Finite Group Databasebeta

← C4×#17988749 #33091614

Subgroups — C4×#17988749 #33091614

Order 18688.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988749C211yesmaximal, characteristic
2C2×C4×#11924018C211yesmaximal, characteristic, complemented
3C2×C4×#11924016C211yesmaximal, characteristic, complemented
4C4×#14556570C211yesmaximal, characteristic, complemented
5#22610272C211yesmaximal, characteristic, complemented
6#22610265C211yesmaximal, characteristic, complemented
7#22610243C211yesmaximal, characteristic, complemented
8#22610199C211yesmaximal, characteristic, complemented
9#22610178C211yesmaximal, characteristic, complemented
10#22610130C211yesmaximal, characteristic, complemented
11#22609871C211yesmaximal, characteristic
12C4×#14556515C211yesmaximal, characteristic, complemented
13C4×#14556512C211yesmaximal, characteristic, complemented
14C4×C22⋊#10596831C211yesmaximal, characteristic, complemented
15C2×C4×#41×C73C211yesmaximal, characteristic
16C22×#11924018C2211yescharacteristic
17C22×#11924016C2211yescharacteristic
18C2×#14556570C2211yescharacteristic
19C2×C4×Dic146C2211yescharacteristic
20#17988749C418yesdirect product factor
21C4×#11924018—24no—
22C4×#11924016—24no—
23C2×#14556524C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556515C2211yescharacteristic
26C2×#14556515C2211yescharacteristic
27C2×#14556515C2211yescharacteristic
28C2×#14556514C2211yescharacteristic
29C2×#14556514C2211yescharacteristic
30C2×#14556512C2211yescharacteristic
31C2×#14556512C2211yescharacteristic
32C2×#14556512C2211yescharacteristic
33C2×C22⋊#10596831C2211yescharacteristic
34C2×C22⋊#10596831C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36C2×C4×#10596831C2211yescharacteristic
37#17988493C2211yescharacteristic
38#17988485C2211yescharacteristic
39#17988471—21no—
40#17988460—21no—
41#17988447C2211yescharacteristic
42C4×#11924007—21no—
43C4×C4⋊Dic73C2211yescharacteristic
44C4×C22⋊Dic73—21no—
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51C22×#41×C73C2211yescharacteristic
52C4×#41×C73—24no—
53C4×#41×C73—24no—
54C2×C4×Q8×C73C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic
56C2×C4×D4×C73—21no—
57C2×C4×D4×C73—21no—
58C2×C4×D4×C73C2211yescharacteristic
59C2×C4×D4×C73C2211yescharacteristic
60C2×#117×C73—21no—
61C2×#117×C73C2211yescharacteristic
62C22×C42×C73—21no—
63C22×C42×C73C2211yescharacteristic
64C22×Dic146C2311yescharacteristic
65C2×#11924018—22no—
66C2×#11924018—22no—
67C2×#11924018C2×C414yescomplemented
68C2×#11924016—22no—
69C2×#11924016—22no—
70C2×#11924016C2×C414yescomplemented
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556570—22no—
76#14556570C2×C414yescomplemented
77C4×Dic146—22no—
78C4×Dic146—22no—
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C4⋊Dic73C2311yescharacteristic
81C2×C4⋊Dic73C2311yescharacteristic
82C2×#11924007—21no—
83C2×#11924007—21no—
84C2×#11924007—21no—
85C2×C22⋊Dic73—21no—
86C2×C22⋊Dic73—21no—
87C2×C4×Dic73—21no—
88C2×C4×Dic73—21no—
89#14556524—22no—
90#14556522—22no—
91#14556515—22no—
92#14556515—22no—
93#14556515C2×C414yescomplemented
94#14556514—22no—
95#14556514—22no—
96#14556512—22no—
97#14556512—22no—
98#14556512C2×C414yescomplemented
99C22⋊#10596831—22no—
100C22⋊#10596831C2×C414yescomplemented
