Finite Group Databasebeta

← C3×#86737 #11905880

Subgroups — C3×#86737 #11905880

Order 1152.

3129 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×C3×#1007C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5C3×Q8×#67C211yesmaximal, characteristic, complemented
6C3×#5677C213yesmaximal, complemented
7C3×#5668C213yesmaximal, complemented
8C3×#5632C213yesmaximal, complemented
9C3×#5629C213yesmaximal, complemented
10C3×#5608C213yesmaximal, complemented
11C3×#5599C213yesmaximal, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
14C3×#5552C213yesmaximal, complemented
15C3×#5548C213yesmaximal, complemented
16C3×#3497—31nomaximal
17#86737C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic
20C3×#1010—28no—
21C3×#1007—28no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yes—
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2213yes—
26C2×C3×D3×Q8C2211yescharacteristic
27C2×C3×#237C2213yes—
28C2×C3×#237C2213yes—
29C2×C3×#235C2213yes—
30C2×C3×#235C2213yes—
31C2×C3×#235C2213yes—
32C22×C3×Dic6C2213yes—
33C32×#124C2213yes—
34C32×C22⋊Q8C2213yes—
35C32×#121C2213yes—
36C32×C4×Q8C2211yescharacteristic
37C32×C4×D4C2213yes—
38C3×#946C2213yes—
39C3×Q8×Dic3C2211yescharacteristic
40C3×#944C2213yes—
41C3×#940C2213yes—
42C3×#940C2213yes—
43C3×#939C2216yes—
44C3×#938C2213yes—
45C3×#938C2213yes—
46C3×#930C2213yes—
47C3×C4×#67C2213yes—
48C3×C4×#67C2213yes—
49C3×#924C2213yes—
50C3×#897C2213yes—
51C3×#896C2216yes—
52C3×#895C2213yes—
53C3×#895C2213yes—
54C3×D3×C4⋊C4C2213yes—
55C3×#888C2213yes—
56C3×#887C2213yes—
57C3×#885C2213yes—
58C3×#885C2213yes—
59C3×#884C2211yescharacteristic
60C3×#884C2213yes—
61C3×#884C2216yes—
62C3×#884C2216yes—
63C3×#67⋊C4C2216yes—
64C3×#67⋊C4C2216yes—
65C3×#878C2216yes—
66C3×#875C2213yes—
67C3×C4×D12C2213yes—
68C3×C42×D3C2213yes—
69C3×C4×Dic6C2213yes—
70C2×C3×2−1+4—31no—
71C2×C3×2−1+4—31no—
72C2×#1010C2×C311yescharacteristic, complemented
73C2×#1007C2×C311yescharacteristic, complemented
74C3×#550—31no—
75C3×#550—33no—
76C3×D4×Q8—31no—
77C3×D4×Q8—33no—
78C3×#548—21no—
79C3×#548—33no—
80C3×#548—31no—
81C3×#548—33no—
82C3×#548D311yescharacteristic, complemented
83C3×#548C2×C311yescharacteristic, complemented
84C3×#537—33no—
85C3×#537—33no—
86C3×#532—33no—
87C3×#532—33no—
88C2×C3×C4×Q8—31no—
89#5834C2×C311yescharacteristic, complemented
90Q8×#67C2×C311yescharacteristic, complemented
91#5677C2×C313yescomplemented
92#5668C2×C313yescomplemented
93#5632C2×C313yescomplemented
94#5629C2×C313yescomplemented
95#5608C2×C313yescomplemented
96#5599C2×C313yescomplemented
97#5576C2×C311yescharacteristic, complemented
98C4×D3×Q8C2×C311yescharacteristic, complemented
99#5552C2×C313yescomplemented
100#5548C2×C313yescomplemented
101C32×#41—24no—
102C2×C32×Q8—24no—
103C2×C32×Q8C2313yes—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C2×C32×D4C2313yes—
