Finite Group Databasebeta

← C3×#71700 #11792002

Subgroups — C3×#71700 #11792002

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C22⋊Q8C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×C3×#924C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2001—31nomaximal
9#71700C311yesmaximal, characteristic, direct product factor
10C22×C32×Q8C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C32×C22⋊Q8—22no—
14C32×C22⋊Q8—22no—
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C22⋊C4—21no—
18C2×C3×#217—21no—
19C2×C3×#216—22no—
20C2×C3×#216—22no—
21C2×C3×#216—22no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924—22no—
24C3×#924—22no—
25C2×C3×Dic3⋊C4—21no—
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#835—22no—
29C3×#830—22no—
30C3×#810—22no—
31C22×C3×Q16—31no—
32C2×C3×C22⋊Q8—21no—
33C2×C3×C22⋊Q8—31no—
34C2×C3×C22⋊Q8D311yescharacteristic
35C2×C3×C22⋊Q8C2×C311yescharacteristic
36C22×#216C2×C311yescharacteristic, complemented
37C2×#924C2×C311yescharacteristic
38C2×C3×#103—31no—
39C2×C3×#103—31no—
40C2×C3×C22⋊C8—31no—
41C2×#835C2×C311yescharacteristic, complemented
42C2×#830C2×C311yescharacteristic
43C2×#810C2×C311yescharacteristic, complemented
44C3×#340—31no—
45#4529C2×C311yescharacteristic, complemented
46C24×C32D411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8D412yes—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—21no—
59C22×C32×C4—21no—
60C22×C32×C4—21no—
61C22×C32×C4D411yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71C32×C4⋊C4—24no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4D412yes—
74C32×C22⋊C4—24no—
75C3×#217—24no—
76C3×#216—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3D412yes—
79C3×Dic3⋊C4—24no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84C2×C3×C3⋊C8—21no—
85C2×C3×C3⋊C8D412yes—
86#2001—31noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8—31no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C22×C311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2×D311yescharacteristic
93C23×C3×C4C22×C311yescharacteristic
94C22×Dic6C22×C311yescharacteristic
95C2×C3×Q16—62no—
96C2×C3×Q16—62no—
97C2×C3×Q16—62no—
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C3×C22⋊Q8—24no—
101C3×C22⋊Q8—24no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—62no—
107C3×C22⋊Q8—62no—
108C2×C3×C4⋊C4—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—61no—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C4⋊C4C22×C311yescharacteristic
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—61no—
120C2×#217—21no—
121C2×#216—22no—
122C2×#216—22no—
123C2×#216—22no—
124C2×C4⋊Dic3C22×C311yescharacteristic
125#924—22no—
126#924—22no—
127C2×Dic3⋊C4—21no—
128C22×C3⋊C8C22×C311yescharacteristic
129C22×C3⋊C8C22×C311yescharacteristic
130C3×#103—62no—
131C3×#103—62no—
132C3×C22⋊C8—62no—
133#835—22no—
134#830—22no—
135#810—22no—
136C23×C32—21no—
137C23×C32—21no—
138C23×C32—21no—
139C23×C32—21no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32Q1612yescomplemented
143C23×C32C2×D411yescharacteristic
144C32×Q8—22no—
145C32×Q8—22no—
146C32×Q8—41no—
147C32×Q8—41no—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4—41no—
156C2×C32×C4—41no—
157C2×C32×C4—41no—
158C2×C32×C4—41no—
159C2×C32×C4—41no—
160C2×C32×C4—41no—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4111yescharacteristic
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—41no—
176C3×Dic6—41no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—41no—
179C22×Q16—31no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8C3×D311yescharacteristic
182C2×#103—31no—
183C2×#103—31no—
184C2×C22⋊C8—31no—
185#340—31no—
186C24×C3—21no—
187C24×C3#6711yescharacteristic
188C24×C3C3×D411yescharacteristic
189C2×C3×Q8—22no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×Q8—41no—
