Finite Group Databasebeta

← C3×#84013 #11886655

Subgroups — C3×#84013 #11886655

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 987 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#577C211yesmaximal, characteristic, complemented
2C3×#5838C211yesmaximal, characteristic, complemented
3C3×#5836C211yesmaximal, characteristic, complemented
4C3×#5771C211yesmaximal, characteristic, complemented
5C3×#5246C211yesmaximal, characteristic, complemented
6C3×#5242C211yesmaximal, characteristic, complemented
7C3×#5205C211yesmaximal, characteristic, complemented
8C3×#5204C211yesmaximal, characteristic, complemented
9C3×#5201C211yesmaximal, characteristic, complemented
10C3×#5200C211yesmaximal, characteristic, complemented
11C3×#5197C211yesmaximal, characteristic, complemented
12C3×#5177C211yesmaximal, characteristic, complemented
13C3×#5167C211yesmaximal, characteristic, complemented
14C3×#5145C211yesmaximal, characteristic, complemented
15C3×#5143C211yesmaximal, characteristic, complemented
16C3×#3289—31nomaximal
17#84013C311yesmaximal, characteristic, direct product factor
18C32×2−1+4C2211yescharacteristic
19C32×H(5,𝔽2)C2211yescharacteristic
20C3×#1010C2211yescharacteristic
21C3×#1010C2211yescharacteristic, complemented
22C32×#137—21no—
23C32×#137C2211yescharacteristic
24C32×AGL(1,ℤ/8)—21no—
25C32×AGL(1,ℤ/8)C2211yescharacteristic
26C32×#135—21no—
27C32×#135C2211yescharacteristic
28C2×C32×SD16—21no—
29C2×C32×SD16C2211yescharacteristic
30C32×#131C2211yescharacteristic
31C3×#951—21no—
32C3×#951—21no—
33C3×#951C2211yescharacteristic
34C3×#951C2211yescharacteristic
35C3×#951C2211yescharacteristic
36C3×#951C2211yescharacteristic, complemented
37C3×#950—21no—
38C3×#950—21no—
39C3×#950C2211yescharacteristic
40C3×#948C2211yescharacteristic
41C3×#948C2211yescharacteristic, complemented
42C3×#944C2211yescharacteristic, complemented
43C2×C3×#216—21no—
44C2×C3×#216C2211yescharacteristic, complemented
45C3×#942—21no—
46C3×#942C2211yescharacteristic, complemented
47C3×#936C2211yescharacteristic
48C2×C3×#214—21no—
49C2×C3×#214C2211yescharacteristic
50C3×#932—21no—
51C3×#932C2211yescharacteristic
52C3×D3×Q16—21no—
53C3×#915—21no—
54C3×#915—21no—
55C3×#912—21no—
56C2×C3×Dic12C2211yescharacteristic, complemented
57C3×#901C2211yescharacteristic, complemented
58C3×#837C2211yescharacteristic
59C3×#837C2211yescharacteristic
60C3×#837C2211yescharacteristic, complemented
61C3×#836C2211yescharacteristic, complemented
62C3×#833C2211yescharacteristic
63C3×#825C2211yescharacteristic, complemented
64C3×#824C2211yescharacteristic, complemented
65C3×#824C2211yescharacteristic, complemented
66C3×#822C2211yescharacteristic, complemented
67C3×#819C2211yescharacteristic, complemented
68C3×#815C2211yescharacteristic, complemented
69C3×#578—31no—
70C3×#578—31no—
71C3×#577—21no—
72C3×#577—31no—
73C3×#577D311yescharacteristic, complemented
74C3×#577C2×C311yescharacteristic, complemented
75#5838C2×C311yescharacteristic, complemented
76#5836C2×C311yescharacteristic, complemented
77#5771C2×C311yescharacteristic, complemented
78C3×#497—31no—
79C3×#473—31no—
