96no—
507C2×C3×Dic3—92no—
508C2×C3×Dic3—92no—
509C2×C3×Dic3—92no—
510C2×C3×Dic3—186no—
511C2×C3×Dic3—186no—
512C2×C3×Dic3—183no—
513C2×C3×Dic3—182no—
514C2×C3×Dic3—182no—
515C2×C3×Dic3—181no—
516C2×C3×Dic3—183no—
517C2×C3×Dic3—181no—
518C23×C9—43no—
519C23×C9—83no—
520C22×D9—123no—
521C2×C22⋊C9—212no—
522C2×C22⋊C9—26no—
523C2×C22⋊C9—26no—
524C2×C22⋊C9—23no—
525C2×C22⋊C9C3×#6716yescomplemented
526C2×C22⋊C9C22×C3×D313yes—
527(C22⋊C9)⋊C2—66no—
528#611—1212no—
529C2×Dic9—123no—
530C2×#120—271noSylow
531C2×C33—22no—
532C2×C33—31no—
533C2×C33—31no—
534C2×C33—32no—
535C2×C33—62no—
536C2×C33GL(2,ℤ/4)12yes—
537C2×C33C22×S411yescharacteristic
538C3×C3⋊D3—122no—
539C2×3−1+2—46no—
540C2×3−1+2—43no—
541C2×3−1+2—86no—
542C2×3−1+2—83no—
543C2×3−1+2—86no—
544C2×3−1+2—812no—
545C2×C3×C9—42no—
546C2×C3×C9—41no—
547C2×C3×C9—82no—
548C2×C3×C9—84no—
549C2×C3×C9—82no—
550C2×C3×C9—81no—
551C3⋊D9—82no—
552AGL(1,ℤ/9)—246no—
553C24×C3—26no—
554C24×C3—22no—
555C24×C3—33no—
556C24×C3—31no—
557C24×C3—31no—
558C24×C3—31no—
559C24×C3—33no—
560C24×C3—31no—
561C24×C3—36no—
562C24×C3—32no—
563C24×C3—32no—
564C24×C3—31no—
565C24×C3—32no—
566C24×C3—62no—
567C24×C3—64no—
568C24×C3—61no—
569C24×C3—61no—
570C24×C3—62no—
571C24×C3—63no—
572C24×C3—63no—
573C24×C3—66no—
574C24×C3—66no—
575C24×C3—62no—
576C24×C3—64no—
577C24×C3—62no—
578C24×C3—612no—
579C24×C3—61no—
580C24×C3—62no—
581C24×C3—271no—
582C24×C3C2×AGL(1,ℤ/9)13yes—
583C24×C3C2×AGL(1,ℤ/9)16yescomplemented
584C24×C3C2×C3×C3⋊D311yescharacteristic
585C24×C3C2×C3×C3⋊D312yes—
586C23×D3—91no—
587C23×D3—93no—
588C2×C3×D4—272no—
589C2×C3×D4—274no—
590C2×C3×D4—274no—
591C2×C3×D4—272no—
592C2×C3×D4—542no—
593C2×C3×D4—544no—
594C2×C3×D4—542no—
595C2×C3×D4—541no—
596C2×C3×D4—542no—
597C2×C3×D4—541no—
598C22×C3×C4—271no—
599C22×C3×C4—271no—
600C22×C3×C4—271no—
601C2×#67—96no—
602C2×#67—912no—
603C2×#67—92no—
604C2×#67—94no—
605C2×#67—94no—
606C2×#67—912no—
607C2×#67—96no—
608C2×#67—92no—
609C2×#67—186no—
610C2×#67—182no—
611C2×#67—1812no—
612C2×#67—184no—
613C2×#67—182no—
614C2×#67—186no—
615C2×#67—181no—
616C2×#67—183no—
617C2×#67—186no—
618C2×#67—183no—
619C2×#67—182no—
620C2×#67—181no—
621C22×Dic3—91no—
622C22×Dic3—91no—
623C22×Dic3—93no—
624C22×Dic3—93no—
625C22×Dic3—91no—
626C22×Dic3—93no—
627C3×C22⋊C4—272no—
628C3×C22⋊C4—274no—
629C3×C22⋊C4—274no—
630C3×C22⋊C4—272no—
631#217—96no—
632#217—912no—
633#217—94no—
634#217—92no—
635#217—94no—
636#217—912no—
637#217—96no—
638#217—92no—
639C22×C32—22no—
640C22×C32—24no—
641C22×C32—22no—
