Finite Group Databasebeta

← C109×#25162 #42143156

Subgroups — C109×#25162 #42143156

Order 27904.

1240 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C109C211yesmaximal, characteristic, complemented
2C2×#449×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×C4×D8×C109C211yesmaximal, characteristic, complemented
5C109×#2428C211yesmaximal, characteristic, complemented
6C109×#2339C211yesmaximal, characteristic, complemented
7C109×#2068C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2033C211yesmaximal, characteristic, complemented
10C109×#2014C211yesmaximal, characteristic, complemented
11C109×#1968C211yesmaximal, characteristic, complemented
12C109×#1923C211yesmaximal, characteristic, complemented
13C109×#1879C211yesmaximal, characteristic, complemented
14C109×#1877C211yesmaximal, characteristic, complemented
15C109×#1864C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C2×#127×C109C2211yescharacteristic
22C2×#121×C109—21no—
23C2×#121×C109C2211yescharacteristic
24C2×#121×C109C2211yescharacteristic
25C2×C4×D4×C109C2211yescharacteristic
26C2×C4×D4×C109C2211yescharacteristic
27C2×C4×D4×C109C2211yescharacteristic
28#459×C109—24no—
29#449×C109—24no—
30#449×C109—24no—
31C4×D8×C109—24no—
32C2×#107×C109C2211yescharacteristic
33C2×#106×C109C2211yescharacteristic
34C2×C4⋊C8×C109C2211yescharacteristic
35C2×#103×C109C2211yescharacteristic
36C2×#103×C109C2211yescharacteristic
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×C22⋊C8×C109C2211yescharacteristic
44C2×C22⋊C8×C109C2211yescharacteristic
45C2×C4×C8×C109C2211yescharacteristic
46#394×C109—21no—
47#392×C109—21no—
48#391×C109C2211yescharacteristic
49#391×C109C2211yescharacteristic
50#390×C109C2211yescharacteristic
51#389×C109C2211yescharacteristic
52#386×C109—21no—
53#386×C109—21no—
54#386×C109—21no—
55#381×C109—21no—
56#380×C109C2211yescharacteristic
57C4×C22⋊C4×C109C2211yescharacteristic
58C2×#95×C109—21no—
59#340×C109C2211yescharacteristic
60#340×C109C2211yescharacteristic
61#336×C109C2211yescharacteristic
62#336×C109C2211yescharacteristic
63C2×#41×C109—22no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—41no—
68C2×#41×C109—41no—
69C22×Q8×C109C2311yescharacteristic
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—21no—
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109C2311yescharacteristic
76C22×D4×C109C2311yescharacteristic
77C22×D4×C109C2311yescharacteristic
78C23×C4×C109—21no—
79C23×C4×C109—21no—
80C23×C4×C109—21no—
81C23×C4×C109—21no—
82C23×C4×C109C2311yescharacteristic
83C2×SD16×C109—22no—
84C2×SD16×C109—22no—
85C2×SD16×C109—22no—
86C2×SD16×C109—22no—
87C2×SD16×C109—41no—
88C2×SD16×C109—41no—
89C2×D8×C109—22no—
90C2×D8×C109—22no—
91C2×D8×C109—22no—
92C2×D8×C109—22no—
93C2×D8×C109—22no—
94C2×D8×C109D414yescomplemented
95C22×C8×C109C2311yescharacteristic
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99#127×C109—22no—
100#127×C109—41no—
101#121×C109—22no—
102#121×C109—22no—
103#121×C109—44no—
104#121×C109—41no—
105#121×C109—41no—
106C4×D4×C109—22no—
107C4×D4×C109—22no—
108C4×D4×C109—22no—
109C4×D4×C109—41no—
110C4×D4×C109—41no—
111C4×D4×C109—41no—
112C2×C4⋊C4×C109—21no—
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C22⋊C4×C109—21no—
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×C109D411yescharacteristic
