Finite Group Databasebeta

← C109×#24008 #42142002

Subgroups — C109×#24008 #42142002

Order 27904.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C109C211yesmaximal, characteristic
2C2×#485×C109C211yesmaximal, characteristic, complemented
3C2×#482×C109C211yesmaximal, characteristic, complemented
4C109×#2280C211yesmaximal, characteristic, complemented
5C109×#2036C211yesmaximal, characteristic, complemented
6C109×#2035C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1875C211yesmaximal, characteristic, complemented
10C109×#1873C211yesmaximal, characteristic, complemented
11C109×#1854C211yesmaximal, characteristic, complemented
12C109×#1854C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1788C211yesmaximal, characteristic, complemented
15C109×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C24×C4×C109C2211yescharacteristic
18#525×C109—24no—
19#525×C109—24no—
20C2×#123×C109—21no—
21C2×C22⋊Q8×C109C2211yescharacteristic
22C2×C22⋊Q8×C109C2211yescharacteristic
23C2×#121×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×#120×C109—21no—
26C2×C4×D4×C109—21no—
27C2×C4×D4×C109—21no—
28C2×#117×C109C2211yescharacteristic
29C2×#117×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic
31#485×C109—24no—
32#482×C109—24no—
33C2×#107×C109C2211yescharacteristic, complemented
34C2×#107×C109C2211yescharacteristic, complemented
35C2×#106×C109C2211yescharacteristic, complemented
36C2×#106×C109C2211yescharacteristic, complemented
37C2×#103×C109C2211yescharacteristic, complemented
38C2×#103×C109C2211yescharacteristic, complemented
39C2×#103×C109C2211yescharacteristic, complemented
40C2×#103×C109C2211yescharacteristic, complemented
41C2×#102×C109C2211yescharacteristic, complemented
42C2×#102×C109C2211yescharacteristic, complemented
43C2×#102×C109C2211yescharacteristic, complemented
44C2×#102×C109C2211yescharacteristic, complemented
45C2×C22⋊C8×C109C2211yescharacteristic
46C2×C22⋊C8×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48C2×C22⋊C8×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50C2×C22⋊C8×C109C2211yescharacteristic
51#381×C109—21no—
52#380×C109C2211yescharacteristic
53#380×C109C2211yescharacteristic
54#380×C109C2211yescharacteristic
55#380×C109C2211yescharacteristic
56#379×C109—21no—
57C4×C22⋊C4×C109—21no—
58C4×C22⋊C4×C109—21no—
59#340×C109C2211yescharacteristic, complemented
60#340×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63C25×C109D411yescharacteristic
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—41no—
69C2×#41×C109—41no—
70C22×Q8×C109C2311yescharacteristic
71C22×D4×C109—21no—
72C22×D4×C109—21no—
73C22×D4×C109—21no—
74C22×D4×C109C2311yescharacteristic
75C23×C4×C109—21no—
76C23×C4×C109—22no—
77C23×C4×C109—22no—
78C23×C4×C109—22no—
79C23×C4×C109—22no—
80C23×C4×C109—41no—
81C23×C4×C109—41no—
82C23×C4×C109D411yescharacteristic
83C23×C4×C109D411yescharacteristic
84C23×C4×C109D411yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C23×C4×C109C2311yescharacteristic
88C22×C8×C109C2311yescharacteristic
89C22×C8×C109C2311yescharacteristic
90C22×C8×C109C2311yescharacteristic
91C22×C8×C109C2311yescharacteristic
92#123×C109—28no—
93C22⋊Q8×C109—22no—
94C22⋊Q8×C109—22no—
95C22⋊Q8×C109—22no—
96C22⋊Q8×C109D414yes—
97#121×C109—22no—
98#121×C109—22no—
99#121×C109—22no—
100#121×C109D414yes—
101#120×C109—28no—
102C4×D4×C109—28no—
103C4×D4×C109—28no—
