Finite Group Databasebeta

← C3×#84014 #11886842

Subgroups — C3×#84014 #11886842

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#577C211yesmaximal, characteristic, complemented
2C3×#5837C211yesmaximal, characteristic, complemented
3C3×#5836C211yesmaximal, characteristic, complemented
4C3×#5770C211yesmaximal, characteristic, complemented
5C3×#5246C211yesmaximal, characteristic, complemented
6C3×#5241C211yesmaximal, characteristic, complemented
7C3×#5205C211yesmaximal, characteristic, complemented
8C3×#5203C211yesmaximal, characteristic, complemented
9C3×#5200C211yesmaximal, characteristic, complemented
10C3×#5198C211yesmaximal, characteristic, complemented
11C3×#5196C211yesmaximal, characteristic, complemented
12C3×#5177C211yesmaximal, characteristic, complemented
13C3×#5175C211yesmaximal, characteristic, complemented
14C3×#5144C211yesmaximal, characteristic, complemented
15C3×#5141C211yesmaximal, characteristic, complemented
16C3×#3291—31nomaximal
17#84014C311yesmaximal, characteristic, direct product factor
18C32×2−1+4C2211yescharacteristic
19C32×H(5,𝔽2)C2211yescharacteristic, complemented
20C3×#1010C2211yescharacteristic
21C3×#1009C2211yescharacteristic, complemented
22C32×#137—21no—
23C32×#137C2211yescharacteristic, complemented
24C32×AGL(1,ℤ/8)—21no—
25C32×AGL(1,ℤ/8)C2211yescharacteristic
26C32×#135—21no—
27C32×#135C2211yescharacteristic
28C2×C32×SD16—21no—
29C2×C32×SD16C2211yescharacteristic, complemented
30C32×#131C2211yescharacteristic, complemented
31C3×#951—21no—
32C3×#951C2211yescharacteristic, complemented
33C3×#951C2211yescharacteristic, complemented
34C3×#950—21no—
35C3×#950—21no—
36C3×#950C2211yescharacteristic
37C3×#949—21no—
38C3×#949C2211yescharacteristic
39C3×#949C2211yescharacteristic
40C3×#948C2211yescharacteristic, complemented
41C3×#948C2211yescharacteristic, complemented
42C3×#944C2211yescharacteristic, complemented
43C3×#942—21no—
44C3×#942C2211yescharacteristic, complemented
45C2×C3×#215—21no—
46C2×C3×#215C2211yescharacteristic, complemented
47C3×#940C2211yescharacteristic
48C2×C3×#214—21no—
49C2×C3×#214C2211yescharacteristic, complemented
50C3×#932—21no—
51C3×#932C2211yescharacteristic
52C3×#918—21no—
53C3×#916—21no—
54C3×D3×SD16—21no—
55C3×#911—21no—
56C2×C3×#204C2211yescharacteristic, complemented
57C3×#901C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic, complemented
59C3×#837C2211yescharacteristic, complemented
60C3×#837C2211yescharacteristic, complemented
61C3×#836C2211yescharacteristic, complemented
62C3×#833C2211yescharacteristic, complemented
63C3×#825C2211yescharacteristic, complemented
64C3×#824C2211yescharacteristic, complemented
65C3×#823C2211yescharacteristic, complemented
66C3×#822C2211yescharacteristic, complemented
67C3×#819C2211yescharacteristic, complemented
68C3×C8×Dic3C2211yescharacteristic, complemented
69C3×#577—21no—
70C3×#577—31no—
71C3×#577—31no—
72C3×#577—31no—
73C3×#577D311yescharacteristic, complemented
74C3×#577C2×C311yescharacteristic, complemented
75#5837C2×C311yescharacteristic, complemented
76#5836C2×C311yescharacteristic, complemented
77#5770C2×C311yescharacteristic, complemented
78C3×#492—31no—
79C3×#471—31no—
80C3×#471—31no—
81C3×#471—31no—
82C3×#471—31no—
83C3×#456—31no—
84C3×#456—31no—
