Finite Group Databasebeta

← C2×#22612837 #33245276

Subgroups — C2×#22612837 #33245276

Order 18688.

4198 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D73C211yesmaximal, characteristic
2C22×#14556551C211yesmaximal, characteristic
3C22×#14556551C211yesmaximal, characteristic
4#22612837C2116yesmaximal, direct product factor
5C2×#17988484C211yesmaximal, characteristic, complemented
6C2×#17988482C211yesmaximal, characteristic, complemented
7C2×#17988462C211yesmaximal, characteristic, complemented
8C2×#17988461C211yesmaximal, characteristic, complemented
9C2×#17988458C211yesmaximal, characteristic, complemented
10C2×#17988451C211yesmaximal, characteristic, complemented
11C2×#17988445C211yesmaximal, characteristic, complemented
12C2×#17988444C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
14C22×#14556498C211yesmaximal, characteristic, complemented
15C2×#95×D73C211yesmaximal, characteristic, complemented
16C2×#385×C73C211yesmaximal, characteristic, complemented
17C23×C22⋊D73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C24×Dic73C2211yescharacteristic
20C23×C4×D73C2211yescharacteristic
21C23×C4×D73C2211yescharacteristic
22C23×C4×D73C2211yescharacteristic
23C2×C4×C22⋊D73—28no—
24C2×C4×C22⋊D73C2218yes—
25C2×#14556551—28no—
26C2×#14556551C4116yescomplemented
27C2×#14556551C2218yes—
28C2×#14556551C2218yes—
29C22×C4⋊Dic73C2211yescharacteristic
30C22×C4⋊Dic73C2211yescharacteristic
31C22×#11924007C2211yescharacteristic
32C22×#11924007C2211yescharacteristic
33C22×#11924007C2211yescharacteristic
34C22×#11924007C2211yescharacteristic
35C22×#11924007C2211yescharacteristic
36C22×C22⋊Dic73C2211yescharacteristic
37C22×#11924005C2211yescharacteristic
38C22×#11924005C2211yescharacteristic
39C22×#11924005C2211yescharacteristic
40C22×C4×Dic73C2211yescharacteristic
41C22×C4×Dic73C2211yescharacteristic
42C22×C4×Dic73C2211yescharacteristic
43#17988484C2218yescomplemented
44#17988482C2218yescomplemented
45#17988462C2218yescomplemented
46#17988461C2218yescomplemented
47#17988458C2218yescomplemented
48#17988451C2218yescomplemented
49#17988445C2218yescomplemented
50#17988444C2218yescomplemented
51C4⋊C4×Dic73C2218yescomplemented
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C2×#14556498C2218yescomplemented
61#95×D73C2218yescomplemented
62C24×C4×C73C2211yescharacteristic
63C22×C4⋊C4×C73C2211yescharacteristic
64C22×C4⋊C4×C73C2211yescharacteristic
65C22×C22⋊C4×C73C2211yescharacteristic
66C22×C22⋊C4×C73C2211yescharacteristic
67#385×C73C2218yescomplemented
68C2×#95×C73C2211yescharacteristic
69C2×#95×C73C2211yescharacteristic
70C24×D73C2311yescharacteristic
71C22×C22⋊D73C2×C418yes—
72C22×C22⋊D73D418yes—
73C22×C22⋊D73Q818yes—
74C22×C22⋊D73C2314yes—
75C23×Dic73—24no—
76C23×Dic73—24no—
77C23×Dic73—42no—
78C23×Dic73—42no—
79C23×Dic73—42no—
80C23×Dic73C2×C418yescomplemented