101C4×#10596831—22no—
102C4×#10596831—22no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C2×#41×C73—22no—
109C2×#41×C73—22no—
110C2×#41×C73—22no—
111C2×#41×C73—22no—
112C2×#41×C73—22no—
113C2×#41×C73C2×C414yes—
114C22×Q8×C73C2311yescharacteristic
115C22×D4×C73—21no—
116C22×D4×C73C2311yescharacteristic
117C23×C4×C73—21no—
118C23×C4×C73—21no—
119C23×C4×C73—21no—
120C23×C4×C73D411yescharacteristic
121C23×C4×C73D411yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C4×Q8×C73—22no—
124C4×Q8×C73—22no—
125C4×Q8×C73—22no—
126C4×Q8×C73D414yes—
127C4×D4×C73—28no—
128C4×D4×C73—28no—
129C4×D4×C73—22no—
130C4×D4×C73—22no—
131C4×D4×C73—22no—
132C4×D4×C73D414yes—
133#117×C73—28no—
134#117×C73—22no—
135#117×C73—22no—
136C2×C4⋊C4×C73—21no—
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73—21no—
141C2×C22⋊C4×C73—21no—
142C2×C22⋊C4×C73—21no—
143C2×C42×C73—28no—
144C2×C42×C73—21no—
145C2×C42×C73—21no—
146C2×C42×C73—21no—
147C2×C42×C73—22no—
148C2×C42×C73—22no—
149C2×C42×C73D411yescharacteristic
150C2×C42×C73D411yescharacteristic
151C2×C42×C73C2311yescharacteristic
152C2×C42×C73C2311yescharacteristic
153C2×Dic146—21no—
154C2×Dic146—21no—
155C2×Dic146—21no—
156C2×Dic146—21no—
157C2×Dic146—21no—
158C2×Dic146C22×C412yes—
159C22×Dic73—21no—
160C22×Dic73—21no—
161C22×Dic73—21no—
162C22×Dic73—21no—
163#11924018—28no—
164#11924016—28no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831—21no—
169C2×#10596831—21no—
170C2×#10596831—21no—
171C2×#10596831—21no—
172C2×#10596831—21no—
173C2×#10596831—21no—
174C2×#10596831—21no—
175C2×#10596831C22×C412yes—
176C2×#10596831C22×C412yes—
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73—21no—
180C4⋊Dic73—21no—
181C4⋊Dic73—21no—
182C4⋊Dic73C22×C412yes—
183#11924007—24no—
184#11924007—42no—
185#11924007—42no—
186C22⋊Dic73—24no—
187C22⋊Dic73—42no—
188C4×Dic73—42no—
189C4×Dic73—42no—
190C24×C73—21no—
191C24×C73C2×D411yescharacteristic
192#41×C73—28no—
193#41×C73—28no—
194#41×C73—28no—
195#41×C73—28no—
196C2×Q8×C73—21no—
197C2×Q8×C73—21no—
198C2×Q8×C73—21no—
199C2×Q8×C73C22×C412yes—
200C2×Q8×C73C2×D412yes—
201C2×Q8×C73#4112yes—
202C2×D4×C73—24no—
203C2×D4×C73—24no—
204C2×D4×C73—24no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73C22×C412yes—
209C2×D4×C73C2×D412yes—
210C2×D4×C73#4112yes—
211C22×C4×C73—24no—
212C22×C4×C73—24no—
213C22×C4×C73—21no—
214C22×C4×C73—24no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—24no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—22no—
223C22×C4×C73—22no—
224C22×C4×C73—24no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—41no—
229C22×C4×C73—42no—
230C22×C4×C73—42no—
231C22×C4×C73—42no—
232C22×C4×C73—42no—
233C22×C4×C73C22×C412yes—
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D411yescharacteristic
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73#4112yes—
240C22×C4×C73C2411yescharacteristic
241C4⋊C4×C73—24no—
242C4⋊C4×C73—24no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73C2×D412yes—
246C4⋊C4×C73C2×D412yes—
247C22⋊C4×C73—24no—
248C22⋊C4×C73—24no—
249C22⋊C4×C73—24no—
250C42×C73—24no—
251C42×C73—24no—
252C42×C73—22no—
253C42×C73—24no—
254C42×C73—22no—
255C42×C73—21no—
256C42×C73—21no—
257C42×C73C2×D412yes—
258C42×C73C2×D412yes—