104#117×C109—22no—
105#117×C109—22no—
106#117×C109—22no—
107#117×C109—22no—
108#117×C109—41no—
109#117×C109—41no—
110C2×C4⋊C4×C109—21no—
111C2×C4⋊C4×C109—21no—
112C2×C4⋊C4×C109C2311yescharacteristic
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C42×C109—21no—
130C2×C42×C109—21no—
131C2×C42×C109—21no—
132#107×C109—22no—
133#107×C109—22no—
134#106×C109—22no—
135#106×C109—22no—
136#103×C109—22no—
137#103×C109—22no—
138#103×C109—41no—
139#103×C109—41no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—41no—
143#102×C109—41no—
144C22⋊C8×C109—22no—
145C22⋊C8×C109—22no—
146C22⋊C8×C109—22no—
147C22⋊C8×C109—22no—
148C22⋊C8×C109—41no—
149C22⋊C8×C109—41no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154C24×C109—22no—
155C24×C109—22no—
156C24×C109—22no—
157C24×C109—21no—
158C24×C109—41no—
159C24×C109—41no—
160C24×C109—41no—
161C24×C109—41no—
162C24×C109C2×D411yescharacteristic
163C24×C109C2×D411yescharacteristic
164C24×C109C2×D411yescharacteristic
165#41×C109—44no—
166#41×C109—44no—
167#41×C109—44no—
168#41×C109—44no—
169C2×Q8×C109—21no—
170C2×Q8×C109—21no—
171C2×Q8×C109—21no—
172C2×Q8×C109—21no—
173C2×Q8×C109—21no—
174C2×Q8×C109C2×D412yes—
175C2×D4×C109—24no—
176C2×D4×C109—24no—
177C2×D4×C109—24no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—42no—
184C2×D4×C109—42no—
185C2×D4×C109—42no—
186C2×D4×C109—42no—
187C2×D4×C109—42no—
188C2×D4×C109—42no—
189C2×D4×C109C2×D412yes—
190C22×C4×C109—21no—
191C22×C4×C109—21no—
192C22×C4×C109—21no—
193C22×C4×C109—21no—
194C22×C4×C109—21no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—24no—
199C22×C4×C109—22no—
200C22×C4×C109—22no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—22no—
205C22×C4×C109—22no—
206C22×C4×C109—22no—
207C22×C4×C109—22no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—41no—
219C22×C4×C109—41no—
220C22×C4×C109—41no—
221C22×C4×C109—44no—
222C22×C4×C109—44no—
223C22×C4×C109—44no—
224C22×C4×C109—44no—
225C22×C4×C109—42no—
226C22×C4×C109—42no—
227C22×C4×C109C2×D411yescharacteristic
228C22×C4×C109C2×D411yescharacteristic
229C22×C4×C109C2×D412yes—
230C22×C4×C109C2×D412yes—
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109#4112yes—
233C22×C4×C109#4112yes—
234C22×C4×C109C2411yescharacteristic
235C2×C8×C109—21no—
236C2×C8×C109—21no—
237C2×C8×C109—21no—
238C2×C8×C109—21no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C2×C8×C109—21no—
246C2×C8×C109—21no—
247C4⋊C4×C109—24no—
248C4⋊C4×C109—24no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—21no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—21no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—21no—
259C4⋊C4×C109C2×D412yes—
260C4⋊C4×C109C2×D412yes—
261C22⋊C4×C109—24no—
262C22⋊C4×C109—24no—
263C22⋊C4×C109—24no—
264C22⋊C4×C109—24no—
265C22⋊C4×C109—24no—
266C22⋊C4×C109—42no—
267C22⋊C4×C109—42no—
268C22⋊C4×C109—42no—
269C22⋊C4×C109—42no—
270C22⋊C4×C109—42no—
271C22⋊C4×C109—42no—
272C42×C109—24no—
273C42×C109—42no—
274C42×C109—42no—
275C23×C109—21no—
276C23×C109—21no—
277C23×C109—21no—
278C23×C109—21no—
279C23×C109—21no—
280C23×C109—21no—
281C23×C109—21no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—21no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—21no—
293C23×C109—22no—
294C23×C109—44no—
295C23×C109—44no—
296C23×C109—44no—
297C23×C109—44no—
298C23×C109—44no—
299C23×C109—44no—
