Finite Group Databasebeta

← C109×#32166 #42150160

Subgroups — C109×#32166 #42150160

Order 27904.

772 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2546C211yesmaximal, characteristic, complemented
2C109×#2512C211yesmaximal, characteristic
3C109×#2072C211yesmaximal, characteristic, complemented
4C109×#2055C211yesmaximal, characteristic
5C109×#2043C211yesmaximal, characteristic, complemented
6C109×#2013C211yesmaximal, characteristic
7C109×#2013C211yesmaximal, characteristic
8C109×#2013C211yesmaximal, characteristic
9C109×#1981C211yesmaximal, characteristic, complemented
10C109×#1968C211yesmaximal, characteristic
11C109×#1956C211yesmaximal, characteristic, complemented
12C109×#1927C211yesmaximal, characteristic, complemented
13C109×#1916C211yesmaximal, characteristic, complemented
14C109×#1880C211yesmaximal, characteristic
15C109×#1865C211yesmaximal, characteristic, complemented
16C22×SD16×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C2×C4⋊Q8×C109C2211yescharacteristic
20C2×C4⋊Q8×C109C2211yescharacteristic
21C2×C4⋊Q8×C109C2211yescharacteristic
22C2×#126×C109—21no—
23C2×C4×Q8×C109C2211yescharacteristic
24C2×#106×C109C2211yescharacteristic
25C2×C4⋊C8×C109C2211yescharacteristic
26C2×#103×C109C2211yescharacteristic
27C2×#103×C109C2211yescharacteristic
28C2×#103×C109C2211yescharacteristic
29C2×#103×C109C2211yescharacteristic
30C2×#103×C109C2211yescharacteristic
31C2×#103×C109C2211yescharacteristic
32C2×#103×C109C2211yescharacteristic
33C2×#103×C109C2211yescharacteristic
34C2×#103×C109C2211yescharacteristic
35C2×#102×C109C2211yescharacteristic
36C2×C4×C8×C109C2211yescharacteristic
37#398×C109—21no—
38#398×C109—21no—
39#397×C109—21no—
40#396×C109—21no—
41#391×C109C2211yescharacteristic
42#391×C109C2211yescharacteristic
43#390×C109C2211yescharacteristic
44#390×C109C2211yescharacteristic
45#390×C109C2211yescharacteristic
46#389×C109—21no—
47#389×C109—21no—
48#389×C109C2211yescharacteristic
49#388×C109—21no—
50#384×C109C2211yescharacteristic
51C4×C4⋊C4×C109C2211yescharacteristic
52C4×C4⋊C4×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#336×C109C2211yescharacteristic
56#336×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×Q8×C109C2311yescharacteristic
60C22×Q8×C109C2311yescharacteristic
61C22×Q8×C109C2311yescharacteristic
62C22×D4×C109C2311yescharacteristic
63C2×SD16×C109—22no—
64C2×SD16×C109—22no—
65C2×SD16×C109—41no—
66C2×SD16×C109—41no—
67C2×SD16×C109—41no—
68C2×SD16×C109—41no—
69C2×SD16×C109—41no—
70C2×SD16×C109—41no—
71C2×SD16×C109—41no—
72C22×C8×C109C2311yescharacteristic
73C22×C8×C109C2311yescharacteristic
74C22×C8×C109C2311yescharacteristic
75C22×C8×C109C2311yescharacteristic
76C4⋊Q8×C109—22no—
77C4⋊Q8×C109—22no—
78C4⋊Q8×C109—41no—
79C4⋊Q8×C109—41no—
80C4⋊Q8×C109—41no—
81C4⋊Q8×C109—41no—
82#126×C109—44no—
83C4×Q8×C109—41no—
84C4×Q8×C109—41no—
85C2×C4⋊C4×C109—21no—
86C2×C4⋊C4×C109—21no—
87C2×C4⋊C4×C109—21no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109—21no—
90C2×C4⋊C4×C109—21no—
91C2×C4⋊C4×C109—21no—
92C2×C4⋊C4×C109—21no—
93C2×C4⋊C4×C109—21no—
94C2×C4⋊C4×C109—21no—
95C2×C4⋊C4×C109D411yescharacteristic
96C2×C4⋊C4×C109D411yescharacteristic
97C2×C4⋊C4×C109C2311yescharacteristic
98C2×C4⋊C4×C109C2311yescharacteristic
99C2×C4⋊C4×C109C2311yescharacteristic
100C2×C4⋊C4×C109C2311yescharacteristic
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C42×C109—21no—
108C2×C42×C109—21no—
109C2×C42×C109C2311yescharacteristic
110C2×C42×C109C2311yescharacteristic
111C2×C42×C109C2311yescharacteristic
112#106×C109—41no—
113C4⋊C8×C109—41no—
114#103×C109—22no—
115#103×C109—22no—