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2311yescharacteristic
84C23×Dic73C2314yes—
85C23×Dic73C2311yescharacteristic
86C23×Dic73C2311yescharacteristic
87C23×Dic73C2311yescharacteristic
88C23×Dic73C2314yes—
89C23×Dic73C2311yescharacteristic
90C22×C4×D73—24no—
91C22×C4×D73—24no—
92C22×C4×D73—24no—
93C22×C4×D73—24no—
94C22×C4×D73—42no—
95C22×C4×D73—42no—
96C22×C4×D73—42no—
97C22×C4×D73—42no—
98C22×C4×D73C2×C418yescomplemented
99C22×C4×D73C2314yes—
100C22×C4×D73C2314yes—
101C22×C4×D73C2314yes—
102C4×C22⋊D73—232no—
103#14556551—232no—
104#14556551C2×C4164yescomplemented
105C2×C4⋊Dic73—24no—
106C2×C4⋊Dic73—42no—
107C2×C4⋊Dic73C2314yes—
108C2×C4⋊Dic73C2314yes—
109C2×#11924007—24no—
110C2×#11924007—24no—
111C2×#11924007—42no—
112C2×#11924007—42no—
113C2×#11924007C2×C418yescomplemented
114C2×#11924007C2314yes—
115C2×#11924007C2314yes—
116C2×#11924007C2314yes—
117C2×#11924007C2314yes—
118C2×#11924007C2314yes—
119C2×C22⋊Dic73—24no—
120C2×C22⋊Dic73C2314yes—
121C2×#11924005—24no—
122C2×#11924005—24no—
123C2×#11924005C2×C418yescomplemented
124C2×#11924005C2314yes—
125C2×#11924005C2314yes—
126C2×#11924005C2314yes—
127C2×C4×Dic73—24no—
128C2×C4×Dic73—24no—
129C2×C4×Dic73C2×C418yescomplemented
130C2×C4×Dic73C2314yes—
131C2×C4×Dic73C2314yes—
132C2×C4×Dic73C2314yes—
133#14556498C2314yes—
134#14556498C2314yes—
135#14556498C2314yes—
136#14556498C2314yes—
137#14556498C2314yes—
138#14556498C2314yes—
139#14556498C2314yes—
140#14556498C2314yes—
141C25×C73C2311yescharacteristic
142C23×C4×C73—24no—
143C23×C4×C73—24no—
144C23×C4×C73—42no—
145C23×C4×C73C2311yescharacteristic
146C23×C4×C73C2311yescharacteristic
147C23×C4×C73C2311yescharacteristic
148C23×C4×C73C2314yes—
149C23×C4×C73C2311yescharacteristic
150C23×C4×C73C2311yescharacteristic
151C23×C4×C73C2311yescharacteristic
152C2×C4⋊C4×C73—24no—
153C2×C4⋊C4×C73—42no—
154C2×C4⋊C4×C73C2314yes—
155C2×C4⋊C4×C73C2314yes—
156C2×C22⋊C4×C73—24no—
157C2×C22⋊C4×C73C2×C418yescomplemented
158C2×C22⋊C4×C73C2314yes—
159C2×C22⋊C4×C73C2314yes—
160#95×C73C2314yes—
161#95×C73C2314yes—
162C23×D73—22no—
163C23×D73—22no—
164C23×D73—22no—
165C23×D73—22no—
166C23×D73C22×C414yes—
167C23×D73C2×D414yes—
168C23×D73C2×Q814yes—
169C23×D73C2412yes—
170C2×C22⋊D73C4⋊C4164yescomplemented
171C2×C22⋊D73C22×C4116yes—
172C2×C22⋊D73C2×D4116yes—
173C2×C22⋊D73C2×Q8116yes—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—22no—
179C22×Dic73—22no—
180C22×Dic73—22no—
181C22×Dic73—22no—
182C22×Dic73—22no—
183C22×Dic73—28no—
184C22×Dic73—22no—
185C22×Dic73—22no—
186C22×Dic73—22no—
187C22×Dic73—22no—
188C22×Dic73—22no—
189C22×Dic73—22no—
190C22×Dic73—28no—
191C22×Dic73—416no—
192C22×Dic73—44no—
193C22×Dic73—44no—
194C22×Dic73—44no—
195C22×Dic73—416no—
196C22×Dic73C22×C414yes—
197C22×Dic73C22×C414yes—
198C22×Dic73C22×C414yes—
199C22×Dic73C22×C4116yescomplemented