80C3×#473—31no—
81C3×#471—31no—
82C3×#471—31no—
83C3×#456—31no—
84C3×#456—31no—
85C3×#455—31no—
86C3×#454—31no—
87C3×#444—31no—
88C3×#444—31no—
89#5246C2×C311yescharacteristic, complemented
90#5242C2×C311yescharacteristic, complemented
91#5205C2×C311yescharacteristic, complemented
92#5204C2×C311yescharacteristic, complemented
93#5201C2×C311yescharacteristic, complemented
94#5200C2×C311yescharacteristic, complemented
95#5197C2×C311yescharacteristic, complemented
96#5177C2×C311yescharacteristic, complemented
97#5167C2×C311yescharacteristic, complemented
98#5145C2×C311yescharacteristic, complemented
99#5143C2×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
115C3×D3×Q8—21no—
116C3×D3×Q8—21no—
117C3×#237—21no—
118C3×#237—21no—
119C3×#237—41no—
120C3×#237—41no—
121C3×#235—21no—
122C3×#235—21no—
123C3×#235C2311yescharacteristic
124C2×C3×Dic6—21no—
125C2×C3×Dic6—21no—
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2311yescharacteristic
128C32×Q16—21no—
129C32×Q16D411yescharacteristic
130C32×SD16—21no—
131C32×SD16—21no—
132C32×SD16—21no—
133C32×SD16—21no—
134C32×SD16D411yescharacteristic
135C32×SD16D411yescharacteristic
136C32×D8—21no—
137C32×D8D411yescharacteristic
138C32×M16—21no—
139C32×M16C2311yescharacteristic
140C2×C32×C8—21no—
141C2×C32×C8C2311yescharacteristic
142C3×#217—41no—
143C3×#216—21no—
144C3×#216—21no—
145C3×#216—21no—
146C3×#216—21no—
147C3×#216—21no—
148C3×#216—21no—
149C3×#216—21no—
150C3×#216D411yescharacteristic
151C3×#215—21no—
152C3×#215D411yescharacteristic
153C3×#214—21no—
154C3×#214—21no—
155C3×#214—21no—
156C3×#214—21no—
157C3×#214—21no—
158C3×#214—21no—
159C3×#214—21no—
160C3×#214D411yescharacteristic
161C3×#213—21no—
162C3×#213D411yescharacteristic
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×Dic12—21no—
174C3×Dic12—21no—
175C3×ΓL(1,𝔽25)—21no—
176C3×D3×C8—21no—
177#3289—31noSylow
178C3×2−1+4—21no—
179C3×2−1+4—31no—
180C3×2−1+4—31no—
181C3×2−1+4C2×D311yescharacteristic
182C3×2−1+4C22×C311yescharacteristic
183C3×H(5,𝔽2)—21no—
184C3×H(5,𝔽2)C2×D311yescharacteristic
185C3×H(5,𝔽2)C22×C311yescharacteristic
186#1010C22×C311yescharacteristic
187#1010C22×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—31no—
196C3×#137—31no—
197C3×#137—61no—
198C3×#137—61no—
199C3×#137—61no—
200C3×#137—61no—
201C3×#137—61no—
202C3×#137C2×D311yescharacteristic
203C3×#137C22×C311yescharacteristic
204C3×AGL(1,ℤ/8)—22no—
205C3×AGL(1,ℤ/8)—21no—
206C3×AGL(1,ℤ/8)—21no—
207C3×AGL(1,ℤ/8)—21no—
208C3×AGL(1,ℤ/8)—31no—
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×Q16—31no—
223C2×C3×Q16—31no—
224C2×C3×Q16—61no—
225C2×C3×Q16—61no—
226C2×C3×SD16—22no—
227C2×C3×SD16—21no—
228C2×C3×SD16—21no—
229C2×C3×SD16—21no—
230C2×C3×SD16—31no—
231C2×C3×SD16—61no—
232C2×C3×SD16C2×D311yescharacteristic
233C2×C3×SD16C22×C311yescharacteristic
234C3×#131—21no—
235C3×#131—31no—
236C3×#131—31no—
237C3×#131—31no—
238C3×#131C2×D311yescharacteristic
239C3×#131C22×C311yescharacteristic
240C3×C4⋊Q8—31no—
241C3×#124—31no—
242#951—21no—
243#951—21no—
244#951C22×C311yescharacteristic
245#951C22×C311yescharacteristic
246#951C22×C311yescharacteristic