107C22×C32×C4C2313yes—
108C22×C32×C4C2313yes—
109C2×C3×#67C2313yes—
110C2×C3×#67C2313yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2311yescharacteristic
113C2×C3×#67C2311yescharacteristic
114C2×C3×#67C2313yes—
115C2×C3×#67C2316yes—
116C22×C3×Dic3C2316yes—
117C3×#239—24no—
118C3×#239—212no—
119C3×D3×Q8—24no—
120C3×D3×Q8—212no—
121C3×D3×Q8D418yescomplemented
122C3×#237—212no—
123C3×#237—212no—
124C3×#235—212no—
125C3×#235—212no—
126C3×#235—212no—
127C2×C3×D12C2313yes—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2313yes—
130C2×C3×D12C2313yes—
131C2×C3×C4×D3C2316yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2313yes—
134C2×C3×C4×D3C2313yes—
135C2×C3×C4×D3C2313yes—
136C2×C3×C4×D3C2313yes—
137C2×C3×Dic6—212no—
138C2×C3×Dic6C2313yes—
139C2×C3×Dic6C2313yes—
140C2×C3×Dic6C2313yes—
141C2×C3×Dic6C2313yes—
142C32×C4⋊C4C2313yes—
143C32×C4⋊C4C2313yes—
144C32×C22⋊C4C2316yes—
145C32×C22⋊C4C2313yes—
146C32×C22⋊C4C2311yescharacteristic
147C32×C42C2313yes—
148C3×#217C2313yes—
149C3×#217C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2316yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2311yescharacteristic
154C3×(C2×D3)⋊C4C2313yes—
155C3×C4⋊Dic3C2313yes—
156C3×C4⋊Dic3C2313yes—
157C3×Dic3⋊C4C2316yes—
158C3×Dic3⋊C4C2316yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2311yescharacteristic
161C3×C4×Dic3C2313yes—
162C3×C4×Dic3C2313yes—
163C3×C4×Dic3C2313yes—
164#3497—31noSylow
165C3×2−1+4—68no—
166C3×2−1+4—68no—
167C2×C3×#41—21no—
168C2×C3×#41—33no—
169C2×C3×#41—31no—
170C2×C3×#41—33no—
171C2×C3×#41—33no—
172C2×C3×#41—33no—
173C2×C3×#41—33no—
174C2×C3×#41—33no—
175C2×C3×#41C2×D311yescharacteristic
176C2×C3×#41C22×C311yescharacteristic
177C22×C3×Q8—21no—
178C22×C3×Q8—31no—
179C22×C3×Q8—33no—
180C22×C3×Q8—31no—
181C22×C3×Q8—33no—
182C22×C3×Q8C2×D311yescharacteristic
183C22×C3×Q8C22×C311yescharacteristic
184#1010—28no—
185#1007—28no—
186C2×#239C22×C313yes—
187C2×#239C22×C311yescharacteristic
188C2×D3×Q8C22×C313yes—
189C2×D3×Q8C22×C311yescharacteristic
190C2×D3×Q8C22×C311yescharacteristic
191C2×#237C22×C313yes—
192C2×#237C22×C313yes—
193C2×#235C22×C313yes—
194C2×#235C22×C313yes—
195C2×#235C22×C313yes—
196C22×Dic6C22×C313yes—
197C3×C4⋊Q8—33no—
198C3×C4⋊Q8—33no—
199C3×#127—33no—
200C3×#127—33no—
201C3×#124—23no—
202C3×#124—33no—
203C3×#124—33no—
204C3×#124—33no—
205C3×#124C2×D313yes—
206C3×#124C22×C313yes—
207C3×C22⋊Q8—23no—
208C3×C22⋊Q8—33no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—36no—
211C3×C22⋊Q8—33no—
212C3×C22⋊Q8—36no—
213C3×C22⋊Q8C2×D313yes—
214C3×C22⋊Q8C22×C313yes—
215C3×#121—23no—
216C3×#121—33no—
217C3×#121—33no—
218C3×#121—36no—
219C3×#121—33no—
220C3×#121—33no—
221C3×#121—33no—
222C3×#121—33no—
223C3×#121—31no—
224C3×#121—36no—
225C3×#121—36no—
226C3×#121C2×D313yes—