642C22×C32—21no—
643C22×C32—22no—
644C22×C32—21no—
645C22×C32—32no—
646C22×C32—31no—
647C22×C32—32no—
648C22×C32—32no—
649C22×C32—31no—
650C22×C32—31no—
651C22×C32—34no—
652C22×C32—32no—
653C22×C32—32no—
654C22×C32—31no—
655C22×C32—33no—
656C22×C32—33no—
657C22×C32—36no—
658C22×C32—36no—
659C22×C32—32no—
660C22×C32—32no—
661C22×C32—31no—
662C22×C32—31no—
663C22×C32—36no—
664C22×C32—33no—
665C22×C32—312no—
666C22×C32—34no—
667C22×C32—36no—
668C22×C32—32no—
669C22×C32—33no—
670C22×C32—36no—
671C22×C32—33no—
672C22×C32—66no—
673C22×C32—62no—
674C22×C32—61no—
675C22×C32—62no—
676C22×C32—61no—
677C22×C32—62no—
678C22×C32—66no—
679C22×C32—63no—
680C22×C32—63no—
681C22×C32—63no—
682C22×C32—66no—
683C22×C32—66no—
684C22×C32—66no—
685C22×C32—62no—
686C22×C32—61no—
687C22×C32—64no—
688C22×C32—612no—
689C22×C32—62no—
690C22×C32—62no—
691C22×C32—62no—
692C22×C32—64no—
693C22×C32—62no—
694C22×C32—64no—
695C22×C32—64no—
696C22×C32—64no—
697C22×C32—68no—
698C22×C32—64no—
699C22×C32—61no—
700C22×C32—61no—
701C22×C32—62no—
702C22×C32—62no—
703C22×C32—66no—
704C22×C32—66no—
705C22×C32—612no—
706C22×C32—63no—
707C22×C32—66no—
708C22×C32—66no—
709C22×C32—64no—
710C22×C32—612no—
711C22×C32—64no—
712C22×C32—612no—
713C22×C32—66no—
714C22×C32—64no—
715C22×C32—612no—
716C22×C32—612no—
717C22×C32—624no—
718C22×C32—62no—
719C22×C32—612no—
720C22×C32—68no—
721C22×C32—624no—
722C22×C32—62no—
723C22×C32—62no—
724C22×C32C2×C3×#6711yescharacteristic
725C22×C32C2×#63811yescharacteristic
726C22×C32C2×C3×S411yescharacteristic
727C22×C32C2×C3×S412yes—
728C22×C32C2×C3⋊S412yes—
729C22×C32C2×C3⋊S411yescharacteristic
730C2×C3⋊D3—62no—
731C2×C3⋊D3—62no—
732C2×C3⋊D3—62no—
733C2×C3⋊D3—122no—
734C2×C3⋊D3—122no—
735C2×C3×D3—186no—
736C2×C3×D3—186no—
737C2×C3×D3—182no—
738C2×C3×D3—182no—
739C2×C3×D3—186no—
740C2×C3×D3—182no—
741C2×C3×D3—366no—
742C2×C3×D3—362no—
743C2×C3×D3—366no—
744C2×C3×D3—362no—
745C3⋊Dic3—62no—
746C3⋊Dic3—62no—
747C3⋊Dic3—62no—
748C3×Dic3—186no—
749C3×Dic3—186no—
750C3×Dic3—182no—
751C3×Dic3—182no—
752C3×Dic3—186no—
753C3×Dic3—182no—
754C22×C9—43no—
755C22×C9—46no—
756C22×C9—86no—
757C22×C9—812no—
758C22×C9—83no—
759C22×C9—86no—
760C2×D9—126no—
761C2×D9—246no—
762C22⋊C9—23no—
763C22⋊C9C2×C3×#6713yescomplemented
764Dic9—126no—
765C25C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
766C22×D4—271no—
767C22×D4—271no—
768C22×D4—271no—
769#120—274no—
770#120—274no—
771C2×C22⋊C4—271no—
772C2×C22⋊C4—271no—
773C2×C22⋊C4—271no—
774C33C2×GL(2,ℤ/4)11yescharacteristic