300C23×C109—44no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—41no—
307C23×C109#12012yes—
308C23×C109#12312yes—
309C23×C109#13512yes—
310C23×C109C22×D411yescharacteristic
311Q8×C109—22no—
312Q8×C109—22no—
313Q8×C109—41no—
314Q8×C109—41no—
315D4×C109—22no—
316D4×C109—22no—
317D4×C109—48no—
318D4×C109—48no—
319D4×C109—48no—
320D4×C109—41no—
321D4×C109—41no—
322C2×C4×C109—21no—
323C2×C4×C109—21no—
324C2×C4×C109—21no—
325C2×C4×C109—21no—
326C2×C4×C109—22no—
327C2×C4×C109—22no—
328C2×C4×C109—22no—
329C2×C4×C109—22no—
330C2×C4×C109—22no—
331C2×C4×C109—22no—
332C2×C4×C109—22no—
333C2×C4×C109—22no—
334C2×C4×C109—22no—
335C2×C4×C109—22no—
336C2×C4×C109—21no—
337C2×C4×C109—22no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—44no—
341C2×C4×C109—44no—
342C2×C4×C109—44no—
343C2×C4×C109—48no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—41no—
366C2×C4×C109#12012yes—
367C2×C4×C109#12312yes—
368C2×C4×C109C22×D411yescharacteristic
369C2×C4×C109C22×D411yescharacteristic
370C2×C4×C109C2×#4111yescharacteristic
371C2×C4×C109C2×#4111yescharacteristic
372C2×C4×C109H(5,𝔽2)11yescharacteristic
373C2×C4×C109H(5,𝔽2)11yescharacteristic
374C8×C109—41no—
375C8×C109—41no—
376C8×C109—41no—
377C8×C109—41no—
378C22×C109—22no—
379C22×C109—22no—
380C22×C109—22no—
381C22×C109—22no—
382C22×C109—22no—
383C22×C109—22no—
384C22×C109—22no—
385C22×C109—22no—
386C22×C109—22no—
387C22×C109—416no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—41no—
391C22×C109—41no—
392C22×C109—41no—
393C22×C109—41no—
394C22×C109—41no—
395C22×C109—41no—
396C22×C109—41no—
397C22×C109—41no—
398C22×C109—41no—
399C22×C109—41no—
400C22×C109—42no—
401C22×C109—42no—
402C22×C109—42no—
403C22×C109—81no—
404C22×C109—81no—
405C22×C109—81no—
406C22×C109—81no—
407C22×C109C2×#12011yescharacteristic
408C22×C109C2×#12311yescharacteristic
409C22×C109#53411yescharacteristic
410C22×C109C2×#13511yescharacteristic
411C22×C109#57511yescharacteristic
412C22×C109#57511yescharacteristic
413C22×C109#57511yescharacteristic
414C4×C109—22no—
415C4×C109—22no—
416C4×C109—41no—
417C4×C109—42no—
418C4×C109—42no—
419C4×C109—42no—
420C4×C109—81no—
421C4×C109—81no—
422C4×C109—81no—
423C4×C109—81no—
424C4×C109#54611yescharacteristic
425C4×C109#54611yescharacteristic
426C4×C109#54611yescharacteristic
427C4×C109#54611yescharacteristic
428#24008C10911yesmaximal, characteristic, direct product factor, Sylow
429C2×C109—42no—
430C2×C109—42no—
431C2×C109—42no—
432C2×C109—82no—
433C2×C109#240511yescharacteristic
434C2×C109#300211yescharacteristic
435C2×C109#300511yescharacteristic
436C2×C109#309111yescharacteristic
437C2×C109#309311yescharacteristic
438C2×C109#319111yescharacteristic
439C2×C109#319711yescharacteristic
440C2×#525C2×C10911yescharacteristic
441C2×#485C2×C10911yescharacteristic, complemented
442C2×#482C2×C10911yescharacteristic, complemented
443#2280C2×C10911yescharacteristic, complemented
444#2036C2×C10911yescharacteristic, complemented
445#2035C2×C10911yescharacteristic, complemented
446#2034C2×C10911yescharacteristic, complemented
447#2033C2×C10911yescharacteristic, complemented
448#1875C2×C10911yescharacteristic, complemented
449#1873C2×C10911yescharacteristic, complemented
450#1854C2×C10911yescharacteristic, complemented
451#1854C2×C10911yescharacteristic, complemented
452#1788C2×C10911yescharacteristic, complemented
453#1788C2×C10911yescharacteristic, complemented