227C3×#121C22×C313yes—
228C3×C4×Q8—21no—
229C3×C4×Q8—31no—
230C3×C4×Q8—33no—
231C3×C4×Q8—33no—
232C3×C4×Q8C2×D311yescharacteristic
233C3×C4×Q8C22×C311yescharacteristic
234C3×C4×D4—23no—
235C3×C4×D4—33no—
236C3×C4×D4—33no—
237C3×C4×D4—36no—
238C3×C4×D4—36no—
239C3×C4×D4—33no—
240C3×C4×D4C2×D313yes—
241C3×C4×D4C22×C313yes—
242C2×C3×C4⋊C4—33no—
243C2×C3×C42—33no—
244#946C22×C313yes—
245Q8×Dic3C22×C311yescharacteristic
246#944C22×C313yes—
247#940C22×C313yes—
248#940C22×C313yes—
249#939C22×C316yes—
250#938C22×C313yes—
251#938C22×C313yes—
252#930C22×C313yes—
253C4×#67C22×C313yes—
254C4×#67C22×C313yes—
255#924C22×C313yes—
256#897C22×C313yes—
257#896C22×C316yes—
258#895C22×C313yes—
259#895C22×C313yes—
260D3×C4⋊C4C22×C313yes—
261#888C22×C313yes—
262#887C22×C313yes—
263#885C22×C313yes—
264#885C22×C313yes—
265#884C22×C313yes—
266#884C22×C316yes—
267#884C22×C316yes—
268#884C22×C311yescharacteristic
269#67⋊C4C22×C316yes—
270#67⋊C4C22×C316yes—
271#878C22×C316yes—
272#875C22×C313yes—
273C4×D12C22×C313yes—
274C42×D3C22×C313yes—
275C4×Dic6C22×C313yes—
276C23×C32C2411yescharacteristic
277C23×C32C2413yes—
278C22×C3×D3C2413yes—
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C32×Q8—26no—
282C32×Q8C2×D414yes—
283C32×D4—26no—
284C32×D4—43no—
285C2×C32×C4—26no—
286C2×C32×C4—26no—
287C2×C32×C4C2411yescharacteristic
288C2×C32×C4C2413yes—
289C2×C32×C4C2413yes—
290C2×C32×C4C2411yescharacteristic
291C2×C32×C4C2413yes—
292C3×#67—22no—
293C3×#67—26no—
294C3×#67—26no—
295C3×#67—26no—
296C3×#67—26no—
297C3×#67—22no—
298C3×#67—46no—
299C2×C3×Dic3—212no—
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C3×D12—22no—
306C3×D12—26no—
307C3×D12—26no—
308C3×D12—43no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—212no—
312C3×C4×D3—22no—
313C3×C4×D3—43no—
314C3×C4×D3C2×D4112yes—
315C3×Dic6—26no—
316C3×Dic6—26no—
317C3×Dic6—26no—
318C3×Dic6C2×D4112yes—
319C2×2−1+4—31no—
320C2×2−1+4—31no—
321#550—31no—
322#550—33no—
323D4×Q8—31no—
324D4×Q8—33no—
325#548—33no—
326#548—31no—
327#548—33no—
328#548C3×D311yescharacteristic, complemented
329#537—33no—
330#537—33no—
331#532—33no—
332#532—33no—
333C2×C4×Q8—31no—
334C3×#41—24no—
335C3×#41—24no—
336C3×#41—44no—
337C3×#41—612no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—612no—
341C3×#41—612no—
342C3×#41—612no—
343C3×#41—64no—
344C2×C3×Q8—24no—
345C2×C3×Q8—24no—
346C2×C3×Q8—21no—
347C2×C3×Q8—23no—
348C2×C3×Q8—38no—
349C2×C3×Q8—33no—
350C2×C3×Q8—33no—
351C2×C3×Q8—33no—
352C2×C3×Q8—33no—
353C2×C3×Q8—44no—
354C2×C3×Q8—612no—
355C2×C3×Q8—612no—
356C2×C3×Q8—64no—
357C2×C3×Q8C22×D313yes—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C23×C313yes—
360C2×C3×Q8C23×C311yescharacteristic
361C2×C3×D4—23no—
362C2×C3×D4—23no—
363C2×C3×D4—31no—
364C2×C3×D4—33no—
365C2×C3×D4—31no—
366C2×C3×D4—33no—
367C2×C3×D4—33no—
368C2×C3×D4—33no—