204C2×C3×Q8—41no—
205C2×C3×Q8—41no—
206C2×C3×Q8—61no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8#6712yes—
212C2×C3×Q8C3×D412yes—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—41no—
236C22×C3×C4—41no—
237C22×C3×C4—41no—
238C22×C3×C4—41no—
239C22×C3×C4—61no—
240C22×C3×C4—61no—
241C22×C3×C4#6711yescharacteristic
242C22×C3×C4C3×D411yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C23×C311yescharacteristic
245C22×Dic3—21no—
246C22×Dic3—21no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6C3×D412yes—
253C3×Q16—68no—
254C2×C3×C8—32no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8—61no—
258C2×C3×C8—61no—
259C2×C3×C8—61no—
260C3×C4⋊C4—28no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—32no—
268C3×C4⋊C4—64no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4#6712yes—
271C3×C4⋊C4C3×D412yes—
272C3×C22⋊C4—28no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—24no—
275C3×C22⋊C4—64no—
276#217—24no—
277#216—28no—
278C4⋊Dic3—21no—
279C4⋊Dic3C3×D412yes—
280Dic3⋊C4—24no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8C3×D412yes—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32#12011yescharacteristic
295C22×C32#12011yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32C2×Q1611yescharacteristic
298C22×C32#13511yescharacteristic
299C22×C32#13711yescharacteristic
300C22×C32#13711yescharacteristic
301C32×C4—41no—
302C32×C4—42no—
303C32×C4—42no—
304C32×C4#12011yescharacteristic
305C32×C4#12111yescharacteristic
306C32×C4#12111yescharacteristic
307C32×C4#12711yescharacteristic
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×Q8—31no—
311C22×Q8C2×C3×D311yescharacteristic
312C23×C4C2×C3×D311yescharacteristic
313C2×Q16—62no—
314C2×Q16—62no—
315C2×Q16—62no—
316C22×C8—31no—
317C22×C8—31no—
318C22⋊Q8—22no—
319C22⋊Q8—22no—
320C22⋊Q8—62no—
321C22⋊Q8—62no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—61no—
325C2×C4⋊C4C2×C3×D311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—61no—
328#103—62no—
329#103—62no—
330C22⋊C8—62no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3#21612yescomplemented
352C23×C3C3×Q1612yescomplemented
353C23×C3C2×#6711yescharacteristic
354C23×C3C2×C3×D411yescharacteristic
355C3×Q8—22no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—22no—
359C3×Q8—42no—
360C3×Q8—42no—
361C3×Q8—42no—
362C3×Q8—42no—
363C3×Q8—41no—
364C3×Q8—41no—
365C3×Q8—41no—
366C3×Q8—41no—
367C3×Q8—62no—
368C3×Q8—62no—
369C3×Q8—121no—
370C3×Q8—121no—
371C2×C3×C4—24no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—121no—
419C2×C3×C4—121no—
420C2×C3×C4—121no—
421C2×C3×C4—121no—
422C2×C3×C4D3×D411yescharacteristic
423C2×C3×C4D3×D411yescharacteristic
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4#23711yescharacteristic
426C2×C3×C4C2×#6711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×C3×D411yescharacteristic
429C2×C3×C4C2×C3×D411yescharacteristic
430C2×C3×C4C2×C3×D411yescharacteristic
431C2×C3×C4C2×C3×D411yescharacteristic
432C2×C3×C4C2×C3×D411yescharacteristic
433C2×C3×C4C3×#4111yescharacteristic
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440Dic6—22no—
441Dic6—22no—
442Dic6—41no—
443Dic6—41no—
444C3×C8—62no—
445C3×C8—121no—
446C3⋊C8—22no—
447C3⋊C8—41no—
448C2×C32—42no—
449C2×C32#39211yescharacteristic
450C2×C32#45111yescharacteristic
451C2×C32#45111yescharacteristic
452C2×C32#45211yescharacteristic
453C2×C32#45211yescharacteristic
454C2×C32#46711yescharacteristic
455C2×C32#47011yescharacteristic
456C24C3×#6711yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—32no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8C3×#6712yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4C3×#6711yescharacteristic
480C22×C4C22×C3×D311yescharacteristic
481Q16—68no—
482C2×C8—32no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—61no—
