Finite Group Databasebeta

← C2×#11734380 #13522892

Subgroups — C2×#11734380 #13522892

Order 1792.

3678 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6499C211yesmaximal, characteristic, complemented
2C22×#6502C211yesmaximal, characteristic
3C22×#6451C211yesmaximal, characteristic, complemented
4C22×#6448C211yesmaximal, characteristic, complemented
5C2×C7×#394C211yesmaximal, characteristic, complemented
6C2×#89762C211yesmaximal, characteristic, complemented
7C2×#89733C211yesmaximal, characteristic, complemented
8C2×#89719C211yesmaximal, characteristic, complemented
9C2×#89729C211yesmaximal, characteristic, complemented
10C2×#89729C211yesmaximal, characteristic, complemented
11C2×#89723C211yesmaximal, characteristic, complemented
12C2×#89714C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic7C211yesmaximal, characteristic, complemented
14#11734380C2116yesmaximal, direct product factor
15C2×#89445C211yesmaximal, characteristic, complemented
16C2×#89421C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C23×C22⋊D7C2211yescharacteristic
19C23×C22⋊D7C2211yescharacteristic
20C24×Dic7C2211yescharacteristic
21C23×Dic14C2211yescharacteristic
22C23×Dic14C2211yescharacteristic
23C22×C7×C4⋊C4C2211yescharacteristic
24C22×C7×C22⋊C4C2211yescharacteristic
25C22×C7×C22⋊C4C2211yescharacteristic
26C22×C7×C22⋊C4C2211yescharacteristic
27C22×C7×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic7C2211yescharacteristic
29C22×C22⋊Dic7C2211yescharacteristic
30C22×C22⋊Dic7C2211yescharacteristic
31C22×C22⋊Dic7C2211yescharacteristic
32C22×C22⋊Dic7C2211yescharacteristic
33C2×#6502—28no—
34C2×#6502C2218yes—
35C2×#6499—28no—
36C2×#6499C2218yescomplemented
37C22×(C2×D7)⋊C4C2211yescharacteristic
38C22×(C2×D7)⋊C4C2211yescharacteristic
39C22×(C2×D7)⋊C4C2211yescharacteristic
40C22×(C2×D7)⋊C4C2211yescharacteristic
41C22×(C2×D7)⋊C4C2211yescharacteristic
42C22×C4⋊Dic7C2211yescharacteristic
43C22×Dic7⋊C4C2211yescharacteristic
44C22×Dic7⋊C4C2211yescharacteristic
45C22×Dic7⋊C4C2211yescharacteristic
46C22×C4×Dic7C2211yescharacteristic
47C22×C4×Dic7C2211yescharacteristic
48C22×C4×Dic7C2211yescharacteristic
49C22×C4×Dic7C2211yescharacteristic
50C2×#6451—28no—
51C2×#6451C2218yescomplemented
52C2×#6448—28no—
53C2×#6448C2218yescomplemented
54C7×#394C2218yescomplemented
55C2×C7×#95C2211yescharacteristic
56C2×C7⋊#95C2211yescharacteristic
57C2×C7⋊#95C2211yescharacteristic
58C2×C7⋊#95C2211yescharacteristic
59C2×C7⋊#95C2211yescharacteristic
60C2×C7⋊#95C2211yescharacteristic
61#89762C2218yescomplemented
62#89733C2218yescomplemented
63#89729C2218yescomplemented
64#89729C2218yescomplemented
65#89723C2218yescomplemented
66#89719C2218yescomplemented
67#89714C2218yescomplemented