247#951C22×C311yescharacteristic, complemented
248#950—21no—
249#950—21no—
250#950C22×C311yescharacteristic
251#948C22×C311yescharacteristic
252#948C22×C311yescharacteristic, complemented
253#944C22×C311yescharacteristic, complemented
254C2×#216—21no—
255C2×#216C22×C311yescharacteristic, complemented
256#942—21no—
257#942C22×C311yescharacteristic, complemented
258#936C22×C311yescharacteristic
259C2×#214—21no—
260C2×#214C22×C311yescharacteristic
261#932—21no—
262#932C22×C311yescharacteristic
263D3×Q16—21no—
264#915—21no—
265#915—21no—
266#912—21no—
267C2×Dic12C22×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×#101—31no—
278C3×#100—31no—
279C3×#97—31no—
280#837C22×C311yescharacteristic
281#837C22×C311yescharacteristic
282#837C22×C311yescharacteristic, complemented
283#836C22×C311yescharacteristic, complemented
284#833C22×C311yescharacteristic
285#825C22×C311yescharacteristic, complemented
286#824C22×C311yescharacteristic, complemented
287#824C22×C311yescharacteristic, complemented
288#822C22×C311yescharacteristic, complemented
289#819C22×C311yescharacteristic, complemented
290#815C22×C311yescharacteristic, complemented
291C23×C32—21no—
292C23×C32—41no—
293C32×Q8—21no—
294C32×Q8—21no—
295C32×Q8—41no—
296C32×Q8C2×D411yescharacteristic
297C32×Q8C2×D411yescharacteristic
298C32×Q8C2×D411yescharacteristic
299C32×D4—21no—
300C32×D4—21no—
301C32×D4—21no—
302C32×D4—21no—
303C32×D4—21no—
304C32×D4—41no—
305C32×D4—41no—
306C32×D4—41no—
307C32×D4C2×D411yescharacteristic
308C32×D4C2×D411yescharacteristic
309C32×D4C2×D411yescharacteristic
310C2×C32×C4—21no—
311C2×C32×C4—21no—
312C2×C32×C4—21no—
313C2×C32×C4—21no—
314C2×C32×C4—41no—
315C2×C32×C4—41no—
316C2×C32×C4—41no—
317C2×C32×C4C2411yescharacteristic
318C3×#67—21no—
319C3×#67—41no—
320C3×#67—41no—
321C2×C3×Dic3—21no—
322C2×C3×Dic3—21no—
323C2×C3×Dic3—21no—
324C2×C3×Dic3—41no—
325C2×C3×Dic3—41no—
326C3×D12C2×D411yescharacteristic
327C3×C4×D3—21no—
328C3×C4×D3—41no—
329C3×C4×D3—41no—
330C3×Dic6—21no—
331C3×Dic6—21no—
332C3×Dic6—21no—
333C3×Dic6—21no—
334C3×Dic6—41no—
335C3×Dic6—41no—
336C3×Dic6C2×D411yescharacteristic
337C32×C8—21no—
338C32×C8C2×D411yescharacteristic
339C32×C8C2×D411yescharacteristic
340C3×C3⋊C8—21no—
341C3×C3⋊C8—21no—
342C3×C3⋊C8—21no—
343C3×C3⋊C8C2×D411yescharacteristic
344C3×C3⋊C8C2×D411yescharacteristic
345#578—31no—
346#578—31no—
347#577—31no—
348#577C3×D311yescharacteristic, complemented
349#497—31no—
350#473—31no—
351#473—31no—
352#471—31no—
353#471—31no—
354#456—31no—
355#456—31no—
356#455—31no—
357#454—31no—
358#444—31no—
359#444—31no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—21no—
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—31no—
374C3×#41—41no—
375C3×#41—41no—
376C3×#41—41no—
377C3×#41—41no—
378C3×#41—42no—
379C3×#41—61no—
380C3×#41—61no—
381C3×#41—61no—
382C3×#41—61no—
383C3×#41—121no—
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—31no—
399C2×C3×Q8—41no—
400C2×C3×Q8—61no—
401C2×C3×Q8—61no—
402C2×C3×Q8—61no—
403C2×C3×Q8—61no—
404C2×C3×Q8C22×D311yescharacteristic
405C2×C3×Q8C23×C311yescharacteristic
406C2×C3×D4—22no—