488C4⋊C4—24no—
489C4⋊C4—21no—
490C4⋊C4—32no—
491C4⋊C4—64no—
492C4⋊C4—61no—
493C4⋊C4C3×#6712yes—
494C22⋊C4—24no—
495C22⋊C4—64no—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3#93711yescharacteristic
525C22×C3#93911yescharacteristic
526C22×C3#94211yescharacteristic
527C22×C3C2×#21611yescharacteristic
528C22×C3#95011yescharacteristic
529C22×C3#95111yescharacteristic
530C22×C3#95311yescharacteristic
531C22×C3C3×#12011yescharacteristic
532C22×C3C3×#12011yescharacteristic
533C22×C3C3×#12111yescharacteristic
534C22×C3C2×C3×Q1611yescharacteristic
535C22×C3C3×#13511yescharacteristic
536C22×C3C3×#13711yescharacteristic
537C22×C3C3×#13711yescharacteristic
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—42no—
543C3×C4—44no—
544C3×C4—44no—
545C3×C4—41no—
546C3×C4—42no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—122no—
552C3×C4—122no—
553C3×C4#93711yescharacteristic
554C3×C4#93811yescharacteristic
555C3×C4#93911yescharacteristic
556C3×C4#94011yescharacteristic
557C3×C4C3×#12011yescharacteristic
558C3×C4C3×#12111yescharacteristic
559C3×C4C3×#12111yescharacteristic
560C3×C4C3×#12711yescharacteristic
561Dic3—42no—
562Dic3—42no—
563C32#200111yescharacteristic, complemented, Sylow
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23C3×#21612yescomplemented
571C23C2×C3×#6711yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—62no—
577Q8—62no—
578Q8—121no—
579Q8—121no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4C3×D3×D411yescharacteristic
600C2×C4C3×D3×D411yescharacteristic
601C2×C4C3×D3×D411yescharacteristic
602C2×C4C3×#23711yescharacteristic
603C2×C4C2×C3×#6711yescharacteristic
604C2×C4C2×C3×#6711yescharacteristic
605C8—62no—
606C8—121no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—44no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3#504711yescharacteristic
618C2×C3#505011yescharacteristic
619C2×C3#505111yescharacteristic
620C2×C3#505211yescharacteristic
621C2×C3#522311yescharacteristic
622C2×C3#522811yescharacteristic
623C2×C3#523911yescharacteristic
624C2×C3C3×#39211yescharacteristic
625C2×C3C3×#45111yescharacteristic
626C2×C3C3×#45111yescharacteristic
627C2×C3C3×#45211yescharacteristic
628C2×C3C3×#45211yescharacteristic
629C2×C3C3×#46711yescharacteristic
630C2×C3C3×#47011yescharacteristic
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22C3×#93711yescharacteristic
639C22C3×#93911yescharacteristic
640C22C3×#94211yescharacteristic
641C22C2×C3×#21611yescharacteristic
642C22C3×#95011yescharacteristic
643C22C3×#95111yescharacteristic
644C22C3×#95311yescharacteristic
645C4—41no—
646C4—42no—
647C4—42no—
648C4—122no—
649C4—122no—
650C4C3×#93711yescharacteristic
651C4C3×#93811yescharacteristic
652C4C3×#93911yescharacteristic
653C4C3×#94011yescharacteristic
654C3—21no—
655C3#7170011yescharacteristic, direct product factor
656C3C3×#200111yescharacteristic, complemented
657C2—42no—
658C2C3×#504711yescharacteristic
659C2C3×#505011yescharacteristic
660C2C3×#505111yescharacteristic
661C2C3×#505211yescharacteristic
662C2C3×#522311yescharacteristic
663C2C3×#522811yescharacteristic
664C2C3×#523911yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C3×#2001
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
4. C2×C3×#835C2semidirect
6. C2×C3×#810C2semidirect
7. C3×#4529C2semidirect
9. #71700C3direct (N × H)
36. C22×#216C2×C3semidirect
41. C2×#835C2×C3semidirect
43. C2×#810C2×C3semidirect
45. #4529C2×C3semidirect
142. C23×C32Q16semidirect
351. C23×C3#216semidirect
352. C23×C3C3×Q16semidirect
563. C32#2001semidirect
570. C23C3×#216semidirect
655. C3#71700direct (N × H)
656. C3C3×#2001semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C22⋊Q82
C22×C3×#2162
C2×C3×#9242
C2×C3×#8352
C2×C3×#8302
C2×C3×#8102
C3×#45292
C3×#20013
#717003