116#103×C109—41no—
117#103×C109—41no—
118#103×C109—41no—
119#103×C109—41no—
120#103×C109—41no—
121#103×C109—41no—
122#103×C109—41no—
123#102×C109—41no—
124C4×C8×C109—41no—
125#95×C109—21no—
126#95×C109—21no—
127#95×C109—21no—
128#95×C109—21no—
129#95×C109—21no—
130#95×C109—21no—
131#95×C109D411yescharacteristic
132#95×C109D411yescharacteristic
133C24×C109—21no—
134C2×Q8×C109—21no—
135C2×Q8×C109—21no—
136C2×Q8×C109—21no—
137C2×Q8×C109—21no—
138C2×Q8×C109—21no—
139C2×Q8×C109—21no—
140C2×Q8×C109—21no—
141C2×Q8×C109—21no—
142C2×Q8×C109—21no—
143C2×Q8×C109—21no—
144C2×Q8×C109—21no—
145C2×Q8×C109—21no—
146C2×Q8×C109—21no—
147C2×Q8×C109—21no—
148C2×Q8×C109—21no—
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109#4112yes—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C22×C4×C109—21no—
159C22×C4×C109—21no—
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109C2×D411yescharacteristic
166C22×C4×C109C2×D411yescharacteristic
167C22×C4×C109C2×D411yescharacteristic
168C22×C4×C109C2×D411yescharacteristic
169C22×C4×C109C2×D411yescharacteristic
170C22×C4×C109C2×D411yescharacteristic
171C22×C4×C109C2411yescharacteristic
172SD16×C109—44no—
173SD16×C109—44no—
174SD16×C109—44no—
175C2×C8×C109—21no—
176C2×C8×C109—21no—
177C2×C8×C109—21no—
178C2×C8×C109—21no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109#4112yes—
187C4⋊C4×C109—22no—
188C4⋊C4×C109—21no—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—21no—
196C4⋊C4×C109—42no—
197C4⋊C4×C109—42no—
198C4⋊C4×C109—42no—
199C4⋊C4×C109—42no—
200C4⋊C4×C109—42no—
201C4⋊C4×C109—42no—
202C4⋊C4×C109—42no—
203C4⋊C4×C109—42no—
204C4⋊C4×C109—42no—
205C4⋊C4×C109—81no—
206C4⋊C4×C109SD1614yescomplemented
207C22⋊C4×C109—42no—
208C22⋊C4×C109—42no—
209C22⋊C4×C109—42no—
210C22⋊C4×C109—42no—
211C22⋊C4×C109—81no—
212C22⋊C4×C109—81no—
213C42×C109—21no—
214C42×C109—21no—
215C42×C109—21no—
216C42×C109—21no—
217C42×C109—21no—
218C42×C109—21no—
219C42×C109—42no—
220C42×C109—42no—
221C23×C109—41no—
222C23×C109—41no—
223C23×C109—41no—
224C23×C109—41no—
225C23×C109—41no—
226C23×C109—41no—
227C23×C109—41no—
228C23×C109C22×D411yescharacteristic
229Q8×C109—22no—
230Q8×C109—22no—
231Q8×C109—41no—
232Q8×C109—41no—
233Q8×C109—41no—
234Q8×C109—41no—
235Q8×C109—41no—
236Q8×C109—41no—
237Q8×C109—41no—
238Q8×C109—41no—
239Q8×C109—41no—
240Q8×C109—41no—
241D4×C109—41no—
242D4×C109—41no—
243D4×C109—41no—
244D4×C109—41no—
245C2×C4×C109—21no—
246C2×C4×C109—21no—
247C2×C4×C109—21no—
248C2×C4×C109—21no—
249C2×C4×C109—21no—
250C2×C4×C109—21no—
251C2×C4×C109—21no—
252C2×C4×C109—21no—
253C2×C4×C109—21no—
254C2×C4×C109—21no—
255C2×C4×C109—22no—
256C2×C4×C109—21no—
257C2×C4×C109—21no—
258C2×C4×C109—21no—
259C2×C4×C109—21no—
260C2×C4×C109—41no—
261C2×C4×C109—41no—
262C2×C4×C109—41no—
263C2×C4×C109—41no—
264C2×C4×C109—41no—
265C2×C4×C109—41no—
266C2×C4×C109—41no—
267C2×C4×C109—41no—
268C2×C4×C109—41no—
269C2×C4×C109—41no—
270C2×C4×C109—41no—
271C2×C4×C109—41no—
272C2×C4×C109—41no—
273C2×C4×C109—41no—
274C2×C4×C109—41no—
275C2×C4×C109—41no—
276C2×C4×C109—41no—
277C2×C4×C109—41no—
278C2×C4×C109—41no—
279C2×C4×C109—41no—
280C2×C4×C109C2×SD1612yes—
281C2×C4×C109C2×SD1612yes—
282C2×C4×C109C2×SD1612yes—
283C2×C4×C109#13712yes—
284C2×C4×C109C2×#4111yescharacteristic
285C2×C4×C109C2×#4111yescharacteristic
286C2×C4×C109H(5,𝔽2)11yescharacteristic
287C2×C4×C109H(5,𝔽2)11yescharacteristic
288C2×C4×C109H(5,𝔽2)11yescharacteristic
289C2×C4×C109H(5,𝔽2)11yescharacteristic
290C8×C109—22no—
291C8×C109—41no—
292C8×C109—41no—
293C8×C109—41no—
294C22×C109—81no—
295C22×C109—81no—
296C22×C109—81no—
297C22×C109—81no—