85C3×#453—31no—
86C3×#453—31no—
87C3×#443—31no—
88C3×#443—31no—
89#5246C2×C311yescharacteristic, complemented
90#5241C2×C311yescharacteristic, complemented
91#5205C2×C311yescharacteristic, complemented
92#5203C2×C311yescharacteristic, complemented
93#5200C2×C311yescharacteristic, complemented
94#5198C2×C311yescharacteristic, complemented
95#5196C2×C311yescharacteristic, complemented
96#5177C2×C311yescharacteristic, complemented
97#5175C2×C311yescharacteristic, complemented
98#5144C2×C311yescharacteristic, complemented
99#5141C2×C311yescharacteristic, complemented
100C32×#41—21no—
101C32×#41—21no—
102C32×#41—21no—
103C32×#41—21no—
104C32×#41—41no—
105C32×#41C2311yescharacteristic
106C32×#41C2311yescharacteristic
107C32×#41C2311yescharacteristic
108C2×C32×Q8—21no—
109C2×C32×Q8—21no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4—21no—
112C2×C32×D4—21no—
113C2×C32×D4—41no—
114C2×C32×D4C2311yescharacteristic
115C2×C3×#67—41no—
116C3×#239—21no—
117C3×D3×Q8—21no—
118C3×#237—21no—
119C3×#237—41no—
120C3×D3×D4—21no—
121C3×D3×D4—41no—
122C3×#235—21no—
123C3×#235—21no—
124C3×#235C2311yescharacteristic
125C2×C3×D12—21no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×Dic6—21no—
128C2×C3×Dic6C2311yescharacteristic
129C32×Q16—21no—
130C32×Q16D411yescharacteristic, complemented
131C32×SD16—21no—
132C32×SD16—21no—
133C32×SD16—21no—
134C32×SD16—21no—
135C32×SD16D411yescharacteristic, complemented
136C32×SD16D411yescharacteristic, complemented
137C32×D8—21no—
138C32×D8D411yescharacteristic, complemented
139C32×M16—21no—
140C32×M16C2311yescharacteristic
141C2×C32×C8—21no—
142C2×C32×C8C2311yescharacteristic
143C3×#216—21no—
144C3×#216—21no—
145C3×#216—21no—
146C3×#216D411yescharacteristic, complemented
147C3×#215—21no—
148C3×#215—21no—
149C3×#215—21no—
150C3×#215—21no—
151C3×#215—21no—
152C3×#215D411yescharacteristic, complemented
153C3×#214—21no—
154C3×#214—21no—
155C3×#214—21no—
156C3×#214—21no—
157C3×#214—21no—
158C3×#214D411yescharacteristic, complemented
159C3×#213—21no—
160C3×#213—21no—
161C3×#213—21no—
162C3×#213D411yescharacteristic, complemented
163C3×Dic3⋊C4—41no—
164C3×C4×Dic3C2311yescharacteristic
165C3×#208—21no—
166C3×#208—21no—
167C3×#208C2311yescharacteristic
168C3×#208C2311yescharacteristic
169C3×#208C2311yescharacteristic
170C2×C3×C3⋊C8—21no—
171C2×C3×C3⋊C8—21no—
172C2×C3×C3⋊C8C2311yescharacteristic
173C3×#204—21no—
174C3×#204—21no—
175C3×ΓL(1,𝔽25)—21no—
176C3×D3×C8—21no—
177#3291—31noSylow
178C3×2−1+4—21no—
179C3×2−1+4—31no—
180C3×2−1+4C2×D311yescharacteristic
181C3×2−1+4C22×C311yescharacteristic
182C3×H(5,𝔽2)—21no—
183C3×H(5,𝔽2)—31no—
184C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
185C3×H(5,𝔽2)C22×C311yescharacteristic, complemented
186#1010C22×C311yescharacteristic
187#1009C22×C311yescharacteristic, complemented
188C3×#137—22no—
189C3×#137—21no—
190C3×#137—21no—
191C3×#137—21no—
192C3×#137—31no—
193C3×#137—31no—
194C3×#137—31no—
195C3×#137—61no—
196C3×#137—61no—
197C3×#137—61no—
198C3×#137C2×D311yescharacteristic, complemented
199C3×#137C22×C311yescharacteristic, complemented
200C3×AGL(1,ℤ/8)—22no—
201C3×AGL(1,ℤ/8)—21no—
202C3×AGL(1,ℤ/8)—21no—
203C3×AGL(1,ℤ/8)—21no—
204C3×AGL(1,ℤ/8)—31no—
205C3×AGL(1,ℤ/8)—31no—
206C3×AGL(1,ℤ/8)—31no—
