Finite Group Databasebeta

← C109×#22427 #42140421

Subgroups — C109×#22427 #42140421

Order 27904.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic
2C2×#436×C109C211yesmaximal, characteristic, complemented
3C2×#417×C109C211yesmaximal, characteristic, complemented
4C2×#418×C109C211yesmaximal, characteristic, complemented
5C109×#2352C211yesmaximal, characteristic, complemented
6C109×#1983C211yesmaximal, characteristic, complemented
7C109×#1958C211yesmaximal, characteristic, complemented
8C109×#1895C211yesmaximal, characteristic, complemented
9C109×#1894C211yesmaximal, characteristic, complemented
10C109×#1874C211yesmaximal, characteristic, complemented
11C109×#1873C211yesmaximal, characteristic, complemented
12C109×#1804C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C109C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic
19C22×M16×C109C2211yescharacteristic, complemented
20#546×C109—24no—
21#546×C109C418yescomplemented
22C2×#124×C109C2211yescharacteristic
23C2×#123×C109—21no—
24C2×C22⋊Q8×C109C2211yescharacteristic
25C2×#121×C109—21no—
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109—21no—
28C2×C4×D4×C109C2211yescharacteristic
29C2×C4×D4×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic
31C22×C4⋊C4×C109C2211yescharacteristic, complemented
32C22×C22⋊C4×C109—21no—
33#436×C109—24no—
34C2×C4⋊C8×C109C2211yescharacteristic, complemented
35#418×C109—24no—
36#417×C109—24no—
37C2×#103×C109C2211yescharacteristic, complemented
38C2×#103×C109C2211yescharacteristic, complemented
39C2×#103×C109C2211yescharacteristic, complemented
40C2×#103×C109C2211yescharacteristic, complemented
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×C22⋊C8×C109C2211yescharacteristic
50C2×C22⋊C8×C109C2211yescharacteristic, complemented
51C2×C4×C8×C109C2211yescharacteristic, complemented
52#388×C109—21no—
53#387×C109—21no—
54#386×C109—21no—
55#382×C109C2211yescharacteristic, complemented
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic, complemented
58C4×C4⋊C4×C109C2211yescharacteristic, complemented
59C4×C22⋊C4×C109—21no—
60#340×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#340×C109C2211yescharacteristic, complemented
64C25×C109—21no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—41no—
69C2×#41×C109—41no—
70C2×#41×C109C2×C414yes—
71C22×Q8×C109C2311yescharacteristic
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—22no—
78C22×D4×C109—41no—
79C22×D4×C109—41no—
80C22×D4×C109C2×C414yescomplemented
81C22×D4×C109D411yescharacteristic
82C22×D4×C109C2311yescharacteristic
83C22×D4×C109C2311yescharacteristic
84C23×C4×C109—21no—
85C23×C4×C109—21no—
86C23×C4×C109—21no—
87C23×C4×C109C2311yescharacteristic
88C23×C4×C109C2311yescharacteristic
89C2×M16×C109—22no—
90C2×M16×C109—22no—
91C2×M16×C109—22no—
92C2×M16×C109—22no—
93C2×M16×C109—41no—
94C2×M16×C109—41no—
95C22×C8×C109C2311yescharacteristic
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99#124×C109—22no—
100#124×C109C2×C414yescomplemented
101#123×C109—28no—
102C22⋊Q8×C109—22no—
103C22⋊Q8×C109C2×C414yescomplemented
104#121×C109—22no—
105#121×C109—28no—
106#121×C109C2×C414yes—
107#120×C109—28no—
108C4×D4×C109—22no—
109C4×D4×C109C2×C414yes—
110C4×D4×C109C2×C414yescomplemented
111C4×D4×C109D414yes—
112#117×C109—22no—
113#117×C109—41no—
114C2×C4⋊C4×C109—21no—
115C2×C4⋊C4×C109—22no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109—41no—
118C2×C4⋊C4×C109D411yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C4⋊C4×C109C2311yescharacteristic
122C2×C4⋊C4×C109C2311yescharacteristic
123C2×C4⋊C4×C109C2311yescharacteristic
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—28no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109D411yescharacteristic