200C22×Dic73C2×D414yes—
201C22×Dic73C2×Q814yes—
202C22×Dic73#4114yes—
203C22×Dic73C2412yes—
204C22×Dic73C2412yes—
205C22×Dic73C2412yes—
206C22×Dic73C2412yes—
207C22×Dic73C2412yes—
208C22×Dic73C2412yes—
209C22×Dic73C2412yes—
210C2×C4×D73—28no—
211C2×C4×D73—28no—
212C2×C4×D73—28no—
213C2×C4×D73—28no—
214C2×C4×D73—416no—
215C2×C4×D73—44no—
216C2×C4×D73—44no—
217C2×C4×D73—44no—
218C2×C4×D73—44no—
219C2×C4×D73—416no—
220C2×C4×D73—416no—
221C2×C4×D73C22×C4116yescomplemented
222C4⋊Dic73—28no—
223C4⋊Dic73—44no—
224#11924007—28no—
225#11924007—28no—
226#11924007—44no—
227#11924007—44no—
228#11924007C22×C4116yescomplemented
229C22⋊Dic73—28no—
230#11924005—28no—
231#11924005—28no—
232#11924005C22×C4116yescomplemented
233C4×Dic73—28no—
234C4×Dic73—28no—
235C4×Dic73C22×C4116yescomplemented
236C24×C73—22no—
237C24×C73—22no—
238C24×C73—22no—
239C24×C73—22no—
240C24×C73C22×C414yes—
241C24×C73C2×D414yes—
242C24×C73C2×Q814yes—
243C24×C73C2412yes—
244C24×C73C2411yescharacteristic
245C22×C4×C73—22no—
246C22×C4×C73—22no—
247C22×C4×C73—22no—
248C22×C4×C73—22no—
249C22×C4×C73—22no—
250C22×C4×C73—22no—
251C22×C4×C73—22no—
252C22×C4×C73—22no—
253C22×C4×C73—22no—
254C22×C4×C73—28no—
255C22×C4×C73—22no—
256C22×C4×C73—22no—
257C22×C4×C73—22no—
258C22×C4×C73—22no—
259C22×C4×C73—22no—
260C22×C4×C73—22no—
261C22×C4×C73—28no—
262C22×C4×C73—44no—
263C22×C4×C73—416no—
264C22×C4×C73C22×C414yes—
265C22×C4×C73C22×C414yes—
266C22×C4×C73#4114yes—
267C22×C4×C73C2412yes—
268C22×C4×C73C2412yes—
269C22×C4×C73C2412yes—
270C22×C4×C73C2412yes—
271C22×C4×C73C2412yes—
272C22×C4×C73C2412yes—
273C4⋊C4×C73—28no—
274C4⋊C4×C73—44no—
275C22⋊C4×C73—28no—
276C22⋊C4×C73C22×C4116yescomplemented
277C23×C73—28no—
278C23×C73—28no—
279C23×C73—28no—
280C23×C73—28no—
281C23×C73—28no—
282C23×C73—28no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73C2×C4⋊C4116yes—
288C23×C73C23×C414yes—
289C23×C73C23×C412yes—
290C23×C73C22×D414yes—
291C23×C73C22×D412yes—
292C23×C73C22×Q814yes—
293C23×C73C22×Q812yes—
294C23×C73C2×#4112yes—
295C23×C73C2×#4112yes—
296C23×C73H(5,𝔽2)12yes—
297C23×C73H(5,𝔽2)12yes—
298C23×C73C2511yescharacteristic
299C22×D73—28no—
300C22×D73—28no—
301C22×D73—28no—
302C22×D73—28no—
303C22×D73—28no—
304C22×D73—28no—
305C22×D73—22no—
306C22×D73—22no—
307C22×D73—22no—
308C22×D73—22no—
309C22×D73C2×C4⋊C4116yes—
310C22×D73C23×C414yes—
311C22×D73C22×D414yes—
312C22×D73C22×Q814yes—
313C2×C4×C73—28no—
314C2×C4×C73—28no—
315C2×C4×C73—28no—
316C2×C4×C73—22no—
317C2×C4×C73—22no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—416no—
332C2×C4×C73—44no—
333C2×C4×C73—44no—
334C2×C4×C73—44no—
335C2×C4×C73C23×C414yes—
336C2×C4×C73C23×C414yes—
337C2×C4×C73C2×#4114yes—
338C22⋊D73C2×C4⋊C4164yescomplemented
339C2×Dic73—28no—
340C2×Dic73—28no—
341C2×Dic73—28no—
342C2×Dic73—22no—
343C2×Dic73—22no—
344C2×Dic73—22no—
