Finite Group Databasebeta

← C3×#85901 #11904738

Subgroups — C3×#85901 #11904738

Order 1152.

3191 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C32×#520C211yesmaximal, characteristic, complemented
4C3×#5576C212yesmaximal, complemented
5C3×Q8×D12C212yesmaximal, complemented
6C3×#5555C216yesmaximal, complemented
7C3×#5554C216yesmaximal, complemented
8C3×#5526C213yesmaximal, complemented
9C3×#5524C213yesmaximal, complemented
10C3×#5510C213yesmaximal, complemented
11C2×C3×#897C213yesmaximal, complemented
12C3×#3489—31nomaximal
13#85901C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×#1010—28no—
16C3×D3×#41—28no—
17C2×C3×#239C2211yescharacteristic
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2213yes—
21C2×C3×#237C2216yescomplemented
22C2×C3×D3×D4C2213yes—
23C2×C3×#235C2213yes—
24C2×C3×#235C2213yescomplemented
25C22×C3×C4×D3C2213yes—
26C22×C3×Dic6C2213yescomplemented
27C32×C4×Q8C2212yescomplemented
28C32×C4×D4C2216yescomplemented
29C32×#117C2213yescomplemented
30C2×C32×C4⋊C4C2213yescomplemented
31C3×#930C22112yescomplemented
32C2×C3×(C2×D3)⋊C4C2216yes—
33C2×C3×C4⋊Dic3C2216yescomplemented
34C3×#897C2213yes—
35C3×#897C2216yes—
36C3×#897C2216yescomplemented
37C3×#897C2216yescomplemented
38C3×#897C2216yescomplemented
39C3×#897C2213yescomplemented
40C3×#895C2211yescharacteristic
41C3×#895C2213yescomplemented
42C3×#895C2216yescomplemented
43C3×#886C2216yescomplemented
44C3×#886C22112yescomplemented
45C3×#882C2216yes—
46C3×#875C2216yescomplemented
47C3×C4×D12C2216yes—
48C3×C4×D12C2216yescomplemented
49C3×#869C2216yescomplemented
50C2×C3×2−1+4—31no—
51C22×C3×#41—31no—
52C2×#1010C2×C311yescharacteristic, complemented
53C2×D3×#41C2×C311yescharacteristic, complemented
54C3×D4×Q8—32no—
55C3×#548—32no—
56C3×#547—36no—
57C3×#546—36no—
58C3×#537—33no—
59C3×#536—33no—
60C3×#525—33no—
61C2×C3×C22⋊Q8—33no—
62C3×#520—21no—
63C3×#520D311yescharacteristic, complemented
64C3×#520C2×C311yescharacteristic, complemented
65#5576C2×C312yescomplemented
66Q8×D12C2×C312yescomplemented
67#5555C2×C316yescomplemented
68#5554C2×C316yescomplemented
69#5526C2×C313yescomplemented
70#5524C2×C313yescomplemented
71#5510C2×C313yescomplemented
72C2×#897C2×C313yescomplemented
73C23×C3×D3C2313yes—
74C32×#41D418yescomplemented
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4C2313yes—
77C22×C32×C4C2316yes—
78C22×C32×C4C2313yes—
79C2×C3×#67C2316yes—
80C2×C3×#67C2316yes—
81C22×C3×Dic3C2313yes—
82C22×C3×Dic3C2316yes—
83C3×#239—24no—
84C3×D3×Q8—24no—
85C3×D3×Q8—28no—
86C3×#237—212no—
87C3×#237—224no—
88C3×D3×D4—212no—
89C3×#235—212no—
90C3×#235—212no—
91C2×C3×D12C2312yes—
92C2×C3×D12C2311yescharacteristic
93C2×C3×D12C2313yes—
94C2×C3×D12C2316yes—
95C2×C3×C4×D3—212no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2313yes—
98C2×C3×C4×D3C2316yes—
99C2×C3×C4×D3C2313yes—
