Finite Group Databasebeta

← #13178694

Subgroups — #13178694

Order 1728.

1276 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64149C211yesmaximal, characteristic
2C3×#64145C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723726C212yesmaximal, complemented
5#11723724C212yesmaximal, complemented
6#11723720C212yesmaximal, complemented
7#11723718C212yesmaximal, complemented
8C4×#6296C211yesmaximal, characteristic, complemented
9#11723691C211yesmaximal, characteristic, complemented
10#11723677C211yesmaximal, characteristic, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595210—31nomaximal
13#10595199—31nomaximal
14#10595198—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C22×C3×C3⋊Dic3C2212yes—
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6296C2211yescharacteristic
22C2×#6294C2212yes—
23C3×#3757C2212yes—
24C3×#3757C2212yes—
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C3×C4×C3⋊Dic3C2211yescharacteristic
28C3×C4×C3⋊Dic3C2211yescharacteristic
29C3×C4×C3⋊Dic3C2211yescharacteristic
30#88815C2212yes—
31#88815C2211yescharacteristic
32#88815C2211yescharacteristic
33#88815C2211yescharacteristic
34#88814C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2212yes—
38#64149D311yescharacteristic
39#64145D311yescharacteristic, complemented
40D4×C3⋊Dic3D311yescharacteristic, complemented
41C3×#940—31no—
42C3×#940—31no—
43C3×#940—61no—
44C3×#936—31no—
45C3×#936—31no—
46C3×#936—61no—
47C3×D4×Dic3—31no—
48C3×D4×Dic3—31no—
49C3×D4×Dic3—61no—
50#63975—32no—
51#67⋊Dic3—32no—
52Dic3×#67—32no—
53#63969—32no—
54#63969—32no—
55#63966—32no—
56#63962—32no—
57#63961—32no—
58#63959—32no—
59#63959—32no—
60#63953—32no—
61#63952—32no—
62C4×#627—31no—
63C4×#627—31no—
64C4×#627—31no—
65#63898—31no—
66#63894—31no—
67Dic3×D12—31no—
68#63864—31no—
69#63863—31no—
70#63860—31no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C23×C33C2312yes—
75C22×C3×C3⋊D3C2312yes—
76C33×D4—22no—
77C2×C33×C4C2311yescharacteristic
78C3×#638—24no—
79C3×#638—42no—
80C2×C3×C3⋊Dic3—42no—
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2312yes—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4⋊(C3⋊D3)—22no—
90C3×#634—22no—
91#6296—22no—
92#6294—42no—
93#5713—91no—
94#5681—91no—
95#5559—91no—
96C2×C32×D4—21no—
97C2×C32×D4—21no—
98C2×C32×D4—21no—
99C2×C32×D4—41no—
100C2×C32×D4C2×D311yescharacteristic
101C2×C32×D4C2×D311yescharacteristic
102C2×C32×D4C2×D311yescharacteristic
103C2×#638C2×D312yes—
104C2×#638C2×D312yes—
105C22×C3⋊Dic3C2×D312yes—
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
107C2×#634C2×D311yescharacteristic
108C2×C3×#67—32no—
109C2×C3×#67—32no—
110C2×C3×#67—32no—
111C2×C3×#67—32no—
112C2×C3×#67—62no—
113C2×C3×#67—62no—
114C22×C3×Dic3—32no—
115C22×C3×Dic3—32no—
116C22×C3×Dic3—62no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—61no—
120C2×C3×Dic6—31no—
121C2×C3×Dic6—31no—
122C2×C3×Dic6—61no—
123C2×#627—31no—
124C2×#627—31no—
125C2×#627—31no—
126C2×#624—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129#3757C2×D312yes—