126C2×C22⋊C4×C109D411yescharacteristic
127C2×C42×C109C2311yescharacteristic
128C2×C42×C109C2311yescharacteristic
129#107×C109—22no—
130#106×C109—41no—
131C4⋊C8×C109—22no—
132#103×C109—22no—
133#103×C109—22no—
134#102×C109—22no—
135#102×C109—22no—
136#102×C109—22no—
137#102×C109—22no—
138#102×C109—41no—
139#102×C109D414yescomplemented
140C22⋊C8×C109—22no—
141C22⋊C8×C109—22no—
142C4×C8×C109—22no—
143#95×C109—21no—
144#95×C109—21no—
145#95×C109—21no—
146#95×C109—21no—
147#95×C109—21no—
148#95×C109—21no—
149#95×C109D411yescharacteristic
150#95×C109D411yescharacteristic
151C24×C109—21no—
152C24×C109—21no—
153C24×C109—21no—
154C24×C109C2×D411yescharacteristic
155#41×C109—44no—
156#41×C109—44no—
157#41×C109—44no—
158#41×C109—44no—
159C2×Q8×C109—21no—
160C2×Q8×C109—21no—
161C2×Q8×C109—21no—
162C2×Q8×C109—21no—
163C2×Q8×C109—21no—
164C2×Q8×C109#4112yes—
165C2×D4×C109—24no—
166C2×D4×C109—21no—
167C2×D4×C109—21no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—21no—
174C2×D4×C109—21no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—42no—
181C2×D4×C109—42no—
182C2×D4×C109—42no—
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×C109—42no—
190C2×D4×C109—81no—
191C2×D4×C109—81no—
192C2×D4×C109—81no—
193C2×D4×C109—81no—
194C2×D4×C109C2×D412yes—
195C2×D4×C109C2×D412yes—
196C2×D4×C109C2×D412yes—
197C2×D4×C109#4112yes—
198C22×C4×C109—24no—
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—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—42no—
211C22×C4×C109—42no—
212C22×C4×C109—42no—
213C22×C4×C109—42no—
214C22×C4×C109—42no—
215C22×C4×C109—42no—
216C22×C4×C109—42no—
217C22×C4×C109—42no—
218C22×C4×C109—81no—
219C22×C4×C109—81no—
220C22×C4×C109—81no—
221C22×C4×C109C2×D411yescharacteristic
222C22×C4×C109C2×D411yescharacteristic
223C22×C4×C109C2×D411yescharacteristic
224C22×C4×C109C2×D411yescharacteristic
225C22×C4×C109C2×D411yescharacteristic
226C22×C4×C109C2411yescharacteristic
227SD16×C109—44no—
228SD16×C109—44no—
229D8×C109—28no—
230D8×C109—44no—
231C2×C8×C109—21no—
232C2×C8×C109—21no—
233C2×C8×C109—21no—
234C2×C8×C109—21no—
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×C109C2×D412yes—
242C2×C8×C109C2×D412yes—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109—21no—
246C4⋊C4×C109—21no—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—42no—
251C4⋊C4×C109C2×D412yes—
252C22⋊C4×C109—22no—
253C22⋊C4×C109—22no—
254C22⋊C4×C109—42no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—42no—
257C22⋊C4×C109—42no—
258C22⋊C4×C109—42no—
259C22⋊C4×C109—42no—
260C22⋊C4×C109—81no—
261C22⋊C4×C109—81no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109—21no—
265C42×C109—21no—
266C23×C109—22no—
267C23×C109—22no—
268C23×C109—22no—
269C23×C109—21no—
270C23×C109—22no—
271C23×C109—21no—
272C23×C109—21no—
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—21no—
276C23×C109—21no—
277C23×C109—41no—
278C23×C109—41no—
279C23×C109—41no—
280C23×C109—41no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—41no—
285C23×C109—41no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—41no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109C22×D411yescharacteristic
295Q8×C109—22no—
296Q8×C109—22no—
297Q8×C109—41no—
298Q8×C109—41no—
299D4×C109—22no—
300D4×C109—22no—