207C3×AGL(1,ℤ/8)—61no—
208C3×AGL(1,ℤ/8)—61no—
209C3×AGL(1,ℤ/8)—61no—
210C3×AGL(1,ℤ/8)C2×D311yescharacteristic
211C3×AGL(1,ℤ/8)C22×C311yescharacteristic
212C3×#135—22no—
213C3×#135—21no—
214C3×#135—21no—
215C3×#135—21no—
216C3×#135—31no—
217C3×#135—61no—
218C3×#135—61no—
219C3×#135—61no—
220C3×#135C2×D311yescharacteristic
221C3×#135C22×C311yescharacteristic
222C2×C3×SD16—22no—
223C2×C3×SD16—21no—
224C2×C3×SD16—21no—
225C2×C3×SD16—21no—
226C2×C3×SD16—31no—
227C2×C3×SD16—31no—
228C2×C3×SD16—31no—
229C2×C3×SD16—61no—
230C2×C3×SD16—61no—
231C2×C3×SD16—61no—
232C2×C3×SD16C2×D311yescharacteristic, complemented
233C2×C3×SD16C22×C311yescharacteristic, complemented
234C3×#131—21no—
235C3×#131—31no—
236C3×#131—31no—
237C3×#131—31no—
238C3×#131C2×D311yescharacteristic, complemented
239C3×#131C22×C311yescharacteristic, complemented
240C3×C4⋊Q8—31no—
241C3×#127—31no—
242#951—21no—
243#951C22×C311yescharacteristic, complemented
244#951C22×C311yescharacteristic, complemented
245#950—21no—
246#950—21no—
247#950C22×C311yescharacteristic
248#949—21no—
249#949C22×C311yescharacteristic
250#949C22×C311yescharacteristic
251#948C22×C311yescharacteristic, complemented
252#948C22×C311yescharacteristic, complemented
253#944C22×C311yescharacteristic, complemented
254#942—21no—
255#942C22×C311yescharacteristic, complemented
256C2×#215—21no—
257C2×#215C22×C311yescharacteristic, complemented
258#940C22×C311yescharacteristic
259C2×#214—21no—
260C2×#214C22×C311yescharacteristic, complemented
261#932—21no—
262#932C22×C311yescharacteristic
263#918—21no—
264#916—21no—
265D3×SD16—21no—
266#911—21no—
267C2×#204C22×C311yescharacteristic, complemented
268#901C22×C311yescharacteristic, complemented
269C3×#108—31no—
270C3×#108—31no—
271C3×#104—31no—
272C3×#104—31no—
273C3×#104—31no—
274C3×#104—31no—
275C3×#101—31no—
276C3×#101—31no—
277C3×#100—31no—
278C3×#100—31no—
279C3×C4×C8—31no—
280#837C22×C311yescharacteristic, complemented
281#837C22×C311yescharacteristic, complemented
282#837C22×C311yescharacteristic, complemented
283#836C22×C311yescharacteristic, complemented
284#833C22×C311yescharacteristic, complemented
285#825C22×C311yescharacteristic, complemented
286#824C22×C311yescharacteristic, complemented
287#823C22×C311yescharacteristic, complemented
288#822C22×C311yescharacteristic, complemented
289#819C22×C311yescharacteristic, complemented
290C8×Dic3C22×C311yescharacteristic, complemented
291C23×C32—21no—
292C23×C32—41no—
293C22×C3×D3—21no—
294C22×C3×D3—41no—
295C32×Q8—21no—
296C32×Q8—21no—
297C32×Q8—41no—
298C32×Q8C2×D411yescharacteristic
299C32×Q8C2×D411yescharacteristic
300C32×Q8C2×D411yescharacteristic
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—21no—
305C32×D4—21no—
306C32×D4—41no—
307C32×D4—41no—
308C32×D4—41no—
309C32×D4C2×D411yescharacteristic
310C32×D4C2×D411yescharacteristic
311C32×D4C2×D411yescharacteristic
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—21no—
315C2×C32×C4—21no—
316C2×C32×C4—41no—
317C2×C32×C4—41no—
318C2×C32×C4—41no—
319C2×C32×C4C2411yescharacteristic
320C3×#67—21no—
321C3×#67—41no—
322C3×#67—41no—
323C3×#67—82no—
324C2×C3×Dic3—21no—
325C2×C3×Dic3—21no—
326C2×C3×Dic3—41no—
327C3×D12—21no—
328C3×D12—21no—
329C3×D12—41no—
330C3×D12C2×D411yescharacteristic
