Finite Group Databasebeta

← C109×#24017 #42142011

Subgroups — C109×#24017 #42142011

Order 27904.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C109C211yesmaximal, characteristic
2C2×#485×C109C211yesmaximal, characteristic, complemented
3C2×#482×C109C211yesmaximal, characteristic, complemented
4C109×#2311C211yesmaximal, characteristic, complemented
5C109×#2036C211yesmaximal, characteristic, complemented
6C109×#2035C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1874C211yesmaximal, characteristic, complemented
10C109×#1872C211yesmaximal, characteristic, complemented
11C109×#1853C211yesmaximal, characteristic, complemented
12C109×#1852C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1788C211yesmaximal, characteristic, complemented
15C109×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18#537×C109—24no—
19#537×C109—24no—
20C2×C22⋊Q8×C109—21no—
21C2×C22⋊Q8×C109C2211yescharacteristic
22C2×C22⋊Q8×C109C2211yescharacteristic
23C2×#121×C109—21no—
24C2×#121×C109—21no—
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#121×C109C2211yescharacteristic
28C2×#117×C109C2211yescharacteristic
29C22×C4⋊C4×C109C2211yescharacteristic
30C22×C4⋊C4×C109C2211yescharacteristic
31#485×C109—24no—
32#482×C109—24no—
33C2×#107×C109C2211yescharacteristic
34C2×#107×C109C2211yescharacteristic
35C2×#106×C109C2211yescharacteristic
36C2×#106×C109C2211yescharacteristic
37C2×#103×C109C2211yescharacteristic
38C2×#103×C109C2211yescharacteristic
39C2×#103×C109C2211yescharacteristic
40C2×#103×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
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#391×C109—21no—
52#390×C109—21no—
53#386×C109—21no—
54#386×C109—21no—
55#380×C109C2211yescharacteristic
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic
58#380×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic
62#340×C109C2211yescharacteristic
63C2×#41×C109—22no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—22no—
71C2×#41×C109—41no—
72C2×#41×C109—41no—
73C2×#41×C109—41no—
74C2×#41×C109—41no—
75C22×Q8×C109D411yescharacteristic
76C22×Q8×C109C2311yescharacteristic
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109D411yescharacteristic
81C22×D4×C109D411yescharacteristic
82C22×D4×C109D411yescharacteristic
83C22×D4×C109C2311yescharacteristic
84C23×C4×C109—21no—
85C23×C4×C109—21no—
86C23×C4×C109—21no—
87C23×C4×C109C2311yescharacteristic
88C23×C4×C109C2311yescharacteristic
89C23×C4×C109C2311yescharacteristic
90C22×C8×C109C2311yescharacteristic
91C22×C8×C109C2311yescharacteristic
92C22×C8×C109C2311yescharacteristic
93C22×C8×C109C2311yescharacteristic
94C22⋊Q8×C109—28no—
95C22⋊Q8×C109—22no—
96C22⋊Q8×C109—22no—
97C22⋊Q8×C109—22no—
98C22⋊Q8×C109D414yes—
99#121×C109—28no—
100#121×C109—28no—
101#121×C109—28no—
102#121×C109—22no—
103#121×C109—22no—
104#121×C109—22no—
105#121×C109D414yes—
106#117×C109—22no—
107#117×C109—22no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C4⋊C4×C109—21no—
111C2×C4⋊C4×C109—22no—
112C2×C4⋊C4×C109—22no—
113C2×C4⋊C4×C109—21no—
114C2×C4⋊C4×C109—41no—
115C2×C4⋊C4×C109—41no—
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C4⋊C4×C109C2311yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C4⋊C4×C109C2311yescharacteristic
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×C22⋊C4×C109—21no—
130C2×C22⋊C4×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—21no—
155C24×C109C2×D411yescharacteristic
156C24×C109C2×D411yescharacteristic
157C24×C109C2×D411yescharacteristic
158#41×C109—44no—
159#41×C109—44no—
160#41×C109—44no—
161#41×C109—44no—
162#41×C109—44no—
163#41×C109—44no—
164#41×C109—44no—
165#41×C109—44no—
166C2×Q8×C109—22no—
167C2×Q8×C109—22no—