7753−1+2—43no—
7763−1+2—83no—
777C3×C9—41no—
778C3×C9—81no—
779C23×C3—26no—
780C23×C3—22no—
781C23×C3—31no—
782C23×C3—31no—
783C23×C3—33no—
784C23×C3—33no—
785C23×C3—36no—
786C23×C3—31no—
787C23×C3—32no—
788C23×C3—36no—
789C23×C3—32no—
790C23×C3—31no—
791C23×C3—32no—
792C23×C3—32no—
793C23×C3—32no—
794C23×C3—34no—
795C23×C3—31no—
796C23×C3—32no—
797C23×C3—312no—
798C23×C3—34no—
799C23×C3—32no—
800C23×C3—31no—
801C23×C3—32no—
802C23×C3—33no—
803C23×C3—36no—
804C23×C3—36no—
805C23×C3—32no—
806C23×C3—31no—
807C23×C3—31no—
808C23×C3—62no—
809C23×C3—64no—
810C23×C3—61no—
811C23×C3—61no—
812C23×C3—62no—
813C23×C3—62no—
814C23×C3—61no—
815C23×C3—62no—
816C23×C3—62no—
817C23×C3—63no—
818C23×C3—63no—
819C23×C3—66no—
820C23×C3—66no—
821C23×C3—64no—
822C23×C3—612no—
823C23×C3—63no—
824C23×C3—66no—
825C23×C3—66no—
826C23×C3—66no—
827C23×C3—62no—
828C23×C3—66no—
829C23×C3—62no—
830C23×C3—66no—
831C23×C3—62no—
832C23×C3—63no—
833C23×C3—61no—
834C23×C3—612no—
835C23×C3—64no—
836C23×C3—66no—
837C23×C3—62no—
838C23×C3—62no—
839C23×C3—62no—
840C23×C3—64no—
841C23×C3—62no—
842C23×C3—61no—
843C23×C3—62no—
844C23×C3—62no—
845C23×C3—64no—
846C23×C3—612no—
847C23×C3—64no—
848C23×C3—64no—
849C23×C3—64no—
850C23×C3—612no—
851C23×C3—64no—
852C23×C3—612no—
853C23×C3—612no—
854C23×C3—66no—
855C23×C3—68no—
856C23×C3—64no—
857C23×C3—624no—
858C23×C3—612no—
859C23×C3—68no—
860C23×C3—624no—
861C23×C3—62no—
862C23×C3—61no—
863C23×C3—61no—
864C23×C3—272no—
865C23×C3—541no—
866C23×C3—542no—
867C23×C3—542no—
868C23×C3—541no—
869C23×C3#611⋊C316yescomplemented
870C23×C3((C22⋊C9)⋊C2)⋊C313yescomplemented
871C23×C3C22×AGL(1,ℤ/9)13yes—
872C23×C3C3×#63812yes—
873C23×C3C3×C3⋊S411yescharacteristic
874C23×C3C22×C3×C3⋊D311yescharacteristic
875C22×D3—96no—
876C22×D3—92no—
877C22×D3—186no—
878C22×D3—186no—
879C22×D3—182no—
880C22×D3—182no—
881C22×D3—183no—
882C22×D3—181no—
883C22×D3—181no—
884C22×D3—183no—
885C3×D4—544no—
886C3×D4—542no—
887C3×D4—548no—
888C3×D4—544no—
889C3×D4—542no—
890C3×D4—544no—
891C2×C3×C4—272no—
892C2×C3×C4—272no—
893C2×C3×C4—272no—
894C2×C3×C4—542no—
895C2×C3×C4—542no—
896C2×C3×C4—541no—
897C2×C3×C4—541no—
898#67—1812no—
899#67—186no—
900#67—184no—
901#67—182no—
902#67—1824no—
903#67—188no—
904#67—1812no—
905#67—184no—
906#67—184no—
907#67—1812no—
908#67—186no—
909#67—182no—
910C2×Dic3—96no—
911C2×Dic3—96no—
912C2×Dic3—92no—
913C2×Dic3—92no—
914C2×Dic3—96no—
915C2×Dic3—92no—
916C2×Dic3—186no—
917C2×Dic3—186no—
918C2×Dic3—182no—
919C2×Dic3—182no—
920C2×Dic3—183no—