134C2×C22⋊C4×C109D411yescharacteristic
135C2×C42×C109—21no—
136C2×C42×C109—21no—
137C2×C42×C109C2311yescharacteristic
138C4⋊C8×C109—22no—
139#103×C109—22no—
140#103×C109—22no—
141#103×C109—41no—
142#103×C109—41no—
143#102×C109—22no—
144#102×C109—22no—
145#102×C109—22no—
146#102×C109—22no—
147#102×C109—22no—
148#102×C109—41no—
149#102×C109—41no—
150#102×C109D414yescomplemented
151C22⋊C8×C109—22no—
152C22⋊C8×C109—22no—
153C4×C8×C109—22no—
154#95×C109—21no—
155#95×C109—21no—
156#95×C109—21no—
157#95×C109—21no—
158#95×C109—21no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—24no—
162C24×C109—42no—
163C24×C109—42no—
164C24×C109—42no—
165C24×C109—42no—
166C24×C109—81no—
167C24×C109—81no—
168C24×C109C2×D411yescharacteristic
169C24×C109C2×D411yescharacteristic
170#41×C109—28no—
171#41×C109—44no—
172#41×C109—44no—
173#41×C109—44no—
174C2×Q8×C109—21no—
175C2×Q8×C109—21no—
176C2×Q8×C109—21no—
177C2×Q8×C109—21no—
178C2×Q8×C109—21no—
179C2×Q8×C109C22×C412yes—
180C2×D4×C109—28no—
181C2×D4×C109—24no—
182C2×D4×C109—24no—
183C2×D4×C109—24no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—21no—
191C2×D4×C109—21no—
192C2×D4×C109—44no—
193C2×D4×C109—44no—
194C2×D4×C109—44no—
195C2×D4×C109—41no—
196C2×D4×C109—41no—
197C2×D4×C109—42no—
198C2×D4×C109—42no—
199C2×D4×C109—42no—
200C2×D4×C109—42no—
201C2×D4×C109—81no—
202C2×D4×C109—81no—
203C2×D4×C109C22⋊C414yes—
204C2×D4×C109C22×C412yes—
205C2×D4×C109C22×C412yes—
206C2×D4×C109C2×D412yes—
207C2×D4×C109#4112yes—
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—21no—
219C22×C4×C109—24no—
220C22×C4×C109—24no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—42no—
225C22×C4×C109—42no—
226C22×C4×C109—42no—
227C22×C4×C109—42no—
228C22×C4×C109—81no—
229C22×C4×C109—81no—
230C22×C4×C109—81no—
231C22×C4×C109C22×C412yes—
232C22×C4×C109C22×C412yes—
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109C2×D411yescharacteristic
235C22×C4×C109C2×D411yescharacteristic
236C22×C4×C109C2×D411yescharacteristic
237C22×C4×C109C2×D412yes—
238C22×C4×C109C2×D412yes—
239C22×C4×C109C2411yescharacteristic
240M16×C109—44no—
241M16×C109—44no—
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—
249C2×C8×C109—21no—
250C2×C8×C109—21no—
251C2×C8×C109—21no—
252C2×C8×C109—21no—
253C2×C8×C109C2×D412yes—
254C4⋊C4×C109—24no—
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—21no—
263C4⋊C4×C109—42no—
264C4⋊C4×C109C22⋊C414yes—
265C4⋊C4×C109C22×C412yes—
266C4⋊C4×C109C2×D412yes—
267C22⋊C4×C109—24no—
268C22⋊C4×C109—24no—
269C22⋊C4×C109—24no—
270C22⋊C4×C109—24no—
271C22⋊C4×C109—24no—
272C22⋊C4×C109—42no—
273C22⋊C4×C109—42no—
274C22⋊C4×C109—81no—
275C22⋊C4×C109C22⋊C414yes—
276C22⋊C4×C109C22⋊C414yes—
277C42×C109—42no—
278C42×C109—81no—
279C42×C109C22×C412yes—
280C42×C109C2×D412yes—
281C23×C109—22no—
282C23×C109—21no—
283C23×C109—21no—
284C23×C109—22no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—22no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—21no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—22no—
297C23×C109—48no—
298C23×C109—48no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—41no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—84no—
310C23×C109—84no—
311C23×C109—84no—
312C23×C109—84no—
313C23×C109—84no—
314C23×C109C2×C22⋊C412yes—
315C23×C109C2×C22⋊C412yes—
316C23×C109C22×D411yescharacteristic
317Q8×C109—22no—
318Q8×C109—22no—
319Q8×C109—41no—
320Q8×C109—41no—
321D4×C109—22no—
322D4×C109—22no—
323D4×C109—22no—
324D4×C109—22no—
325D4×C109—22no—
326D4×C109—44no—
327D4×C109—48no—
328D4×C109—48no—
329D4×C109—41no—
330D4×C109—41no—
331D4×C109—84no—
332D4×C109C4×D414yes—
333C2×C4×C109—21no—
334C2×C4×C109—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—21no—
