Finite Group Databasebeta

← C3×#10595232 #13174795

Subgroups — C3×#10595232 #13174795

Order 1728.

1582 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×#3798C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C3×#63978C212yesmaximal, complemented
6C3×#63971C212yesmaximal, complemented
7C3×#63970C212yesmaximal, complemented
8C3×#63964C212yesmaximal, complemented
9C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10C3×#63871C211yesmaximal, characteristic, complemented
11C3×#63856C211yesmaximal, characteristic, complemented
12C3×#5833—31nomaximal
13C3×#5608—31nomaximal
14#10595232C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×C4×C3⋊D3C2211yescharacteristic
18C2×C32×#67C2212yes—
19C2×C32×#67C2212yes—
20C22×C32×Dic3C2212yes—
21C32×#237—24no—
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×C4×D3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×C3×#627C2211yescharacteristic
26C2×C3×#626C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#625C2211yescharacteristic
29C2×C3×D3×Dic3C2212yes—
30C3×#3798—24no—
31C3×#3757C2212yes—
32C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C32×#217C2212yes—
34C32×C4⋊Dic3C2211yescharacteristic
35C3×#3724C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C32×#41—31no—
41C2×C3×#237—21no—
42C2×C3×#237D311yescharacteristic, complemented
43C2×C3×#237C2×C311yescharacteristic, complemented
44C2×C3×#235—31no—
45C2×C3×#235—31no—
46C2×#3798C2×C311yescharacteristic, complemented
47C32×#121—31no—
48#64147C2×C311yescharacteristic, complemented
49C3×#946—31no—
50C3×#946—31no—
51C3×#939—32no—
52C3×#939—32no—
53C3×#939—32no—
54C3×#938—21no—
55C3×#938—31no—
56C3×#938—31no—
57C3×#938—32no—
58C3×#938—61no—
59C3×#938D311yescharacteristic, complemented
60C3×#938C2×C311yescharacteristic, complemented
61C3×#930—32no—
62C2×C3×C4⋊Dic3—31no—
63C3×#924—31no—
64C3×#924—32no—
65C3×#897—31no—
66C3×D3×C4⋊C4—31no—
67C3×#884—32no—
68C3×#878—32no—
69#63978C2×C312yescomplemented
70#63971C2×C312yescomplemented
71#63970C2×C312yescomplemented
72#63964C2×C312yescomplemented
73D3×C4⋊Dic3C2×C311yescharacteristic, complemented
74#63871C2×C311yescharacteristic, complemented
75#63856C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C22×C32×D3C2311yescharacteristic
80C33×D4—22no—
81C2×C33×C4C2311yescharacteristic
82C3×#638—42no—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C3×C4×C3⋊D3—22no—
86C32×#67—24no—
87C32×#67—42no—
88C2×C32×Dic3—24no—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2312yes—
92C2×C32×Dic3C2311yescharacteristic
93C32×C4×D3—22no—
94C32×C4×D3D414yescomplemented
95C32×Dic6—22no—
96C3×#627—22no—
97C3×#626—22no—
98C3×#626—22no—
99C3×#625—22no—
100C3×D3×Dic3—42no—
101C3×#537—91no—
102#5833—31no—
103#5608—31no—
104C32×#41—64no—
105C2×C32×Q8—31no—
106C2×C32×D4—21no—
107C2×C32×D4—21no—
108C2×C32×D4—21no—
109C2×C32×D4—32no—
110C2×C32×D4—32no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C22×C311yescharacteristic
115C22×C32×C4—31no—
116C22×C32×C4—32no—
117C22×C32×C4—31no—
118C2×#638C22×C312yes—
119C2×C4×C3⋊D3C22×C311yescharacteristic
120C2×C3×#67—22no—
121C2×C3×#67—22no—
122C2×C3×#67—31no—
123C2×C3×#67—31no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—31no—
127C2×C3×#67—31no—
128C2×C3×#67—62no—
129C2×C3×#67C2×D312yes—