100C2×C3×C4×D3C2313yes—
101C2×C3×Dic6—212no—
102C2×C3×Dic6C2313yes—
103C2×C3×Dic6C2316yes—
104C2×C3×Dic6C2313yes—
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2313yes—
107C32×C4⋊C4C2316yes—
108C32×C22⋊C4C2316yes—
109C32×C42C2316yes—
110C3×(C2×D3)⋊C4C2316yes—
111C3×(C2×D3)⋊C4C2316yes—
112C3×(C2×D3)⋊C4C2312yes—
113C3×(C2×D3)⋊C4C23112yes—
114C3×(C2×D3)⋊C4C2316yes—
115C3×C4⋊Dic3C2316yes—
116C3×C4⋊Dic3C2316yes—
117C3×C4⋊Dic3C23112yes—
118#3489—31noSylow
119C3×2−1+4—68no—
120C2×C3×#41—21no—
121C2×C3×#41—31no—
122C2×C3×#41—33no—
123C2×C3×#41—36no—
124C2×C3×#41—33no—
125C2×C3×#41—33no—
126C2×C3×#41—68no—
127C2×C3×#41C2×D311yescharacteristic
128C2×C3×#41C22×C311yescharacteristic
129C22×C3×Q8—31no—
130C22×C3×Q8—32no—
131C22×C3×Q8—33no—
132C22×C3×D4—33no—
133C23×C3×C4—33no—
134#1010—28no—
135D3×#41—28no—
136C2×#239C22×C311yescharacteristic
137C2×D3×Q8C22×C311yescharacteristic
138C2×D3×Q8C22×C312yescomplemented
139C2×#237C22×C313yes—
140C2×#237C22×C316yescomplemented
141C2×D3×D4C22×C313yes—
142C2×#235C22×C313yes—
143C2×#235C22×C313yescomplemented
144C22×C4×D3C22×C313yes—
145C22×Dic6C22×C313yescomplemented
146C3×C4⋊Q8—36no—
147C3×#124—36no—
148C3×#123—36no—
149C3×#123—312no—
150C3×C22⋊Q8—33no—
151C3×C22⋊Q8—36no—
152C3×C22⋊Q8—36no—
153C3×C22⋊Q8—36no—
154C3×C22⋊Q8—33no—
155C3×C22⋊Q8—36no—
156C3×#121—312no—
157C3×#121—31no—
158C3×#121—33no—
159C3×#121—36no—
160C3×#120—36no—
161C3×C4×Q8—22no—
162C3×C4×Q8C2×D312yescomplemented
163C3×C4×Q8C22×C312yescomplemented
164C3×C4×D4—26no—
165C3×C4×D4—36no—
166C3×C4×D4—36no—
167C3×C4×D4C2×D316yescomplemented
168C3×C4×D4C22×C316yescomplemented
169C3×#117—23no—
170C3×#117C2×D313yescomplemented
171C3×#117C22×C313yescomplemented
172C2×C3×C4⋊C4—23no—
173C2×C3×C4⋊C4—36no—
174C2×C3×C4⋊C4C2×D313yescomplemented
175C2×C3×C4⋊C4C22×C313yescomplemented
176C2×C3×C22⋊C4—36no—
177#930C22×C3112yescomplemented
178C2×(C2×D3)⋊C4C22×C316yes—
179C2×C4⋊Dic3C22×C316yescomplemented
180#897C22×C313yes—
181#897C22×C316yes—
182#897C22×C316yescomplemented
183#897C22×C316yescomplemented
184#897C22×C316yescomplemented
185#897C22×C313yescomplemented
186#895C22×C311yescharacteristic
187#895C22×C313yescomplemented
188#895C22×C316yescomplemented
189#886C22×C316yescomplemented
190#886C22×C3112yescomplemented
191#882C22×C316yes—
192#875C22×C316yescomplemented
193C4×D12C22×C316yes—
194C4×D12C22×C316yescomplemented
195#869C22×C316yescomplemented
196C23×C32C2413yes—
197C22×C3×D3—26no—
198C22×C3×D3—26no—
199C22×C3×D3—43no—
200C22×C3×D3C2413yes—
201C22×C3×D3C2412yes—
202C22×C3×D3C2411yescharacteristic
203C32×Q8C2×D414yes—
204C32×D4C2×D4112yes—
205C2×C32×C4—46no—
206C2×C32×C4C2×D4112yes—
207C2×C32×C4C2412yes—
208C2×C32×C4C2416yes—
209C2×C32×C4C2413yes—
210C2×C32×C4C2411yescharacteristic
211C3×#67—212no—
212C3×#67—212no—
213C2×C3×Dic3—212no—
214C2×C3×Dic3—26no—