341C2×C4×C109—22no—
342C2×C4×C109—22no—
343C2×C4×C109—22no—
344C2×C4×C109—22no—
345C2×C4×C109—22no—
346C2×C4×C109—22no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—48no—
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—41no—
367C2×C4×C109—41no—
368C2×C4×C109—84no—
369C2×C4×C109—84no—
370C2×C4×C109C2×C22⋊C412yes—
371C2×C4×C109C2×C22⋊C412yes—
372C2×C4×C109C2×C22⋊C412yes—
373C2×C4×C109C2×C22⋊C412yes—
374C2×C4×C109C23×C411yescharacteristic
375C2×C4×C109C22×D411yescharacteristic
376C2×C4×C109C22×D411yescharacteristic
377C2×C4×C109C2×#4111yescharacteristic
378C2×C4×C109H(5,𝔽2)11yescharacteristic
379C2×C4×C109H(5,𝔽2)11yescharacteristic
380C8×C109—22no—
381C8×C109—41no—
382C8×C109—41no—
383C8×C109—41no—
384C22×C109—22no—
385C22×C109—22no—
386C22×C109—24no—
387C22×C109—22no—
388C22×C109—22no—
389C22×C109—22no—
390C22×C109—22no—
391C22×C109—42no—
392C22×C109—42no—
393C22×C109—41no—
394C22×C109—41no—
395C22×C109—42no—
396C22×C109—41no—
397C22×C109—41no—
398C22×C109—42no—
399C22×C109—41no—
400C22×C109—41no—
401C22×C109—42no—
402C22×C109—41no—
403C22×C109—41no—
404C22×C109—42no—
405C22×C109—42no—
406C22×C109—42no—
407C22×C109—42no—
408C22×C109—816no—
409C22×C109—81no—
410C22×C109—81no—
411C22×C109—81no—
412C22×C109—81no—
413C22×C109C22×C22⋊C411yescharacteristic
414C22×C109D4211yescharacteristic
415C22×C109#54611yescharacteristic
416C22×C109#57511yescharacteristic
417C22×C109#57511yescharacteristic
418C22×C109#57611yescharacteristic
419C22×C109#57711yescharacteristic
420C4×C109—22no—
421C4×C109—22no—
422C4×C109—22no—
423C4×C109—22no—
424C4×C109—42no—
425C4×C109—42no—
426C4×C109—42no—
427C4×C109—81no—
428C4×C109—81no—
429C4×C109—81no—
430C4×C109C2×C4×D411yescharacteristic
431C4×C109#51811yescharacteristic
432C4×C109D4211yescharacteristic
433C4×C109#54611yescharacteristic
434#22427C10911yesmaximal, characteristic, direct product factor, Sylow
435C2×C109—42no—
436C2×C109—42no—
437C2×C109—44no—
438C2×C109—82no—
439C2×C109D4×C22⋊C411yescharacteristic
440C2×C109#289611yescharacteristic
441C2×C109#289711yescharacteristic
442C2×C109#327311yescharacteristic
443C2×C109#327511yescharacteristic
444C2×C109#332211yescharacteristic
445C2×C109#332311yescharacteristic
446C2×#546C2×C10911yescharacteristic
447C2×#436C2×C10911yescharacteristic, complemented
448C2×#417C2×C10911yescharacteristic, complemented
449C2×#418C2×C10911yescharacteristic, complemented
450#2352C2×C10911yescharacteristic, complemented
451#1983C2×C10911yescharacteristic, complemented
452#1958C2×C10911yescharacteristic, complemented
453#1895C2×C10911yescharacteristic, complemented
454#1894C2×C10911yescharacteristic, complemented
455#1874C2×C10911yescharacteristic, complemented
456#1873C2×C10911yescharacteristic, complemented
457#1804C2×C10911yescharacteristic, complemented
458#1788C2×C10911yescharacteristic, complemented
459#1786C2×C10911yescharacteristic, complemented
460C4×#102C2×C10911yescharacteristic, complemented
461C109#2242711yescharacteristic, direct product factor, Sylow
462C22×#41C22×C10911yescharacteristic
463C23×D4C22×C10911yescharacteristic
464C22×M16C22×C10911yescharacteristic
465C22×M16C22×C10911yescharacteristic, complemented
466#546—24no—
467#546C4×C10918yescomplemented
468C2×#124C22×C10911yescharacteristic
469C2×#123—21no—
470C2×C22⋊Q8C22×C10911yescharacteristic
471C2×#121—21no—
472C2×#121C22×C10911yescharacteristic
473C2×#120—21no—
474C2×C4×D4C22×C10911yescharacteristic
475C2×C4×D4C22×C10911yescharacteristic
476C2×#117C22×C10911yescharacteristic
477C22×C4⋊C4C22×C10911yescharacteristic, complemented
478C22×C22⋊C4—21no—
479#436—24no—
480C2×C4⋊C8C22×C10911yescharacteristic, complemented
481#418—24no—
482#417—24no—
483C2×#103C22×C10911yescharacteristic, complemented