130#3757C2×D312yes—
131#3757C2×D312yes—
132C4⋊(C3⋊Dic3)C2×D311yescharacteristic
133C4×C3⋊Dic3C2×D311yescharacteristic
134C4×C3⋊Dic3C2×D311yescharacteristic
135C4×C3⋊Dic3C2×D311yescharacteristic
136C3×#217—32no—
137C3×#217—32no—
138C3×#217—32no—
139C3×#217—32no—
140C3×#217—32no—
141C3×#217—32no—
142C3×#217—62no—
143C3×#217—62no—
144C3×#217—62no—
145C3×C4⋊Dic3—31no—
146C3×C4⋊Dic3—31no—
147C3×C4⋊Dic3—61no—
148C3×C4×Dic3—31no—
149C3×C4×Dic3—31no—
150C3×C4×Dic3—31no—
151C3×C4×Dic3—31no—
152C3×C4×Dic3—31no—
153C3×C4×Dic3—31no—
154C3×C4×Dic3—61no—
155C3×C4×Dic3—61no—
156C3×C4×Dic3—61no—
157#3724—32no—
158#3724—31no—
159#3724—31no—
160#3724—31no—
161Dic3⋊Dic3—32no—
162Dic3⋊Dic3—32no—
163Dic3⋊Dic3—31no—
164Dic3⋊Dic3—31no—
165Dic3⋊Dic3—31no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169#3722—32no—
170#3722—32no—
171#3722—32no—
172(C2×D3)⋊Dic3—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178Dic32—32no—
179Dic32—32no—
180Dic32—32no—
181C22×C33—22no—
182C22×C33—22no—
183C22×C33—22no—
184C22×C33C2411yescharacteristic
185C2×C3×C3⋊D3—22no—
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C33×C4#4112yes—
189C3×C3⋊Dic3—21no—
190C3×C3⋊Dic3—21no—
191C3×C3⋊Dic3—22no—
192C3×C3⋊Dic3—21no—
193C3×C3⋊Dic3—21no—
194C3×C3⋊Dic3—21no—
195C3×C3⋊Dic3—22no—
196C3×C3⋊Dic3#4112yes—
197C3×#127—91no—
198C3×#124—91no—
199C3×C4×D4—91no—
200#947—91no—
201Q8×Dic3—91no—
202#940—31no—
203#940—31no—
204#940—61no—
205#936—31no—
206#936—31no—
207#936—61no—
208#936—91no—
209#936—92no—
210#935—92no—
211#935—92no—
212D4×Dic3—31no—
213D4×Dic3—31no—
214D4×Dic3—61no—
215D4×Dic3—91no—
216D4×Dic3—92no—
217#929—92no—
218C4×#67—92no—
219#893—91no—
220#887—91no—
221#886—92no—
222#885—92no—
223#885—92no—
224#883—92no—
225#883—92no—
226#67⋊C4—92no—
227#875—91no—
228C4×D12—91no—
229C4×Dic6—91no—
230C4×Dic6—91no—
231C4×Dic6—91no—
232C4×Dic6—91no—
233C23×C32—22no—
234C23×C32—22no—
235C23×C32—22no—
236C23×C32—42no—
237C23×C32C22×D312yes—
238C23×C32C22×D312yes—
239C23×C32C22×D312yes—
240C22×C3⋊D3C22×D312yes—
241C22×C3×D3—32no—
242C22×C3×D3—32no—
243C22×C3×D3—62no—
244C32×D4—22no—
245C32×D4—24no—
246C32×D4—22no—
247C32×D4—22no—
248C32×D4—42no—
249C32×D4—42no—
250C32×D4—44no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—41no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258#638—24no—
259#638—42no—
260C2×C3⋊Dic3—42no—
261C2×C3⋊Dic3C22×D312yes—
262C2×C3⋊Dic3C22×D312yes—
263C2×C3⋊Dic3C22×D311yescharacteristic
264C2×C3⋊Dic3C22×D311yescharacteristic
265C2×C3⋊Dic3C22×D311yescharacteristic
266C2×C3⋊Dic3C22×D311yescharacteristic
267C2×C3⋊Dic3C22×D311yescharacteristic
268C2×C3⋊Dic3C22×D311yescharacteristic
269C4⋊(C3⋊D3)—22no—
270#634—22no—
271C3×#67—64no—
272C3×#67—64no—
273C3×#67—124no—
274C3×#67—122no—
275C3×#67—122no—
276C3×#67—124no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3—32no—
280C2×C3×Dic3—32no—
281C2×C3×Dic3—32no—
282C2×C3×Dic3—32no—
283C2×C3×Dic3—31no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—31no—