130C2×C3×#67C2×D312yes—
131C2×C3×#67C22×C312yes—
132C2×C3×#67C22×C312yes—
133C22×C3×Dic3—22no—
134C22×C3×Dic3—32no—
135C22×C3×Dic3C2×D312yes—
136C22×C3×Dic3C22×C312yes—
137C3×#237—28no—
138C3×#237—24no—
139C3×#237—24no—
140C3×#235—64no—
141C3×#235—64no—
142C2×C3×D12—31no—
143C2×C3×D12—31no—
144C2×C3×C4×D3—21no—
145C2×C3×C4×D3—21no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—32no—
149C2×C3×C4×D3—61no—
150C2×C3×C4×D3C2×D311yescharacteristic
151C2×C3×C4×D3C2×D311yescharacteristic
152C2×C3×C4×D3C22×C311yescharacteristic
153C2×C3×C4×D3C22×C311yescharacteristic
154C2×C3×Dic6—21no—
155C2×C3×Dic6—31no—
156C2×C3×Dic6—31no—
157C2×C3×Dic6C2×D311yescharacteristic
158C2×C3×Dic6C22×C311yescharacteristic
159C2×#627C22×C311yescharacteristic
160C2×#626C22×C311yescharacteristic
161C2×#626C22×C311yescharacteristic
162C2×#625C22×C311yescharacteristic
163C2×D3×Dic3C22×C312yes—
164#3798—24no—
165C32×C4⋊C4—31no—
166C32×C22⋊C4—32no—
167#3757C22×C312yes—
168C4⋊(C3⋊Dic3)C22×C311yescharacteristic
169C3×#217—22no—
170C3×#217—32no—
171C3×#217—32no—
172C3×#217—32no—
173C3×#217—62no—
174C3×#217C2×D312yes—
175C3×#217C22×C312yes—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4—32no—
178C3×(C2×D3)⋊C4—32no—
179C3×C4⋊Dic3—21no—
180C3×C4⋊Dic3—31no—
181C3×C4⋊Dic3—31no—
182C3×C4⋊Dic3—32no—
183C3×C4⋊Dic3—32no—
184C3×C4⋊Dic3—61no—
185C3×C4⋊Dic3C2×D311yescharacteristic
186C3×C4⋊Dic3C22×C311yescharacteristic
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—32no—
189C3×Dic3⋊C4—32no—
190C3×Dic3⋊C4—32no—
191#3724C22×C312yes—
192Dic3⋊Dic3C22×C312yes—
193Dic3⋊Dic3C22×C312yes—
194#3722C22×C312yes—
195(C2×D3)⋊Dic3C22×C312yes—
196C22×C33—22no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2411yescharacteristic
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C32×D3—21no—
204C2×C32×D3—21no—
205C2×C32×D3—21no—
206C2×C32×D3—21no—
207C2×C32×D3—21no—
208C2×C32×D3C2×D412yes—
209C33×C4C2×D412yes—
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—22no—
212C32×Dic3—22no—
213C32×Dic3—21no—
214C32×Dic3—22no—
215C32×Dic3C2×D412yes—
216C2×C3×#41—31no—
217C2×C3×#41—31no—
218C2×C3×#41—61no—
219C2×C3×#41—91no—
220C2×#237C3×D311yescharacteristic, complemented
221C2×#235—31no—
222C2×#235—31no—
223C3×C22⋊Q8—92no—
224C3×C22⋊Q8—91no—
225C3×C22⋊Q8—91no—
226C3×#121—31no—
227C3×#121—31no—
228C3×#121—61no—
229C3×#121—92no—
230C3×#121—92no—
231C3×#121—92no—
232C3×#121—91no—
233C2×C3×C4⋊C4—91no—
234#946—31no—
235#946—31no—
236#939—32no—
237#939—32no—
238#939—32no—
239#938—31no—
240#938—31no—
241#938—32no—
242#938—61no—
243#938C3×D311yescharacteristic, complemented
244#930—32no—
245C2×C4⋊Dic3—31no—
246#924—31no—
247#924—32no—
248#897—31no—
249D3×C4⋊C4—31no—
250#884—32no—
251#878—32no—
252C23×C32—22no—
253C23×C32—22no—
254C23×C32—22no—
255C23×C32—31no—
256C23×C32—31no—
257C23×C32—42no—
258C23×C32C22×D312yes—
259C23×C32C22×D312yes—
260C23×C32C23×C312yes—
261C22×C3⋊D3C23×C311yescharacteristic
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—31no—
265C22×C3×D3—31no—
266C22×C3×D3—61no—
267C22×C3×D3C22×D311yescharacteristic
268C22×C3×D3C22×D311yescharacteristic
269C22×C3×D3C23×C311yescharacteristic
270C22×C3×D3C23×C311yescharacteristic
271C32×Q8—62no—
272C32×D4—22no—
273C32×D4—24no—
274C32×D4—22no—
275C32×D4—22no—