921C2×Dic3—181no—
922C2×Dic3—181no—
923C2×Dic3—183no—
924C2×C32—22no—
925C2×C32—24no—
926C2×C32—22no—
927C2×C32—22no—
928C2×C32—21no—
929C2×C32—31no—
930C2×C32—31no—
931C2×C32—32no—
932C2×C32—33no—
933C2×C32—33no—
934C2×C32—36no—
935C2×C32—31no—
936C2×C32—31no—
937C2×C32—32no—
938C2×C32—33no—
939C2×C32—36no—
940C2×C32—66no—
941C2×C32—61no—
942C2×C32—61no—
943C2×C32—62no—
944C2×C32—63no—
945C2×C32—63no—
946C2×C32—66no—
947C2×C32—64no—
948C2×C32—612no—
949C2×C32—66no—
950C2×C32—62no—
951C2×C32—62no—
952C2×C32C3×GL(2,ℤ/4)12yes—
953C2×C32#6426912yes—
954C2×C32C22×C3×S411yescharacteristic
955C2×C32C22×C3⋊S411yescharacteristic
956C3⋊D3—122no—
957C3×D3—366no—
958C3×D3—362no—
959C2×C9—46no—
960C2×C9—43no—
961C2×C9—86no—
962C2×C9—812no—
963C2×C9—86no—
964C2×C9—83no—
965D9—246no—
966C24—22no—
967C24—31no—
968C24—31no—
969C24—32no—
970C24—62no—
971C24—271no—
972C24C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
973C24C2×C3⋊AGL(1,ℤ/9)12yescomplemented
974C2×D4—272no—
975C2×D4—274no—
976C2×D4—274no—
977C2×D4—272no—
978C2×D4—542no—
979C2×D4—544no—
980C2×D4—542no—
981C2×D4—541no—
982C2×D4—542no—
983C2×D4—541no—
984C22×C4—271no—
985C22×C4—271no—
986C22×C4—271no—
987C22⋊C4—272no—
988C22⋊C4—274no—
989C22⋊C4—274no—
990C22⋊C4—272no—
991C22×C3—26no—
992C22×C3—22no—
993C22×C3—36no—
994C22×C3—33no—
995C22×C3—32no—
996C22×C3—31no—
997C22×C3—31no—
998C22×C3—31no—
999C22×C3—32no—
1000C22×C3—32no—
1001C22×C3—33no—
1002C22×C3—33no—
1003C22×C3—36no—
1004C22×C3—36no—
1005C22×C3—32no—
1006C22×C3—32no—
1007C22×C3—31no—
1008C22×C3—31no—
1009C22×C3—312no—
1010C22×C3—34no—
1011C22×C3—32no—
1012C22×C3—31no—
1013C22×C3—34no—
1014C22×C3—32no—
1015C22×C3—36no—
1016C22×C3—32no—
1017C22×C3—31no—
1018C22×C3—31no—
1019C22×C3—32no—
1020C22×C3—62no—
1021C22×C3—64no—
1022C22×C3—62no—
1023C22×C3—61no—
1024C22×C3—61no—
1025C22×C3—61no—
1026C22×C3—62no—
1027C22×C3—62no—
1028C22×C3—62no—
1029C22×C3—66no—
1030C22×C3—63no—
1031C22×C3—63no—
1032C22×C3—63no—
1033C22×C3—66no—
1034C22×C3—66no—
1035C22×C3—64no—
1036C22×C3—612no—
1037C22×C3—66no—
1038C22×C3—66no—
1039C22×C3—62no—
1040C22×C3—66no—
1041C22×C3—612no—
1042C22×C3—62no—
1043C22×C3—64no—
1044C22×C3—63no—
1045C22×C3—61no—
1046C22×C3—66no—
1047C22×C3—62no—
1048C22×C3—62no—
1049C22×C3—62no—
1050C22×C3—64no—
1051C22×C3—61no—
1052C22×C3—62no—
1053C22×C3—62no—
1054C22×C3—64no—
1055C22×C3—612no—
1056C22×C3—64no—
1057C22×C3—64no—
1058C22×C3—62no—
1059C22×C3—64no—
1060C22×C3—612no—
1061C22×C3—64no—
1062C22×C3—68no—
1063C22×C3—612no—
1064C22×C3—624no—