369C2×C3×D4—36no—
370C2×C3×D4—31no—
371C2×C3×D4—33no—
372C2×C3×D4—33no—
373C2×C3×D4—33no—
374C2×C3×D4C22×D313yes—
375C2×C3×D4C22×D313yes—
376C2×C3×D4C23×C313yes—
377C2×C3×D4C23×C313yes—
378C22×C3×C4—23no—
379C22×C3×C4—23no—
380C22×C3×C4—33no—
381C22×C3×C4—36no—
382C22×C3×C4—31no—
383C22×C3×C4—36no—
384C22×C3×C4—33no—
385C22×C3×C4—33no—
386C22×C3×C4—33no—
387C22×C3×C4C22×D313yes—
388C22×C3×C4C22×D313yes—
389C22×C3×C4C23×C313yes—
390C22×C3×C4C23×C313yes—
391C2×#67C23×C313yes—
392C2×#67C23×C313yes—
393C2×#67C23×C313yes—
394C2×#67C23×C311yescharacteristic
395C2×#67C23×C311yescharacteristic
396C2×#67C23×C313yes—
397C2×#67C23×C316yes—
398C22×Dic3C23×C316yes—
399#239—24no—
400#239—212no—
401D3×Q8—24no—
402D3×Q8—212no—
403D3×Q8C3×D418yescomplemented
404#237—212no—
405#237—212no—
406#235—212no—
407#235—212no—
408#235—212no—
409C2×D12C23×C313yes—
410C2×D12C23×C313yes—
411C2×D12C23×C311yescharacteristic
412C2×D12C23×C313yes—
413C2×C4×D3C23×C311yescharacteristic
414C2×C4×D3C23×C313yes—
415C2×C4×D3C23×C313yes—
416C2×C4×D3C23×C316yes—
417C2×C4×D3C23×C313yes—
418C2×C4×D3C23×C313yes—
419C2×Dic6—212no—
420C2×Dic6C23×C313yes—
421C2×Dic6C23×C313yes—
422C2×Dic6C23×C313yes—
423C2×Dic6C23×C313yes—
424C3×C4⋊C4—23no—
425C3×C4⋊C4—23no—
426C3×C4⋊C4—36no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—33no—
429C3×C4⋊C4—36no—
430C3×C4⋊C4—33no—
431C3×C4⋊C4—33no—
432C3×C4⋊C4C22×D313yes—
433C3×C4⋊C4C22×D313yes—
434C3×C4⋊C4C23×C313yes—
435C3×C4⋊C4C23×C313yes—
436C3×C22⋊C4—21no—
437C3×C22⋊C4—23no—
438C3×C22⋊C4—26no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—33no—
441C3×C22⋊C4—33no—
442C3×C22⋊C4—31no—
443C3×C22⋊C4—33no—
444C3×C22⋊C4—33no—
445C3×C22⋊C4—36no—
446C3×C22⋊C4C22×D313yes—
447C3×C22⋊C4C22×D316yes—
448C3×C22⋊C4C22×D311yescharacteristic
449C3×C22⋊C4C23×C316yes—
450C3×C22⋊C4C23×C313yes—
451C3×C22⋊C4C23×C311yescharacteristic
452C3×C42—23no—
453C3×C42—33no—
454C3×C42—33no—
455C3×C42—33no—
456C3×C42C22×D313yes—
457C3×C42C23×C313yes—
458#217C23×C313yes—
459#217C23×C313yes—
460(C2×D3)⋊C4C23×C311yescharacteristic
461(C2×D3)⋊C4C23×C313yes—
462(C2×D3)⋊C4C23×C316yes—
463(C2×D3)⋊C4C23×C313yes—
464(C2×D3)⋊C4C23×C313yes—
465C4⋊Dic3C23×C313yes—
466C4⋊Dic3C23×C313yes—
467Dic3⋊C4C23×C316yes—
468Dic3⋊C4C23×C316yes—
469Dic3⋊C4C23×C313yes—
470Dic3⋊C4C23×C311yescharacteristic
471C4×Dic3C23×C313yes—
472C4×Dic3C23×C313yes—
473C4×Dic3C23×C313yes—
474C22×C32—21no—
475C22×C32—23no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—23no—
479C22×C32—23no—
480C22×C32C2511yescharacteristic
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—23no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—23no—
489C2×C3×D3C22×D412yes—
490C32×C4—21no—
491C32×C4—23no—
492C32×C4—21no—
493C32×C4—23no—
494C32×C4C22×D416yes—
495C3×Dic3—21no—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3C22×D416yes—