454#1779C2×C10911yescharacteristic, complemented
455C109#2400811yescharacteristic, direct product factor, Sylow
456C22×#41C22×C10911yescharacteristic
457C24×C4C22×C10911yescharacteristic
458#525—24no—
459#525—24no—
460C2×#123—21no—
461C2×C22⋊Q8C22×C10911yescharacteristic
462C2×C22⋊Q8C22×C10911yescharacteristic
463C2×#121C22×C10911yescharacteristic
464C2×#121C22×C10911yescharacteristic
465C2×#120—21no—
466C2×C4×D4—21no—
467C2×C4×D4—21no—
468C2×#117C22×C10911yescharacteristic
469C2×#117C22×C10911yescharacteristic
470C2×#117C22×C10911yescharacteristic
471#485—24no—
472#482—24no—
473C2×#107C22×C10911yescharacteristic, complemented
474C2×#107C22×C10911yescharacteristic, complemented
475C2×#106C22×C10911yescharacteristic, complemented
476C2×#106C22×C10911yescharacteristic, complemented
477C2×#103C22×C10911yescharacteristic, complemented
478C2×#103C22×C10911yescharacteristic, complemented
479C2×#103C22×C10911yescharacteristic, complemented
480C2×#103C22×C10911yescharacteristic, complemented
481C2×#102C22×C10911yescharacteristic, complemented
482C2×#102C22×C10911yescharacteristic, complemented
483C2×#102C22×C10911yescharacteristic, complemented
484C2×#102C22×C10911yescharacteristic, complemented
485C2×C22⋊C8C22×C10911yescharacteristic
486C2×C22⋊C8C22×C10911yescharacteristic
487C2×C22⋊C8C22×C10911yescharacteristic
488C2×C22⋊C8C22×C10911yescharacteristic
489C2×C22⋊C8C22×C10911yescharacteristic
490C2×C22⋊C8C22×C10911yescharacteristic
491#381—21no—
492#380C22×C10911yescharacteristic
493#380C22×C10911yescharacteristic
494#380C22×C10911yescharacteristic
495#380C22×C10911yescharacteristic
496#379—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499#340C22×C10911yescharacteristic, complemented
500#340C22×C10911yescharacteristic, complemented
501#340C22×C10911yescharacteristic, complemented
502#340C22×C10911yescharacteristic, complemented
503C25D4×C10911yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C10911yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C10911yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C10911yescharacteristic
523C23×C4D4×C10911yescharacteristic
524C23×C4D4×C10911yescharacteristic
525C23×C4C23×C10911yescharacteristic
526C23×C4C23×C10911yescharacteristic
527C23×C4C23×C10911yescharacteristic
528C22×C8C23×C10911yescharacteristic
529C22×C8C23×C10911yescharacteristic
530C22×C8C23×C10911yescharacteristic
531C22×C8C23×C10911yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C10914yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C10914yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C10911yescharacteristic
553C2×C4⋊C4C23×C10911yescharacteristic
554C2×C4⋊C4C23×C10911yescharacteristic
555C2×C4⋊C4C23×C10911yescharacteristic
556C2×C4⋊C4C23×C10911yescharacteristic
557C2×C4⋊C4C23×C10911yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C10911yescharacteristic
603C24C2×D4×C10911yescharacteristic
604C24C2×D4×C10911yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C10912yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C10912yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C10911yescharacteristic
668C22×C4C2×D4×C10911yescharacteristic
669C22×C4C2×D4×C10912yes—
670C22×C4C2×D4×C10912yes—
671C22×C4C2×D4×C10911yescharacteristic
672C22×C4#41×C10912yes—
673C22×C4#41×C10912yes—
674C22×C4C24×C10911yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C10912yes—