68C22⋊C4×Dic7C2218yescomplemented
69#89445C2218yescomplemented
70#89421C2218yescomplemented
71C2×#2491—71nomaximal, Sylow
72C25×C7C2311yescharacteristic
73C25×C7C2311yescharacteristic
74C24×D7C2311yescharacteristic
75C22×C7×D4—24no—
76C22×C7×D4—24no—
77C22×C7×D4—42no—
78C22×C7×D4C2314yes—
79C23×C4×C7C2311yescharacteristic
80C23×C4×C7C2311yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×C4×C7C2311yescharacteristic
84C22×C22⋊D7—24no—
85C22×C22⋊D7—24no—
86C22×C22⋊D7—24no—
87C22×C22⋊D7—24no—
88C22×C22⋊D7—24no—
89C22×C22⋊D7—42no—
90C22×C22⋊D7C2314yes—
91C22×C22⋊D7C2314yes—
92C23×Dic7—24no—
93C23×Dic7—24no—
94C23×Dic7—24no—
95C23×Dic7C2311yescharacteristic
96C23×Dic7C2311yescharacteristic
97C23×Dic7C2311yescharacteristic
98C23×Dic7C2314yes—
99C23×Dic7C2311yescharacteristic
100C23×Dic7C2311yescharacteristic
101C23×Dic7C2311yescharacteristic
102C23×Dic7C2311yescharacteristic
103C22×Dic14—24no—
104C22×Dic14—24no—
105C22×Dic14—24no—
106C22×Dic14—24no—
107C22×Dic14—42no—
108C22×Dic14—42no—
109C22×Dic14C2314yes—
110C22×Dic14C2314yes—
111C2×C7×C4⋊C4—24no—
112C2×C7×C4⋊C4C2314yes—
113C2×C7×C22⋊C4—24no—
114C2×C7×C22⋊C4—24no—
115C2×C7×C22⋊C4—24no—
116C2×C7×C22⋊C4—42no—
117C2×C7×C22⋊C4C2314yes—
118C2×C7×C22⋊C4C2314yes—
119C2×C7×C22⋊C4C2314yes—
120C2×C7×C22⋊C4C2314yes—
121C2×C22⋊Dic7—24no—
122C2×C22⋊Dic7—24no—
123C2×C22⋊Dic7—24no—
124C2×C22⋊Dic7—24no—
125C2×C22⋊Dic7D418yescomplemented
126C2×C22⋊Dic7C2314yes—
127C2×C22⋊Dic7C2314yes—
128C2×C22⋊Dic7C2314yes—
129C2×C22⋊Dic7C2314yes—
130C2×C22⋊Dic7C2314yes—
131#6502—232no—
132#6499—232no—
133C2×(C2×D7)⋊C4—24no—
134C2×(C2×D7)⋊C4—24no—
135C2×(C2×D7)⋊C4—24no—
136C2×(C2×D7)⋊C4—24no—
137C2×(C2×D7)⋊C4—42no—
138C2×(C2×D7)⋊C4C2314yes—
139C2×(C2×D7)⋊C4C2314yes—
140C2×(C2×D7)⋊C4C2314yes—
141C2×(C2×D7)⋊C4C2314yes—
142C2×(C2×D7)⋊C4C2314yes—
143C2×C4⋊Dic7—24no—
144C2×C4⋊Dic7C2314yes—
145C2×Dic7⋊C4—24no—
146C2×Dic7⋊C4—24no—
147C2×Dic7⋊C4D418yes—
148C2×Dic7⋊C4C2314yes—
149C2×Dic7⋊C4C2314yes—
150C2×Dic7⋊C4C2314yes—
151C2×C4×Dic7—24no—
152C2×C4×Dic7—24no—
153C2×C4×Dic7—24no—
154C2×C4×Dic7—24no—
155C2×C4×Dic7C2314yes—
156C2×C4×Dic7C2314yes—
157C2×C4×Dic7C2314yes—
158C2×C4×Dic7C2314yes—
159#6451—232no—
160#6448—232no—
161C7×#95C2314yes—
162C7⋊#95C2314yes—
163C7⋊#95C2314yes—
164C7⋊#95C2314yes—
165C7⋊#95C2314yes—
166C7⋊#95C2314yes—
167C22×C4⋊Q8—71no—
168C22×#124—71no—
169C22×#124—71no—
170C22×#121—71no—
171#2491—716no—
172C2×#394—71no—
173C2×#394D711yescharacteristic, complemented
174C2×#393—71no—
175C2×#393—71no—
176C2×#390—71no—
177C2×#390—71no—
178C2×#388—71no—
179C2×#388—71no—
180C2×#380—71no—
181C2×C4×C4⋊C4—71no—
182C2×C4×C22⋊C4—71no—
183C24×C7—22no—
184C24×C7—22no—
185C24×C7—22no—
186C24×C7—22no—
187C24×C7—22no—
188C24×C7—22no—
189C24×C7—22no—
190C24×C7—22no—