215C2×C3×Dic3C2413yes—
216C2×C3×Dic3C2411yescharacteristic
217C2×C3×Dic3C2416yes—
218C3×D12—24no—
219C3×D12—22no—
220C3×D12—26no—
221C3×D12—46no—
222C3×C4×D3—22no—
223C3×C4×D3—26no—
224C3×C4×D3—26no—
225C3×C4×D3—26no—
226C3×C4×D3—212no—
227C3×Dic6—26no—
228C3×Dic6—212no—
229C3×Dic6—26no—
230C2×2−1+4—31no—
231C22×#41—31no—
232D4×Q8—32no—
233#548—32no—
234#547—36no—
235#546—36no—
236#537—33no—
237#536—33no—
238#525—33no—
239C2×C22⋊Q8—33no—
240#520C3×D311yescharacteristic, complemented
241C24×C3—33no—
242C23×D3C23×C313yes—
243C3×#41—28no—
244C3×#41—64no—
245C3×#41—612no—
246C3×#41—624no—
247C3×#41—612no—
248C3×#41—612no—
249C3×#41D1218yescomplemented
250C3×#41C3×D418yescomplemented
251C2×C3×Q8—21no—
252C2×C3×Q8—33no—
253C2×C3×Q8—36no—
254C2×C3×Q8—33no—
255C2×C3×Q8—64no—
256C2×C3×Q8—68no—
257C2×C3×Q8—612no—
258C2×C3×Q8C22×D311yescharacteristic
259C2×C3×Q8C23×C311yescharacteristic
260C2×C3×D4—23no—
261C2×C3×D4—36no—
262C2×C3×D4—36no—
263C2×C3×D4—32no—
264C2×C3×D4—31no—
265C2×C3×D4—33no—
266C2×C3×D4—36no—
267C2×C3×D4—612no—
268C2×C3×D4C22×D313yes—
269C2×C3×D4C23×C313yes—
270C22×C3×C4—23no—
271C22×C3×C4—26no—
272C22×C3×C4—36no—
273C22×C3×C4—33no—
274C22×C3×C4—36no—
275C22×C3×C4—33no—
276C22×C3×C4—33no—
277C22×C3×C4—31no—
278C22×C3×C4—33no—
279C22×C3×C4—612no—
280C22×C3×C4C22×D316yes—
281C22×C3×C4C22×D313yes—
282C22×C3×C4C23×C316yes—
283C22×C3×C4C23×C313yes—
284C2×#67C23×C316yes—
285C2×#67C23×C316yes—
286C22×Dic3C23×C313yes—
287C22×Dic3C23×C316yes—
288#239—24no—
289D3×Q8—24no—
290D3×Q8—28no—
291#237—212no—
292#237—224no—
293D3×D4—212no—
294#235—212no—
295#235—212no—
296C2×D12C23×C312yes—
297C2×D12C23×C313yes—
298C2×D12C23×C311yescharacteristic
299C2×D12C23×C316yes—
300C2×C4×D3—212no—
301C2×C4×D3C23×C313yes—
302C2×C4×D3C23×C316yes—
303C2×C4×D3C23×C313yes—
304C2×C4×D3C23×C311yescharacteristic
305C2×C4×D3C23×C313yes—
306C2×Dic6—212no—
307C2×Dic6C23×C313yes—
308C2×Dic6C23×C316yes—
309C2×Dic6C23×C313yes—
310C3×C4⋊C4—23no—
311C3×C4⋊C4—26no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—36no—
314C3×C4⋊C4—312no—
315C3×C4⋊C4—36no—
316C3×C4⋊C4C22×D313yes—
317C3×C4⋊C4C22×D316yes—
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C4⋊C4C23×C311yescharacteristic
320C3×C4⋊C4C23×C313yes—
321C3×C4⋊C4C23×C316yes—
322C3×C22⋊C4—26no—
323C3×C22⋊C4—36no—
324C3×C22⋊C4—312no—
325C3×C22⋊C4—32no—
326C3×C22⋊C4—36no—
327C3×C22⋊C4—36no—
328C3×C22⋊C4C22×D316yes—
329C3×C22⋊C4C23×C316yes—
330C3×C42—26no—
331C3×C42C22×D316yes—
332C3×C42C23×C316yes—
333(C2×D3)⋊C4C23×C316yes—
334(C2×D3)⋊C4C23×C316yes—
335(C2×D3)⋊C4C23×C312yes—
336(C2×D3)⋊C4C23×C316yes—
337(C2×D3)⋊C4C23×C3112yes—
338C4⋊Dic3C23×C316yes—
339C4⋊Dic3C23×C3112yes—
340C4⋊Dic3C23×C316yes—
341C22×C32—23no—
342C22×C32—23no—
343C22×C32C22×D416yes—
344C22×C32C2511yescharacteristic
345C2×C3×D3—21no—
346C2×C3×D3—21no—
347C2×C3×D3—22no—