298C22×C109—81no—
299C22×C109—81no—
300C22×C109—81no—
301C22×C109#53511yescharacteristic
302C22×C109#54611yescharacteristic
303C22×C109#55011yescharacteristic
304C22×C109C22×SD1611yescharacteristic
305C22×C109C2×#13711yescharacteristic
306C22×C109#57711yescharacteristic
307C22×C109#57811yescharacteristic
308C4×C109—22no—
309C4×C109—22no—
310C4×C109—22no—
311C4×C109—22no—
312C4×C109—41no—
313C4×C109—42no—
314C4×C109—41no—
315C4×C109—81no—
316C4×C109—81no—
317C4×C109—81no—
318C4×C109—81no—
319C4×C109—81no—
320C4×C109—81no—
321C4×C109#53811yescharacteristic
322C4×C109#53811yescharacteristic
323C4×C109#55311yescharacteristic
324C4×C109#56011yescharacteristic
325#32166C10911yesmaximal, characteristic, direct product factor, Sylow
326C2×C109—161no—
327C2×C109#271411yescharacteristic
328C2×C109#320611yescharacteristic
329C2×C109#322511yescharacteristic
330C2×C109#329811yescharacteristic
331C2×C109#332011yescharacteristic
332C2×C109#339211yescharacteristic
333C2×C109#339811yescharacteristic
334#2546C2×C10911yescharacteristic, complemented
335#2512C2×C10911yescharacteristic
336#2072C2×C10911yescharacteristic, complemented
337#2055C2×C10911yescharacteristic
338#2043C2×C10911yescharacteristic, complemented
339#2013C2×C10911yescharacteristic
340#2013C2×C10911yescharacteristic
341#2013C2×C10911yescharacteristic
342#1981C2×C10911yescharacteristic, complemented
343#1968C2×C10911yescharacteristic
344#1956C2×C10911yescharacteristic, complemented
345#1927C2×C10911yescharacteristic, complemented
346#1916C2×C10911yescharacteristic, complemented
347#1880C2×C10911yescharacteristic
348#1865C2×C10911yescharacteristic, complemented
349C109#3216611yescharacteristic, direct product factor, Sylow
350C22×SD16C22×C10911yescharacteristic
351C22×SD16C22×C10911yescharacteristic
352C22×SD16C22×C10911yescharacteristic
353C2×C4⋊Q8C22×C10911yescharacteristic
354C2×C4⋊Q8C22×C10911yescharacteristic
355C2×C4⋊Q8C22×C10911yescharacteristic
356C2×#126—21no—
357C2×C4×Q8C22×C10911yescharacteristic
358C2×#106C22×C10911yescharacteristic
359C2×C4⋊C8C22×C10911yescharacteristic
360C2×#103C22×C10911yescharacteristic
361C2×#103C22×C10911yescharacteristic
362C2×#103C22×C10911yescharacteristic
363C2×#103C22×C10911yescharacteristic
364C2×#103C22×C10911yescharacteristic
365C2×#103C22×C10911yescharacteristic
366C2×#103C22×C10911yescharacteristic
367C2×#103C22×C10911yescharacteristic
368C2×#103C22×C10911yescharacteristic
369C2×#102C22×C10911yescharacteristic
370C2×C4×C8C22×C10911yescharacteristic
371#398—21no—
372#398—21no—
373#397—21no—
374#396—21no—
375#391C22×C10911yescharacteristic
376#391C22×C10911yescharacteristic
377#390C22×C10911yescharacteristic
378#390C22×C10911yescharacteristic
379#390C22×C10911yescharacteristic
380#389—21no—
381#389—21no—
382#389C22×C10911yescharacteristic
383#388—21no—
384#384C22×C10911yescharacteristic
385C4×C4⋊C4C22×C10911yescharacteristic
386C4×C4⋊C4C22×C10911yescharacteristic
387#340C22×C10911yescharacteristic
388#340C22×C10911yescharacteristic
389#336C22×C10911yescharacteristic
390#336C22×C10911yescharacteristic
391#336C22×C10911yescharacteristic
392#336C22×C10911yescharacteristic
393C22×Q8C23×C10911yescharacteristic
394C22×Q8C23×C10911yescharacteristic
395C22×Q8C23×C10911yescharacteristic
396C22×D4C23×C10911yescharacteristic
397C2×SD16—22no—
398C2×SD16—22no—
399C2×SD16—41no—
400C2×SD16—41no—
401C2×SD16—41no—
402C2×SD16—41no—
403C2×SD16—41no—
404C2×SD16—41no—
405C2×SD16—41no—
406C22×C8C23×C10911yescharacteristic
407C22×C8C23×C10911yescharacteristic
408C22×C8C23×C10911yescharacteristic
409C22×C8C23×C10911yescharacteristic