331C3×C4×D3—21no—
332C3×C4×D3—41no—
333C3×C4×D3—41no—
334C3×Dic6—21no—
335C3×Dic6—21no—
336C3×Dic6—41no—
337C3×Dic6C2×D411yescharacteristic
338C32×C8—21no—
339C32×C8C2×D411yescharacteristic
340C32×C8C2×D411yescharacteristic
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8—21no—
344C3×C3⋊C8C2×D411yescharacteristic
345C3×C3⋊C8C2×D411yescharacteristic
346#577—31no—
347#577—31no—
348#577—31no—
349#577C3×D311yescharacteristic, complemented
350#492—31no—
351#471—31no—
352#471—31no—
353#471—31no—
354#471—31no—
355#456—31no—
356#456—31no—
357#453—31no—
358#453—31no—
359#443—31no—
360#443—31no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—21no—
364C3×#41—21no—
365C3×#41—21no—
366C3×#41—21no—
367C3×#41—21no—
368C3×#41—21no—
369C3×#41—21no—
370C3×#41—21no—
371C3×#41—21no—
372C3×#41—21no—
373C3×#41—21no—
374C3×#41—31no—
375C3×#41—41no—
376C3×#41—41no—
377C3×#41—41no—
378C3×#41—41no—
379C3×#41—42no—
380C3×#41—61no—
381C3×#41—61no—
382C3×#41—61no—
383C3×#41—61no—
384C3×#41—121no—
385C3×#41C22×D311yescharacteristic
386C3×#41C22×D311yescharacteristic
387C3×#41C22×D311yescharacteristic
388C3×#41C23×C311yescharacteristic
389C3×#41C23×C311yescharacteristic
390C3×#41C23×C311yescharacteristic
391C2×C3×Q8—22no—
392C2×C3×Q8—21no—
393C2×C3×Q8—21no—
394C2×C3×Q8—21no—
395C2×C3×Q8—21no—
396C2×C3×Q8—21no—
397C2×C3×Q8—31no—
398C2×C3×Q8—41no—
399C2×C3×Q8—61no—
400C2×C3×Q8—61no—
401C2×C3×Q8C22×D311yescharacteristic
402C2×C3×Q8C23×C311yescharacteristic
403C2×C3×D4—22no—
404C2×C3×D4—21no—
405C2×C3×D4—21no—
406C2×C3×D4—21no—
407C2×C3×D4—21no—
408C2×C3×D4—21no—
409C2×C3×D4—31no—
410C2×C3×D4—41no—
411C2×C3×D4—41no—
412C2×C3×D4—41no—
413C2×C3×D4—42no—
414C2×C3×D4—61no—
415C2×C3×D4—61no—
416C2×C3×D4—121no—
417C2×C3×D4—121no—
418C2×C3×D4C22×D311yescharacteristic
419C2×C3×D4C23×C311yescharacteristic
420C2×#67—41no—
421#239—21no—
422D3×Q8—21no—
423#237—21no—
424#237—41no—
425D3×D4—21no—
426D3×D4—41no—
427#235—21no—
428#235—21no—
429#235C23×C311yescharacteristic
430C2×D12—21no—
431C2×D12C23×C311yescharacteristic
432C2×Dic6—21no—
433C2×Dic6C23×C311yescharacteristic
434C3×Q16—22no—
435C3×Q16—21no—
436C3×Q16—21no—
437C3×Q16—21no—
438C3×Q16—31no—
439C3×Q16—61no—
440C3×Q16—61no—
441C3×Q16—61no—
442C3×Q16#6711yescharacteristic, complemented
443C3×Q16C3×D411yescharacteristic, complemented
444C3×SD16—22no—
445C3×SD16—22no—
446C3×SD16—22no—
447C3×SD16—22no—
448C3×SD16—21no—
449C3×SD16—21no—
450C3×SD16—21no—
451C3×SD16—21no—
452C3×SD16—21no—
453C3×SD16—21no—
454C3×SD16—21no—
455C3×SD16—21no—
456C3×SD16—21no—
457C3×SD16—21no—
458C3×SD16—31no—
459C3×SD16—31no—
460C3×SD16—61no—
461C3×SD16—61no—
462C3×SD16—61no—
463C3×SD16—61no—
464C3×SD16—61no—
465C3×SD16—61no—
466C3×SD16—61no—
467C3×SD16—61no—
468C3×SD16—61no—
469C3×SD16—61no—
470C3×SD16—61no—
471C3×SD16—61no—
472C3×SD16#6711yescharacteristic, complemented
473C3×SD16#6711yescharacteristic, complemented
474C3×SD16C3×D411yescharacteristic, complemented
475C3×SD16C3×D411yescharacteristic, complemented
476C3×D8—22no—
477C3×D8—21no—
478C3×D8—21no—
479C3×D8—21no—
480C3×D8—31no—
481C3×D8—61no—
482C3×D8—61no—
483C3×D8—61no—
484C3×D8#6711yescharacteristic, complemented
485C3×D8C3×D411yescharacteristic, complemented
486C3×M16—22no—
487C3×M16—21no—
488C3×M16—21no—