168C2×Q8×C109—21no—
169C2×Q8×C109—21no—
170C2×Q8×C109—21no—
171C2×Q8×C109—21no—
172C2×Q8×C109—21no—
173C2×Q8×C109—41no—
174C2×Q8×C109C2×D412yes—
175C2×D4×C109—24no—
176C2×D4×C109—22no—
177C2×D4×C109—22no—
178C2×D4×C109—22no—
179C2×D4×C109—22no—
180C2×D4×C109—24no—
181C2×D4×C109—24no—
182C2×D4×C109—22no—
183C2×D4×C109—22no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—41no—
190C2×D4×C109—41no—
191C2×D4×C109—41no—
192C2×D4×C109—42no—
193C2×D4×C109—42no—
194C2×D4×C109—81no—
195C2×D4×C109—81no—
196C2×D4×C109—81no—
197C2×D4×C109—81no—
198C2×D4×C109C2×D412yes—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—24no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—24no—
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—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—42no—
223C22×C4×C109—42no—
224C22×C4×C109—42no—
225C22×C4×C109—81no—
226C22×C4×C109—81no—
227C22×C4×C109—81no—
228C22×C4×C109—81no—
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D412yes—
232C22×C4×C109C2×D412yes—
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109#4112yes—
235C22×C4×C109#4112yes—
236C22×C4×C109C2411yescharacteristic
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—
247C2×C8×C109—21no—
248C2×C8×C109—21no—
249C4⋊C4×C109—24no—
250C4⋊C4×C109—24no—
251C4⋊C4×C109—24no—
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×C109—21no—
260C4⋊C4×C109—21no—
261C4⋊C4×C109—21no—
262C4⋊C4×C109—42no—
263C4⋊C4×C109C2×D412yes—
264C4⋊C4×C109C2×D412yes—
265C22⋊C4×C109—24no—
266C22⋊C4×C109—24no—
267C22⋊C4×C109—24no—
268C22⋊C4×C109—24no—
269C22⋊C4×C109—42no—
270C22⋊C4×C109—81no—
271C22⋊C4×C109—81no—
272C22⋊C4×C109—81no—
273C22⋊C4×C109—81no—
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—22no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—21no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109#12012yes—
302C23×C109#12312yes—
303C23×C109C22×D411yescharacteristic
304Q8×C109—22no—
305Q8×C109—22no—
306Q8×C109—44no—
307Q8×C109—41no—
308Q8×C109—41no—
309D4×C109—22no—
310D4×C109—22no—
311D4×C109—44no—
312D4×C109—44no—
313D4×C109—44no—
314D4×C109—48no—
315D4×C109—41no—
316D4×C109—41no—
317D4×C109—84no—
318D4×C109—84no—
319C2×C4×C109—21no—
320C2×C4×C109—21no—
321C2×C4×C109—21no—
322C2×C4×C109—21no—
323C2×C4×C109—22no—
324C2×C4×C109—22no—
325C2×C4×C109—22no—
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—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—48no—
338C2×C4×C109—41no—
339C2×C4×C109—41no—
340C2×C4×C109—41no—
341C2×C4×C109—41no—
342C2×C4×C109—41no—
343C2×C4×C109—41no—
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—84no—
361C2×C4×C109—84no—
362C2×C4×C109#12012yes—
363C2×C4×C109#12312yes—
364C2×C4×C109C22×D411yescharacteristic
365C2×C4×C109C22×D411yescharacteristic
366C2×C4×C109C2×#4111yescharacteristic
367C2×C4×C109C2×#4111yescharacteristic
368C2×C4×C109H(5,𝔽2)11yescharacteristic
369C2×C4×C109H(5,𝔽2)11yescharacteristic
370C8×C109—41no—
371C8×C109—41no—
372C8×C109—41no—
373C8×C109—41no—
374C22×C109—22no—
375C22×C109—22no—
376C22×C109—22no—
377C22×C109—22no—
378C22×C109—22no—
379C22×C109—22no—
380C22×C109—41no—
381C22×C109—41no—
382C22×C109—41no—
383C22×C109—41no—
384C22×C109—41no—
385C22×C109—41no—
386C22×C109—41no—
387C22×C109—41no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—42no—
391C22×C109—41no—
392C22×C109—41no—
393C22×C109—41no—
394C22×C109—41no—
395C22×C109—42no—
396C22×C109—41no—
397C22×C109—42no—
398C22×C109—81no—
399C22×C109—81no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109C2×#12011yescharacteristic
403C22×C109C2×#12311yescharacteristic
404C22×C109#53411yescharacteristic
405C22×C109#57611yescharacteristic