345C2×Dic73—22no—
346C2×Dic73—22no—
347C2×Dic73—22no—
348C2×Dic73—22no—
349C2×Dic73—22no—
350C2×Dic73—22no—
351C2×Dic73—22no—
352C2×Dic73—22no—
353C2×Dic73—22no—
354C2×Dic73—22no—
355C2×Dic73—22no—
356C2×Dic73—22no—
357C2×Dic73—416no—
358C2×Dic73—416no—
359C2×Dic73—44no—
360C2×Dic73—44no—
361C2×Dic73—44no—
362C2×Dic73C2×C4⋊C4116yes—
363C2×Dic73C23×C414yes—
364C2×Dic73C23×C414yes—
365C2×Dic73C23×C414yes—
366C2×Dic73C22×D414yes—
367C2×Dic73C22×Q814yes—
368C2×Dic73C2×#4114yes—
369C4×D73—416no—
370C4×D73—416no—
371C4×D73—416no—
372C22×C73—232no—
373C22×C73—24no—
374C22×C73—24no—
375C22×C73—24no—
376C22×C73—24no—
377C22×C73—24no—
378C22×C73—24no—
379C22×C73C22×C4⋊C418yes—
380C22×C73C22×C4⋊C414yes—
381C22×C73C4×#4114yes—
382C22×C73#51814yes—
383C22×C73#54614yes—
384C22×C73#54614yes—
385C22×C73#55414yes—
386C22×C73#55414yes—
387C22×C73C24×C411yescharacteristic
388C22×C73C23×D411yescharacteristic
389C22×C73C23×Q811yescharacteristic
390C22×C73C22×#4111yescharacteristic
391C22×C73C22×#4111yescharacteristic
392C22×C73C2×H(5,𝔽2)11yescharacteristic
393C22×C73C2×H(5,𝔽2)11yescharacteristic
394C2×D73—232no—
395C2×D73—24no—
396C2×D73—24no—
397C2×D73—24no—
398C2×D73—24no—
399C2×D73—24no—
400C2×D73—24no—
401C2×D73C22×C4⋊C418yes—
402C4×C73—24no—
403C4×C73—24no—
404C4×C73—24no—
405C4×C73—42no—
406C4×C73—42no—
407C4×C73—42no—
408Dic73—24no—
409Dic73—24no—
410Dic73—24no—
411Dic73—42no—
412Dic73—42no—
413Dic73—42no—
414Dic73C22×C4⋊C418yes—
415C2×#2349—731nomaximal, Sylow
416C2×C73—28no—
417C2×C73#234918yescomplemented
418C2×C73C23×C4⋊C411yescharacteristic
419C2×C73C2×C4×#4111yescharacteristic
420C2×C73C2×#51811yescharacteristic
421C2×C73C2×#54611yescharacteristic
422C2×C73C2×#54611yescharacteristic
423C2×C73C2×#55411yescharacteristic
424C2×C73C2×#55411yescharacteristic
425D73—28no—
426C22×C4×D4—731no—
427C22×C4×D4—731no—
428C22×C4×D4—731no—
429#2349—7316no—
430C2×#389—731no—
431C2×#389—731no—
432C2×#385—731no—
433C2×#385—731no—
434C2×#385—731no—
435C2×#385D7311yescharacteristic, complemented
436C2×#382—731no—
437C2×#380—731no—
438C2×#380—731no—
439C2×C4×C4⋊C4—731no—
440C22×#95—731no—
441C22×#95—731no—
442C73C2×#234911yescharacteristic, complemented, Sylow
443C23×D4—731no—
444C24×C4—731no—
445C24×C4—731no—
446C24×C4—731no—
447C24×C4—731no—
448C24×C4—731no—
449C24×C4C2×D7311yescharacteristic
450C2×C4×D4—738no—
451C2×C4×D4—7316no—
452C2×C4×D4—738no—
453C2×C4×D4—738no—
454C2×C4×D4—1468no—
455C2×C4×D4—1468no—
456C22×C4⋊C4—731no—
457C22×C4⋊C4—731no—
458C22×C4⋊C4—731no—
459C22×C4⋊C4—731no—
460C22×C4⋊C4—731no—
461C22×C4⋊C4—731no—
462C22×C4⋊C4—731no—
463C22×C4⋊C4C2×D7311yescharacteristic
464C22×C4⋊C4C2×D7311yescharacteristic
465C22×C22⋊C4—731no—
466C22×C22⋊C4—731no—
467C22×C22⋊C4—731no—
468C22×C22⋊C4—731no—
469C22×C22⋊C4C2×D7311yescharacteristic
470C22×C22⋊C4C2×D7311yescharacteristic