489C3×M16—21no—
490C3×M16—31no—
491C3×M16—31no—
492C3×M16—31no—
493C3×M16—61no—
494C3×M16—61no—
495C3×M16—61no—
496C3×M16C22×D311yescharacteristic
497C3×M16C23×C311yescharacteristic
498C2×C3×C8—22no—
499C2×C3×C8—21no—
500C2×C3×C8—21no—
501C2×C3×C8—21no—
502C2×C3×C8—31no—
503C2×C3×C8—61no—
504C2×C3×C8—61no—
505C2×C3×C8—61no—
506C2×C3×C8C22×D311yescharacteristic
507C2×C3×C8C23×C311yescharacteristic
508C3×C4⋊C4—121no—
509C3×C42—31no—
510#216—21no—
511#216—21no—
512#216—21no—
513#216C3×D411yescharacteristic, complemented
514#215—21no—
515#215—21no—
516#215—21no—
517#215—21no—
518#215—21no—
519#215C3×D411yescharacteristic, complemented
520#214—21no—
521#214—21no—
522#214—21no—
523#214—21no—
524#214—21no—
525#214C3×D411yescharacteristic, complemented
526#213—21no—
527#213—21no—
528#213—21no—
529#213C3×D411yescharacteristic, complemented
530Dic3⋊C4—41no—
531C4×Dic3C23×C311yescharacteristic
532#208—21no—
533#208—21no—
534#208C23×C311yescharacteristic
535#208C23×C311yescharacteristic
536#208C23×C311yescharacteristic
537C2×C3⋊C8—21no—
538C2×C3⋊C8—21no—
539C2×C3⋊C8C23×C311yescharacteristic
540#204—21no—
541#204—21no—
542ΓL(1,𝔽25)—21no—
543D3×C8—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—21no—
547C22×C32—41no—
548C22×C32—81no—
549C22×C32—161no—
550C22×C32H(5,𝔽2)11yescharacteristic
551C2×C3×D3—21no—
552C2×C3×D3—41no—
553C2×C3×D3—81no—
554C2×C3×D3—161no—
555C32×C4—21no—
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—41no—
559C32×C4C22×D411yescharacteristic
560C32×C4C22×D411yescharacteristic
561C3×Dic3—22no—
562C3×Dic3—21no—
563C3×Dic3—41no—
5642−1+4—31no—
5652−1+4C2×C3×D311yescharacteristic
566H(5,𝔽2)—31no—
567H(5,𝔽2)C2×C3×D311yescharacteristic, complemented
568#137—21no—
569#137—31no—
570#137—31no—
571#137—31no—
572#137—61no—
573#137—61no—
574#137—61no—
575#137C2×C3×D311yescharacteristic, complemented
576AGL(1,ℤ/8)—21no—
577AGL(1,ℤ/8)—31no—
578AGL(1,ℤ/8)—31no—
579AGL(1,ℤ/8)—31no—
580AGL(1,ℤ/8)—61no—
581AGL(1,ℤ/8)—61no—
582AGL(1,ℤ/8)—61no—
583AGL(1,ℤ/8)C2×C3×D311yescharacteristic
584#135—21no—
585#135—31no—
586#135—61no—
587#135—61no—
588#135—61no—
589#135C2×C3×D311yescharacteristic
590C2×SD16—21no—
591C2×SD16—31no—
592C2×SD16—31no—
593C2×SD16—31no—
594C2×SD16—61no—
595C2×SD16—61no—
596C2×SD16—61no—
597C2×SD16C2×C3×D311yescharacteristic, complemented
598#131—31no—
599#131—31no—
600#131—31no—
601#131C2×C3×D311yescharacteristic, complemented
602C4⋊Q8—31no—
603#127—31no—
604#108—31no—
605#108—31no—
606#104—31no—
607#104—31no—
608#104—31no—
609#104—31no—
610#101—31no—
611#101—31no—
612#100—31no—
613#100—31no—
614C4×C8—31no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—42no—
621C23×C3—61no—
622C23×C3—121no—
623C22×D3—21no—
624C22×D3—41no—
625C3×Q8—22no—
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—21no—
630C3×Q8—21no—
631C3×Q8—21no—
632C3×Q8—21no—
633C3×Q8—31no—
634C3×Q8—41no—
635C3×Q8—41no—
636C3×Q8—41no—
637C3×Q8—42no—
638C3×Q8—61no—
639C3×Q8—61no—
640C3×Q8—121no—
641C3×Q8D3×D411yescharacteristic
642C3×Q8C2×#6711yescharacteristic
643C3×Q8C2×#6711yescharacteristic
644C3×Q8C2×C3×D411yescharacteristic
645C3×Q8C2×C3×D411yescharacteristic
646C3×Q8C2×C3×D411yescharacteristic
647C3×D4—22no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—21no—