259C23×C73—22no—
260C23×C73—21no—
261C23×C73—22no—
262C23×C73—21no—
263C23×C73—22no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73C4×D412yes—
273C23×C73C22×D411yescharacteristic
274Q8×C73—22no—
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73C4×D414yes—
278D4×C73—216no—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—22no—
282D4×C73C4×D414yes—
283C2×C4×C73—216no—
284C2×C4×C73—22no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
288C2×C4×C73—21no—
289C2×C4×C73—22no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—21no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—44no—
303C2×C4×C73—48no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—44no—
309C2×C4×C73—48no—
310C2×C4×C73C4×D412yes—
311C2×C4×C73#12012yes—
312C2×C4×C73#12012yes—
313C2×C4×C73#13512yes—
314C2×C4×C73#13512yes—
315C2×C4×C73#13712yes—
316C2×C4×C73C23×C411yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73C2×#4111yescharacteristic
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—41no—
325C2×Dic73—41no—
326C2×Dic73—41no—
327C2×Dic73—41no—
328C2×Dic73—41no—
329C2×Dic73—41no—
330C2×Dic73—41no—
331C2×Dic73—41no—
332C2×Dic73—41no—
333C2×Dic73—41no—
334Dic146—22no—
335Dic146—22no—
336Dic146—41no—
337Dic146—41no—
338#10596831—22no—
339#10596831—22no—
340#10596831—41no—
341#10596831—41no—
342C22×C73—22no—
343C22×C73—22no—
344C22×C73—22no—
345C22×C73—24no—
346C22×C73—41no—
347C22×C73—42no—
348C22×C73—41no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73—41no—
353C22×C73—42no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73C2×C4×D411yescharacteristic
357C22×C73C2×#12011yescharacteristic
358C22×C73#52511yescharacteristic
359C22×C73C2×#13511yescharacteristic
360C22×C73C2×#13511yescharacteristic
361C22×C73C2×#13711yescharacteristic
362C22×C73#57511yescharacteristic
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—22no—
366C4×C73—24no—
367C4×C73—41no—
368C4×C73—42no—
369C4×C73—42no—
370C4×C73#45214yescomplemented
371C4×C73C2×C4×D411yescharacteristic
372C4×C73C2×C4×D411yescharacteristic
373C4×C73#52511yescharacteristic
374C4×C73#52511yescharacteristic
375Dic73—42no—
376Dic73—42no—
377Dic73—81no—
378Dic73—81no—
379C4×#452—731nomaximal, Sylow
380C2×C73—42no—
381C2×C73—44no—
382C2×C73C4×#12011yescharacteristic
383C2×C73C4×#13511yescharacteristic
384C2×C73C4×#13711yescharacteristic
385C2×C73C2×#45211yescharacteristic
386C2×C73#300211yescharacteristic
387C2×C73#310211yescharacteristic
388C2×C73#310711yescharacteristic
389C2×C4×#41D7311yescharacteristic
390C2×#452—731no—
391C2×C4×Q16—731no—
392C2×C4×SD16—731no—
393C4×C22⋊Q8—731no—
394#1878—731no—
395#1877—731no—
396#1873—731no—
397#1865—731no—
398#1862—731no—
399#1854—731no—
400#1788—731no—
401C4×#103—731no—
402C4×#102—731no—
403C4×C22⋊C8—731no—
404C73C4×#45211yescharacteristic, complemented, Sylow
405C22×#41C2×D7311yescharacteristic
406C22×Q16—731no—
407C22×SD16—731no—
408C2×C22⋊Q8—731no—
409C4×#41—24no—
410C4×#41—24no—
411C2×C4×Q8—731no—
412C2×C4×Q8C2×D7311yescharacteristic
413C2×C4×Q8C2×D7311yescharacteristic
414C2×C4×D4—21no—
415C2×C4×D4—21no—
416C2×C4×D4C2×D7311yescharacteristic
417C2×C4×D4C2×D7311yescharacteristic
418C2×#117—21no—
419C2×#117C2×D7311yescharacteristic
420C22×C42—21no—