191C24×C7—22no—
192C24×C7—22no—
193C24×C7—22no—
194C24×C7—22no—
195C24×C7—22no—
196C24×C7C2×D414yes—
197C24×C7C2412yes—
198C24×C7C2412yes—
199C24×C7C2411yescharacteristic
200C23×D7—22no—
201C23×D7—22no—
202C23×D7—22no—
203C23×D7—22no—
204C23×D7—22no—
205C23×D7—22no—
206C23×D7—22no—
207C23×D7C2412yes—
208C2×C7×D4—28no—
209C2×C7×D4—28no—
210C2×C7×D4—44no—
211C2×C7×D4—416no—
212C22×C4×C7—22no—
213C22×C4×C7—22no—
214C22×C4×C7—22no—
215C22×C4×C7—22no—
216C22×C4×C7—22no—
217C22×C4×C7—22no—
218C22×C4×C7—22no—
219C22×C4×C7—22no—
220C22×C4×C7—22no—
221C22×C4×C7—22no—
222C22×C4×C7—22no—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7C2×D414yes—
226C22×C4×C7#4114yes—
227C22×C4×C7C2412yes—
228C22×C4×C7C2412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2412yes—
231C22×C4×C7C2412yes—
232C2×C22⋊D7—28no—
233C2×C22⋊D7—28no—
234C2×C22⋊D7—28no—
235C2×C22⋊D7—28no—
236C2×C22⋊D7—28no—
237C2×C22⋊D7—44no—
238C2×C22⋊D7—416no—
239C2×C22⋊D7—416no—
240C22×Dic7—22no—
241C22×Dic7—22no—
242C22×Dic7—22no—
243C22×Dic7—22no—
244C22×Dic7—22no—
245C22×Dic7—22no—
246C22×Dic7—22no—
247C22×Dic7—22no—
248C22×Dic7—22no—
249C22×Dic7—22no—
250C22×Dic7—22no—
251C22×Dic7—22no—
252C22×Dic7—22no—
253C22×Dic7—22no—
254C22×Dic7—22no—
255C22×Dic7—28no—
256C22×Dic7—28no—
257C22×Dic7—28no—
258C22×Dic7—416no—
259C22×Dic7C2×D414yes—
260C22×Dic7C2×D414yes—
261C22×Dic7C2×D414yes—
262C22×Dic7C2×D414yes—
263C22×Dic7#4114yes—
264C22×Dic7#4114yes—
265C22×Dic7C2412yes—
266C22×Dic7C2412yes—
267C22×Dic7C2412yes—
268C22×Dic7C2412yes—
269C22×Dic7C2412yes—
270C22×Dic7C2412yes—
271C22×Dic7C2412yes—
272C2×Dic14—28no—
273C2×Dic14—28no—
274C2×Dic14—28no—
275C2×Dic14—28no—
276C2×Dic14—44no—
277C2×Dic14—44no—
278C2×Dic14—416no—
279C2×Dic14—416no—
280C7×C4⋊C4—28no—
281C7×C22⋊C4—28no—
282C7×C22⋊C4—28no—
283C7×C22⋊C4—28no—
284C7×C22⋊C4—44no—
285C22⋊Dic7—28no—
286C22⋊Dic7—28no—
287C22⋊Dic7—28no—
288C22⋊Dic7—28no—
289C22⋊Dic7C2×D4116yescomplemented
290(C2×D7)⋊C4—28no—
291(C2×D7)⋊C4—28no—
292(C2×D7)⋊C4—28no—
293(C2×D7)⋊C4—28no—
294(C2×D7)⋊C4—44no—
295C4⋊Dic7—28no—
296Dic7⋊C4—28no—
297Dic7⋊C4—28no—
298Dic7⋊C4C2×D4116yes—
299C4×Dic7—28no—
300C4×Dic7—28no—
301C4×Dic7—28no—
302C4×Dic7—28no—
303C23×Q8—71no—
304C23×Q8—71no—
305C23×D4—71no—
306C23×D4—71no—
307C23×D4C2×D711yescharacteristic
308C24×C4—71no—
309C2×C4⋊Q8—78no—
310C2×C4⋊Q8—148no—
311C2×#124—78no—
312C2×#124—78no—
313C2×#124—148no—
314C2×#124—148no—
315C2×#121—78no—
316C2×#121—148no—
317C22×C4⋊C4—71no—
318C22×C4⋊C4—71no—
319C22×C4⋊C4—71no—
320C22×C4⋊C4—71no—
321C22×C4⋊C4C2×D711yescharacteristic
322C22×C22⋊C4—71no—
323C22×C22⋊C4—71no—
324C22×C22⋊C4—71no—
325C22×C22⋊C4—71no—
326C22×C22⋊C4—71no—
327C22×C22⋊C4—71no—
328C22×C22⋊C4—71no—
329C22×C22⋊C4—71no—
330C22×C22⋊C4—71no—