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—22no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—21no—
658C3×D4—21no—
659C3×D4—21no—
660C3×D4—21no—
661C3×D4—21no—
662C3×D4—31no—
663C3×D4—41no—
664C3×D4—41no—
665C3×D4—41no—
666C3×D4—41no—
667C3×D4—41no—
668C3×D4—41no—
669C3×D4—41no—
670C3×D4—42no—
671C3×D4—41no—
672C3×D4—41no—
673C3×D4—42no—
674C3×D4—42no—
675C3×D4—61no—
676C3×D4—61no—
677C3×D4—61no—
678C3×D4—121no—
679C3×D4—121no—
680C3×D4—121no—
681C3×D4—242no—
682C3×D4D3×D411yescharacteristic
683C3×D4C2×#6711yescharacteristic
684C3×D4C2×#6711yescharacteristic
685C3×D4C2×C3×D411yescharacteristic
686C3×D4C2×C3×D411yescharacteristic
687C3×D4C2×C3×D411yescharacteristic
688C2×C3×C4—22no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—21no—
697C2×C3×C4—21no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—42no—
708C2×C3×C4—42no—
709C2×C3×C4—42no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—61no—
713C2×C3×C4—121no—
714C2×C3×C4—121no—
715C2×C3×C4—121no—
716C2×C3×C4C23×D311yescharacteristic
717C2×C3×C4C24×C311yescharacteristic
718#67—21no—
719#67—41no—
720#67—41no—
721#67—82no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—41no—
725D12—21no—
726D12—21no—
727D12—41no—
728D12C2×C3×D411yescharacteristic
729C4×D3—21no—
730C4×D3—41no—
731C4×D3—41no—
732Dic6—21no—
733Dic6—21no—
734Dic6—41no—
735Dic6C2×C3×D411yescharacteristic
736C3×C8—22no—
737C3×C8—21no—
738C3×C8—21no—
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—31no—
742C3×C8—31no—
743C3×C8—61no—
744C3×C8—61no—
745C3×C8—61no—
746C3×C8C2×#6711yescharacteristic
747C3×C8C2×#6711yescharacteristic
748C3×C8C2×C3×D411yescharacteristic
749C3×C8C2×C3×D411yescharacteristic
750C3⋊C8—21no—
751C3⋊C8—21no—
752C3⋊C8—21no—
753C3⋊C8C2×C3×D411yescharacteristic
754C3⋊C8C2×C3×D411yescharacteristic
755C2×C32—21no—
756C2×C32—41no—
757C2×C32—41no—
758C2×C32—41no—
759C2×C32—81no—
760C2×C32D4211yescharacteristic
761C3×D3—41no—
762C3×D3—81no—
763#41—21no—
764#41—21no—
765#41—21no—
766#41—21no—
767#41—31no—
768#41—41no—
769#41—61no—
770#41—61no—
771#41—61no—
772#41—61no—
773#41—121no—
774#41C22×C3×D311yescharacteristic
775#41C22×C3×D311yescharacteristic
776#41C22×C3×D311yescharacteristic
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—31no—
780C2×Q8—61no—
781C2×Q8—61no—
782C2×Q8C22×C3×D311yescharacteristic
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—31no—
786C2×D4—41no—
787C2×D4—61no—
788C2×D4—61no—
789C2×D4—121no—
790C2×D4—121no—
791C2×D4C22×C3×D311yescharacteristic
792Q16—21no—
793Q16—31no—
794Q16—61no—
795Q16—61no—
796Q16—61no—
797Q16C3×#6711yescharacteristic, complemented
798SD16—21no—
799SD16—21no—
800SD16—21no—
801SD16—21no—
802SD16—31no—
803SD16—31no—
804SD16—61no—
805SD16—61no—
806SD16—61no—
807SD16—61no—
808SD16—61no—
809SD16—61no—
810SD16—61no—
811SD16—61no—
812SD16—61no—
813SD16—61no—
814SD16—61no—
815SD16—61no—
816SD16C3×#6711yescharacteristic, complemented
817SD16C3×#6711yescharacteristic, complemented
818D8—21no—
819D8—31no—
820D8—61no—
821D8—61no—
822D8—61no—
823D8C3×#6711yescharacteristic, complemented
824M16—21no—
825M16—31no—
826M16—31no—
827M16—31no—
828M16—61no—
829M16—61no—
830M16—61no—
831M16C22×C3×D311yescharacteristic
832C2×C8—21no—
833C2×C8—31no—
834C2×C8—61no—