1065C22×C3—66no—
1066C22×C3—64no—
1067C22×C3—612no—
1068C22×C3—68no—
1069C22×C3—624no—
1070C22×C3—612no—
1071C22×C3—66no—
1072C22×C3—62no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—62no—
1076C22×C3—542no—
1077C22×C3—542no—
1078C22×C3—542no—
1079C22×C3—1082no—
1080C22×C3—1082no—
1081C22×C3C2×#611⋊C313yescomplemented
1082C22×C3C2×((C22⋊C9)⋊C2)⋊C313yes—
1083C22×C3C2×((C22⋊C9)⋊C2)⋊C316yescomplemented
1084C22×C3C2×C3×#63811yescharacteristic
1085C22×C3C2×C3×C3⋊S411yescharacteristic
1086C22×C3C2×C3×C3⋊S412yes—
1087C2×D3—186no—
1088C2×D3—186no—
1089C2×D3—182no—
1090C2×D3—182no—
1091C2×D3—186no—
1092C2×D3—182no—
1093C2×D3—366no—
1094C2×D3—362no—
1095C2×D3—366no—
1096C2×D3—362no—
1097C3×C4—542no—
1098C3×C4—542no—
1099C3×C4—542no—
1100Dic3—186no—
1101Dic3—186no—
1102Dic3—182no—
1103Dic3—182no—
1104Dic3—186no—
1105Dic3—182no—
1106C32—21no—
1107C32—33no—
1108C32C2×C3×GL(2,ℤ/4)11yescharacteristic
1109C32C2×#6426911yescharacteristic
1110C9—43no—
1111C9—83no—
1112C23—22no—
1113C23—31no—
1114C23—31no—
1115C23—32no—
1116C23—32no—
1117C23—34no—
1118C23—31no—
1119C23—32no—
1120C23—32no—
1121C23—62no—
1122C23—62no—
1123C23—62no—
1124C23—61no—
1125C23—64no—
1126C23—62no—
1127C23—64no—
1128C23—272no—
1129C23—541no—
1130C23—542no—
1131C23—542no—
1132C23—541no—
1133C23#1061998012yescomplemented
1134C23C3⋊(((C22⋊C9)⋊C2)⋊C3)11yescharacteristic, complemented
1135C23C22×C3⋊AGL(1,ℤ/9)11yescharacteristic
1136D4—544no—
1137D4—542no—
1138D4—548no—
1139D4—544no—
1140D4—542no—
1141D4—544no—
1142C2×C4—272no—
1143C2×C4—272no—
1144C2×C4—272no—
1145C2×C4—542no—
1146C2×C4—542no—
1147C2×C4—541no—
1148C2×C4—541no—
1149C2×C3—26no—
1150C2×C3—22no—
1151C2×C3—31no—
1152C2×C3—31no—
1153C2×C3—32no—
1154C2×C3—33no—
1155C2×C3—33no—
1156C2×C3—36no—
1157C2×C3—31no—
1158C2×C3—31no—
1159C2×C3—32no—
1160C2×C3—31no—
1161C2×C3—32no—
1162C2×C3—62no—
1163C2×C3—64no—
1164C2×C3—61no—
1165C2×C3—61no—
1166C2×C3—62no—
1167C2×C3—63no—
1168C2×C3—63no—
1169C2×C3—66no—
1170C2×C3—64no—
1171C2×C3—62no—
1172C2×C3—612no—
1173C2×C3—66no—
1174C2×C3—62no—
1175C2×C3—61no—
1176C2×C3—62no—
1177C2×C3—1082no—
1178C2×C3#63694⋊C316yescomplemented
1179C2×C3C22×((C22⋊C9)⋊C2)⋊C313yes—
1180C2×C3C3×#6426912yes—
1181C2×C3C22×C3×C3⋊S411yescharacteristic
1182D3—366no—
1183D3—362no—
1184C22—22no—
1185C22—32no—
1186C22—31no—
1187C22—31no—
1188C22—31no—
1189C22—32no—
1190C22—32no—
1191C22—34no—
1192C22—32no—
1193C22—62no—
1194C22—62no—
1195C22—64no—
1196C22—61no—
1197C22—62no—
1198C22—64no—
1199C22—62no—
1200C22—542no—