331C22×C22⋊C4—71no—
332C22×C22⋊C4C2×D711yescharacteristic
333C22×C22⋊C4C2×D711yescharacteristic
334C22×C22⋊C4C2×D711yescharacteristic
335C22×C22⋊C4C2×D711yescharacteristic
336C22×C42—71no—
337C22×C42—71no—
338C22×C42—71no—
339C22×C42—71no—
340#394—78no—
341#394C2×D718yescomplemented
342#393—78no—
343#393—78no—
344#390—78no—
345#390—78no—
346#388—78no—
347#388—78no—
348#380—78no—
349C4×C4⋊C4—78no—
350C4×C22⋊C4—78no—
351C2×#95—71no—
352C2×#95—71no—
353C2×#95—71no—
354C2×#95—71no—
355C2×#95—71no—
356C2×#95C2×D711yescharacteristic
357C23×C7—28no—
358C23×C7—28no—
359C23×C7—28no—
360C23×C7—22no—
361C23×C7—22no—
362C23×C7—22no—
363C23×C7—22no—
364C23×C7—22no—
365C23×C7—22no—
366C23×C7—22no—
367C23×C7—22no—
368C23×C7—22no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—44no—
374C23×C7—44no—
375C23×C7—44no—
376C23×C7—44no—
377C23×C7—44no—
378C23×C7—44no—
379C23×C7—44no—
380C23×C7—44no—
381C23×C7—44no—
382C23×C7—44no—
383C23×C7—44no—
384C23×C7C22×D414yes—
385C23×C7C22×D412yes—
386C23×C7C22×D412yes—
387C23×C7C2×#4112yes—
388C23×C7C2×#4112yes—
389C23×C7C2×#4112yes—
390C23×C7H(5,𝔽2)12yes—
391C23×C72−1+412yes—
392C23×C7C2511yescharacteristic
393C22×D7—22no—
394C22×D7—22no—
395C22×D7—22no—
396C22×D7—22no—
397C22×D7—22no—
398C22×D7—22no—
399C22×D7—22no—
400C22×D7—44no—
401C22×D7—44no—
402C22×D7—44no—
403C22×D7—44no—
404C22×D7—44no—
405C22×D7—44no—
406C22×D7—44no—
407C7×D4—416no—
408C2×C4×C7—28no—
409C2×C4×C7—28no—
410C2×C4×C7—22no—
411C2×C4×C7—22no—
412C2×C4×C7—22no—
413C2×C4×C7—22no—
414C2×C4×C7—22no—
415C2×C4×C7—22no—
416C2×C4×C7—22no—
417C2×C4×C7—22no—
418C2×C4×C7—22no—
419C2×C4×C7—22no—
420C2×C4×C7—22no—
421C2×C4×C7—22no—
422C2×C4×C7—22no—
423C2×C4×C7—44no—
424C2×C4×C7—44no—
425C2×C4×C7—44no—
426C2×C4×C7C22×D414yes—
427C2×C4×C7C2×#4114yes—
428C22⋊D7—416no—
429C22⋊D7—416no—
430C2×Dic7—28no—
431C2×Dic7—28no—
432C2×Dic7—28no—
433C2×Dic7—22no—
434C2×Dic7—22no—
435C2×Dic7—22no—
436C2×Dic7—22no—
437C2×Dic7—22no—
438C2×Dic7—22no—
439C2×Dic7—22no—
440C2×Dic7—22no—
441C2×Dic7—22no—
442C2×Dic7—22no—
443C2×Dic7—22no—
444C2×Dic7—22no—
445C2×Dic7—22no—
446C2×Dic7—22no—
447C2×Dic7—22no—
448C2×Dic7—44no—
449C2×Dic7—44no—
450C2×Dic7—44no—
451C2×Dic7—416no—
452C2×Dic7#124116yescomplemented
453C2×Dic7C22×D414yes—
454C2×Dic7C22×D414yes—
455C2×Dic7C22×D414yes—
456C2×Dic7C22×D414yes—
457C2×Dic7C2×#4114yes—
458C2×Dic7C2×#4114yes—
459Dic14—416no—
460Dic14—416no—
461C25—71no—
462C25C22×D711yescharacteristic
463C25C22×D711yescharacteristic
464C22×Q8—74no—
465C22×Q8—74no—
466C22×Q8—144no—
467C22×Q8—144no—
468C22×Q8—144no—
469C22×Q8—144no—
470C22×Q8—282no—
471C22×Q8—282no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—42no—
475C22×D4—74no—
476C22×D4—74no—
477C22×D4—144no—