700C4⋊C4C2×D4×C10912yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C10912yes—
748C23#123×C10912yes—
749C23#135×C10912yes—
750C23C22×D4×C10911yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C10912yes—
807C2×C4#123×C10912yes—
808C2×C4C22×D4×C10911yescharacteristic
809C2×C4C22×D4×C10911yescharacteristic
810C2×C4C2×#41×C10911yescharacteristic
811C2×C4C2×#41×C10911yescharacteristic
812C2×C4H(5,𝔽2)×C10911yescharacteristic
813C2×C4H(5,𝔽2)×C10911yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C10911yescharacteristic
848C22C2×#123×C10911yescharacteristic
849C22#534×C10911yescharacteristic
850C22C2×#135×C10911yescharacteristic
851C22#575×C10911yescharacteristic
852C22#575×C10911yescharacteristic
853C22#575×C10911yescharacteristic
854C4—22no—
855C4—22no—
856C4—42no—
857C4—42no—
858C4—41no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4#546×C10911yescharacteristic
865C4#546×C10911yescharacteristic
866C4#546×C10911yescharacteristic
867C4#546×C10911yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C109×#240511yescharacteristic
873C2C109×#300211yescharacteristic
874C2C109×#300511yescharacteristic
875C2C109×#309111yescharacteristic
876C2C109×#309311yescharacteristic
877C2C109×#319111yescharacteristic
878C2C109×#319711yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#525×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C24×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C109C2semidirect
3. C2×#482×C109C2semidirect
4. C109×#2280C2semidirect
5. C109×#2036C2semidirect
6. C109×#2035C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#1875C2semidirect
10. C109×#1873C2semidirect
11. C109×#1854C2semidirect
12. C109×#1854C2semidirect
13. C109×#1788C2semidirect
14. C109×#1788C2semidirect
15. C109×#1779C2semidirect
33. C2×#107×C109C22semidirect
34. C2×#107×C109C22semidirect
35. C2×#106×C109C22semidirect
36. C2×#106×C109C22semidirect
37. C2×#103×C109C22semidirect
38. C2×#103×C109C22semidirect
39. C2×#103×C109C22semidirect
40. C2×#103×C109C22semidirect
41. C2×#102×C109C22semidirect
42. C2×#102×C109C22semidirect
43. C2×#102×C109C22semidirect
44. C2×#102×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
428. #24008C109direct (N × H)
441. C2×#485C2×C109semidirect
442. C2×#482C2×C109semidirect
443. #2280C2×C109semidirect
444. #2036C2×C109semidirect
445. #2035C2×C109semidirect
446. #2034C2×C109semidirect
447. #2033C2×C109semidirect
448. #1875C2×C109semidirect
449. #1873C2×C109semidirect
450. #1854C2×C109semidirect
451. #1854C2×C109semidirect
452. #1788C2×C109semidirect
453. #1788C2×C109semidirect
454. #1779C2×C109semidirect
455. C109#24008direct (N × H)
473. C2×#107C22×C109semidirect
474. C2×#107C22×C109semidirect
475. C2×#106C22×C109semidirect
476. C2×#106C22×C109semidirect
477. C2×#103C22×C109semidirect
478. C2×#103C22×C109semidirect
479. C2×#103C22×C109semidirect
480. C2×#103C22×C109semidirect
481. C2×#102C22×C109semidirect
482. C2×#102C22×C109semidirect
483. C2×#102C22×C109semidirect
484. C2×#102C22×C109semidirect
499. #340C22×C109semidirect
500. #340C22×C109semidirect
501. #340C22×C109semidirect
502. #340C22×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1092
C2×#485×C1092
C2×#482×C1092
C109×#22802
C109×#20362
C109×#20352
C109×#20342
C109×#20332
C109×#18752
C109×#18732
C109×#18542
C109×#17882
C109×#17792
#24008109