835C2×C8—61no—
836C2×C8—61no—
837C2×C8C22×C3×D311yescharacteristic
838C4⋊C4—121no—
839C42—31no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—21no—
843C22×C3—21no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—42no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—61no—
854C22×C3—81no—
855C22×C3—81no—
856C22×C3—121no—
857C22×C3—161no—
858C22×C3—161no—
859C22×C3—161no—
860C22×C3—162no—
861C22×C3—241no—
862C22×C3—481no—
863C22×C3#100411yescharacteristic
864C22×C3C3×H(5,𝔽2)11yescharacteristic
865C2×D3—21no—
866C2×D3—41no—
867C2×D3—81no—
868C2×D3—161no—
869C3×C4—22no—
870C3×C4—21no—
871C3×C4—21no—
872C3×C4—21no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—21no—
877C3×C4—21no—
878C3×C4—41no—
879C3×C4—41no—
880C3×C4—42no—
881C3×C4—41no—
882C3×C4—41no—
883C3×C4—62no—
884C3×C4—61no—
885C3×C4—121no—
886C3×C4C2×D3×D411yescharacteristic
887C3×C4C22×#6711yescharacteristic
888C3×C4C22×C3×D411yescharacteristic
889C3×C4C22×C3×D411yescharacteristic
890Dic3—22no—
891Dic3—21no—
892Dic3—41no—
893C32#329111yescharacteristic, complemented, Sylow
894C23—21no—
895C23—41no—
896C23—61no—
897C23—121no—
898Q8—21no—
899Q8—21no—
900Q8—31no—
901Q8—41no—
902Q8—61no—
903Q8—61no—
904Q8—121no—
905Q8C3×D3×D411yescharacteristic
906Q8C2×C3×#6711yescharacteristic
907Q8C2×C3×#6711yescharacteristic
908D4—21no—
909D4—21no—
910D4—21no—
911D4—21no—
912D4—21no—
913D4—31no—
914D4—41no—
915D4—41no—
916D4—41no—
917D4—61no—
918D4—61no—
919D4—61no—
920D4—121no—
921D4—121no—
922D4—121no—
923D4—242no—
924D4C3×D3×D411yescharacteristic
925D4C2×C3×#6711yescharacteristic
926D4C2×C3×#6711yescharacteristic
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—121no—
938C2×C4—121no—
939C2×C4—121no—
940C2×C4C23×C3×D311yescharacteristic
941C8—21no—
942C8—31no—
943C8—31no—
944C8—61no—
945C8—61no—
946C8—61no—
947C8C2×C3×#6711yescharacteristic
948C8C2×C3×#6711yescharacteristic
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—42no—
954C2×C3—41no—
955C2×C3—41no—
956C2×C3—41no—
957C2×C3—41no—
958C2×C3—41no—
959C2×C3—41no—
960C2×C3—81no—
961C2×C3—81no—
962C2×C3—82no—
963C2×C3—81no—
964C2×C3—81no—
965C2×C3—121no—
966C2×C3—241no—
967C2×C3D4×#6711yescharacteristic
968C2×C3C3×D4211yescharacteristic
969D3—41no—
970D3—81no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—41no—
975C22—61no—
976C22—81no—
977C22—121no—
978C22—161no—
979C22—241no—
980C22—481no—
981C22C3×#100411yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—41no—
986C4—62no—
987C4—61no—
988C4—121no—
989C4C2×C3×D3×D411yescharacteristic
990C4C22×C3×#6711yescharacteristic
991C3—21no—
992C3#8401411yescharacteristic, direct product factor
993C3C3×#329111yescharacteristic, complemented
994C2—21no—
995C2—41no—
996C2—41no—
997C2—41no—
998C2—81no—
999C2—121no—
1000C2—241no—
1001C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC2×C3D4×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#577C2
socleC2×C32D42
hypercenterC3×#577D3
hypocenterC3C3×#3291
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#577

Complements

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

NH ≅ G/Ntype
1. C32×#577C2semidirect
2. C3×#5837C2semidirect
3. C3×#5836C2semidirect
4. C3×#5770C2semidirect
5. C3×#5246C2semidirect
6. C3×#5241C2semidirect
7. C3×#5205C2semidirect