287C2×C3×Dic3—31no—
288C2×C3×Dic3—31no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—61no—
294C2×C3×Dic3—61no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—61no—
297C2×C3×Dic3—61no—
298C2×C3×Dic3—61no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—62no—
301C2×C3×Dic3—122no—
302C2×C3×Dic3—122no—
303C2×C3×Dic3—124no—
304C3×D12—62no—
305C3×D12—62no—
306C3×D12—122no—
307C3×Dic6—62no—
308C3×Dic6—62no—
309C3×Dic6—122no—
310#627—62no—
311#627—62no—
312#627—62no—
313#624—122no—
314D3×Dic3—122no—
315D3×Dic3—122no—
316#559—271noSylow
317C2×C33—42no—
318C2×C33C2×#4111yescharacteristic
319C2×C33C2×#4111yescharacteristic
320C2×C33H(5,𝔽2)11yescharacteristic
321C3×C3⋊D3—42no—
322C2×C3×Q8—91no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—41no—
327C2×C3×D4—92no—
328C2×C3×D4—92no—
329C2×C3×D4—91no—
330C2×C3×D4D3211yescharacteristic
331C2×C3×D4D3211yescharacteristic
332C2×C3×D4D3211yescharacteristic
333C22×C3×C4—92no—
334C2×#67—32no—
335C2×#67—32no—
336C2×#67—32no—
337C2×#67—32no—
338C2×#67—62no—
339C2×#67—62no—
340C22×Dic3—32no—
341C22×Dic3—32no—
342C22×Dic3—62no—
343C22×Dic3—92no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×C4×D3—92no—
348C2×C4×D3—92no—
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C2×Dic6—91no—
353C2×Dic6—91no—
354C2×Dic6—91no—
355C3×C4⋊C4—91no—
356C3×C22⋊C4—92no—
357C3×C22⋊C4—92no—
358C3×C22⋊C4—92no—
359C3×C42—91no—
360C3×C42—91no—
361C3×C42—91no—
362#217—32no—
363#217—32no—
364#217—32no—
365#217—32no—
366#217—32no—
367#217—32no—
368#217—62no—
369#217—62no—
370#217—62no—
371#217—92no—
372#217—92no—
373#217—92no—
374(C2×D3)⋊C4—92no—
375(C2×D3)⋊C4—92no—
376(C2×D3)⋊C4—92no—
377(C2×D3)⋊C4—92no—
378(C2×D3)⋊C4—92no—
379(C2×D3)⋊C4—92no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—91no—
384C4⋊Dic3—91no—
385C4⋊Dic3—91no—
386C4⋊Dic3—92no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—92no—
394Dic3⋊C4—92no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—92no—
405C4×Dic3—92no—
406C4×Dic3—92no—
407C22×C32—22no—
408C22×C32—24no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—22no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—41no—
421C22×C32—42no—
422C22×C32—42no—
423C22×C32—44no—
424C22×C32—42no—
425C22×C32—42no—
426C22×C32—42no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32—42no—
430C22×C32—82no—
431C22×C32—82no—
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3—22no—
438C2×C3×D3—62no—
439C2×C3×D3—62no—
440C2×C3×D3—62no—
441C2×C3×D3—62no—
442C2×C3×D3—62no—
443C2×C3×D3—62no—
444C2×C3×D3—122no—
445C2×C3×D3—122no—
446C2×C3×D3—122no—
447C32×C4—22no—
448C32×C4—22no—
449C32×C4—22no—
450C32×C4—42no—
451C32×C4#23512yes—
452C32×C4#23712yes—
453C32×C4#23712yes—
454C3⋊Dic3—21no—
455C3⋊Dic3—21no—
456C3⋊Dic3—22no—
457C3⋊Dic3—22no—
458C3⋊Dic3—21no—
459C3⋊Dic3—21no—
460C3⋊Dic3—21no—
461C3⋊Dic3#23712yes—
462C3×Dic3—32no—
463C3×Dic3—32no—
464C3×Dic3—62no—
465C3×Dic3—62no—
466C3×Dic3—62no—
467C3×Dic3—62no—