1201C22—542no—
1202C22—542no—
1203C22—1082no—
1204C22—1082no—
1205C22C2×#1061998011yescharacteristic, complemented
1206C22C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)11yescharacteristic
1207C22C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)12yescomplemented
1208C4—542no—
1209C4—542no—
1210C4—542no—
1211C3—31no—
1212C3—61no—
1213C3C2×#63694⋊C313yescomplemented
1214C3C2×C3×#6426911yescharacteristic
1215C2—22no—
1216C2—31no—
1217C2—31no—
1218C2—32no—
1219C2—62no—
1220C2—1082no—
1221C2#7222015212yesdirect product factor
1222C2C22×C3⋊(((C22⋊C9)⋊C2)⋊C3)11yescharacteristic
subgroupG/H
centerC22C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)
commutator, cosocleC2×C3×C22⋊C9C23×C3
FrattiniC2×C3C22×C3×C3⋊S4
FittingC25×C33D3
socleC24×C32C2×C3×D3
hypercenterC23C3⋊(((C22⋊C9)⋊C2)⋊C3)
hypocenterC3×C22⋊C9C2×C3×D4
LCSG ▷ C2×C3×C22⋊C9 ▷ C3×C22⋊C9
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(#1094⋊C4)C2semidirect
2. C22×C3⋊(((C22⋊C9)⋊C2)⋊C3)C2semidirect
3. C23×C3×#1094C2semidirect
4. #72220152C2direct (N × H)
6. C2×#11722396C3semidirect
10. C22×C3×#1094C22semidirect
12. C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)C22semidirect
14. C3⋊(#1094⋊C4)C22semidirect
20. C23×#1094D3semidirect
22. C23×C3×C22⋊C9C2×C3semidirect
23. C22×C3⋊((C22⋊C9)⋊C2)C2×C3semidirect
30. #11722396C2×C3semidirect
31. C2×C3⋊((C22⋊C9)⋊C4)C2×C3semidirect
37. C2×C3×#1094D4semidirect
72. C22×#1094C2×D3semidirect
78. C22×C3×C22⋊C9C22×C3semidirect
80. C2×C3⋊((C22⋊C9)⋊C2)C22×C3semidirect
89. C3⋊((C22⋊C9)⋊C4)C22×C3semidirect
96. C3×#1094C2×D4semidirect
112. C23×C22⋊C9C3×D3semidirect
178. C2×#1094#67semidirect
184. C2×C3×C22⋊C9C3×D4semidirect
278. C22×C22⋊C9C2×C3×D3semidirect
339. #1094C2×#67semidirect
341. C3×C22⋊C9C2×C3×D4semidirect
346. C25×C3AGL(1,ℤ/9)semidirect
525. C2×C22⋊C9C3×#67semidirect
583. C24×C3C2×AGL(1,ℤ/9)semidirect
763. C22⋊C9C2×C3×#67semidirect
765. C25C3⋊AGL(1,ℤ/9)semidirect
869. C23×C3#611⋊C3semidirect
870. C23×C3((C22⋊C9)⋊C2)⋊C3semidirect
973. C24C2×C3⋊AGL(1,ℤ/9)semidirect
1081. C22×C3C2×#611⋊C3semidirect
1083. C22×C3C2×((C22⋊C9)⋊C2)⋊C3semidirect
1133. C23#10619980semidirect
1134. C23C3⋊(((C22⋊C9)⋊C2)⋊C3)semidirect
1178. C2×C3#63694⋊C3semidirect
1205. C22C2×#10619980semidirect
1207. C22C2×C3⋊(((C22⋊C9)⋊C2)⋊C3)semidirect
1213. C3C2×#63694⋊C3semidirect
1221. C2#72220152direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3⋊(#1094⋊C4)2
C22×C3⋊(((C22⋊C9)⋊C2)⋊C3)2
C23×C3×#10942
#722201522
C2×C3×#641623
C2×#117223963
C2×#63694⋊C33
C2×#106199804