276C32×D4—42no—
277C32×D4—42no—
278C32×D4—44no—
279C32×D4—64no—
280C32×D4—122no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—31no—
285C2×C32×C4—34no—
286C2×C32×C4—32no—
287C2×C32×C4—31no—
288C2×C32×C4—32no—
289C2×C32×C4—41no—
290C2×C32×C4—64no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D311yescharacteristic
293C2×C32×C4C22×D311yescharacteristic
294C2×C32×C4C23×C311yescharacteristic
295#638—42no—
296C2×C3⋊Dic3C23×C312yes—
297C2×C3⋊Dic3C23×C311yescharacteristic
298C4×C3⋊D3—22no—
299C3×#67—28no—
300C3×#67—24no—
301C3×#67—24no—
302C3×#67—42no—
303C3×#67—42no—
304C3×#67—44no—
305C3×#67—62no—
306C3×#67—62no—
307C3×#67—62no—
308C3×#67—62no—
309C3×#67—122no—
310C3×#67—122no—
311C3×#67—124no—
312C2×C3×Dic3—28no—
313C2×C3×Dic3—24no—
314C2×C3×Dic3—24no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—21no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—32no—
320C2×C3×Dic3—31no—
321C2×C3×Dic3—32no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—62no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—122no—
326C2×C3×Dic3C22×D311yescharacteristic
327C2×C3×Dic3C22×D312yes—
328C2×C3×Dic3C22×D312yes—
329C2×C3×Dic3C22×D311yescharacteristic
330C2×C3×Dic3C23×C312yes—
331C2×C3×Dic3C23×C312yes—
332C2×C3×Dic3C23×C311yescharacteristic
333C2×C3×Dic3C23×C311yescharacteristic
334C3×D12—62no—
335C3×D12—62no—
336C3×C4×D3—22no—
337C3×C4×D3—22no—
338C3×C4×D3—24no—
339C3×C4×D3—42no—
340C3×C4×D3—62no—
341C3×C4×D3—62no—
342C3×C4×D3—122no—
343C3×C4×D3—122no—
344C3×C4×D3#6714yescomplemented
345C3×C4×D3C3×D414yescomplemented
346C3×Dic6—24no—
347C3×Dic6—22no—
348C3×Dic6—22no—
349C3×Dic6—62no—
350C3×Dic6—62no—
351#627—22no—
352#626—22no—
353#626—22no—
354#625—22no—
355D3×Dic3—42no—
356#537—91noSylow
357C2×C33—42no—
358C2×C33C22×D411yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C2×C332−1+411yescharacteristic
361C3×C3⋊D3—41no—
362C32×D3—22no—
363C32×D3—41no—
364C3×#41—64no—
365C3×#41—64no—
366C3×#41—68no—
367C3×#41—184no—
368C2×C3×Q8—31no—
369C2×C3×Q8—31no—
370C2×C3×Q8—61no—
371C2×C3×Q8—91no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—32no—
376C2×C3×D4—32no—
377C2×C3×D4—32no—
378C2×C3×D4—32no—
379C2×C3×D4—41no—
380C2×C3×D4—62no—
381C2×C3×D4—62no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—92no—
386C2×C3×D4D3211yescharacteristic
387C2×C3×D4C2×C3×D311yescharacteristic
388C2×C3×D4C2×C3×D311yescharacteristic
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—32no—
392C22×C3×C4—32no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—61no—
396C22×C3×C4—61no—
397C22×C3×C4—62no—
398C22×C3×C4—92no—
399C22×C3×C4—91no—
400C2×#67—31no—
401C2×#67—31no—
402C2×#67—32no—
403C2×#67—32no—
404C2×#67—31no—
405C2×#67—31no—
406C2×#67—62no—
407C2×#67C2×C3×D312yes—
408C2×#67C2×C3×D312yes—
409C22×Dic3—32no—
410C22×Dic3C2×C3×D312yes—
411#237—24no—
412#235—64no—
413#235—64no—
414C2×D12—31no—
415C2×D12—31no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—32no—
419C2×C4×D3—61no—
420C2×C4×D3C2×C3×D311yescharacteristic
421C2×C4×D3C2×C3×D311yescharacteristic
422C2×Dic6—31no—
423C2×Dic6—31no—
424C2×Dic6C2×C3×D311yescharacteristic
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—61no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—92no—
430C3×C4⋊C4—92no—