301D4×C109—22no—
302D4×C109—22no—
303D4×C109—22no—
304D4×C109—48no—
305D4×C109—41no—
306D4×C109—41no—
307D4×C109—41no—
308D4×C109—41no—
309D4×C109—41no—
310D4×C109—41no—
311D4×C109—84no—
312D4×C109—84no—
313D4×C109—84no—
314D4×C109—84no—
315D4×C109#12114yescomplemented
316C2×C4×C109—21no—
317C2×C4×C109—21no—
318C2×C4×C109—21no—
319C2×C4×C109—21no—
320C2×C4×C109—21no—
321C2×C4×C109—22no—
322C2×C4×C109—21no—
323C2×C4×C109—21no—
324C2×C4×C109—22no—
325C2×C4×C109—21no—
326C2×C4×C109—21no—
327C2×C4×C109—21no—
328C2×C4×C109—21no—
329C2×C4×C109—21no—
330C2×C4×C109—21no—
331C2×C4×C109—48no—
332C2×C4×C109—41no—
333C2×C4×C109—41no—
334C2×C4×C109—41no—
335C2×C4×C109—41no—
336C2×C4×C109—41no—
337C2×C4×C109—41no—
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—84no—
350C2×C4×C109—84no—
351C2×C4×C109—84no—
352C2×C4×C109#13512yes—
353C2×C4×C109AGL(1,ℤ/8)12yes—
354C2×C4×C109C22×D411yescharacteristic
355C2×C4×C109C22×D411yescharacteristic
356C2×C4×C109C2×#4111yescharacteristic
357C2×C4×C109C2×#4111yescharacteristic
358C2×C4×C109H(5,𝔽2)11yescharacteristic
359C2×C4×C109H(5,𝔽2)11yescharacteristic
360C8×C109—22no—
361C8×C109—22no—
362C8×C109—41no—
363C8×C109—41no—
364C22×C109—24no—
365C22×C109—42no—
366C22×C109—42no—
367C22×C109—42no—
368C22×C109—42no—
369C22×C109—42no—
370C22×C109—42no—
371C22×C109—41no—
372C22×C109—41no—
373C22×C109—41no—
374C22×C109—42no—
375C22×C109—41no—
376C22×C109—41no—
377C22×C109—42no—
378C22×C109—42no—
379C22×C109—41no—
380C22×C109—41no—
381C22×C109—81no—
382C22×C109—81no—
383C22×C109—81no—
384C22×C109—81no—
385C22×C109—81no—
386C22×C109—81no—
387C22×C109—81no—
388C22×C109—81no—
389C22×C109—81no—
390C22×C109—81no—
391C22×C109—81no—
392C22×C109#52511yescharacteristic
393C22×C109D4211yescharacteristic
394C22×C109D4211yescharacteristic
395C22×C109C2×#13511yescharacteristic
396C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
397C22×C109#57611yescharacteristic
398C22×C109#57711yescharacteristic
399C4×C109—22no—
400C4×C109—22no—
401C4×C109—41no—
402C4×C109—42no—
403C4×C109—42no—
404C4×C109—41no—
405C4×C109—41no—
406C4×C109—81no—
407C4×C109—81no—
408C4×C109—81no—
409C4×C109C2×#12111yescharacteristic
410C4×C109#53811yescharacteristic
411C4×C109#54611yescharacteristic
412C4×C109#54611yescharacteristic
413#25162C10911yesmaximal, characteristic, direct product factor, Sylow
414C2×C109—44no—
415C2×C109—81no—
416C2×C109—82no—
417C2×C109—161no—
418C2×C109#242411yescharacteristic
419C2×C109#310611yescharacteristic
420C2×C109#311911yescharacteristic
421C2×C109#326411yescharacteristic
422C2×C109#327211yescharacteristic
423C2×C109#328011yescharacteristic
424C2×C109#328411yescharacteristic
425C2×#459C2×C10911yescharacteristic, complemented
426C2×#449C2×C10911yescharacteristic, complemented
427C2×#449C2×C10911yescharacteristic, complemented
428C2×C4×D8C2×C10911yescharacteristic, complemented
429#2428C2×C10911yescharacteristic, complemented
430#2339C2×C10911yescharacteristic, complemented
431#2068C2×C10911yescharacteristic, complemented
432#2034C2×C10911yescharacteristic, complemented
433#2033C2×C10911yescharacteristic, complemented
434#2014C2×C10911yescharacteristic, complemented
435#1968C2×C10911yescharacteristic, complemented
436#1923C2×C10911yescharacteristic, complemented