421C22×C42C2×D7311yescharacteristic
422#452—738no—
423C4×Q16—1464no—
424C4×SD16—1464no—
425C2×#107—731no—
426C2×#106—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×#103—731no—
431C2×#103—731no—
432C2×#102—731no—
433C2×#102—731no—
434C2×#102—731no—
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×C4×C8—731no—
438C2×C4×C8—731no—
439#391—731no—
440#389—731no—
441#387—1461no—
442#385—1461no—
443#380—731no—
444C4×C4⋊C4—731no—
445C4×C4⋊C4—1461no—
446C4×C22⋊C4—1461no—
447#340—731no—
448#340—731no—
449#340—731no—
450#340—731no—
451#336—731no—
452#336—731no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41C4×D7314yes—
459C22×Q8—731no—
460C22×Q8C22×D7311yescharacteristic
461C22×D4—21no—
462C22×D4C22×D7311yescharacteristic
463C23×C4—21no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C22⋊D7311yescharacteristic
467C23×C4C22⋊D7311yescharacteristic
468C23×C4C22×D7311yescharacteristic
469C2×Q16—734no—
470C2×Q16—1462no—
471C2×Q16—1462no—
472C2×SD16—734no—
473C2×SD16—1462no—
474C2×SD16—1462no—
475C22×C8—731no—
476C22×C8—731no—
477C22×C8—731no—
478C22×C8—731no—
479C22⋊Q8—734no—
480C22⋊Q8—1462no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—1462no—
485C4×Q8—1462no—
486C4×Q8C22⋊D7314yes—
487C4×D4—28no—
488C4×D4—28no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4C22⋊D7314yes—
493#117—28no—
494#117—22no—
495#117—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—1461no—
502C2×C4⋊C4—1461no—
503C2×C4⋊C4—1461no—
504C2×C4⋊C4C22×D7311yescharacteristic
505C2×C4⋊C4C22×D7311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C42—28no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—21no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—1461no—
518C2×C42—1461no—
519C2×C42C22⋊D7311yescharacteristic
520C2×C42C22⋊D7311yescharacteristic
521C2×C42C22×D7311yescharacteristic
522C2×C42C22×D7311yescharacteristic
523#107—1462no—
524#106—1462no—
525#103—734no—
526#103—1462no—
527#103—1462no—
528#103—1462no—
529#103—1462no—
530#102—734no—
531#102—1462no—
532#102—1462no—
533C22⋊C8—734no—
534C22⋊C8—1462no—
535C4×C8—1462no—
536C4×C8—1462no—
537#95—1461no—
538#95—1461no—
539#95—1461no—
540#95—1461no—
541#95—1461no—
542C24—21no—
543C24C2×C22⋊D7311yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—732no—
552C2×Q8—1461no—
553C2×Q8—1461no—
554C2×Q8—1461no—
555C2×Q8—1461no—
556C2×Q8—1461no—
557C2×Q8C2×C4×D7312yes—
558C2×Q8C2×C22⋊D7312yes—
559C2×Q8#1192402812yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C2×C4×D7312yes—
567C2×D4C2×C22⋊D7312yes—
568C2×D4#1192402812yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4C2×C4×D7312yes—
596C22×C4C2×C22⋊D7311yescharacteristic
597C22×C4C2×C22⋊D7311yescharacteristic
598C22×C4C2×C22⋊D7311yescharacteristic
599C22×C4C2×C22⋊D7311yescharacteristic
600C22×C4C2×C22⋊D7311yescharacteristic
601C22×C4#1192402812yes—
602C22×C4C23×D7311yescharacteristic
603Q16—1468no—
604SD16—1468no—
605C2×C8—732no—
606C2×C8—732no—
607C2×C8—1461no—
608C2×C8—1461no—
609C2×C8—1461no—
610C2×C8—1461no—
611C2×C8—1461no—
612C2×C8—1461no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—2922no—
622C4⋊C4—2922no—
623C4⋊C4—732no—
624C4⋊C4—1461no—
625C4⋊C4—1461no—
626C4⋊C4—1461no—
627C4⋊C4—1461no—
628C4⋊C4—1464no—
629C4⋊C4—1461no—
630C4⋊C4C2×C22⋊D7312yes—