471C22×C42—731no—
472C22×C42—731no—
473C22×C42—731no—
474#389—738no—
475#389—738no—
476#385—738no—
477#385—738no—
478#385—738no—
479#385C2×D7318yescomplemented
480#382—738no—
481#380—738no—
482#380—738no—
483C4×C4⋊C4—738no—
484C2×#95—738no—
485C2×#95—731no—
486C2×#95—731no—
487C2×#95—731no—
488C2×#95—731no—
489C2×#95—731no—
490C2×#95—731no—
491C2×#95—731no—
492C2×#95—731no—
493C2×#95—738no—
494C2×#95C2×D7311yescharacteristic
495C2×#95C2×D7311yescharacteristic
496C25—731no—
497C25C22×D7311yescharacteristic
498C22×D4—738no—
499C22×D4—738no—
500C22×D4—738no—
501C22×D4—734no—
502C23×C4—24no—
503C23×C4—24no—
504C23×C4—42no—
505C23×C4—2922no—
506C23×C4—2922no—
507C23×C4—2922no—
508C23×C4—2922no—
509C23×C4—2922no—
510C23×C4—2922no—
511C23×C4—2922no—
512C23×C4—738no—
513C23×C4—734no—
514C23×C4—738no—
515C23×C4—734no—
516C23×C4—734no—
517C23×C4—734no—
518C23×C4—734no—
519C23×C4—731no—
520C23×C4—731no—
521C23×C4—731no—
522C23×C4—731no—
523C23×C4—731no—
524C23×C4—731no—
525C23×C4—731no—
526C23×C4—1464no—
527C23×C4—1464no—
528C23×C4—1464no—
529C23×C4—1464no—
530C23×C4—1464no—
531C23×C4—1464no—
532C23×C4C22×D7311yescharacteristic
533C23×C4C22×D7311yescharacteristic
534C23×C4C22×D7311yescharacteristic
535C23×C4C22×D7314yes—
536C23×C4C22×D7311yescharacteristic
537C23×C4C22×D7311yescharacteristic
538C23×C4C22×D7311yescharacteristic
539C4×D4—7364no—
540C4×D4—14632no—
541C4×D4—14632no—
542C2×C4⋊C4—24no—
543C2×C4⋊C4—42no—
544C2×C4⋊C4—2922no—
545C2×C4⋊C4—2922no—
546C2×C4⋊C4—2922no—
547C2×C4⋊C4—734no—
548C2×C4⋊C4—734no—
549C2×C4⋊C4—734no—
550C2×C4⋊C4—738no—
551C2×C4⋊C4—734no—
552C2×C4⋊C4—734no—
553C2×C4⋊C4—734no—
554C2×C4⋊C4—734no—
555C2×C4⋊C4—1464no—
556C2×C4⋊C4—1464no—
557C2×C4⋊C4—1464no—
558C2×C4⋊C4C22×D7314yes—
559C2×C4⋊C4C22×D7314yes—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—738no—
562C2×C22⋊C4—734no—
563C2×C22⋊C4—734no—
564C2×C22⋊C4—734no—
565C2×C22⋊C4—734no—
566C2×C22⋊C4—1464no—
567C2×C22⋊C4—1464no—
568C2×C22⋊C4—1464no—
569C2×C22⋊C4C4×D7318yescomplemented
570C2×C22⋊C4C22×D7314yes—
571C2×C22⋊C4C22×D7314yes—
572C2×C42—738no—
573C2×C42—734no—
574C2×C42—734no—
575C2×C42—734no—
576C2×C42—1464no—
577C2×C42—1464no—
578#95—734no—
579#95—734no—
580#95—734no—
581#95—734no—
582#95—734no—
583#95—734no—
584#95—734no—
585#95—734no—
586#95C22×D7314yes—
587#95C22×D7314yes—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—734no—
593C24—734no—
594C24—734no—
595C24—732no—
596C24—1462no—
597C24—1462no—
598C24—1462no—
599C24—1462no—
600C24C2×C4×D7314yes—
601C24D4×D7314yes—
602C24Q8×D7314yes—
603C24C23×D7312yes—
604C24C23×D7311yescharacteristic
605C2×D4—7364no—
606C2×D4—7316no—
607C2×D4—7316no—
608C2×D4—7316no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—28no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—28no—
626C22×C4—44no—
627C22×C4—416no—
628C22×C4—29216no—