407C2×C3×D4—21no—
408C2×C3×D4—21no—
409C2×C3×D4—21no—
410C2×C3×D4—21no—
411C2×C3×D4—21no—
412C2×C3×D4—41no—
413C2×C3×D4—41no—
414C2×C3×D4—41no—
415C2×C3×D4—42no—
416C2×C3×D4C22×D311yescharacteristic
417C2×C3×D4C23×C311yescharacteristic
418D3×Q8—21no—
419D3×Q8—21no—
420#237—21no—
421#237—21no—
422#237—41no—
423#237—41no—
424#235—21no—
425#235—21no—
426#235C23×C311yescharacteristic
427C2×Dic6—21no—
428C2×Dic6—21no—
429C2×Dic6C23×C311yescharacteristic
430C2×Dic6C23×C311yescharacteristic
431C3×Q16—22no—
432C3×Q16—21no—
433C3×Q16—21no—
434C3×Q16—21no—
435C3×Q16—31no—
436C3×Q16—61no—
437C3×Q16—61no—
438C3×Q16—61no—
439C3×Q16—61no—
440C3×Q16—61no—
441C3×Q16—61no—
442C3×Q16—61no—
443C3×Q16—61no—
444C3×Q16—61no—
445C3×Q16#6711yescharacteristic
446C3×Q16C3×D411yescharacteristic
447C3×SD16—22no—
448C3×SD16—22no—
449C3×SD16—22no—
450C3×SD16—22no—
451C3×SD16—21no—
452C3×SD16—21no—
453C3×SD16—21no—
454C3×SD16—21no—
455C3×SD16—21no—
456C3×SD16—21no—
457C3×SD16—21no—
458C3×SD16—21no—
459C3×SD16—21no—
460C3×SD16—21no—
461C3×SD16—31no—
462C3×SD16—31no—
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#6711yescharacteristic
472C3×SD16#6711yescharacteristic
473C3×SD16C3×D411yescharacteristic
474C3×SD16C3×D411yescharacteristic
475C3×D8—22no—
476C3×D8—21no—
477C3×D8—21no—
478C3×D8—21no—
479C3×D8—31no—
480C3×D8—61no—
481C3×D8#6711yescharacteristic
482C3×D8C3×D411yescharacteristic
483C3×M16—22no—
484C3×M16—21no—
485C3×M16—21no—
486C3×M16—21no—
487C3×M16—31no—
488C3×M16—31no—
489C3×M16—31no—
490C3×M16—61no—
491C3×M16—61no—
492C3×M16—61no—
493C3×M16C22×D311yescharacteristic
494C3×M16C23×C311yescharacteristic
495C2×C3×C8—22no—
496C2×C3×C8—21no—
497C2×C3×C8—21no—
498C2×C3×C8—21no—
499C2×C3×C8—31no—
500C2×C3×C8—61no—
501C2×C3×C8—61no—
502C2×C3×C8—61no—
503C2×C3×C8C22×D311yescharacteristic
504C2×C3×C8C23×C311yescharacteristic
505C3×C4⋊C4—121no—
506C3×C22⋊C4—121no—
507C3×C42—31no—
508#217—41no—
509#216—21no—
510#216—21no—
511#216—21no—
512#216—21no—
513#216—21no—
514#216—21no—
515#216—21no—
516#216C3×D411yescharacteristic
517#215—21no—
518#215C3×D411yescharacteristic
519#214—21no—
520#214—21no—
521#214—21no—
522#214—21no—
523#214—21no—
524#214—21no—
525#214—21no—
526#214C3×D411yescharacteristic
527#213—21no—
528#213C3×D411yescharacteristic
529Dic3⋊C4—41no—
530C4×Dic3C23×C311yescharacteristic
531#208—21no—
532#208—21no—
533#208C23×C311yescharacteristic
534#208C23×C311yescharacteristic
535#208C23×C311yescharacteristic
536C2×C3⋊C8—21no—
537C2×C3⋊C8—21no—
538C2×C3⋊C8C23×C311yescharacteristic
539Dic12—21no—
540Dic12—21no—
541ΓL(1,𝔽25)—21no—
542D3×C8—21no—
543C22×C32—21no—
544C22×C32—21no—
545C22×C32—21no—
546C22×C32—41no—
547C22×C32—81no—
548C22×C32—161no—
549C22×C32H(5,𝔽2)11yescharacteristic
550C2×C3×D3—21no—
551C32×C4—21no—
552C32×C4—21no—
553C32×C4—21no—
554C32×C4—41no—
555C32×C4C22×D411yescharacteristic
556C32×C4C22×D411yescharacteristic
557C3×Dic3—21no—
558C3×Dic3—41no—
559C3×Dic3—41no—
560C3×Dic3—41no—
5612−1+4—31no—
5622−1+4—31no—
5632−1+4C2×C3×D311yescharacteristic
564H(5,𝔽2)C2×C3×D311yescharacteristic
565#137—21no—
566#137—31no—