431C3×C4⋊C4—91no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—62no—
435C3×C22⋊C4—92no—
436C3×C22⋊C4—92no—
437C3×C22⋊C4—92no—
438#217—32no—
439#217—32no—
440#217—32no—
441#217—62no—
442#217C2×C3×D312yes—
443(C2×D3)⋊C4—32no—
444(C2×D3)⋊C4—32no—
445(C2×D3)⋊C4—32no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—32no—
449C4⋊Dic3—32no—
450C4⋊Dic3—61no—
451C4⋊Dic3C2×C3×D311yescharacteristic
452Dic3⋊C4—32no—
453Dic3⋊C4—32no—
454Dic3⋊C4—32no—
455Dic3⋊C4—32no—
456C22×C32—22no—
457C22×C32—24no—
458C22×C32—22no—
459C22×C32—22no—
460C22×C32—22no—
461C22×C32—22no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—21no—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32—32no—
470C22×C32—41no—
471C22×C32—42no—
472C22×C32—42no—
473C22×C32—44no—
474C22×C32—42no—
475C22×C32—42no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—61no—
481C22×C32—61no—
482C22×C32—61no—
483C22×C32—61no—
484C22×C32—61no—
485C22×C32—82no—
486C22×C32—82no—
487C22×C32C23×D311yescharacteristic
488C22×C32C23×D311yescharacteristic
489C22×C32C24×C311yescharacteristic
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—21no—
495C2×C3×D3—21no—
496C2×C3×D3—21no—
497C2×C3×D3—22no—
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—21no—
503C2×C3×D3—21no—
504C2×C3×D3—22no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—41no—
509C2×C3×D3—62no—
510C2×C3×D3—61no—
511C2×C3×D3—61no—
512C2×C3×D3—61no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—61no—
516C2×C3×D3—121no—
517C2×C3×D3—121no—
518C2×C3×D3C2×#6712yes—
519C2×C3×D3C2×C3×D412yes—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C32×C4—32no—
524C32×C4—42no—
525C32×C4—62no—
526C32×C4—62no—
527C32×C4—61no—
528C32×C4D3×D412yes—
529C32×C4C2×#6712yes—
530C32×C4C2×C3×D412yes—
531C3⋊Dic3—21no—
532C3⋊Dic3—22no—
533C3×Dic3—24no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—22no—
537C3×Dic3—21no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—41no—
542C3×Dic3—42no—
543C3×Dic3—61no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—61no—
547C3×Dic3—121no—
548C3×Dic3—122no—
549C3×Dic3C2×#6712yes—
550C3×Dic3C2×C3×D412yes—
551C2×#41—31no—
552C2×#41—91no—
553C22⋊Q8—92no—
554C22⋊Q8—91no—
555C22⋊Q8—91no—
556#121—31no—
557#121—92no—
558#121—92no—
559#121—92no—
560#121—91no—
561C2×C4⋊C4—91no—
562C33#53711yescharacteristic, complemented, Sylow
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—31no—
567C23×C3—31no—
568C23×C3—31no—
569C23×C3—31no—
570C23×C3—42no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—91no—
574C23×C3C2×D3212yes—
575C23×C3C22×C3×D312yes—
576C23×C3C22×C3×D312yes—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—61no—
580C22×D3C22×C3×D311yescharacteristic
581C22×D3C22×C3×D311yescharacteristic
582C3×Q8—64no—
583C3×Q8—62no—
584C3×Q8—62no—
585C3×Q8—182no—
586C3×D4—24no—
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—22no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—44no—
593C3×D4—64no—
594C3×D4—64no—
595C3×D4—68no—
596C3×D4—122no—
597C3×D4—122no—
598C3×D4—124no—
599C3×D4—182no—
600C3×D4—182no—
601C3×D4—182no—
602C3×D4—362no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—31no—
607C2×C3×C4—31no—
608C2×C3×C4—34no—
609C2×C3×C4—34no—
610C2×C3×C4—31no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—31no—