478C22×D4—144no—
479C22×D4—144no—
480C22×D4—144no—
481C22×D4—144no—
482C22×D4—282no—
483C22×D4C22×D714yes—
484C23×C4—71no—
485C23×C4—71no—
486C23×C4—71no—
487C23×C4—71no—
488C23×C4—74no—
489C23×C4—71no—
490C23×C4—71no—
491C23×C4—71no—
492C23×C4—144no—
493C23×C4—144no—
494C23×C4—144no—
495C23×C4C22×D711yescharacteristic
496C23×C4C22×D711yescharacteristic
497C23×C4C22×D711yescharacteristic
498C23×C4C22×D711yescharacteristic
499C23×C4C22×D711yescharacteristic
500C4⋊Q8—1432no—
501#124—1432no—
502#124—1432no—
503#121—1432no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—78no—
506C2×C4⋊C4—74no—
507C2×C4⋊C4—74no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—144no—
511C2×C4⋊C4—144no—
512C2×C4⋊C4—144no—
513C2×C4⋊C4C22×D714yes—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—78no—
519C2×C22⋊C4—74no—
520C2×C22⋊C4—74no—
521C2×C22⋊C4—74no—
522C2×C22⋊C4—74no—
523C2×C22⋊C4—74no—
524C2×C22⋊C4—74no—
525C2×C22⋊C4—74no—
526C2×C22⋊C4—74no—
527C2×C22⋊C4—74no—
528C2×C22⋊C4—74no—
529C2×C22⋊C4—144no—
530C2×C22⋊C4—144no—
531C2×C22⋊C4—144no—
532C2×C22⋊C4—144no—
533C2×C22⋊C4—144no—
534C2×C22⋊C4—144no—
535C2×C22⋊C4—144no—
536C2×C22⋊C4—144no—
537C2×C22⋊C4—282no—
538C2×C22⋊C4C22×D714yes—
539C2×C22⋊C4C22×D714yes—
540C2×C22⋊C4C22×D714yes—
541C2×C22⋊C4C22×D714yes—
542C2×C42—74no—
543C2×C42—74no—
544C2×C42—74no—
545C2×C42—74no—
546C2×C42—144no—
547C2×C42—144no—
548C2×C42—144no—
549C2×C42—144no—
550#95—74no—
551#95—74no—
552#95—74no—
553#95—74no—
554#95—74no—
555#95C22×D714yes—
556C22×C7—24no—
557C22×C7—24no—
558C22×C7—24no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—42no—
562C22×C7—42no—
563C22×C7—416no—
564C22×C7—42no—
565C22×C7—42no—
566C22×C7—42no—
567C22×C7—42no—
568C22×C7—42no—
569C22×C7—42no—
570C22×C7—42no—
571C22×C7—88no—
572C22×C7C2×#12414yes—
573C22×C7#53214yes—
574C22×C7#54214yes—
575C22×C7D4214yes—
576C22×C7#54714yes—
577C22×C7#54814yes—
578C22×C7#55514yes—
579C22×C7C23×D411yescharacteristic
580C22×C7C23×D411yescharacteristic
581C22×C7C22×#4111yescharacteristic
582C22×C7C22×#4111yescharacteristic
583C22×C7C22×#4111yescharacteristic
584C22×C7C2×H(5,𝔽2)11yescharacteristic
585C22×C7C2×2−1+411yescharacteristic
586C2×D7—42no—
587C2×D7—42no—
588C2×D7—42no—
589C2×D7—42no—
590C2×D7—42no—
591C2×D7—42no—
592C2×D7—42no—
593C2×D7—88no—
594C4×C7—24no—
595C4×C7—24no—
596C4×C7—42no—
597C4×C7—42no—
598C4×C7—42no—
599Dic7—24no—
600Dic7—24no—
601Dic7—24no—
602Dic7—42no—
603Dic7—42no—
604Dic7—42no—
605Dic7C2×#12418yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—72no—
620C24—142no—
621C24—142no—
622C24—142no—
623C24—142no—
624C24—142no—
625C24—142no—
626C24—142no—
627C24D4×D714yes—
628C24C23×D712yes—
629C24C23×D712yes—
630C24C23×D711yescharacteristic
631C2×Q8—148no—