437#1879C2×C10911yescharacteristic, complemented
438#1877C2×C10911yescharacteristic, complemented
439#1864C2×C10911yescharacteristic, complemented
440C109#2516211yescharacteristic, direct product factor, Sylow
441C22×#41C22×C10911yescharacteristic
442C22×SD16C22×C10911yescharacteristic
443C22×SD16C22×C10911yescharacteristic
444C22×D8C22×C10911yescharacteristic
445C22×D8C22×C10911yescharacteristic
446C2×#127C22×C10911yescharacteristic
447C2×#121—21no—
448C2×#121C22×C10911yescharacteristic
449C2×#121C22×C10911yescharacteristic
450C2×C4×D4C22×C10911yescharacteristic
451C2×C4×D4C22×C10911yescharacteristic
452C2×C4×D4C22×C10911yescharacteristic
453#459—24no—
454#449—24no—
455#449—24no—
456C4×D8—24no—
457C2×#107C22×C10911yescharacteristic
458C2×#106C22×C10911yescharacteristic
459C2×C4⋊C8C22×C10911yescharacteristic
460C2×#103C22×C10911yescharacteristic
461C2×#103C22×C10911yescharacteristic
462C2×#102C22×C10911yescharacteristic
463C2×#102C22×C10911yescharacteristic
464C2×#102C22×C10911yescharacteristic
465C2×#102C22×C10911yescharacteristic
466C2×#102C22×C10911yescharacteristic
467C2×#102C22×C10911yescharacteristic
468C2×C22⋊C8C22×C10911yescharacteristic
469C2×C22⋊C8C22×C10911yescharacteristic
470C2×C4×C8C22×C10911yescharacteristic
471#394—21no—
472#392—21no—
473#391C22×C10911yescharacteristic
474#391C22×C10911yescharacteristic
475#390C22×C10911yescharacteristic
476#389C22×C10911yescharacteristic
477#386—21no—
478#386—21no—
479#386—21no—
480#381—21no—
481#380C22×C10911yescharacteristic
482C4×C22⋊C4C22×C10911yescharacteristic
483C2×#95—21no—
484#340C22×C10911yescharacteristic
485#340C22×C10911yescharacteristic
486#336C22×C10911yescharacteristic
487#336C22×C10911yescharacteristic
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—41no—
493C2×#41—41no—
494C22×Q8C23×C10911yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C23×C10911yescharacteristic
501C22×D4C23×C10911yescharacteristic
502C22×D4C23×C10911yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C23×C10911yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8D4×C10914yescomplemented
520C22×C8C23×C10911yescharacteristic
521C22×C8C23×C10911yescharacteristic
522C22×C8C23×C10911yescharacteristic
523C22×C8C23×C10911yescharacteristic
524#127—22no—
525#127—41no—
526#121—22no—
527#121—22no—
528#121—44no—
529#121—41no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C10911yescharacteristic
539C2×C4⋊C4C23×C10911yescharacteristic
540C2×C4⋊C4C23×C10911yescharacteristic
541C2×C4⋊C4C23×C10911yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C10911yescharacteristic
551C2×C22⋊C4D4×C10911yescharacteristic
552C2×C42C23×C10911yescharacteristic
553C2×C42C23×C10911yescharacteristic
554#107—22no—
555#106—41no—
556C4⋊C8—22no—
557#103—22no—
558#103—22no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C10914yescomplemented
565C22⋊C8—22no—
566C22⋊C8—22no—
567C4×C8—22no—
568#95—21no—
569#95—21no—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C10911yescharacteristic
575#95D4×C10911yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C10911yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8#41×C10912yes—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C10912yes—
620C2×D4C2×D4×C10912yes—
621C2×D4C2×D4×C10912yes—