615C2×C3×C4—32no—
616C2×C3×C4—41no—
617C2×C3×C4—64no—
618C2×C3×C4—61no—
619C2×C3×C4—62no—
620C2×C3×C4—61no—
621C2×C3×C4—62no—
622C2×C3×C4—64no—
623C2×C3×C4—64no—
624C2×C3×C4—68no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—92no—
628C2×C3×C4—91no—
629C2×C3×C4—122no—
630C2×C3×C4—182no—
631C2×C3×C4—362no—
632C2×C3×C4C2×D3211yescharacteristic
633C2×C3×C4C22×C3×D311yescharacteristic
634C2×C3×C4C22×C3×D311yescharacteristic
635#67—24no—
636#67—42no—
637#67—62no—
638#67—62no—
639#67—62no—
640#67—62no—
641#67—122no—
642#67—122no—
643#67—124no—
644C2×Dic3—24no—
645C2×Dic3—32no—
646C2×Dic3—31no—
647C2×Dic3—32no—
648C2×Dic3—31no—
649C2×Dic3—62no—
650C2×Dic3—61no—
651C2×Dic3—122no—
652C2×Dic3C22×C3×D311yescharacteristic
653C2×Dic3C22×C3×D312yes—
654C2×Dic3C22×C3×D312yes—
655C2×Dic3C22×C3×D311yescharacteristic
656D12—62no—
657D12—62no—
658C4×D3—22no—
659C4×D3—62no—
660C4×D3—62no—
661C4×D3—122no—
662C4×D3—122no—
663C4×D3C3×#6714yescomplemented
664Dic6—22no—
665Dic6—62no—
666Dic6—62no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—41no—
677C2×C32—41no—
678C2×C32—41no—
679C2×C32—42no—
680C2×C32—44no—
681C2×C32—42no—
682C2×C32—42no—
683C2×C32—62no—
684C2×C32—82no—
685C2×C32—82no—
686C2×C32—84no—
687C2×C32—121no—
688C2×C32C2×D3×D411yescharacteristic
689C2×C32#100411yescharacteristic
690C2×C32#100911yescharacteristic
691C2×C32#101011yescharacteristic
692C2×C32#101011yescharacteristic
693C2×C32C22×#6711yescharacteristic
694C2×C32C22×C3×D411yescharacteristic
695C2×C32C3×H(5,𝔽2)11yescharacteristic
696C2×C32C3×2−1+411yescharacteristic
697C3⋊D3—41no—
698C3×D3—22no—
699C3×D3—22no—
700C3×D3—42no—
701C3×D3—42no—
702C3×D3—41no—
703C3×D3—41no—
704C3×D3—122no—
705C3×D3—121no—
706C3×D3—121no—
707#41—64no—
708#41—184no—
709C2×Q8—31no—
710C2×Q8—91no—
711C2×D4—32no—
712C2×D4—32no—
713C2×D4—91no—
714C2×D4—91no—
715C2×D4—91no—
716C2×D4—92no—
717C2×D4C3×D3211yescharacteristic
718C22×C4—31no—
719C22×C4—32no—
720C22×C4—31no—
721C22×C4—92no—
722C22×C4—91no—
723C4⋊C4—31no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C4⋊C4—91no—
728C22⋊C4—32no—
729C22⋊C4—92no—
730C22⋊C4—92no—
731C22⋊C4—92no—
732C22×C3—24no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—32no—
746C22×C3—32no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—44no—
756C22×C3—41no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—61no—
762C22×C3—61no—
763C22×C3—61no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—61no—
768C22×C3—61no—
769C22×C3—82no—
770C22×C3—82no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—181no—
776C22×C3—181no—
777C22×C3—181no—
778C22×C3C22×D3211yescharacteristic
779C22×C3C23×C3×D311yescharacteristic
780C22×C3C23×C3×D311yescharacteristic
781C2×D3—21no—
782C2×D3—21no—
783C2×D3—21no—
784C2×D3—21no—
785C2×D3—21no—
786C2×D3—62no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—121no—
794C2×D3—121no—
795C2×D3C2×C3×#6712yes—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—32no—
800C3×C4—32no—
801C3×C4—42no—
802C3×C4—62no—
803C3×C4—64no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—61no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—61no—
810C3×C4—121no—
811C3×C4—122no—
812C3×C4—182no—
813C3×C4—181no—
814C3×C4D3×#6712yes—
815C3×C4C3×D3×D412yes—
816C3×C4C2×C3×#6712yes—
817Dic3—21no—