631C4⋊C4C2×C22⋊D7312yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—2922no—
636C22⋊C4—1464no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—24no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—2922no—
645C42—2922no—
646C42C2×C22⋊D7312yes—
647C42C2×C22⋊D7312yes—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C4×C22⋊D7312yes—
662C23C22×C22⋊D7311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—2921no—
667Q8—2921no—
668Q8—1462no—
669Q8—1462no—
670Q8C4×C22⋊D7314yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4C4×C22⋊D7314yes—
676C2×C4—216no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—44no—
702C2×C4—48no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—1462no—
714C2×C4—1462no—
715C2×C4C4×C22⋊D7312yes—
716C2×C4#1455656012yes—
717C2×C4#1455656012yes—
718C2×C4#1455661112yes—
719C2×C4#1455661112yes—
720C2×C4#1455662112yes—
721C2×C4C22×C4×D7311yescharacteristic
722C2×C4C22×C22⋊D7311yescharacteristic
723C2×C4C22×C22⋊D7311yescharacteristic
724C2×C4C2×#1192402811yescharacteristic
725C2×C4C2×#1192402811yescharacteristic
726C2×C4C2×#1192402811yescharacteristic
727C8—2921no—
728C8—2921no—
729C8—1462no—
730C8—1462no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—24no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22C2×C4×C22⋊D7311yescharacteristic
746C22C2×#1455656011yescharacteristic
747C22#1798909811yescharacteristic
748C22C2×#1455661111yescharacteristic
749C22C2×#1455661111yescharacteristic
750C22C2×#1455662111yescharacteristic
751C22#1798938511yescharacteristic
752C4—22no—
753C4—22no—
754C4—22no—
755C4—24no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—2922no—
760C4—2922no—
761C4—5841no—
762C4—5841no—
763C4#1798874914yesdirect product factor
764C4C2×C4×C22⋊D7311yescharacteristic
765C4C2×C4×C22⋊D7311yescharacteristic
766C4#1798909811yescharacteristic
767C4#1798909811yescharacteristic
768C2—42no—
769C2—44no—
770C2C4×#1455656011yescharacteristic
771C2C4×#1455661111yescharacteristic
772C2C4×#1455662111yescharacteristic
773C2C2×#1798874911yescharacteristic
774C2#2261914911yescharacteristic
775C2#2261994911yescharacteristic
776C2#2262000211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC2×C4×#41×C73C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenterC2×C4×#41D73
hypocenterC73C4×#452
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11924018C2semidirect
3. C2×C4×#11924016C2semidirect
4. C4×#14556570C2semidirect
5. #22610272C2semidirect
6. #22610265C2semidirect
7. #22610243C2semidirect
8. #22610199C2semidirect
9. #22610178C2semidirect
10. #22610130C2semidirect
12. C4×#14556515C2semidirect
13. C4×#14556512C2semidirect
14. C4×C22⋊#10596831C2semidirect
20. #17988749C4direct (N × H)
67. C2×#11924018C2×C4semidirect
70. C2×#11924016C2×C4semidirect
76. #14556570C2×C4semidirect
93. #14556515C2×C4semidirect
98. #14556512C2×C4semidirect
100. C22⋊#10596831C2×C4semidirect
370. C4×C73#452semidirect
404. C73C4×#452semidirect
763. C4#17988749direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179887492
C2×C4×#119240182
C2×C4×#119240162
C4×#145565702
#226102722
#226102652
#226102432
#226101992
#226101782
#226101302
#226098712
C4×#145565152
C4×#145565122
C4×C22⋊#105968312
C2×C4×#41×C732
C4×#45273