406C22×C109#57711yescharacteristic
407C22×C109#57711yescharacteristic
408C22×C109#57811yescharacteristic
409C4×C109—22no—
410C4×C109—22no—
411C4×C109—41no—
412C4×C109—42no—
413C4×C109—42no—
414C4×C109—42no—
415C4×C109—81no—
416C4×C109—81no—
417C4×C109—81no—
418C4×C109—81no—
419C4×C109#54611yescharacteristic
420C4×C109#54611yescharacteristic
421C4×C109#54611yescharacteristic
422C4×C109#54611yescharacteristic
423#24017C10911yesmaximal, characteristic, direct product factor, Sylow
424C2×C109—42no—
425C2×C109—42no—
426C2×C109—81no—
427C2×C109—82no—
428C2×C109#240511yescharacteristic
429C2×C109#301211yescharacteristic
430C2×C109#301311yescharacteristic
431C2×C109#309811yescharacteristic
432C2×C109#309911yescharacteristic
433C2×C109#319811yescharacteristic
434C2×C109#320111yescharacteristic
435C2×#537C2×C10911yescharacteristic
436C2×#485C2×C10911yescharacteristic, complemented
437C2×#482C2×C10911yescharacteristic, complemented
438#2311C2×C10911yescharacteristic, complemented
439#2036C2×C10911yescharacteristic, complemented
440#2035C2×C10911yescharacteristic, complemented
441#2034C2×C10911yescharacteristic, complemented
442#2033C2×C10911yescharacteristic, complemented
443#1874C2×C10911yescharacteristic, complemented
444#1872C2×C10911yescharacteristic, complemented
445#1853C2×C10911yescharacteristic, complemented
446#1852C2×C10911yescharacteristic, complemented
447#1788C2×C10911yescharacteristic, complemented
448#1788C2×C10911yescharacteristic, complemented
449#1780C2×C10911yescharacteristic, complemented
450C109#2401711yescharacteristic, direct product factor, Sylow
451C22×#41C22×C10911yescharacteristic
452C22×#41C22×C10911yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C10911yescharacteristic
457C2×C22⋊Q8C22×C10911yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C10911yescharacteristic
462C2×#121C22×C10911yescharacteristic
463C2×#117C22×C10911yescharacteristic
464C22×C4⋊C4C22×C10911yescharacteristic
465C22×C4⋊C4C22×C10911yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C10911yescharacteristic
469C2×#107C22×C10911yescharacteristic
470C2×#106C22×C10911yescharacteristic
471C2×#106C22×C10911yescharacteristic
472C2×#103C22×C10911yescharacteristic
473C2×#103C22×C10911yescharacteristic
474C2×#103C22×C10911yescharacteristic
475C2×#103C22×C10911yescharacteristic
476C2×#102C22×C10911yescharacteristic
477C2×#102C22×C10911yescharacteristic
478C2×#102C22×C10911yescharacteristic
479C2×#102C22×C10911yescharacteristic
480C2×C22⋊C8C22×C10911yescharacteristic
481C2×C22⋊C8C22×C10911yescharacteristic
482C2×C22⋊C8C22×C10911yescharacteristic
483C2×C22⋊C8C22×C10911yescharacteristic
484C2×C22⋊C8C22×C10911yescharacteristic
485C2×C22⋊C8C22×C10911yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C10911yescharacteristic
491#380C22×C10911yescharacteristic
492#380C22×C10911yescharacteristic
493#380C22×C10911yescharacteristic
494#340C22×C10911yescharacteristic
495#340C22×C10911yescharacteristic
496#340C22×C10911yescharacteristic
497#340C22×C10911yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C10911yescharacteristic
511C22×Q8C23×C10911yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C10911yescharacteristic
516C22×D4D4×C10911yescharacteristic
517C22×D4D4×C10911yescharacteristic
518C22×D4C23×C10911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10911yescharacteristic
523C23×C4C23×C10911yescharacteristic
524C23×C4C23×C10911yescharacteristic
525C22×C8C23×C10911yescharacteristic
526C22×C8C23×C10911yescharacteristic
527C22×C8C23×C10911yescharacteristic
528C22×C8C23×C10911yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C10914yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C10914yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C10911yescharacteristic