622C2×D4#41×C10912yes—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C2×D4×C10911yescharacteristic
647C22×C4C2×D4×C10911yescharacteristic
648C22×C4C2×D4×C10911yescharacteristic
649C22×C4C2×D4×C10911yescharacteristic
650C22×C4C2×D4×C10911yescharacteristic
651C22×C4C24×C10911yescharacteristic
652SD16—44no—
653SD16—44no—
654D8—28no—
655D8—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C2×D4×C10912yes—
667C2×C8C2×D4×C10912yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—42no—
676C4⋊C4C2×D4×C10912yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23C22×D4×C10911yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—84no—
737D4—84no—
738D4—84no—
739D4—84no—
740D4#121×C10914yescomplemented
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—84no—
777C2×C4#135×C10912yes—
778C2×C4AGL(1,ℤ/8)×C10912yes—
779C2×C4C22×D4×C10911yescharacteristic
780C2×C4C22×D4×C10911yescharacteristic
781C2×C4C2×#41×C10911yescharacteristic
782C2×C4C2×#41×C10911yescharacteristic
783C2×C4H(5,𝔽2)×C10911yescharacteristic
784C2×C4H(5,𝔽2)×C10911yescharacteristic
785C8—22no—
786C8—22no—
787C8—41no—
788C8—41no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22#525×C10911yescharacteristic
818C22D42×C10911yescharacteristic
819C22D42×C10911yescharacteristic
820C22C2×#135×C10911yescharacteristic
821C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
822C22#576×C10911yescharacteristic
823C22#577×C10911yescharacteristic
824C4—22no—
825C4—22no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—42no—
831C4—81no—
832C4—81no—
833C4—81no—
834C4C2×#121×C10911yescharacteristic
835C4#538×C10911yescharacteristic
836C4#546×C10911yescharacteristic
837C4#546×C10911yescharacteristic
838C2—44no—
839C2—81no—
840C2—82no—
841C2—161no—
842C2C109×#242411yescharacteristic
843C2C109×#310611yescharacteristic
844C2C109×#311911yescharacteristic
845C2C109×#326411yescharacteristic
846C2C109×#327211yescharacteristic
847C2C109×#328011yescharacteristic
848C2C109×#328411yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C109C2semidirect
2. C2×#449×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×C4×D8×C109C2semidirect
5. C109×#2428C2semidirect
6. C109×#2339C2semidirect
7. C109×#2068C2semidirect
8. C109×#2034C2semidirect
9. C109×#2033C2semidirect
10. C109×#2014C2semidirect
11. C109×#1968C2semidirect
12. C109×#1923C2semidirect
13. C109×#1879C2semidirect
14. C109×#1877C2semidirect
15. C109×#1864C2semidirect
94. C2×D8×C109D4semidirect
139. #102×C109D4semidirect
315. D4×C109#121semidirect
413. #25162C109direct (N × H)
425. C2×#459C2×C109semidirect
426. C2×#449C2×C109semidirect
427. C2×#449C2×C109semidirect
428. C2×C4×D8C2×C109semidirect
429. #2428C2×C109semidirect
430. #2339C2×C109semidirect
431. #2068C2×C109semidirect
432. #2034C2×C109semidirect
433. #2033C2×C109semidirect
434. #2014C2×C109semidirect
435. #1968C2×C109semidirect
436. #1923C2×C109semidirect
437. #1879C2×C109semidirect
438. #1877C2×C109semidirect
439. #1864C2×C109semidirect
440. C109#25162direct (N × H)
519. C2×D8D4×C109semidirect
564. #102D4×C109semidirect
740. D4#121×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1092
C2×#449×C1092
C2×C4×D8×C1092
C109×#24282
C109×#23392
C109×#20682
C109×#20342
C109×#20332
C109×#20142
C109×#19682
C109×#19232
C109×#18792
C109×#18772
C109×#18642
#25162109