499C3×Dic32−1+412yescomplemented
5002−1+4—68no—
5012−1+4—68no—
502C2×#41—33no—
503C2×#41—31no—
504C2×#41—33no—
505C2×#41—33no—
506C2×#41—33no—
507C2×#41—33no—
508C2×#41—33no—
509C2×#41C2×C3×D311yescharacteristic
510C22×Q8—31no—
511C22×Q8—33no—
512C22×Q8—31no—
513C22×Q8—33no—
514C22×Q8C2×C3×D311yescharacteristic
515C4⋊Q8—33no—
516C4⋊Q8—33no—
517#127—33no—
518#127—33no—
519#124—33no—
520#124—33no—
521#124—33no—
522#124C2×C3×D313yes—
523C22⋊Q8—33no—
524C22⋊Q8—33no—
525C22⋊Q8—36no—
526C22⋊Q8—33no—
527C22⋊Q8—36no—
528C22⋊Q8C2×C3×D313yes—
529#121—33no—
530#121—33no—
531#121—36no—
532#121—33no—
533#121—33no—
534#121—33no—
535#121—33no—
536#121—31no—
537#121—36no—
538#121—36no—
539#121C2×C3×D313yes—
540C4×Q8—31no—
541C4×Q8—33no—
542C4×Q8—33no—
543C4×Q8C2×C3×D311yescharacteristic
544C4×D4—33no—
545C4×D4—33no—
546C4×D4—36no—
547C4×D4—36no—
548C4×D4—33no—
549C4×D4C2×C3×D313yes—
550C2×C4⋊C4—33no—
551C2×C42—33no—
552C23×C3—21no—
553C23×C3—23no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D313yes—
559C23×C3C24×C311yescharacteristic
560C23×C3C24×C313yes—
561C22×D3C24×C313yes—
562C22×D3C24×C311yescharacteristic
563C22×D3C24×C311yescharacteristic
564C3×Q8—26no—
565C3×Q8—26no—
566C3×Q8—24no—
567C3×Q8—312no—
568C3×Q8—46no—
569C3×Q8—66no—
570C3×Q8—66no—
571C3×Q8—66no—
572C3×Q8D3×D414yes—
573C3×Q8C2×C3×D414yes—
574C3×D4—26no—
575C3×D4—26no—
576C3×D4—46no—
577C3×D4—43no—
578C3×D4—43no—
579C3×D4—46no—
580C3×D4—62no—
581C3×D4—66no—
582C3×D4—62no—
583C3×D4—66no—
584C3×D4—66no—
585C3×D4—66no—
586C3×D4—62no—
587C3×D4—66no—
588C3×D4—66no—
589C3×D4—123no—
590C3×D4—126no—
591C2×C3×C4—26no—
592C2×C3×C4—26no—
593C2×C3×C4—26no—
594C2×C3×C4—26no—
595C2×C3×C4—23no—
596C2×C3×C4—21no—
597C2×C3×C4—23no—
598C2×C3×C4—23no—
599C2×C3×C4—21no—
600C2×C3×C4—31no—
601C2×C3×C4—33no—
602C2×C3×C4—312no—
603C2×C3×C4—33no—
604C2×C3×C4—33no—
605C2×C3×C4—31no—
606C2×C3×C4—46no—
607C2×C3×C4—46no—
608C2×C3×C4—62no—
609C2×C3×C4—612no—
610C2×C3×C4—612no—
611C2×C3×C4—66no—
612C2×C3×C4—66no—
613C2×C3×C4—123no—
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D313yes—
616C2×C3×C4C23×D311yescharacteristic
617C2×C3×C4C23×D313yes—
618C2×C3×C4C23×D313yes—
619C2×C3×C4C24×C311yescharacteristic
620C2×C3×C4C24×C313yes—
621C2×C3×C4C24×C313yes—
622C2×C3×C4C24×C311yescharacteristic
623C2×C3×C4C24×C313yes—
624#67—22no—
625#67—26no—
626#67—26no—
627#67—26no—
628#67—26no—
629#67—22no—
630#67—46no—
631C2×Dic3—212no—
632C2×Dic3C24×C313yes—
633C2×Dic3C24×C313yes—
634C2×Dic3C24×C311yescharacteristic
635C2×Dic3C24×C313yes—
636C2×Dic3C24×C311yescharacteristic
637D12—22no—
638D12—26no—
639D12—26no—
640D12—43no—
641C4×D3—26no—
642C4×D3—26no—
643C4×D3—212no—
644C4×D3—22no—
645C4×D3—43no—
646C4×D3C2×C3×D4112yes—
647Dic6—26no—
648Dic6—26no—
649Dic6—26no—
650Dic6C2×C3×D4112yes—