629C22×C4—2924no—
630C22×C4—2924no—
631C22×C4—2924no—
632C22×C4—29216no—
633C22×C4—2924no—
634C22×C4—29216no—
635C22×C4—29216no—
636C22×C4—2924no—
637C22×C4—2924no—
638C22×C4—2924no—
639C22×C4—29216no—
640C22×C4—7316no—
641C22×C4—7316no—
642C22×C4—734no—
643C22×C4—734no—
644C22×C4—734no—
645C22×C4—732no—
646C22×C4—734no—
647C22×C4—734no—
648C22×C4—734no—
649C22×C4—732no—
650C22×C4—732no—
651C22×C4—732no—
652C22×C4—732no—
653C22×C4—732no—
654C22×C4—732no—
655C22×C4—1468no—
656C22×C4—1468no—
657C22×C4—1468no—
658C22×C4—1468no—
659C22×C4—1462no—
660C22×C4—1462no—
661C22×C4—1462no—
662C22×C4—1468no—
663C22×C4—1462no—
664C22×C4—1462no—
665C22×C4—1462no—
666C22×C4—1462no—
667C22×C4—1462no—
668C22×C4—1462no—
669C22×C4—1468no—
670C22×C4—1462no—
671C22×C4—1462no—
672C22×C4—1462no—
673C22×C4—1462no—
674C22×C4—1462no—
675C22×C4—1462no—
676C22×C4C2×C4×D7314yes—
677C22×C4C2×C4×D7314yes—
678C22×C4#1192402714yes—
679C22×C4C23×D7312yes—
680C22×C4C23×D7312yes—
681C22×C4C23×D7312yes—
682C22×C4C23×D7312yes—
683C22×C4C23×D7312yes—
684C22×C4C23×D7312yes—
685C4⋊C4—28no—
686C4⋊C4—44no—
687C4⋊C4—2924no—
688C4⋊C4—2924no—
689C4⋊C4—2924no—
690C4⋊C4—7316no—
691C4⋊C4—1468no—
692C4⋊C4—1468no—
693C4⋊C4—1468no—
694C22⋊C4—28no—
695C22⋊C4—7316no—
696C22⋊C4—1468no—
697C22⋊C4—1468no—
698C22⋊C4—1468no—
699C22⋊C4C2×C4×D73116yescomplemented
700C42—7316no—
701C42—1468no—
702C42—1468no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—734no—
714C23—734no—
715C23—734no—
716C23—7316no—
717C23—1462no—
718C23—1462no—
719C23—1462no—
720C23—1462no—
721C23—1468no—
722C23—1468no—
723C23—1468no—
724C23—1468no—
725C23—1468no—
726C23—1468no—
727C23C4⋊C4×D73116yes—
728C23C22×C4×D7314yes—
729C23C22×C4×D7312yes—
730C23C2×D4×D7314yes—
731C23C2×D4×D7312yes—
732C23C2×Q8×D7314yes—
733C23C2×Q8×D7312yes—
734C23#41×D7312yes—
735C23C2×#1192402712yes—
736C23#1455663612yes—
737C23#1455663712yes—
738C23C24×D7311yescharacteristic
739D4—7364no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—28no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—416no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—29216no—
763C2×C4—29216no—
764C2×C4—29216no—
765C2×C4—2924no—
766C2×C4—2924no—
767C2×C4—2924no—
768C2×C4—29216no—
769C2×C4—29216no—
770C2×C4—734no—
771C2×C4—734no—
772C2×C4—734no—
773C2×C4—7316no—
774C2×C4—734no—
775C2×C4—734no—
776C2×C4—734no—
777C2×C4—1462no—
778C2×C4—1462no—
779C2×C4—1462no—
780C2×C4—1462no—
781C2×C4—1462no—
782C2×C4—1462no—
783C2×C4—1462no—
784C2×C4—1462no—
785C2×C4—1462no—
786C2×C4—1462no—
787C2×C4—1462no—
788C2×C4—1462no—
789C2×C4—1462no—
790C2×C4—1462no—
791C2×C4—1462no—
792C2×C4—1468no—
793C2×C4—1468no—
794C2×C4—1468no—
795C2×C4C22×C4×D7314yes—
796C2×C4C22×C4×D7314yes—
797C2×C4C2×#1192402714yes—
798C22—232no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—738no—
806C22—14632no—
807C22—1464no—