567#137—31no—
568#137—31no—
569#137—31no—
570#137—31no—
571#137—61no—
572#137—61no—
573#137—61no—
574#137—61no—
575#137—61no—
576#137C2×C3×D311yescharacteristic
577AGL(1,ℤ/8)—21no—
578AGL(1,ℤ/8)—31no—
579AGL(1,ℤ/8)—61no—
580AGL(1,ℤ/8)C2×C3×D311yescharacteristic
581#135—21no—
582#135—31no—
583#135—61no—
584#135—61no—
585#135—61no—
586#135C2×C3×D311yescharacteristic
587C2×Q16—31no—
588C2×Q16—31no—
589C2×Q16—61no—
590C2×Q16—61no—
591C2×SD16—21no—
592C2×SD16—31no—
593C2×SD16—61no—
594C2×SD16C2×C3×D311yescharacteristic
595#131—31no—
596#131—31no—
597#131—31no—
598#131C2×C3×D311yescharacteristic
599C4⋊Q8—31no—
600#124—31no—
601#108—31no—
602#108—31no—
603#104—31no—
604#104—31no—
605#104—31no—
606#104—31no—
607#101—31no—
608#101—31no—
609#101—31no—
610#100—31no—
611#97—31no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—41no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—42no—
618C3×Q8—22no—
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—21no—
622C3×Q8—21no—
623C3×Q8—21no—
624C3×Q8—21no—
625C3×Q8—21no—
626C3×Q8—31no—
627C3×Q8—41no—
628C3×Q8—41no—
629C3×Q8—41no—
630C3×Q8—42no—
631C3×Q8—61no—
632C3×Q8—61no—
633C3×Q8—61no—
634C3×Q8—61no—
635C3×Q8—121no—
636C3×Q8—121no—
637C3×Q8D3×D411yescharacteristic
638C3×Q8C2×#6711yescharacteristic
639C3×Q8C2×#6711yescharacteristic
640C3×Q8C2×C3×D411yescharacteristic
641C3×Q8C2×C3×D411yescharacteristic
642C3×Q8C2×C3×D411yescharacteristic
643C3×D4—22no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—21no—
647C3×D4—21no—
648C3×D4—21no—
649C3×D4—21no—
650C3×D4—22no—
651C3×D4—21no—
652C3×D4—21no—
653C3×D4—21no—
654C3×D4—21no—
655C3×D4—21no—
656C3×D4—21no—
657C3×D4—21no—
658C3×D4—31no—
659C3×D4—41no—
660C3×D4—41no—
661C3×D4—41no—
662C3×D4—41no—
663C3×D4—41no—
664C3×D4—41no—
665C3×D4—41no—
666C3×D4—42no—
667C3×D4—41no—
668C3×D4—41no—
669C3×D4—42no—
670C3×D4—42no—
671C3×D4—61no—
672C3×D4—121no—
673C3×D4—121no—
674C3×D4D3×D411yescharacteristic
675C3×D4C2×#6711yescharacteristic
676C3×D4C2×#6711yescharacteristic
677C3×D4C2×C3×D411yescharacteristic
678C3×D4C2×C3×D411yescharacteristic
679C3×D4C2×C3×D411yescharacteristic
680C2×C3×C4—22no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—42no—
700C2×C3×C4—42no—
701C2×C3×C4—42no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—121no—
707C2×C3×C4—121no—
708C2×C3×C4—121no—
709C2×C3×C4—121no—
710C2×C3×C4C23×D311yescharacteristic
711C2×C3×C4C24×C311yescharacteristic
712#67—21no—
713#67—41no—
714#67—41no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—41no—
719C2×Dic3—41no—
720D12C2×C3×D411yescharacteristic
721C4×D3—21no—
722C4×D3—41no—
723C4×D3—41no—
724Dic6—21no—
725Dic6—21no—
726Dic6—21no—
727Dic6—21no—
728Dic6—41no—
729Dic6—41no—
730Dic6C2×C3×D411yescharacteristic
731C3×C8—22no—
732C3×C8—21no—
733C3×C8—21no—
734C3×C8—21no—
735C3×C8—21no—
736C3×C8—31no—
737C3×C8—31no—
738C3×C8—61no—
739C3×C8—61no—
740C3×C8—61no—
741C3×C8C2×#6711yescharacteristic
742C3×C8C2×#6711yescharacteristic
743C3×C8C2×C3×D411yescharacteristic
744C3×C8C2×C3×D411yescharacteristic
745C3⋊C8—21no—
746C3⋊C8—21no—
747C3⋊C8—21no—
748C3⋊C8C2×C3×D411yescharacteristic