818Dic3—22no—
819Dic3—22no—
820Dic3—61no—
821Dic3—62no—
822Dic3—62no—
823Dic3—61no—
824Dic3—121no—
825Dic3—122no—
826Dic3C2×C3×#6712yes—
827C32—21no—
828C32—21no—
829C32—21no—
830C32—41no—
831C32#560811yescharacteristic, complemented
832C32#583311yescharacteristic, complemented
833C32C3×#53711yescharacteristic, complemented
834C23—31no—
835C23—31no—
836C23—91no—
837C23C2×C3×D3212yes—
838Q8—62no—
839Q8—182no—
840D4—22no—
841D4—64no—
842D4—122no—
843D4—182no—
844D4—182no—
845D4—182no—
846D4—362no—
847C2×C4—31no—
848C2×C4—34no—
849C2×C4—31no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—64no—
853C2×C4—62no—
854C2×C4—92no—
855C2×C4—91no—
856C2×C4—182no—
857C2×C4—362no—
858C2×C4C2×C3×D3211yescharacteristic
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—44no—
869C2×C3—42no—
870C2×C3—42no—
871C2×C3—42no—
872C2×C3—41no—
873C2×C3—41no—
874C2×C3—41no—
875C2×C3—62no—
876C2×C3—62no—
877C2×C3—82no—
878C2×C3—82no—
879C2×C3—84no—
880C2×C3—122no—
881C2×C3—122no—
882C2×C3—121no—
883C2×C3—121no—
884C2×C3—361no—
885C2×C3#6430911yescharacteristic
886C2×C3#6431411yescharacteristic
887C2×C3C2×D3×#6711yescharacteristic
888C2×C3C2×C3×D3×D411yescharacteristic
889C2×C3C3×#100411yescharacteristic
890C2×C3C3×#100911yescharacteristic
891C2×C3C3×#101011yescharacteristic
892C2×C3C3×#101011yescharacteristic
893C2×C3C22×C3×#6711yescharacteristic
894D3—22no—
895D3—41no—
896D3—122no—
897D3—121no—
898D3—121no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—32no—
903C22—61no—
904C22—61no—
905C22—61no—
906C22—61no—
907C22—61no—
908C22—181no—
909C22—181no—
910C22—181no—
911C22C22×C3×D3211yescharacteristic
912C4—32no—
913C4—62no—
914C4—61no—
915C4—62no—
916C4—181no—
917C4—182no—
918C4C3×D3×#6712yes—
919C3—21no—
920C3—21no—
921C3—21no—
922C3—41no—
923C3#1059523211yescharacteristic, direct product factor
924C3C3×#560811yescharacteristic, complemented
925C3C3×#583311yescharacteristic, complemented
926C2—42no—
927C2—62no—
928C2—121no—
929C2—361no—
930C2C3×#6430911yescharacteristic
931C2C3×#6431411yescharacteristic
932C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×#3798C2semidirect
3. C3×#64147C2semidirect
4. C32×#938C2semidirect
5. C3×#63978C2semidirect
6. C3×#63971C2semidirect
7. C3×#63970C2semidirect
8. C3×#63964C2semidirect
9. C3×D3×C4⋊Dic3C2semidirect
10. C3×#63871C2semidirect
11. C3×#63856C2semidirect
14. #10595232C3direct (N × H)
42. C2×C3×#237D3semidirect
43. C2×C3×#237C2×C3semidirect
46. C2×#3798C2×C3semidirect
48. #64147C2×C3semidirect
59. C3×#938D3semidirect
60. C3×#938C2×C3semidirect
69. #63978C2×C3semidirect
70. #63971C2×C3semidirect
71. #63970C2×C3semidirect
72. #63964C2×C3semidirect
73. D3×C4⋊Dic3C2×C3semidirect
74. #63871C2×C3semidirect
75. #63856C2×C3semidirect
94. C32×C4×D3D4semidirect
220. C2×#237C3×D3semidirect
243. #938C3×D3semidirect
344. C3×C4×D3#67semidirect
345. C3×C4×D3C3×D4semidirect
562. C33#537semidirect
663. C4×D3C3×#67semidirect
831. C32#5608semidirect
832. C32#5833semidirect
833. C32C3×#537semidirect
923. C3#10595232direct (N × H)
924. C3C3×#5608semidirect
925. C3C3×#5833semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×#37982
C3×#641472
C32×#9382
C3×#639782
C3×#639712
C3×#639702
C3×#639642
C3×D3×C4⋊Dic32
C3×#638712
C3×#638562
C3×#58333
C3×#56083
#105952323