651C2×C32—41no—
652C2×C32—43no—
653C2×C32C23×D411yescharacteristic
654C2×C32C2×2−1+411yescharacteristic
655C2×C32#58511yescharacteristic
656C3×D3—22no—
657C3×D3—43no—
658C3×D3—41no—
659#41—24no—
660#41—612no—
661#41—612no—
662#41—612no—
663#41—612no—
664#41—612no—
665#41—612no—
666#41—64no—
667C2×Q8—24no—
668C2×Q8—38no—
669C2×Q8—33no—
670C2×Q8—33no—
671C2×Q8—33no—
672C2×Q8—33no—
673C2×Q8—612no—
674C2×Q8—612no—
675C2×Q8—64no—
676C2×Q8C22×C3×D313yes—
677C2×Q8C22×C3×D311yescharacteristic
678C2×D4—31no—
679C2×D4—33no—
680C2×D4—31no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—33no—
684C2×D4—36no—
685C2×D4—31no—
686C2×D4—33no—
687C2×D4—33no—
688C2×D4—33no—
689C2×D4C22×C3×D313yes—
690C2×D4C22×C3×D313yes—
691C22×C4—33no—
692C22×C4—36no—
693C22×C4—31no—
694C22×C4—36no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4C22×C3×D313yes—
699C22×C4C22×C3×D313yes—
700C4⋊C4—36no—
701C4⋊C4—33no—
702C4⋊C4—31no—
703C4⋊C4—33no—
704C4⋊C4—36no—
705C4⋊C4—33no—
706C4⋊C4C22×C3×D313yes—
707C4⋊C4C22×C3×D313yes—
708C22⋊C4—33no—
709C22⋊C4—33no—
710C22⋊C4—33no—
711C22⋊C4—31no—
712C22⋊C4—33no—
713C22⋊C4—33no—
714C22⋊C4—36no—
715C22⋊C4C22×C3×D313yes—
716C22⋊C4C22×C3×D316yes—
717C22⋊C4C22×C3×D311yescharacteristic
718C42—33no—
719C42—33no—
720C42—33no—
721C42C22×C3×D313yes—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—23no—
725C22×C3—21no—
726C22×C3—23no—
727C22×C3—21no—
728C22×C3—23no—
729C22×C3—23no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—23no—
733C22×C3—23no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—32no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—43no—
740C22×C3—43no—
741C22×C3—43no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—63no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—63no—
748C22×C3—61no—
749C22×C3—63no—
750C22×C3C24×D311yescharacteristic
751C22×C3C25×C311yescharacteristic
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—23no—
755C2×D3—21no—
756C2×D3—23no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—23no—
760C2×D3C22×C3×D412yes—
761C3×C4—21no—
762C3×C4—23no—
763C3×C4—23no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—23no—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—26no—
770C3×C4—36no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—43no—
774C3×C4—43no—
775C3×C4—41no—
776C3×C4—63no—
777C3×C4—61no—
778C3×C4—63no—
779C3×C4C2×D3×D416yes—
780C3×C4C22×C3×D416yes—
781Dic3—21no—
782Dic3—23no—
783Dic3—23no—
784Dic3C22×C3×D416yes—
785Dic3C3×2−1+412yescomplemented
786C32#349711yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—33no—
790C23C23×C3×D311yescharacteristic
791C23C23×C3×D313yes—
792Q8—26no—
793Q8—312no—
794Q8—66no—
795Q8—66no—
796Q8—66no—
797Q8C3×D3×D414yes—
798D4—26no—
799D4—43no—
800D4—62no—
801D4—66no—
802D4—66no—
803D4—66no—
804D4—62no—
805D4—66no—