749C3⋊C8C2×C3×D411yescharacteristic
750C2×C32—21no—
751C2×C32—41no—
752C2×C32—41no—
753C2×C32—41no—
754C2×C32—81no—
755C2×C32D4211yescharacteristic
756C3×D3—41no—
757#41—21no—
758#41—21no—
759#41—21no—
760#41—21no—
761#41—31no—
762#41—41no—
763#41—61no—
764#41—61no—
765#41—61no—
766#41—61no—
767#41—121no—
768#41—121no—
769#41C22×C3×D311yescharacteristic
770#41C22×C3×D311yescharacteristic
771#41C22×C3×D311yescharacteristic
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—31no—
775C2×Q8—31no—
776C2×Q8—61no—
777C2×Q8—61no—
778C2×Q8—61no—
779C2×Q8—61no—
780C2×Q8C22×C3×D311yescharacteristic
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4C22×C3×D311yescharacteristic
785Q16—21no—
786Q16—31no—
787Q16—61no—
788Q16—61no—
789Q16—61no—
790Q16—61no—
791Q16—61no—
792Q16—61no—
793Q16—61no—
794Q16—61no—
795Q16—61no—
796Q16C3×#6711yescharacteristic
797SD16—21no—
798SD16—21no—
799SD16—21no—
800SD16—21no—
801SD16—31no—
802SD16—31no—
803SD16—61no—
804SD16—61no—
805SD16—61no—
806SD16—61no—
807SD16—61no—
808SD16—61no—
809SD16—61no—
810SD16—61no—
811SD16C3×#6711yescharacteristic
812SD16C3×#6711yescharacteristic
813D8—21no—
814D8—31no—
815D8—61no—
816D8C3×#6711yescharacteristic
817M16—21no—
818M16—31no—
819M16—31no—
820M16—31no—
821M16—61no—
822M16—61no—
823M16—61no—
824M16C22×C3×D311yescharacteristic
825C2×C8—21no—
826C2×C8—31no—
827C2×C8—61no—
828C2×C8—61no—
829C2×C8—61no—
830C2×C8C22×C3×D311yescharacteristic
831C4⋊C4—121no—
832C22⋊C4—121no—
833C42—31no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—42no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—61no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—161no—
851C22×C3—161no—
852C22×C3—161no—
853C22×C3—162no—
854C22×C3#100411yescharacteristic
855C22×C3C3×H(5,𝔽2)11yescharacteristic
856C2×D3—21no—
857C3×C4—22no—
858C3×C4—21no—
859C3×C4—21no—
860C3×C4—21no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—21no—
866C3×C4—41no—
867C3×C4—41no—
868C3×C4—42no—
869C3×C4—41no—
870C3×C4—41no—
871C3×C4—61no—
872C3×C4—121no—
873C3×C4—121no—
874C3×C4—121no—
875C3×C4C2×D3×D411yescharacteristic
876C3×C4C22×#6711yescharacteristic
877C3×C4C22×C3×D411yescharacteristic
878C3×C4C22×C3×D411yescharacteristic
879Dic3—21no—
880Dic3—41no—
881Dic3—41no—
882Dic3—41no—
883C32#328911yescharacteristic, complemented, Sylow
884C23—21no—
885C23—41no—
886Q8—21no—
887Q8—21no—
888Q8—31no—
889Q8—41no—
890Q8—61no—
891Q8—61no—
892Q8—61no—
893Q8—61no—
894Q8—121no—
895Q8—121no—
896Q8C3×D3×D411yescharacteristic
897Q8C2×C3×#6711yescharacteristic
898Q8C2×C3×#6711yescharacteristic
899D4—21no—
900D4—21no—
901D4—21no—
902D4—21no—
903D4—21no—
904D4—31no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—61no—
909D4—121no—
910D4—121no—
911D4C3×D3×D411yescharacteristic
912D4C2×C3×#6711yescharacteristic
913D4C2×C3×#6711yescharacteristic
914C2×C4—21no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—61no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—61no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4—121no—
928C2×C4—121no—
929C2×C4C23×C3×D311yescharacteristic
930C8—21no—
931C8—31no—