348C2×C3×D3—23no—
349C2×C3×D3—22no—
350C2×C3×D3—23no—
351C2×C3×D3—22no—
352C2×C3×D3—23no—
353C2×C3×D3—412no—
354C2×C3×D32−1+412yescomplemented
355C32×C4—22no—
356C32×C4—26no—
357C32×C4C22×D412yes—
358C32×C4C22×D416yes—
359C3×Dic3—26no—
360C3×Dic3—23no—
361C3×Dic3—21no—
3622−1+4—68no—
363C2×#41—31no—
364C2×#41—36no—
365C2×#41—33no—
366C2×#41—33no—
367C2×#41—33no—
368C2×#41—68no—
369C2×#41C2×C3×D311yescharacteristic
370C22×Q8—32no—
371C22×Q8—31no—
372C22×Q8—33no—
373C22×D4—33no—
374C23×C4—33no—
375C4⋊Q8—36no—
376#124—36no—
377#123—36no—
378#123—312no—
379C22⋊Q8—33no—
380C22⋊Q8—36no—
381C22⋊Q8—36no—
382C22⋊Q8—36no—
383C22⋊Q8—33no—
384C22⋊Q8—36no—
385#121—312no—
386#121—31no—
387#121—33no—
388#121—36no—
389#120—36no—
390C4×Q8C2×C3×D312yescomplemented
391C4×D4—36no—
392C4×D4—36no—
393C4×D4C2×C3×D316yescomplemented
394#117C2×C3×D313yescomplemented
395C2×C4⋊C4—36no—
396C2×C4⋊C4C2×C3×D313yescomplemented
397C2×C22⋊C4—36no—
398C23×C3—23no—
399C23×C3—31no—
400C23×C3—33no—
401C23×C3—32no—
402C23×C3—66no—
403C23×C3—66no—
404C23×C3—123no—
405C23×C3C23×D313yes—
406C23×C3C24×C313yes—
407C22×D3—26no—
408C22×D3—26no—
409C22×D3—43no—
410C22×D3C24×C313yes—
411C22×D3C24×C312yes—
412C22×D3C24×C311yescharacteristic
413C3×Q8—24no—
414C3×Q8—66no—
415C3×Q8—612no—
416C3×Q8—66no—
417C3×Q8C2×D1214yes—
418C3×Q8C2×C3×D414yes—
419C3×D4—212no—
420C3×D4—64no—
421C3×D4—612no—
422C3×D4—612no—
423C3×D4—66no—
424C3×D4—62no—
425C3×D4—126no—
426C3×D4C2×D12112yes—
427C3×D4C2×C3×D4112yes—
428C2×C3×C4—23no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—26no—
432C2×C3×C4—212no—
433C2×C3×C4—36no—
434C2×C3×C4—31no—
435C2×C3×C4—33no—
436C2×C3×C4—46no—
437C2×C3×C4—46no—
438C2×C3×C4—66no—
439C2×C3×C4—612no—
440C2×C3×C4—62no—
441C2×C3×C4—66no—
442C2×C3×C4—66no—
443C2×C3×C4—66no—
444C2×C3×C4—612no—
445C2×C3×C4—86no—
446C2×C3×C4C2×D12112yes—
447C2×C3×C4C2×C3×D4112yes—
448C2×C3×C4C23×D312yes—
449C2×C3×C4C23×D316yes—
450C2×C3×C4C23×D313yes—
451C2×C3×C4C23×D311yescharacteristic
452C2×C3×C4C24×C312yes—
453C2×C3×C4C24×C316yes—
454C2×C3×C4C24×C313yes—
455C2×C3×C4C24×C311yescharacteristic
456#67—212no—
457#67—212no—
458C2×Dic3—212no—
459C2×Dic3—26no—
460C2×Dic3C24×C313yes—
461C2×Dic3C24×C311yescharacteristic
462C2×Dic3C24×C316yes—
463D12—24no—
464D12—22no—
465D12—26no—
466D12—46no—
467C4×D3—22no—
468C4×D3—26no—
469C4×D3—26no—
470C4×D3—26no—
471C4×D3—212no—
472Dic6—26no—
473Dic6—212no—
474Dic6—26no—
475C2×C32—26no—
476C2×C32C23×D411yescharacteristic
477C2×C32C2×2−1+411yescharacteristic
478C2×C32#58511yescharacteristic
479C3×D3—22no—
480C3×D3—42no—
481C3×D3—43no—
482C24—33no—
483#41—64no—
484#41—612no—
485#41—624no—
486#41—612no—
487#41—612no—
488#41C3×D1218yescomplemented
489C2×Q8—33no—
490C2×Q8—36no—
491C2×Q8—33no—
492C2×Q8—64no—
493C2×Q8—68no—
494C2×Q8—612no—
495C2×Q8C22×C3×D311yescharacteristic
496C2×D4—36no—