632C2×Q8—148no—
633C2×Q8—148no—
634C2×Q8—148no—
635C2×Q8—284no—
636C2×Q8—284no—
637C2×Q8—2816no—
638C2×Q8—2816no—
639C2×D4—28no—
640C2×D4—28no—
641C2×D4—44no—
642C2×D4—416no—
643C2×D4—148no—
644C2×D4—148no—
645C2×D4—148no—
646C2×D4—148no—
647C2×D4—148no—
648C2×D4—2816no—
649C2×D4—284no—
650C2×D4—2816no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—74no—
665C22×C4—74no—
666C22×C4—74no—
667C22×C4—72no—
668C22×C4—74no—
669C22×C4—74no—
670C22×C4—74no—
671C22×C4—72no—
672C22×C4—72no—
673C22×C4—72no—
674C22×C4—72no—
675C22×C4—72no—
676C22×C4—72no—
677C22×C4—148no—
678C22×C4—148no—
679C22×C4—148no—
680C22×C4—142no—
681C22×C4—142no—
682C22×C4—142no—
683C22×C4—142no—
684C22×C4—142no—
685C22×C4—142no—
686C22×C4—142no—
687C22×C4—142no—
688C22×C4—142no—
689C22×C4—142no—
690C22×C4—142no—
691C22×C4—142no—
692C22×C4—142no—
693C22×C4—142no—
694C22×C4—142no—
695C22×C4—2816no—
696C22×C4D4×D714yes—
697C22×C4#115914yes—
698C22×C4C23×D712yes—
699C22×C4C23×D712yes—
700C22×C4C23×D712yes—
701C22×C4C23×D712yes—
702C22×C4C23×D712yes—
703C4⋊C4—28no—
704C4⋊C4—716no—
705C4⋊C4—148no—
706C4⋊C4—148no—
707C4⋊C4—148no—
708C22⋊C4—28no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—44no—
712C22⋊C4—716no—
713C22⋊C4—148no—
714C22⋊C4—148no—
715C22⋊C4—148no—
716C22⋊C4—148no—
717C22⋊C4—148no—
718C22⋊C4—148no—
719C22⋊C4—148no—
720C22⋊C4—148no—
721C22⋊C4—284no—
722C42—148no—
723C42—148no—
724C42—148no—
725C42—148no—
726C2×C7—44no—
727C2×C7—82no—
728C2×C7#249118yescomplemented
729C2×C7C22×#12411yescharacteristic
730C2×C7C2×#53211yescharacteristic
731C2×C7C2×#54211yescharacteristic
732C2×C7C2×D4211yescharacteristic
733C2×C7C2×#54711yescharacteristic
734C2×C7C2×#54811yescharacteristic
735C2×C7C2×#55511yescharacteristic
736D7—82no—
737C23—28no—
738C23—28no—
739C23—28no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—142no—
765C23—142no—
766C23—142no—
767C23—142no—
768C23—142no—
769C23—142no—
770C23—142no—
771C23—284no—
772C23—284no—
773C23—284no—
774C23—284no—
775C23—284no—
776C23—284no—
777C23—284no—
778C23C2×D4×D714yes—
779C23C2×D4×D712yes—
780C23C2×D4×D712yes—
781C23C2×#115912yes—
782C23#654812yes—
783C23D7×#4112yes—
784C23D7×#4112yes—
785C23#655412yes—
786C23C24×D711yescharacteristic
787Q8—2816no—
788Q8—2816no—
789D4—416no—
790D4—2816no—
791D4—2816no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—74no—
811C2×C4—74no—
812C2×C4—74no—
813C2×C4—716no—
814C2×C4—74no—
815C2×C4—74no—
816C2×C4—74no—
817C2×C4—148no—
818C2×C4—148no—
819C2×C4—148no—
820C2×C4—142no—
821C2×C4—142no—
822C2×C4—142no—
823C2×C4—142no—
824C2×C4—142no—
825C2×C4—142no—
826C2×C4—142no—
827C2×C4—142no—
828C2×C4—142no—
829C2×C4—142no—
830C2×C4—142no—
831C2×C4—142no—
832C2×C4—142no—
833C2×C4—142no—
834C2×C4—142no—