552C2×C4⋊C4C23×C10911yescharacteristic
553C2×C4⋊C4C23×C10911yescharacteristic
554C2×C4⋊C4C23×C10911yescharacteristic
555C2×C4⋊C4C23×C10911yescharacteristic
556C2×C4⋊C4C23×C10911yescharacteristic
557C2×C22⋊C4—21no—
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×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C10911yescharacteristic
591C24C2×D4×C10911yescharacteristic
592C24C2×D4×C10911yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C10912yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C10912yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
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—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C10911yescharacteristic
665C22×C4C2×D4×C10911yescharacteristic
666C22×C4C2×D4×C10912yes—
667C22×C4C2×D4×C10912yes—
668C22×C4C2×D4×C10911yescharacteristic
669C22×C4#41×C10912yes—
670C22×C4#41×C10912yes—
671C22×C4C24×C10911yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
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—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
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—42no—
698C4⋊C4C2×D4×C10912yes—
699C4⋊C4C2×D4×C10912yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C10912yes—
737C23#123×C10912yes—
738C23C22×D4×C10911yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
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—84no—
796C2×C4—84no—
797C2×C4#120×C10912yes—
798C2×C4#123×C10912yes—
799C2×C4C22×D4×C10911yescharacteristic
800C2×C4C22×D4×C10911yescharacteristic
801C2×C4C2×#41×C10911yescharacteristic
802C2×C4C2×#41×C10911yescharacteristic
803C2×C4H(5,𝔽2)×C10911yescharacteristic
804C2×C4H(5,𝔽2)×C10911yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C10911yescharacteristic
838C22C2×#123×C10911yescharacteristic
839C22#534×C10911yescharacteristic
840C22#576×C10911yescharacteristic
841C22#577×C10911yescharacteristic
842C22#577×C10911yescharacteristic
843C22#578×C10911yescharacteristic
844C4—22no—
845C4—22no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C10911yescharacteristic
855C4#546×C10911yescharacteristic
856C4#546×C10911yescharacteristic
857C4#546×C10911yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C109×#240511yescharacteristic
863C2C109×#301211yescharacteristic
864C2C109×#301311yescharacteristic
865C2C109×#309811yescharacteristic
866C2C109×#309911yescharacteristic
867C2C109×#319811yescharacteristic
868C2C109×#320111yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#537×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C22×#41×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×#2311C2semidirect
5. C109×#2036C2semidirect
6. C109×#2035C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#1874C2semidirect
10. C109×#1872C2semidirect
11. C109×#1853C2semidirect
12. C109×#1852C2semidirect
13. C109×#1788C2semidirect
14. C109×#1788C2semidirect
15. C109×#1780C2semidirect
423. #24017C109direct (N × H)
436. C2×#485C2×C109semidirect
437. C2×#482C2×C109semidirect
438. #2311C2×C109semidirect
439. #2036C2×C109semidirect
440. #2035C2×C109semidirect
441. #2034C2×C109semidirect
442. #2033C2×C109semidirect
443. #1874C2×C109semidirect
444. #1872C2×C109semidirect
445. #1853C2×C109semidirect
446. #1852C2×C109semidirect
447. #1788C2×C109semidirect
448. #1788C2×C109semidirect
449. #1780C2×C109semidirect
450. C109#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#537×C1092
C2×#485×C1092
C2×#482×C1092
C109×#23112
C109×#20362
C109×#20352
C109×#20342
C109×#20332
C109×#18742
C109×#18722
C109×#18532
C109×#18522
C109×#17882
C109×#17802
#24017109