468C3×Dic3—61no—
469C3×Dic3—61no—
470C3×Dic3—62no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—62no—
474C3×Dic3—61no—
475C3×Dic3—61no—
476C3×Dic3—61no—
477C3×Dic3—61no—
478C3×Dic3—62no—
479C3×Dic3—61no—
480C3×Dic3—61no—
481C3×Dic3—122no—
482C3×Dic3—121no—
483C3×Dic3—121no—
484C3×Dic3—121no—
485C3×Dic3—122no—
486#127—91no—
487#124—91no—
488#124—271no—
489#124—272no—
490#123—272no—
491#123—272no—
492C4×Q8—271no—
493C4×Q8—271no—
494C4×D4—91no—
495C4×D4—271no—
496C4×D4—272no—
497C33#55911yescharacteristic, complemented, Sylow
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—42no—
502C23×C3—92no—
503C23×C3C2×D3212yes—
504C23×C3C2×D3212yes—
505C23×C3C2×D3212yes—
506C22×D3—32no—
507C22×D3—32no—
508C22×D3—62no—
509C3×Q8—182no—
510C3×D4—24no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—42no—
515C3×D4—42no—
516C3×D4—44no—
517C3×D4—184no—
518C3×D4—182no—
519C3×D4—362no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—41no—
524C2×C3×C4—91no—
525C2×C3×C4—92no—
526C2×C3×C4—92no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—91no—
531C2×C3×C4—91no—
532C2×C3×C4—362no—
533C2×C3×C4C2×D3211yescharacteristic
534C2×C3×C4C2×D3211yescharacteristic
535C2×C3×C4C2×D3211yescharacteristic
536#67—64no—
537#67—64no—
538#67—124no—
539#67—122no—
540#67—122no—
541#67—124no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—62no—
565C2×Dic3—62no—
566C2×Dic3—122no—
567C2×Dic3—122no—
568C2×Dic3—124no—
569C2×Dic3—362no—
570D12—62no—
571D12—62no—
572D12—122no—
573C4×D3—362no—
574C4×D3—362no—
575Dic6—62no—
576Dic6—62no—
577Dic6—122no—
578Dic6—182no—
579Dic6—182no—
580Dic6—182no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—41no—
591C2×C32—41no—
592C2×C32—41no—
593C2×C32—42no—
594C2×C32—44no—
595C2×C32—42no—
596C2×C32—42no—
597C2×C32—82no—
598C2×C32—82no—
599C2×C32—84no—
600C2×C32C2×#23511yescharacteristic
601C2×C32C2×#23711yescharacteristic
602C2×C32C2×#23711yescharacteristic
603C2×C32C2×#23711yescharacteristic
604C2×C32#100411yescharacteristic
605C2×C32#100411yescharacteristic
606C2×C32D3×#4111yescharacteristic
607C2×C32D3×#4111yescharacteristic
608C2×C32#100911yescharacteristic
609C3⋊D3—42no—
610C3×D3—122no—
611C3×D3—122no—
612C3×D3—242no—
613C2×Q8—91no—
614C2×Q8—271no—
615C2×D4—92no—
616C2×D4—92no—
617C2×D4—91no—
618C2×D4#111311yescharacteristic
619C22×C4—92no—
620C22×C4—272no—
621C4⋊C4—91no—
622C4⋊C4—271no—
623C4⋊C4—271no—
624C4⋊C4—271no—
625C4⋊C4—272no—
626C22⋊C4—92no—
627C22⋊C4—92no—
628C22⋊C4—92no—
629C22⋊C4—272no—
630C22⋊C4—272no—
631C22⋊C4—272no—
632C42—91no—
633C42—91no—
634C42—91no—
635C42—272no—
636C22×C3—24no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—44no—
658C22×C3—41no—
659C22×C3—82no—
660C22×C3—82no—
661C22×C3—182no—
662C22×C3—182no—
663C22×C3—182no—
664C22×C3C22×D3211yescharacteristic
665C22×C3C22×D3211yescharacteristic
666C22×C3C22×D3211yescharacteristic
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—122no—
676C3×C4—22no—
677C3×C4—22no—
678C3×C4—22no—
679C3×C4—42no—