835C2×C4—2816no—
836C2×C4—284no—
837C2×C4—284no—
838C2×C4—284no—
839C2×C4C2×D4×D714yes—
840C2×C4C2×#115914yes—
841C7C2×#249111yescharacteristic, complemented, Sylow
842C22—24no—
843C22—24no—
844C22—24no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—416no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—88no—
858C22—282no—
859C22—282no—
860C22—282no—
861C22—282no—
862C22—282no—
863C22—282no—
864C22—282no—
865C22—568no—
866C22#9028114yes—
867C22#9028714yes—
868C22#9028914yes—
869C22#9030714yes—
870C22#9034614yes—
871C22#9035314yes—
872C22D7×#12414yes—
873C22C22×D4×D711yescharacteristic
874C22C22×D4×D711yescharacteristic
875C22C22×#115911yescharacteristic
876C22C2×#654811yescharacteristic
877C22C2×D7×#4111yescharacteristic
878C22C2×D7×#4111yescharacteristic
879C22C2×#655411yescharacteristic
880C4—24no—
881C4—24no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—78no—
886C4—144no—
887C4—144no—
888C4—144no—
889C4—282no—
890C4—282no—
891C4—282no—
892C2—44no—
893C2—82no—
894C2—562no—
895C2#1173438018yesdirect product factor
896C2C2×#9028111yescharacteristic
897C2C2×#9028711yescharacteristic
898C2C2×#9028911yescharacteristic
899C2C2×#9030711yescharacteristic
900C2C2×#9035311yescharacteristic
901C2C2×#9034611yescharacteristic
902C2C2×D7×#12411yescharacteristic
subgroupG/H
centerC24C23×D7
commutator, cosocleC23×C7C25
FrattiniC23C24×D7
FittingC2×C7×#394C2
socleC24×C7C24
prime radicalC22×#6502C2
hypercenterC2×#394D7
hypocenterC7C2×#2491
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#6499C2semidirect
3. C22×#6451C2semidirect
4. C22×#6448C2semidirect
5. C2×C7×#394C2semidirect
6. C2×#89762C2semidirect
7. C2×#89733C2semidirect
8. C2×#89719C2semidirect
9. C2×#89729C2semidirect
10. C2×#89729C2semidirect
11. C2×#89723C2semidirect
12. C2×#89714C2semidirect
13. C2×C22⋊C4×Dic7C2semidirect
14. #11734380C2direct (N × H)
15. C2×#89445C2semidirect
16. C2×#89421C2semidirect
36. C2×#6499C22semidirect
51. C2×#6451C22semidirect
53. C2×#6448C22semidirect
54. C7×#394C22semidirect
61. #89762C22semidirect
62. #89733C22semidirect
63. #89729C22semidirect
64. #89729C22semidirect
65. #89723C22semidirect
66. #89719C22semidirect
67. #89714C22semidirect
68. C22⋊C4×Dic7C22semidirect
69. #89445C22semidirect
70. #89421C22semidirect
125. C2×C22⋊Dic7D4semidirect
173. C2×#394D7semidirect
289. C22⋊Dic7C2×D4semidirect
341. #394C2×D7semidirect
452. C2×Dic7#124semidirect
605. Dic7C2×#124semidirect
728. C2×C7#2491semidirect
841. C7C2×#2491semidirect
895. C2#11734380direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#64992
C22×#65022
C22×#64512
C22×#64482
C2×C7×#3942
C2×#897622
C2×#897332
C2×#897192
C2×#897292
C2×#897232
C2×#897142
C2×C22⋊C4×Dic72
#117343802
C2×#894452
C2×#894212
C2×#24917