484C2×#103C22×C10911yescharacteristic, complemented
485C2×#103C22×C10911yescharacteristic, complemented
486C2×#103C22×C10911yescharacteristic, complemented
487C2×#102C22×C10911yescharacteristic
488C2×#102C22×C10911yescharacteristic
489C2×#102C22×C10911yescharacteristic
490C2×#102C22×C10911yescharacteristic
491C2×#102C22×C10911yescharacteristic
492C2×#102C22×C10911yescharacteristic
493C2×#102C22×C10911yescharacteristic
494C2×#102C22×C10911yescharacteristic
495C2×C22⋊C8C22×C10911yescharacteristic
496C2×C22⋊C8C22×C10911yescharacteristic, complemented
497C2×C4×C8C22×C10911yescharacteristic, complemented
498#388—21no—
499#387—21no—
500#386—21no—
501#382C22×C10911yescharacteristic, complemented
502#380C22×C10911yescharacteristic
503#380C22×C10911yescharacteristic, complemented
504C4×C4⋊C4C22×C10911yescharacteristic, complemented
505C4×C22⋊C4—21no—
506#340C22×C10911yescharacteristic, complemented
507#340C22×C10911yescharacteristic, complemented
508#340C22×C10911yescharacteristic, complemented
509#340C22×C10911yescharacteristic, complemented
510C25—21no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—22no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41C2×C4×C10914yes—
517C22×Q8C23×C10911yescharacteristic
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×C4×C10914yescomplemented
527C22×D4D4×C10911yescharacteristic
528C22×D4C23×C10911yescharacteristic
529C22×D4C23×C10911yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C10911yescharacteristic
534C23×C4C23×C10911yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C22×C8C23×C10911yescharacteristic
542C22×C8C23×C10911yescharacteristic
543C22×C8C23×C10911yescharacteristic
544C22×C8C23×C10911yescharacteristic
545#124—22no—
546#124C2×C4×C10914yescomplemented
547#123—28no—
548C22⋊Q8—22no—
549C22⋊Q8C2×C4×C10914yescomplemented
550#121—22no—
551#121—28no—
552#121C2×C4×C10914yes—
553#120—28no—
554C4×D4—22no—
555C4×D4C2×C4×C10914yes—
556C4×D4C2×C4×C10914yescomplemented
557C4×D4D4×C10914yes—
558#117—22no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C10911yescharacteristic
565C2×C4⋊C4C23×C10911yescharacteristic
566C2×C4⋊C4C23×C10911yescharacteristic
567C2×C4⋊C4C23×C10911yescharacteristic
568C2×C4⋊C4C23×C10911yescharacteristic
569C2×C4⋊C4C23×C10911yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—28no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C10911yescharacteristic
580C2×C22⋊C4D4×C10911yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C10911yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C10914yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599C4×C8—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C10911yescharacteristic
615C24C2×D4×C10911yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C10912yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C10914yes—
650C2×D4C22×C4×C10912yes—
651C2×D4C22×C4×C10912yes—
652C2×D4C2×D4×C10912yes—
653C2×D4#41×C10912yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C10912yes—
678C22×C4C22×C4×C10912yes—
679C22×C4C2×D4×C10911yescharacteristic
680C22×C4C2×D4×C10911yescharacteristic
681C22×C4C2×D4×C10911yescharacteristic
682C22×C4C2×D4×C10911yescharacteristic
683C22×C4C2×D4×C10912yes—
684C22×C4C2×D4×C10912yes—
685C22×C4C24×C10911yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C10912yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C10914yes—
711C4⋊C4C22×C4×C10912yes—
712C4⋊C4C2×D4×C10912yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C10914yes—
722C22⋊C4C22⋊C4×C10914yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C10912yes—
726C42C2×D4×C10912yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊C4×C10912yes—
761C23C2×C22⋊C4×C10912yes—