497C2×D4—36no—
498C2×D4—32no—
499C2×D4—31no—
500C2×D4—33no—
501C2×D4—36no—
502C2×D4—612no—
503C2×D4C22×C3×D313yes—
504C22×C4—36no—
505C22×C4—33no—
506C22×C4—36no—
507C22×C4—33no—
508C22×C4—33no—
509C22×C4—31no—
510C22×C4—33no—
511C22×C4—612no—
512C22×C4C22×C3×D316yes—
513C22×C4C22×C3×D313yes—
514C4⋊C4—36no—
515C4⋊C4—312no—
516C4⋊C4—36no—
517C4⋊C4C22×C3×D313yes—
518C4⋊C4C22×C3×D316yes—
519C4⋊C4C22×C3×D311yescharacteristic
520C22⋊C4—36no—
521C22⋊C4—312no—
522C22⋊C4—32no—
523C22⋊C4—36no—
524C22⋊C4—36no—
525C22⋊C4C22×C3×D316yes—
526C42C22×C3×D316yes—
527C22×C3—23no—
528C22×C3—23no—
529C22×C3—23no—
530C22×C3—23no—
531C22×C3—26no—
532C22×C3—21no—
533C22×C3—32no—
534C22×C3—43no—
535C22×C3—43no—
536C22×C3—61no—
537C22×C3—61no—
538C22×C3—62no—
539C22×C3—63no—
540C22×C3—62no—
541C22×C3—63no—
542C22×C3—62no—
543C22×C3—63no—
544C22×C3—1212no—
545C22×C3C22×D1216yes—
546C22×C3C22×C3×D416yes—
547C22×C3C24×D311yescharacteristic
548C22×C3C25×C311yescharacteristic
549C2×D3—21no—
550C2×D3—21no—
551C2×D3—22no—
552C2×D3—23no—
553C2×D3—22no—
554C2×D3—23no—
555C2×D3—22no—
556C2×D3—23no—
557C2×D3—412no—
558C2×D3C3×2−1+412yescomplemented
559C3×C4—26no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—26no—
563C3×C4—22no—
564C3×C4—26no—
565C3×C4—46no—
566C3×C4—42no—
567C3×C4—61no—
568C3×C4—63no—
569C3×C4—66no—
570C3×C4C22×D1212yes—
571C3×C4C22×D1216yes—
572C3×C4C22×C3×D412yes—
573C3×C4C22×C3×D416yes—
574Dic3—26no—
575Dic3—23no—
576Dic3—21no—
577C32#348911yescharacteristic, complemented, Sylow
578C23—31no—
579C23—33no—
580C23—32no—
581C23—66no—
582C23—66no—
583C23—123no—
584C23C23×C3×D313yes—
585Q8—66no—
586Q8—612no—
587Q8—66no—
588Q8C2×C3×D1214yes—
589D4—64no—
590D4—612no—
591D4—612no—
592D4—66no—
593D4—62no—
594D4—126no—
595D4C2×C3×D12112yes—
596C2×C4—36no—
597C2×C4—31no—
598C2×C4—33no—
599C2×C4—46no—
600C2×C4—66no—
601C2×C4—612no—
602C2×C4—62no—
603C2×C4—66no—
604C2×C4—66no—
605C2×C4—66no—
606C2×C4—612no—
607C2×C4C2×C3×D12112yes—
608C2×C4C23×C3×D312yes—
609C2×C4C23×C3×D316yes—
610C2×C4C23×C3×D313yes—
611C2×C4C23×C3×D311yescharacteristic
612C2×C3—26no—
613C2×C3—26no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—46no—
618C2×C3—62no—
619C2×C3—123no—
620C2×C3—122no—
621C2×C3C23×D1211yescharacteristic
622C2×C3#596611yescharacteristic
623C2×C3D3×2−1+411yescharacteristic
624C2×C3C23×C3×D411yescharacteristic
625C2×C3C2×C3×2−1+411yescharacteristic
626C2×C3C3×#58511yescharacteristic
627D3—22no—
628D3—43no—
629D3—42no—
630C22—23no—
631C22—23no—
632C22—32no—
633C22—61no—
634C22—61no—
635C22—62no—
636C22—63no—
637C22—62no—
638C22—63no—
639C22—62no—
640C22—63no—
641C22—1212no—
642C22C22×C3×D1216yes—
643C22C24×C3×D311yescharacteristic
644C4—26no—
645C4—22no—
646C4—61no—
647C4—63no—
648C4—66no—
649C4C22×C3×D1212yes—
650C4C22×C3×D1216yes—
651C3—21no—