680C3×C4—92no—
681C3×C4—181no—
682C3×C4—181no—
683C3×C4—181no—
684C3×C4—182no—
685C3×C4—181no—
686C3×C4—181no—
687C3×C4—182no—
688C3×C4#380412yes—
689C3×C4#380412yes—
690C3×C4#380512yes—
691Dic3—32no—
692Dic3—32no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—62no—
701Dic3—61no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—62no—
706Dic3—61no—
707Dic3—61no—
708Dic3—62no—
709Dic3—62no—
710Dic3—122no—
711Dic3—122no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715C32—21no—
716C32—21no—
717C32—21no—
718C32—41no—
719C32#555911yescharacteristic, complemented
720C32#568111yescharacteristic, complemented
721C32#571311yescharacteristic, complemented
722C23—92no—
723C23C2×#111312yes—
724Q8—182no—
725Q8—542no—
726D4—22no—
727D4—184no—
728D4—182no—
729D4—362no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—92no—
737C2×C4—92no—
738C2×C4—362no—
739C2×C4—1082no—
740C2×C4C2×#111311yescharacteristic
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—44no—
751C2×C3—42no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3—41no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—82no—
758C2×C3—82no—
759C2×C3—84no—
760C2×C3—362no—
761C2×C3D3×#23711yescharacteristic
762C2×C3D3×#23711yescharacteristic
763C2×C3#6431211yescharacteristic
764C2×C3#6431311yescharacteristic
765C2×C3#6431411yescharacteristic
766C2×C3#6431411yescharacteristic
767C2×C3C2×#380411yescharacteristic
768C2×C3C2×#380411yescharacteristic
769C2×C3C2×#380511yescharacteristic
770D3—122no—
771D3—122no—
772D3—242no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—182no—
777C22—182no—
778C22—182no—
779C22C22×#111311yescharacteristic
780C4—92no—
781C4—181no—
782C4—181no—
783C4—181no—
784C4—182no—
785C4—181no—
786C4—181no—
787C4—182no—
788C4#8904612yes—
789C3—21no—
790C3—21no—
791C3—21no—
792C3—41no—
793C3#1059519811yescharacteristic, complemented
794C3#1059519911yescharacteristic, complemented
795C3#1059521011yescharacteristic, complemented
796C2—42no—
797C2—362no—
798C2#1172462211yescharacteristic
799C2#1172462311yescharacteristic
800C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
prime radicalC3×#64149C2
hypercenterC2×D4#1113
hypocenterC33#559
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C3×#64145C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723726C2semidirect
5. #11723724C2semidirect
6. #11723720C2semidirect
7. #11723718C2semidirect
8. C4×#6296C2semidirect
9. #11723691C2semidirect
10. #11723677C2semidirect
11. #11723668C2semidirect
39. #64145D3semidirect
40. D4×C3⋊Dic3D3semidirect
497. C33#559semidirect
719. C32#5559semidirect
720. C32#5681semidirect
721. C32#5713semidirect
793. C3#10595198semidirect
794. C3#10595199semidirect
795. C3#10595210semidirect

Maximal subgroups

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

subgroupindex
C3×#641492
C3×#641452
C3×D4×C3⋊Dic32
#117237262
#117237242
#117237202
#117237182
C4×#62962
#117236912
#117236772
#117236682
#105952103
#105951993
#105951983