8. C3×#5203C2semidirect
9. C3×#5200C2semidirect
10. C3×#5198C2semidirect
11. C3×#5196C2semidirect
12. C3×#5177C2semidirect
13. C3×#5175C2semidirect
14. C3×#5144C2semidirect
15. C3×#5141C2semidirect
17. #84014C3direct (N × H)
19. C32×H(5,𝔽2)C22semidirect
21. C3×#1009C22semidirect
23. C32×#137C22semidirect
29. C2×C32×SD16C22semidirect
30. C32×#131C22semidirect
32. C3×#951C22semidirect
33. C3×#951C22semidirect
40. C3×#948C22semidirect
41. C3×#948C22semidirect
42. C3×#944C22semidirect
44. C3×#942C22semidirect
46. C2×C3×#215C22semidirect
49. C2×C3×#214C22semidirect
56. C2×C3×#204C22semidirect
57. C3×#901C22semidirect
58. C3×#837C22semidirect
59. C3×#837C22semidirect
60. C3×#837C22semidirect
61. C3×#836C22semidirect
62. C3×#833C22semidirect
63. C3×#825C22semidirect
64. C3×#824C22semidirect
65. C3×#823C22semidirect
66. C3×#822C22semidirect
67. C3×#819C22semidirect
68. C3×C8×Dic3C22semidirect
73. C3×#577D3semidirect
74. C3×#577C2×C3semidirect
75. #5837C2×C3semidirect
76. #5836C2×C3semidirect
77. #5770C2×C3semidirect
89. #5246C2×C3semidirect
90. #5241C2×C3semidirect
91. #5205C2×C3semidirect
92. #5203C2×C3semidirect
93. #5200C2×C3semidirect
94. #5198C2×C3semidirect
95. #5196C2×C3semidirect
96. #5177C2×C3semidirect
97. #5175C2×C3semidirect
98. #5144C2×C3semidirect
99. #5141C2×C3semidirect
130. C32×Q16D4semidirect
135. C32×SD16D4semidirect
136. C32×SD16D4semidirect
138. C32×D8D4semidirect
146. C3×#216D4semidirect
152. C3×#215D4semidirect
158. C3×#214D4semidirect
162. C3×#213D4semidirect
184. C3×H(5,𝔽2)C2×D3semidirect
185. C3×H(5,𝔽2)C22×C3semidirect
187. #1009C22×C3semidirect
198. C3×#137C2×D3semidirect
199. C3×#137C22×C3semidirect
232. C2×C3×SD16C2×D3semidirect
233. C2×C3×SD16C22×C3semidirect
238. C3×#131C2×D3semidirect
239. C3×#131C22×C3semidirect
243. #951C22×C3semidirect
244. #951C22×C3semidirect
251. #948C22×C3semidirect
252. #948C22×C3semidirect
253. #944C22×C3semidirect
255. #942C22×C3semidirect
257. C2×#215C22×C3semidirect
260. C2×#214C22×C3semidirect
267. C2×#204C22×C3semidirect
268. #901C22×C3semidirect
280. #837C22×C3semidirect
281. #837C22×C3semidirect
282. #837C22×C3semidirect
283. #836C22×C3semidirect
284. #833C22×C3semidirect
285. #825C22×C3semidirect
286. #824C22×C3semidirect
287. #823C22×C3semidirect
288. #822C22×C3semidirect
289. #819C22×C3semidirect
290. C8×Dic3C22×C3semidirect
349. #577C3×D3semidirect
442. C3×Q16#67semidirect
443. C3×Q16C3×D4semidirect
472. C3×SD16#67semidirect
473. C3×SD16#67semidirect
474. C3×SD16C3×D4semidirect
475. C3×SD16C3×D4semidirect
484. C3×D8#67semidirect
485. C3×D8C3×D4semidirect
513. #216C3×D4semidirect
519. #215C3×D4semidirect
525. #214C3×D4semidirect
529. #213C3×D4semidirect
567. H(5,𝔽2)C2×C3×D3semidirect
575. #137C2×C3×D3semidirect
597. C2×SD16C2×C3×D3semidirect
601. #131C2×C3×D3semidirect
797. Q16C3×#67semidirect
816. SD16C3×#67semidirect
817. SD16C3×#67semidirect
823. D8C3×#67semidirect
893. C32#3291semidirect
992. C3#84014direct (N × H)
993. C3C3×#3291semidirect

Maximal subgroups

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

subgroupindex
C32×#5772
C3×#58372
C3×#58362
C3×#57702
C3×#52462
C3×#52412
C3×#52052
C3×#52032
C3×#52002
C3×#51982
C3×#51962
C3×#51772
C3×#51752
C3×#51442
C3×#51412
C3×#32913
#840143