806D4—62no—
807D4—66no—
808D4—66no—
809D4—123no—
810D4—126no—
811C2×C4—26no—
812C2×C4—26no—
813C2×C4—31no—
814C2×C4—33no—
815C2×C4—312no—
816C2×C4—33no—
817C2×C4—31no—
818C2×C4—33no—
819C2×C4—612no—
820C2×C4—62no—
821C2×C4—612no—
822C2×C4—66no—
823C2×C4—66no—
824C2×C4—123no—
825C2×C4C23×C3×D311yescharacteristic
826C2×C4C23×C3×D313yes—
827C2×C4C23×C3×D311yescharacteristic
828C2×C4C23×C3×D313yes—
829C2×C4C23×C3×D313yes—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—42no—
834C2×C3—41no—
835C2×C3—43no—
836C2×C3—41no—
837C2×C3—43no—
838C2×C3—62no—
839C2×C3—83no—
840C2×C3—123no—
841C2×C3—121no—
842C2×C3C22×D3×D411yescharacteristic
843C2×C3#596411yescharacteristic
844C2×C3D3×2−1+411yescharacteristic
845C2×C3C23×C3×D411yescharacteristic
846C2×C3C2×C3×2−1+411yescharacteristic
847C2×C3C3×#58511yescharacteristic
848D3—22no—
849D3—43no—
850D3—41no—
851C22—21no—
852C22—23no—
853C22—21no—
854C22—23no—
855C22—21no—
856C22—23no—
857C22—32no—
858C22—61no—
859C22—61no—
860C22—63no—
861C22—61no—
862C22—61no—
863C22—63no—
864C22—61no—
865C22—63no—
866C22C24×C3×D311yescharacteristic
867C4—21no—
868C4—23no—
869C4—23no—
870C4—21no—
871C4—36no—
872C4—32no—
873C4—63no—
874C4—61no—
875C4—63no—
876C4C2×C3×D3×D416yes—
877C3—21no—
878C3#8673711yescharacteristic, direct product factor
879C3C3×#349711yescharacteristic, complemented
880C2—41no—
881C2—43no—
882C2—62no—
883C2—123no—
884C2—121no—
885C2C22×C3×D3×D411yescharacteristic
886C2C3×#596411yescharacteristic
887C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3497
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×C3×#1007C2semidirect
3. C32×#548C2semidirect
4. C3×#5834C2semidirect
5. C3×Q8×#67C2semidirect
6. C3×#5677C2semidirect
7. C3×#5668C2semidirect
8. C3×#5632C2semidirect
9. C3×#5629C2semidirect
10. C3×#5608C2semidirect
11. C3×#5599C2semidirect
12. C3×#5576C2semidirect
13. C3×C4×D3×Q8C2semidirect
14. C3×#5552C2semidirect
15. C3×#5548C2semidirect
17. #86737C3direct (N × H)
72. C2×#1010C2×C3semidirect
73. C2×#1007C2×C3semidirect
82. C3×#548D3semidirect
83. C3×#548C2×C3semidirect
89. #5834C2×C3semidirect
90. Q8×#67C2×C3semidirect
91. #5677C2×C3semidirect
92. #5668C2×C3semidirect
93. #5632C2×C3semidirect
94. #5629C2×C3semidirect
95. #5608C2×C3semidirect
96. #5599C2×C3semidirect
97. #5576C2×C3semidirect
98. C4×D3×Q8C2×C3semidirect
99. #5552C2×C3semidirect
100. #5548C2×C3semidirect
121. C3×D3×Q8D4semidirect
328. #548C3×D3semidirect
403. D3×Q8C3×D4semidirect
499. C3×Dic32−1+4semidirect
785. Dic3C3×2−1+4semidirect
786. C32#3497semidirect
878. C3#86737direct (N × H)
879. C3C3×#3497semidirect

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×#10072
C32×#5482
C3×#58342
C3×Q8×#672
C3×#56772
C3×#56682
C3×#56322
C3×#56292
C3×#56082
C3×#55992
C3×#55762
C3×C4×D3×Q82
C3×#55522
C3×#55482
C3×#34973
#867373