652C3#8590111yescharacteristic, direct product factor
653C3C3×#348911yescharacteristic, complemented
654C2—26no—
655C2—62no—
656C2—123no—
657C2—122no—
658C2C23×C3×D1211yescharacteristic
659C2C3×#596611yescharacteristic
660C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#520C2
socleC22×C32C25
hypercenterC3×#520D3
hypocenterC3C3×#3489
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#520

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C32×#520C2semidirect
4. C3×#5576C2semidirect
5. C3×Q8×D12C2semidirect
6. C3×#5555C2semidirect
7. C3×#5554C2semidirect
8. C3×#5526C2semidirect
9. C3×#5524C2semidirect
10. C3×#5510C2semidirect
11. C2×C3×#897C2semidirect
13. #85901C3direct (N × H)
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
24. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
27. C32×C4×Q8C22semidirect
28. C32×C4×D4C22semidirect
29. C32×#117C22semidirect
30. C2×C32×C4⋊C4C22semidirect
31. C3×#930C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
36. C3×#897C22semidirect
37. C3×#897C22semidirect
38. C3×#897C22semidirect
39. C3×#897C22semidirect
41. C3×#895C22semidirect
42. C3×#895C22semidirect
43. C3×#886C22semidirect
44. C3×#886C22semidirect
46. C3×#875C22semidirect
48. C3×C4×D12C22semidirect
49. C3×#869C22semidirect
52. C2×#1010C2×C3semidirect
53. C2×D3×#41C2×C3semidirect
63. C3×#520D3semidirect
64. C3×#520C2×C3semidirect
65. #5576C2×C3semidirect
66. Q8×D12C2×C3semidirect
67. #5555C2×C3semidirect
68. #5554C2×C3semidirect
69. #5526C2×C3semidirect
70. #5524C2×C3semidirect
71. #5510C2×C3semidirect
72. C2×#897C2×C3semidirect
74. C32×#41D4semidirect
138. C2×D3×Q8C22×C3semidirect
140. C2×#237C22×C3semidirect
143. C2×#235C22×C3semidirect
145. C22×Dic6C22×C3semidirect
162. C3×C4×Q8C2×D3semidirect
163. C3×C4×Q8C22×C3semidirect
167. C3×C4×D4C2×D3semidirect
168. C3×C4×D4C22×C3semidirect
170. C3×#117C2×D3semidirect
171. C3×#117C22×C3semidirect
174. C2×C3×C4⋊C4C2×D3semidirect
175. C2×C3×C4⋊C4C22×C3semidirect
177. #930C22×C3semidirect
179. C2×C4⋊Dic3C22×C3semidirect
182. #897C22×C3semidirect
183. #897C22×C3semidirect
184. #897C22×C3semidirect
185. #897C22×C3semidirect
187. #895C22×C3semidirect
188. #895C22×C3semidirect
189. #886C22×C3semidirect
190. #886C22×C3semidirect
192. #875C22×C3semidirect
194. C4×D12C22×C3semidirect
195. #869C22×C3semidirect
240. #520C3×D3semidirect
249. C3×#41D12semidirect
250. C3×#41C3×D4semidirect
354. C2×C3×D32−1+4semidirect
390. C4×Q8C2×C3×D3semidirect
393. C4×D4C2×C3×D3semidirect
394. #117C2×C3×D3semidirect
396. C2×C4⋊C4C2×C3×D3semidirect
488. #41C3×D12semidirect
558. C2×D3C3×2−1+4semidirect
577. C32#3489semidirect
652. C3#85901direct (N × H)
653. C3C3×#3489semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×C3×D3×#412
C32×#5202
C3×#55762
C3×Q8×D122
C3×#55552
C3×#55542
C3×#55262
C3×#55242
C3×#55102
C2×C3×#8972
C3×#34893
#859013