410C4⋊Q8—22no—
411C4⋊Q8—22no—
412C4⋊Q8—41no—
413C4⋊Q8—41no—
414C4⋊Q8—41no—
415C4⋊Q8—41no—
416#126—44no—
417C4×Q8—41no—
418C4×Q8—41no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4D4×C10911yescharacteristic
430C2×C4⋊C4D4×C10911yescharacteristic
431C2×C4⋊C4C23×C10911yescharacteristic
432C2×C4⋊C4C23×C10911yescharacteristic
433C2×C4⋊C4C23×C10911yescharacteristic
434C2×C4⋊C4C23×C10911yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C10911yescharacteristic
444C2×C42C23×C10911yescharacteristic
445C2×C42C23×C10911yescharacteristic
446#106—41no—
447C4⋊C8—41no—
448#103—22no—
449#103—22no—
450#103—41no—
451#103—41no—
452#103—41no—
453#103—41no—
454#103—41no—
455#103—41no—
456#103—41no—
457#102—41no—
458C4×C8—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C10911yescharacteristic
466#95D4×C10911yescharacteristic
467C24—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8#41×C10912yes—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4C2×D4×C10911yescharacteristic
500C22×C4C2×D4×C10911yescharacteristic
501C22×C4C2×D4×C10911yescharacteristic
502C22×C4C2×D4×C10911yescharacteristic
503C22×C4C2×D4×C10911yescharacteristic
504C22×C4C2×D4×C10911yescharacteristic
505C22×C4C24×C10911yescharacteristic
506SD16—44no—
507SD16—44no—
508SD16—44no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8#41×C10912yes—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4SD16×C10914yescomplemented
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22×D4×C10911yescharacteristic
563Q8—22no—
564Q8—22no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4C2×SD16×C10912yes—
615C2×C4C2×SD16×C10912yes—
616C2×C4C2×SD16×C10912yes—
617C2×C4#137×C10912yes—
618C2×C4C2×#41×C10911yescharacteristic
619C2×C4C2×#41×C10911yescharacteristic
620C2×C4H(5,𝔽2)×C10911yescharacteristic
621C2×C4H(5,𝔽2)×C10911yescharacteristic
622C2×C4H(5,𝔽2)×C10911yescharacteristic
623C2×C4H(5,𝔽2)×C10911yescharacteristic
624C8—22no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#535×C10911yescharacteristic
636C22#546×C10911yescharacteristic
637C22#550×C10911yescharacteristic
638C22C22×SD16×C10911yescharacteristic
639C22C2×#137×C10911yescharacteristic
640C22#577×C10911yescharacteristic
641C22#578×C10911yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4#538×C10911yescharacteristic
656C4#538×C10911yescharacteristic
657C4#553×C10911yescharacteristic
658C4#560×C10911yescharacteristic
659C2—161no—
660C2C109×#271411yescharacteristic
661C2C109×#320611yescharacteristic
662C2C109×#322511yescharacteristic
663C2C109×#329811yescharacteristic
664C2C109×#332011yescharacteristic
665C2C109×#339211yescharacteristic
666C2C109×#339811yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC22×D4×C109C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C4⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2546C2semidirect
3. C109×#2072C2semidirect
5. C109×#2043C2semidirect
9. C109×#1981C2semidirect
11. C109×#1956C2semidirect
12. C109×#1927C2semidirect
13. C109×#1916C2semidirect
15. C109×#1865C2semidirect
206. C4⋊C4×C109SD16semidirect
325. #32166C109direct (N × H)
334. #2546C2×C109semidirect
336. #2072C2×C109semidirect
338. #2043C2×C109semidirect
342. #1981C2×C109semidirect
344. #1956C2×C109semidirect
345. #1927C2×C109semidirect
346. #1916C2×C109semidirect
348. #1865C2×C109semidirect
349. C109#32166direct (N × H)
540. C4⋊C4SD16×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#25462
C109×#25122
C109×#20722
C109×#20552
C109×#20432
C109×#20132
C109×#19812
C109×#19682
C109×#19562
C109×#19272
C109×#19162
C109×#18802
C109×#18652
#32166109