808C22—1464no—
809C22—1464no—
810C22—1464no—
811C22—1464no—
812C22—1464no—
813C22C2×C4⋊C4×D7318yes—
814C22C2×C4⋊C4×D7314yes—
815C22C4×#1192402714yes—
816C22#1798905914yes—
817C22#1798922414yes—
818C22#1798922914yes—
819C22#1798929114yes—
820C22#1798929514yes—
821C22C23×C4×D7311yescharacteristic
822C22C22×D4×D7311yescharacteristic
823C22C22×Q8×D7311yescharacteristic
824C22C2×#41×D7311yescharacteristic
825C22C22×#1192402711yescharacteristic
826C22C2×#1455663611yescharacteristic
827C22C2×#1455663711yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—2922no—
835C4—2922no—
836C4—2922no—
837C4—738no—
838C4—1464no—
839C4—1464no—
840C4—1464no—
841C2—28no—
842C2—1468no—
843C2#2261283718yesdirect product factor
844C2C22×C4⋊C4×D7311yescharacteristic
845C2C2×C4×#1192402711yescharacteristic
846C2C2×#1798905911yescharacteristic
847C2C2×#1798922411yescharacteristic
848C2C2×#1798922911yescharacteristic
849C2C2×#1798929111yescharacteristic
850C2C2×#1798929511yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#385×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC2×#385D73
hypocenterC73C2×#2349
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. #22612837C2direct (N × H)
5. C2×#17988484C2semidirect
6. C2×#17988482C2semidirect
7. C2×#17988462C2semidirect
8. C2×#17988461C2semidirect
9. C2×#17988458C2semidirect
10. C2×#17988451C2semidirect
11. C2×#17988445C2semidirect
12. C2×#17988444C2semidirect
13. C2×C4⋊C4×Dic73C2semidirect
14. C22×#14556498C2semidirect
15. C2×#95×D73C2semidirect
16. C2×#385×C73C2semidirect
26. C2×#14556551C4semidirect
43. #17988484C22semidirect
44. #17988482C22semidirect
45. #17988462C22semidirect
46. #17988461C22semidirect
47. #17988458C22semidirect
48. #17988451C22semidirect
49. #17988445C22semidirect
50. #17988444C22semidirect
51. C4⋊C4×Dic73C22semidirect
60. C2×#14556498C22semidirect
61. #95×D73C22semidirect
67. #385×C73C22semidirect
80. C23×Dic73C2×C4semidirect
98. C22×C4×D73C2×C4semidirect
104. #14556551C2×C4semidirect
113. C2×#11924007C2×C4semidirect
123. C2×#11924005C2×C4semidirect
129. C2×C4×Dic73C2×C4semidirect
157. C2×C22⋊C4×C73C2×C4semidirect
170. C2×C22⋊D73C4⋊C4semidirect
199. C22×Dic73C22×C4semidirect
221. C2×C4×D73C22×C4semidirect
228. #11924007C22×C4semidirect
232. #11924005C22×C4semidirect
235. C4×Dic73C22×C4semidirect
276. C22⋊C4×C73C22×C4semidirect
338. C22⋊D73C2×C4⋊C4semidirect
417. C2×C73#2349semidirect
435. C2×#385D73semidirect
442. C73C2×#2349semidirect
479. #385C2×D73semidirect
569. C2×C22⋊C4C4×D73semidirect
699. C22⋊C4C2×C4×D73semidirect
843. C2#22612837direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D732
C22×#145565512
#226128372
C2×#179884842
C2×#179884822
C2×#179884622
C2×#179884612
C2×#179884582
C2×#179884512
C2×#179884452
C2×#179884442
C2×C4⋊C4×Dic732
C22×#145564982
C2×#95×D732
C2×#385×C732
C2×#234973