932C8—31no—
933C8—61no—
934C8—61no—
935C8—61no—
936C8C2×C3×#6711yescharacteristic
937C8C2×C3×#6711yescharacteristic
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—41no—
942C2×C3—42no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—81no—
950C2×C3—81no—
951C2×C3—82no—
952C2×C3—81no—
953C2×C3—81no—
954C2×C3—121no—
955C2×C3D4×#6711yescharacteristic
956C2×C3C3×D4211yescharacteristic
957D3—41no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—41no—
962C22—61no—
963C22—81no—
964C22—161no—
965C22C3×#100411yescharacteristic
966C4—21no—
967C4—21no—
968C4—21no—
969C4—41no—
970C4—61no—
971C4—121no—
972C4—121no—
973C4—121no—
974C4C2×C3×D3×D411yescharacteristic
975C4C22×C3×#6711yescharacteristic
976C3—21no—
977C3#8401311yescharacteristic, direct product factor
978C3C3×#328911yescharacteristic, complemented
979C2—21no—
980C2—41no—
981C2—41no—
982C2—41no—
983C2—81no—
984C2—121no—
985C2C3×D4×#6711yescharacteristic
subgroupG/H
centerC2×C3D4×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#577C2
socleC2×C32D42
hypercenterC3×#577D3
hypocenterC3C3×#3289
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×#5838C2semidirect
3. C3×#5836C2semidirect
4. C3×#5771C2semidirect
5. C3×#5246C2semidirect
6. C3×#5242C2semidirect
7. C3×#5205C2semidirect
8. C3×#5204C2semidirect
9. C3×#5201C2semidirect
10. C3×#5200C2semidirect
11. C3×#5197C2semidirect
12. C3×#5177C2semidirect
13. C3×#5167C2semidirect
14. C3×#5145C2semidirect
15. C3×#5143C2semidirect
17. #84013C3direct (N × H)
21. C3×#1010C22semidirect
36. C3×#951C22semidirect
41. C3×#948C22semidirect
42. C3×#944C22semidirect
44. C2×C3×#216C22semidirect
46. C3×#942C22semidirect
56. C2×C3×Dic12C22semidirect
57. C3×#901C22semidirect
60. C3×#837C22semidirect
61. C3×#836C22semidirect
63. C3×#825C22semidirect
64. C3×#824C22semidirect
65. C3×#824C22semidirect
66. C3×#822C22semidirect
67. C3×#819C22semidirect
68. C3×#815C22semidirect
73. C3×#577D3semidirect
74. C3×#577C2×C3semidirect
75. #5838C2×C3semidirect
76. #5836C2×C3semidirect
77. #5771C2×C3semidirect
89. #5246C2×C3semidirect
90. #5242C2×C3semidirect
91. #5205C2×C3semidirect
92. #5204C2×C3semidirect
93. #5201C2×C3semidirect
94. #5200C2×C3semidirect
95. #5197C2×C3semidirect
96. #5177C2×C3semidirect
97. #5167C2×C3semidirect
98. #5145C2×C3semidirect
99. #5143C2×C3semidirect
187. #1010C22×C3semidirect
247. #951C22×C3semidirect
252. #948C22×C3semidirect
253. #944C22×C3semidirect
255. C2×#216C22×C3semidirect
257. #942C22×C3semidirect
267. C2×Dic12C22×C3semidirect
268. #901C22×C3semidirect
282. #837C22×C3semidirect
283. #836C22×C3semidirect
285. #825C22×C3semidirect
286. #824C22×C3semidirect
287. #824C22×C3semidirect
288. #822C22×C3semidirect
289. #819C22×C3semidirect
290. #815C22×C3semidirect
348. #577C3×D3semidirect
883. C32#3289semidirect
977. C3#84013direct (N × H)
978. C3C3×#3289semidirect

Maximal subgroups

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

subgroupindex
C32×#5772
C3×#58382
C3×#58362
C3×#57712
C3×#52462
C3×#52422
C3×#52052
C3×#52042
C3×#52012
C3×#52002
C3×#51972
C3×#51772
C3×#51672
C3×#51452
C3×#51432
C3×#32893
#840133