762C23C22×D4×C10911yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C10914yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C10912yes—
817C2×C4C2×C22⋊C4×C10912yes—
818C2×C4C2×C22⋊C4×C10912yes—
819C2×C4C2×C22⋊C4×C10912yes—
820C2×C4C23×C4×C10911yescharacteristic
821C2×C4C22×D4×C10911yescharacteristic
822C2×C4C22×D4×C10911yescharacteristic
823C2×C4C2×#41×C10911yescharacteristic
824C2×C4H(5,𝔽2)×C10911yescharacteristic
825C2×C4H(5,𝔽2)×C10911yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊C4×C10911yescharacteristic
860C22D42×C10911yescharacteristic
861C22#546×C10911yescharacteristic
862C22#575×C10911yescharacteristic
863C22#575×C10911yescharacteristic
864C22#576×C10911yescharacteristic
865C22#577×C10911yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C10911yescharacteristic
877C4#518×C10911yescharacteristic
878C4D42×C10911yescharacteristic
879C4#546×C10911yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C10911yescharacteristic
885C2C109×#289611yescharacteristic
886C2C109×#289711yescharacteristic
887C2C109×#327311yescharacteristic
888C2C109×#327511yescharacteristic
889C2C109×#332211yescharacteristic
890C2C109×#332311yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutatorC2×C4C23×C4×C109
Frattini, cosocleC22×C4C24×C109
prime radicalC2×#546×C109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#436×C109C2semidirect
3. C2×#417×C109C2semidirect
4. C2×#418×C109C2semidirect
5. C109×#2352C2semidirect
6. C109×#1983C2semidirect
7. C109×#1958C2semidirect
8. C109×#1895C2semidirect
9. C109×#1894C2semidirect
10. C109×#1874C2semidirect
11. C109×#1873C2semidirect
12. C109×#1804C2semidirect
13. C109×#1788C2semidirect
14. C109×#1786C2semidirect
15. C4×#102×C109C2semidirect
19. C22×M16×C109C22semidirect
21. #546×C109C4semidirect
31. C22×C4⋊C4×C109C22semidirect
34. C2×C4⋊C8×C109C22semidirect
37. C2×#103×C109C22semidirect
38. C2×#103×C109C22semidirect
39. C2×#103×C109C22semidirect
40. C2×#103×C109C22semidirect
50. C2×C22⋊C8×C109C22semidirect
51. C2×C4×C8×C109C22semidirect
55. #382×C109C22semidirect
57. #380×C109C22semidirect
58. C4×C4⋊C4×C109C22semidirect
60. #340×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #340×C109C22semidirect
80. C22×D4×C109C2×C4semidirect
100. #124×C109C2×C4semidirect
103. C22⋊Q8×C109C2×C4semidirect
110. C4×D4×C109C2×C4semidirect
150. #102×C109D4semidirect
434. #22427C109direct (N × H)
447. C2×#436C2×C109semidirect
448. C2×#417C2×C109semidirect
449. C2×#418C2×C109semidirect
450. #2352C2×C109semidirect
451. #1983C2×C109semidirect
452. #1958C2×C109semidirect
453. #1895C2×C109semidirect
454. #1894C2×C109semidirect
455. #1874C2×C109semidirect
456. #1873C2×C109semidirect
457. #1804C2×C109semidirect
458. #1788C2×C109semidirect
459. #1786C2×C109semidirect
460. C4×#102C2×C109semidirect
461. C109#22427direct (N × H)
465. C22×M16C22×C109semidirect
467. #546C4×C109semidirect
477. C22×C4⋊C4C22×C109semidirect
480. C2×C4⋊C8C22×C109semidirect
483. C2×#103C22×C109semidirect
484. C2×#103C22×C109semidirect
485. C2×#103C22×C109semidirect
486. C2×#103C22×C109semidirect
496. C2×C22⋊C8C22×C109semidirect
497. C2×C4×C8C22×C109semidirect
501. #382C22×C109semidirect
503. #380C22×C109semidirect
504. C4×C4⋊C4C22×C109semidirect
506. #340C22×C109semidirect
507. #340C22×C109semidirect
508. #340C22×C109semidirect
509. #340C22×C109semidirect
526. C22×D4C2×C4×C109semidirect
546. #124C2×C4×C109semidirect
549. C22⋊Q8C2×C4×C109semidirect
556. C4×D4C2×C4×C109semidirect
596. #102D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1092
C2×#436×C1092
C2×#417×C1092
C2×#418×C1092
C109×#23522
C109×#19832
C109×#19582
C109×#18952
C109×#18942
C109×#18742
C109×#18732
C109×#18042
C109×#17882
C109×#17862
C4×#102×C1092
#22427109